Commit `94470ad726`

94470ad72648783324965722d11f6ccbd04281da

parent: 28b7030e5b

Unsigned

cmc <hello@cleberg.net> · 2026-10-17 23:21 UTC

M0 spike: plan, sky engine, static sky render, APNs probe (!1)

- =PLAN.org=: concept, screens, data sources checked 2026-10-17, Cloudflare backend, milestones, roadmap, M0 results.
- =Packages/MoonriseKit=:
  - =CAstronomy=: Astronomy Engine v2.1.19 C source (MIT).
  - =SkyEngine=: Swift wrapper. Moon, Mars, Jupiter, Saturn match JPL Horizons within 1′ (RA/Dec, alt/az, heliocentric).
  - =SkyRenderer=: stereographic sky, 8,404 BSC5 stars, 88 constellations (ConstellationLines, CC BY 4.0), planets, moon phase, horizon. Mac render of a 1179×2556 frame: 0.09 s. Not measured on a device.
- =spikes/apns-worker=: ES256 provider token via WebCrypto, =/push=, =/probe=. Deployed probe got APNs 403 =InvalidProviderToken= with =apns-id= on 3 of 3 calls, so HTTP/2 to APNs works from a Worker. Worker deleted after.
- =THIRD_PARTY.org=, =.gitignore=.

Tests: =swift test= in =Packages/MoonriseKit= (7 pass); =node --test test/= in =spikes/apns-worker= (1 pass).

Layout: unified · split

.gitignore added +7

@@ -0,0 +1,7 @@
	1	.DS_Store
	2	.build/
	3	.swiftpm/
	4	node_modules/
	5	.wrangler/
	6	.dev.vars
	7	*.p8

PLAN.org added +358

@@ -0,0 +1,358 @@
	1	#+title: Moonrise
	2	#+subtitle: concept and plan
	3
	4	* name
	5	Moonrise. App Store name with a descriptor, e.g. "Moonrise: Sky and
	6	Space", since the bare name is shared and reads as moon-only.
	7
	8	Existing apps (Oct 2026 search), all moon-times utilities: AVIA Moonrise
	9	(id390606204, last updated 2021), Moonrise Moment (id6788237210),
	10	Mooncaster. The descriptor and screenshots need to show the app covers
	11	far more than the moon.
	12
	13	Reserved in App Store Connect 2026-10-17. USPTO search not done.
	14
	15	* Apple identifiers
	16	\| Item \| Value \|
	17	\|-
	18	\| Team ID \| =ZCNAX3VL9D= \|
	19	\| Bundle ID \| =sh.krz.moonrise= \|
	20	\| APNs key \| "Moonrise APNs", key ID =644XS4F2RG=, Sandbox and Production. The .p8 is held outside the repo. \|
	21
	22	* concept
	23	An iPhone app for everything in space: what is overhead tonight, what the
	24	sun is doing, what is launching, where our spacecraft are, and a
	25	reference library for the planets, stars, galaxies and missions.
	26
	27	The lead on every tab is a picture computed from real data or a real
	28	image: the sky above you, the solar system today, the sun this hour, a
	29	rocket on its pad. Text sits underneath, a swipe or tap away.
	30
	31	Free of accounts. Works offline for anything that can be computed;
	32	fetches only live feeds.
	33
	34	* design
	35	After NASA's 1975 Graphics Standards Manual.
	36
	37	- Helvetica Neue (ships with iOS). Tabular figures for all numbers.
	38	- Strict grid, flush left, black hairlines, numbered modules.
	39	- Off-white and ink by day. Near-black with white line work at night.
	40	- One red accent for alerts and emphasis. Not NASA's exact red, no NASA
	41	insignia or worm logotype, nothing that reads as an official NASA app.
	42	- Drawings are technical: orbits as orbits, dimension lines, to-scale
	43	comparisons, Gantt-style mission timelines.
	44	- Night mode: red-on-black for dark-adapted eyes, switched on
	45	automatically after astronomical dusk while the Sky tab is open.
	46	- Motion only where it carries data: planets moving at true relative
	47	speeds, the moon's phase easing while scrubbing time.
	48
	49	Avoid: neon on black, glow, scan lines, hexagons, crosshairs,
	50	monospaced readouts as decoration.
	51
	52	* screens
	53	Five tabs.
	54
	55	** 1. Sky (home)
	56	- Full-screen sky for your location and time: horizon, stars to about
	57	magnitude 6, constellation lines, planets, the moon at its true phase,
	58	the sun below the horizon as a glow at the edge.
	59	- Pans with the device (compass and gyroscope) or by drag. Pinch to zoom.
	60	- Tap any object for a card: name, magnitude, rise and set, distance,
	61	link to its Library page.
	62	- Time scrubber: drag hours forward or back; tap to return to now.
	63	- Alert chips across the top when relevant: aurora (Kp threshold for
	64	your latitude), ISS pass within the hour, launch within the hour,
	65	eclipse or conjunction today.
	66	- Today sheet, pulled up from the bottom:
	67	- Moon: phase, illumination, next quarter.
	68	- Visible tonight: planets with direction, altitude, rise and set.
	69	- ISS passes over the next 3 days.
	70	- Next launch with countdown.
	71	- Space weather: Kp now and forecast.
	72	- Deep space: Voyager 1 distance and light time.
	73
	74	** 2. System
	75	- Top-down orrery of the solar system for today. Log-scaled distances by
	76	default; toggle to true scale.
	77	- Time slider from 1957 to 2050. Planets and spacecraft move together.
	78	- Spacecraft drawn with their trajectories: Voyager 1 and 2, New
	79	Horizons, Juno, Europa Clipper, JUICE, Psyche, Parker Solar Probe,
	80	Lucy, and missions at Mars.
	81	- Tap a planet or spacecraft for its Library page.
	82	- Inset for Earth–Moon space: ISS, JWST at L2, lunar missions.
	83
	84	** 3. Sun
	85	- Latest SDO full-disk image, full width. Swipe between wavelengths:
	86	171 Å (corona), 304 Å (chromosphere), 193 Å, HMI visible light.
	87	- Kp index: bar chart for the last 3 days and the 3-day forecast.
	88	- Aurora oval for your hemisphere (OVATION model) with your location
	89	marked.
	90	- Solar flares: GOES X-ray flux for the last 24 hours, flare classes
	91	marked.
	92	- Plain-language summary in one line: "Quiet", "Minor storm likely
	93	tonight", and similar.
	94
	95	** 4. Launches
	96	- Upcoming launches, each led by the rocket's silhouette drawn to a
	97	common scale.
	98	- Detail: vehicle, mission, payload, orbit, pad on a map, countdown,
	99	launch window, webcast link.
	100	- Live Activity from T−1 hour through orbit insertion.
	101	- Past launches with outcome.
	102
	103	** 5. Library
	104	Every page leads with a drawing or image; facts follow as a spec sheet.
	105
	106	- Solar system: the sun, 8 planets, dwarf planets, major moons. Each has
	107	a dimensioned drawing, a to-scale comparison with Earth, a facts grid,
	108	the missions that visited on a timeline, and a short essay.
	109	- Constellations: all 88. Modern line figure, the plate from a
	110	historical atlas (Bayer, Hevelius, Bode), bright stars, best season,
	111	where it is tonight.
	112	- Stars: bright named stars with type, distance, colour and the origin
	113	of the name.
	114	- Deep sky: the 110 Messier objects, then well-known NGC objects, with
	115	Hubble, Webb or ground images and a scale bar.
	116	- Spacecraft and missions: active and historic. Status, location,
	117	instruments, findings, timeline.
	118	- Later sections: exoplanets, rockets side by side to scale, the history
	119	of exploration as a browsable timeline, a scale view from Earth to the
	120	observable universe.
	121
	122	Search across all of it from the Library tab.
	123
	124	* widgets, Live Activities, notifications
	125	- Lock Screen: moon phase; Kp; next launch countdown.
	126	- Home Screen: tonight's planets; Voyager 1 distance; today's sun image.
	127	- Live Activity: launch countdown through orbit.
	128	- Notifications, each off by default and opt-in: aurora possible at your
	129	latitude; launch in one hour; ISS visible pass in 15 minutes.
	130
	131	* data sources
	132	Checked 2026-10-17 against primary sources unless marked unconfirmed.
	133
	134	\| Source \| Use \| Terms and limits \|
	135	\|-
	136	\| Astronomy Engine v2.1.19 (Don Cross) \| Sun, moon, planet positions; rise, set, phases, eclipses, conjunctions \| MIT, keep notice. No Swift package; C source vendored as an SPM target. Last release 2023-12. \|
	137	\| Yale Bright Star Catalogue (VizieR V/50) \| 9,096 stars with V mag, bundled \| No licence in ReadMe; VizieR says "free in a scientific context", check per catalogue. US-government origin (NSSDC); public domain unconfirmed. \|
	138	\| HYG database \| Star names, distances \| CC BY-SA 4.0; use only if BSC5 is not enough \|
	139	\| IAU boundaries (VizieR VI/49) \| Boundaries \| Same VizieR ambiguity as BSC5 \|
	140	\| Constellation lines: van der Sluys ConstellationLines v1.4 \| Stick figures by HR number, bundled \| CC BY 4.0. Credit: "Constellation lines: Marc van der Sluys, ConstellationLines (doi:10.5281/zenodo.10397192), CC BY 4.0." Stellarium (CC BY-SA, AGPL repo) and d3-celestial (no data licence) rejected. \|
	141	\| OpenNGC \| Messier and NGC object data \| CC BY-SA 4.0; ShareAlike on the data file. Decide before M5. \|
	142	\| NOAA SWPC JSON \| Kp (=json/planetary_k_index_1m.json=), Kp forecast (=products/noaa-planetary-k-index-forecast.json=, array of objects), OVATION (=json/ovation_aurora_latest.json=, ~900 KB), GOES X-ray (=json/goes/primary/xrays-6-hour.json=), alerts (=products/alerts.json=) \| No terms page; US government. =cache-control: max-age=60=: poll at most once a minute. \|
	143	\| NASA SDO \| =assets/img/latest/latest_{512,1024,...}_{0171,0193,0304,HMIIC}.jpg= \| Not copyrighted unless noted. Credit: "Courtesy of NASA/SDO and the AIA, EVE, and HMI science teams." \|
	144	\| JPL Horizons API \| Spacecraft positions (Voyager 1 = -31) \| No published limit; errors come back as HTTP 200, check payload. Cache server-side. \|
	145	\| CelesTrak GP \| =celestrak.org/NORAD/elements/gp.php?CATNR=25544&FORMAT=JSON= \| Updates every 2 h; one download per update. >50 HTTP errors in 2 h blocks the IP. Fetch only from the Worker; stop on any non-200. \|
	146	\| Launch Library 2 v2.3.0 \| =ll.thespacedevs.com/2.3.0/= \| 15 requests/hour anonymous (confirmed). Higher tiers via Patreon; price, commercial and attribution terms unpublished. Ask The Space Devs before launch. \|
	147	\| NASA Image and Video Library \| Planet, mission and spacecraft images \| Generally not copyrighted; acknowledge NASA. Insignia and logotype protected; no implied endorsement; no current astronauts in promotion. \|
	148	\| ESA/Hubble, ESA/Webb, ESO \| Deep-sky images \| CC BY 4.0; full credit line visible next to each image; note modifications. ESO: no commercial use of identifiable people. \|
	149	\| USGS Astrogeology \| Planet and moon maps \| Public domain \|
	150	\| NASA Exoplanet Archive \| Exoplanets (later) \| Public; bundle a snapshot, refresh periodically \|
	151	\| Historical star atlases (LoC, Linda Hall Library, Wikimedia scans) \| Constellation plates \| Works public domain; check each scan's terms \|
	152
	153	Track source and licence per image in the content bundle from day one.
	154
	155	* architecture
	156	- iOS 26+, SwiftUI, Swift 6 language mode. iPhone first; iPad layout in
	157	v1.1.
	158	- Packages:
	159	- =SkyEngine=: Swift wrapper over Astronomy Engine's C library.
	160	Coordinates, rise and set, phases, events, kō-style solar longitude
	161	(shared with the parked seventy-two app).
	162	- =SkyRenderer=: SwiftUI Canvas first; move to Metal if 9,000 stars
	163	plus lines cannot hold 60 fps while panning.
	164	- =Feeds=: typed clients for SWPC, SDO, CelesTrak, the backend. Cached
	165	on disk with per-feed lifetimes.
	166	- =Library=: bundled content (JSON plus images), versioned, updatable
	167	from the backend without an app release.
	168	- Backend on Cloudflare; see [[*backend][backend]].
	169	- No accounts. Device registers an APNs token and a coarse latitude band
	170	for aurora alerts, nothing else.
	171
	172	* backend
	173	Only what the app cannot do alone: cache rate-limited feeds (Launch
	174	Library 2, Horizons), send pushes (aurora, launches), drive launch Live
	175	Activities, ship Library content updates. Positions, phases and ISS passes
	176	are computed on device; ISS pass alerts are local notifications. SWPC and
	177	SDO are public, so the app can fetch them directly if the backend is down.
	178
	179	** Cloudflare products
	180	\| Product \| Role \|
	181	\|-
	182	\| Workers (TypeScript) \| JSON API; APNs sender \|
	183	\| Cron Triggers \| Feed polling \|
	184	\| D1 \| Devices, launches, alert dedupe, Live Activity tokens, ephemeris, content versions \|
	185	\| Workers Cache \| Cache GET responses (=/v1/today= etc.) \|
	186	\| Queues \| Push fan-out with retries, decoupled from polling \|
	187	\| R2 \| Library content packs, widget-sized SDO thumbnails \|
	188	\| Workers secrets \| APNs .p8 key, key ID, team ID; Launch Library 2 key \|
	189	\| Workers Rate Limiting \| Per-IP limits on device registration \|
	190
	191	** APNs from Workers
	192	APNs requires HTTP/2. A Cloudflare engineer stated in workerd issue #4841
	193	(2025-08-20) that production requests pass through Cloudflare's proxy,
	194	which upgrades them to HTTP/2; workerd itself, and so =wrangler dev=, does
	195	not support HTTP/2 and there are no plans to add it. Cloudflare's docs do
	196	not state this. Open-source senders rely on it (e.g.
	197	FiveSheepCo/cloudflare-apns2). Containers (Workers Paid) can run an HTTP/2
	198	sender as a fallback. Spike: =spikes/apns-worker=.
	199
	200	- Sign the ES256 provider JWT with WebCrypto; reuse it for 20–60 minutes
	201	as Apple requires.
	202	- Test pushes against a deployed staging Worker using the sandbox APNs
	203	host, never from local dev.
	204	- Keep the sender behind the push Queue so it can move to Cloudflare
	205	Containers (a small Go or Python sender) if Workers' HTTP/2 stops
	206	working, without touching the rest.
	207	- Delete tokens on HTTP 410.
	208
	209	** jobs
	210	\| Cron \| Job \|
	211	\|-
	212	\| =/5 * * *= \| SWPC: 1-minute Kp, Kp forecast, OVATION aurora, alerts; run aurora engine \|
	213	\| =/10 * * *= \| Launch Library 2 upcoming list \|
	214	\| =* * * * *= \| If a launch is within 1 h: poll it (needs paid LL2 key); push Live Activity updates on status change \|
	215	\| =0 /4 * *= \| CelesTrak ISS and bright satellites \|
	216	\| =15 3 * * *= \| JPL Horizons daily positions for ~20 spacecraft \|
	217
	218	The anonymous Launch Library 2 tier is 15 requests/hour; the 1-minute job
	219	needs a key. CelesTrak: never more than once per 2-hour update.
	220
	221	** data (D1)
	222	- =devices=: APNs token, environment (sandbox/production), 5°
	223	geomagnetic latitude band, UTC offset, preferences (aurora threshold,
	224	launch alerts, quiet hours), last seen.
	225	- =launches=: normalized LL2 cache plus raw JSON.
	226	- =feed_snapshots=: latest result per feed with fetch time and status.
	227	- =alerts_sent=: dedupe key (type, band, storm event).
	228	- =live_activity_tokens=: launch, update token, device; push-to-start
	229	tokens separately.
	230	- =spacecraft_ephemeris=: spacecraft, date, position.
	231	- =content_versions=: pack, version, hash, R2 key.
	232
	233	** API
	234	\| Method and path \| Purpose \|
	235	\|-
	236	\| =GET /v1/today= \| One small payload: next launches, space weather summary, active alerts, spacecraft positions, content version. ETag. \|
	237	\| =GET /v1/launches=, =GET /v1/launches/{id}= \| List, detail \|
	238	\| =GET /v1/spacecraft?ids=&from=&to== \| Recent positions; full history ships in the app \|
	239	\| =GET /v1/content/manifest=, =GET /v1/content/{pack}= \| Library updates from R2 \|
	240	\| =POST/PATCH/DELETE /v1/devices[/{token}]= \| Register, preferences, unregister \|
	241	\| =POST /v1/live-activities= \| Register an update token for a launch \|
	242	\| =GET /healthz= \| Liveness and per-feed staleness \|
	243
	244	** alerts
	245	- Aurora: from Kp forecast and OVATION, find the latitude bands that can
	246	see aurora; notify devices in those bands where it is dark, outside
	247	quiet hours; at most one per band per storm.
	248	- Launches: "launch in one hour" to opted-in devices; push-to-start the
	249	Live Activity (iOS 17.2+); update on countdown, hold, liftoff, staging,
	250	orbit or scrub; end 15 minutes after the outcome.
	251
	252	** privacy and abuse
	253	- Stored per device: push token, 5° latitude band, UTC offset,
	254	preferences. No location, no accounts.
	255	- v1: per-IP rate limits. Later: App Attest verification in the Worker.
	256
	257	** operations
	258	- Repo =moonrise-server= on gitbay; deploy with Wrangler from CI.
	259	- Staging and production Workers with separate D1 databases and APNs
	260	environments.
	261	- Workers Logs for errors; feed staleness in =/healthz=.
	262	- Likely Workers Paid plan (about $5/month) plus an optional Launch
	263	Library 2 key. Check current pricing for Queues and D1 before launch.
	264
	265	* content
	266	The Library is the largest piece of work.
	267
	268	- v1: sun, 8 planets, 5 dwarf planets, ~25 major moons, 88
	269	constellations, ~50 named stars, 110 Messier objects, ~40 missions.
	270	About 320 pages.
	271	- Write in one voice: short essay plus spec sheet per page. Start from
	272	NASA public-domain text where useful, rewritten.
	273	- Drawings for every planet and moon in the house style, generated from
	274	data (radius, oblateness, rings, axial tilt) rather than drawn by hand.
	275
	276	* milestones
	277	- M0, spike. Confirm every source, licence and rate limit above.
	278	Astronomy Engine building from Swift with tests against Horizons.
	279	Static sky render for one place and time. Reserve the name.
	280	- M1, Sky. Live sky with device motion, object cards, time scrubber,
	281	night mode, Today sheet. Moon and planets widgets.
	282	- M2, Sun. SDO images, Kp, aurora oval, flares. Backend up; aurora
	283	push.
	284	- M3, Launches. List, detail, rocket silhouettes, Live Activity.
	285	- M4, System. Orrery with time slider and spacecraft trajectories.
	286	- M5, Library v1. Solar system, constellations, stars, Messier,
	287	missions. Search.
	288	- 1.0 = M1–M5, TestFlight, App Store.
	289
	290	** M0 results (2026-10-17)
	291	- Data sources: checked; see [[*data sources][data sources]]. Open: Launch Library 2
	292	commercial terms, OpenNGC ShareAlike, BSC5 licence statement.
	293	- =Packages/MoonriseKit=:
	294	- =CAstronomy=: Astronomy Engine v2.1.19 C source.
	295	- =SkyEngine=: Swift wrapper. Tests against JPL Horizons (Chicago,
	296	2026-10-17 02:00 UT): apparent RA/Dec and airless alt/az for the Moon,
	297	Mars, Jupiter, Saturn within 1′; heliocentric Jupiter and Saturn within
	298	1′ angular (Saturn 0.00045 AU, about 10″).
	299	- =SkyRenderer=: stereographic projection, 8,404 stars to V 6.5, 88
	300	constellations, planets to mag 6, moon with phase, horizon. Scene
	301	build 0.03 s, Canvas render of a 1179×2556 frame 0.09 s on an Apple
	302	silicon Mac via =ImageRenderer=. Not measured on a device; panning at
	303	60 fps (16 ms per frame) is unproven and likely needs culling,
	304	pre-rendered star layers or Metal.
	305	- =spikes/apns-worker=: ES256 provider token via WebCrypto (unit-tested),
	306	=/push= and a credential-free =/probe=. Deployed as
	307	=moonrise-apns-spike=; =/probe= got APNs JSON responses (403
	308	=InvalidProviderToken= with an =apns-id=) on 3 of 3 calls, so the
	309	deployed Worker reaches the APNs sandbox over HTTP/2. Worker deleted
	310	after the test. A real push still needs an APNs key and a device token.
	311	- Name reserved in App Store Connect; APNs key created (key ID 644XS4F2RG).
	312
	313	* roadmap
	314	** v1: now
	315	Sky, System, Sun, Launches, Library core (above).
	316
	317	** v2: plan, track, more devices
	318	- Events: eclipses, meteor showers, conjunctions, oppositions, each with
	319	an observing plan. Eclipse path maps with local timings; the 2 August
	320	2027 total eclipse (Spain, North Africa, Egypt) is a launch target.
	321	- Deep Space Network Now: which DSN dishes are talking to which
	322	spacecraft.
	323	- More satellites: Tiangong, Hubble, Starlink trains, bright passes.
	324	- Observing log stored as plain text or Org.
	325	- Mars: latest rover raw images, local time at each rover.
	326	- Library: exoplanets, rockets to scale, exploration timeline, scale
	327	view.
	328	- iPad, Mac, Apple Watch complications.
	329
	330	** v3: across time and cultures
	331	- Sky cultures: Chinese, Polynesian, Arabic, Norse and other
	332	constellations over the same stars.
	333	- Historical sky for any date and place, with precession.
	334	- 3D planets from USGS maps; immersive sky and orrery on Vision Pro.
	335	- Guided seasonal sky tours and mission stories.
	336	- Live coverage of major events (e.g. an Artemis landing) on the orrery
	337	with a Live Activity.
	338	- Maybe: smart-telescope pointing (Seestar and similar).
	339
	340	* risks
	341	- Library scope: 320 pages is most of the effort. Ship 1.0 with fewer
	342	pages before adding more.
	343	- Sky render performance and compass accuracy; indoor and urban magnetic
	344	interference makes device-motion panning unreliable, so drag must
	345	always work.
	346	- Third-party feed limits (Launch Library 2) and feed outages: show the
	347	last good data with its age.
	348	- NASA brand rules: the style is borrowed, the branding must not be.
	349	- A crowded category (SkySafari, Night Sky, Stellarium, Next Spaceflight,
	350	SpaceWeatherLive). The case for this app is all of it in one place,
	351	designed well, not depth in any one area.
	352
	353	* open questions
	354	- Pricing: free, paid up front, or free with a one-time unlock for the
	355	Library and alerts.
	356	- Fallback for APNs if Workers' HTTP/2 stops working: Containers sender
	357	vs. a separate small VPS. The M0 probe worked, so this is a contingency.
	358	- Whether the Sky tab needs AR camera overlay at all (current lean: no).

Packages/MoonriseKit/Package.swift added +27

@@ -0,0 +1,27 @@
	1	// swift-tools-version: 6.2
	2	import PackageDescription
	3
	4	let package = Package(
	5	name: "MoonriseKit",
	6	platforms: [.iOS(.v26), .macOS(.v26)],
	7	products: [
	8	.library(name: "SkyEngine", targets: ["SkyEngine"]),
	9	.library(name: "SkyRenderer", targets: ["SkyRenderer"]),
	10	],
	11	targets: [
	12	// Astronomy Engine v2.1.19 (MIT), https://github.com/cosinekitty/astronomy
	13	.target(
	14	name: "CAstronomy",
	15	exclude: ["LICENSE"],
	16	cSettings: [.unsafeFlags(["-w"])]
	17	),
	18	.target(name: "SkyEngine", dependencies: ["CAstronomy"]),
	19	.target(
	20	name: "SkyRenderer",
	21	dependencies: ["SkyEngine"],
	22	resources: [.copy("Resources/bsc5.json"), .copy("Resources/constellations.json")]
	23	),
	24	.testTarget(name: "SkyEngineTests", dependencies: ["SkyEngine"]),
	25	.testTarget(name: "SkyRendererTests", dependencies: ["SkyRenderer"]),
	26	]
	27	)

Packages/MoonriseKit/Sources/CAstronomy/LICENSE added +21

@@ -0,0 +1,21 @@
	1	MIT License
	2
	3	Copyright (c) 2019-2023 Don Cross <cosinekitty@gmail.com>
	4
	5	Permission is hereby granted, free of charge, to any person obtaining a copy
	6	of this software and associated documentation files (the "Software"), to deal
	7	in the Software without restriction, including without limitation the rights
	8	to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
	9	copies of the Software, and to permit persons to whom the Software is
	10	furnished to do so, subject to the following conditions:
	11
	12	The above copyright notice and this permission notice shall be included in all
	13	copies or substantial portions of the Software.
	14
	15	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	16	IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	17	FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
	18	AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
	19	LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
	20	OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
	21	SOFTWARE.

Packages/MoonriseKit/Sources/CAstronomy/astronomy.c added +13058

@@ -0,0 +1,13058 @@
	1	/*
	2	Astronomy Engine for C/C++.
	3	https://github.com/cosinekitty/astronomy
	4
	5	MIT License
	6
	7	Copyright (c) 2019-2023 Don Cross <cosinekitty@gmail.com>
	8
	9	Permission is hereby granted, free of charge, to any person obtaining a copy
	10	of this software and associated documentation files (the "Software"), to deal
	11	in the Software without restriction, including without limitation the rights
	12	to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
	13	copies of the Software, and to permit persons to whom the Software is
	14	furnished to do so, subject to the following conditions:
	15
	16	The above copyright notice and this permission notice shall be included in all
	17	copies or substantial portions of the Software.
	18
	19	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	20	IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	21	FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
	22	AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
	23	LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
	24	OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
	25	SOFTWARE.
	26	*/
	27
	28	#include <math.h>
	29	#include <stdint.h>
	30	#include <stdio.h>
	31	#include <stdlib.h>
	32	#include <string.h>
	33
	34	#if !defined(ASTRONOMY_ENGINE_NO_CURRENT_TIME)
	35	#if defined(__unix__) \|\| defined(__unix) \|\| (defined(__APPLE__) && defined(__MACH__))
	36	#include <sys/time.h>
	37	#elif defined(_WIN32)
	38	#define WIN32_LEAN_AND_MEAN
	39	#include <windows.h>
	40	#else
	41	#include <time.h>
	42	#endif
	43	#endif
	44
	45	#include "astronomy.h"
	46
	47	#ifdef __FAST_MATH__
	48	#error Astronomy Engine does not support "fast math" optimization because it causes incorrect behavior. See: https://github.com/cosinekitty/astronomy/issues/245
	49	#endif
	50
	51	#ifdef __cplusplus
	52	extern "C" {
	53	#endif
	54
	55	/** @cond DOXYGEN_SKIP */
	56	#define PI 3.14159265358979323846
	57
	58	#define PLUTO_NUM_STATES 51
	59	#define PLUTO_TIME_STEP 29200
	60	#define PLUTO_DT 146
	61
	62	#define PLUTO_NSTEPS 201
	63
	64
	65
	66	typedef enum
	67	{
	68	FROM_2000,
	69	INTO_2000
	70	}
	71	precess_dir_t;
	72
	73	typedef struct
	74	{
	75	double x;
	76	double y;
	77	double z;
	78	}
	79	terse_vector_t;
	80
	81	typedef struct
	82	{
	83	double tt; /* J2000 terrestrial time [days] */
	84	terse_vector_t r; /* position [au] */
	85	terse_vector_t v; /* velocity [au/day] */
	86	terse_vector_t a; /* acceleration [au/day^2] */
	87	}
	88	body_grav_calc_t;
	89
	90	typedef struct
	91	{
	92	body_grav_calc_t step[PLUTO_NSTEPS];
	93	}
	94	body_segment_t;
	95
	96	typedef struct
	97	{
	98	double tt; /* Terrestrial Time in J2000 days */
	99	terse_vector_t r; /* position [au] */
	100	terse_vector_t v; /* velocity [au/day] */
	101	}
	102	body_state_t;
	103
	104	typedef struct
	105	{
	106	body_state_t Sun;
	107	body_state_t Jupiter;
	108	body_state_t Saturn;
	109	body_state_t Uranus;
	110	body_state_t Neptune;
	111	}
	112	major_bodies_t;
	113
	114	typedef struct
	115	{
	116	astro_time_t time;
	117	body_state_t gravitators[1 + BODY_SUN];
	118	body_grav_calc_t *bodies;
	119	}
	120	gravsim_endpoint_t;
	121
	122	struct astro_grav_sim_s
	123	{
	124	astro_body_t originBody;
	125	int numBodies;
	126	gravsim_endpoint_t endpoint[2];
	127	gravsim_endpoint_t *prev;
	128	gravsim_endpoint_t *curr;
	129	};
	130
	131	typedef struct
	132	{
	133	double ra;
	134	double dec;
	135	double dist;
	136	}
	137	stardef_t;
	138
	139	/* Mean obliquity of the J2000 ecliptic in radians. */
	140	#define OBLIQ_2000 0.40909260059599012
	141	#define COS_OBLIQ_2000 0.9174821430670688
	142	#define SIN_OBLIQ_2000 0.3977769691083922
	143
	144	/** @endcond */
	145
	146	#define NSTARS 8
	147	static stardef_t StarTable[NSTARS];
	148
	149	#define GetStarPointer(body) (((body) >= BODY_STAR1) && ((body) <= BODY_STAR8) ? &StarTable[(body) - BODY_STAR1] : NULL)
	150
	151	static stardef_t *UserDefinedStar(astro_body_t body)
	152	{
	153	stardef_t *star = GetStarPointer(body);
	154	if (star != NULL && star->dist > 0.0)
	155	return star;
	156	return NULL;
	157	}
	158
	159
	160	/**
	161	* @brief Assign equatorial coordinates to a user-defined star.
	162	*
	163	* Some Astronomy Engine functions allow their `body` parameter to
	164	* be a user-defined fixed point in the sky, loosely called a "star".
	165	* This function assigns a right ascension, declination, and distance
	166	* to one of the eight user-defined stars `BODY_STAR1` .. `BODY_STAR8`.
	167	*
	168	* Stars are not valid until defined. Once defined, they retain their
	169	* definition until re-defined by another call to `Astronomy_DefineStar`.
	170	*
	171	* @param body
	172	* One of the eight user-defined star identifiers: `BODY_STAR1` .. `BODY_STAR8`.
	173	*
	174	* @param ra
	175	* The right ascension to be assigned to the star, expressed in J2000 equatorial coordinates (EQJ).
	176	* The value is in units of sidereal hours, and must be within the half-open range [0, 24).
	177	*
	178	* @param dec
	179	* The declination to be assigned to the star, expressed in J2000 equatorial coordinates (EQJ).
	180	* The value is in units of degrees north (positive) or south (negative) of the J2000 equator,
	181	* and must be within the closed range [-90, +90].
	182	*
	183	* @param distanceLightYears
	184	* The distance between the star and the Sun, expressed in light-years.
	185	* This value is used to calculate the tiny parallax shift as seen by an observer on Earth.
	186	* If you don't know the distance to the star, using a large value like 1000 will generally work well.
	187	* The minimum allowed distance is 1 light-year, which is required to provide certain internal optimizations.
	188	*
	189	* @return
	190	* `ASTRO_SUCCESS` indicates the star has been defined. Any other value indicates an error,
	191	* in which case no change has taken place to any of the star definitions.
	192	*/
	193	astro_status_t Astronomy_DefineStar(astro_body_t body, double ra, double dec, double distanceLightYears)
	194	{
	195	stardef_t *star = GetStarPointer(body);
	196
	197	if (star == NULL)
	198	return ASTRO_INVALID_BODY;
	199
	200	if (!isfinite(ra) \|\| ra < 0.0 \|\| ra >= 24.0)
	201	return ASTRO_INVALID_PARAMETER;
	202
	203	if (!isfinite(dec) \|\| dec < -90.0 \|\| dec > +90.0)
	204	return ASTRO_INVALID_PARAMETER;
	205
	206	if (!isfinite(distanceLightYears) \|\| distanceLightYears < 1.0)
	207	return ASTRO_INVALID_PARAMETER;
	208
	209	star->ra = ra;
	210	star->dec = dec;
	211	star->dist = distanceLightYears * AU_PER_LY;
	212
	213	return ASTRO_SUCCESS;
	214	}
	215
	216	static const terse_vector_t VecZero = { 0.0, 0.0, 0.0 };
	217
	218	static terse_vector_t VecAdd(terse_vector_t a, terse_vector_t b)
	219	{
	220	terse_vector_t c;
	221	c.x = a.x + b.x;
	222	c.y = a.y + b.y;
	223	c.z = a.z + b.z;
	224	return c;
	225	}
	226
	227	static void VecIncr(terse_vector_t *target, terse_vector_t source)
	228	{
	229	target->x += source.x;
	230	target->y += source.y;
	231	target->z += source.z;
	232	}
	233
	234	static void VecDecr(terse_vector_t *target, terse_vector_t source)
	235	{
	236	target->x -= source.x;
	237	target->y -= source.y;
	238	target->z -= source.z;
	239	}
	240
	241	static terse_vector_t VecMul(double s, terse_vector_t v)
	242	{
	243	terse_vector_t p;
	244	p.x = s * v.x;
	245	p.y = s * v.y;
	246	p.z = s * v.z;
	247	return p;
	248	}
	249
	250	static void VecScale(terse_vector_t *target, double scalar)
	251	{
	252	target->x *= scalar;
	253	target->y *= scalar;
	254	target->z *= scalar;
	255	}
	256
	257	static terse_vector_t VecRamp(terse_vector_t a, terse_vector_t b, double ramp)
	258	{
	259	terse_vector_t c;
	260	c.x = (1-ramp)a.x + rampb.x;
	261	c.y = (1-ramp)a.y + rampb.y;
	262	c.z = (1-ramp)a.z + rampb.z;
	263	return c;
	264	}
	265
	266	static terse_vector_t VecMean(terse_vector_t a, terse_vector_t b)
	267	{
	268	terse_vector_t c;
	269	c.x = (a.x + b.x) / 2;
	270	c.y = (a.y + b.y) / 2;
	271	c.z = (a.z + b.z) / 2;
	272	return c;
	273	}
	274
	275	static astro_state_vector_t ExportState(body_state_t terse, astro_time_t time)
	276	{
	277	astro_state_vector_t state;
	278
	279	state.status = ASTRO_SUCCESS;
	280	state.x = terse.r.x;
	281	state.y = terse.r.y;
	282	state.z = terse.r.z;
	283	state.vx = terse.v.x;
	284	state.vy = terse.v.y;
	285	state.vz = terse.v.z;
	286	state.t = time;
	287
	288	return state;
	289	}
	290
	291	static astro_state_vector_t ExportGravCalc(body_grav_calc_t calc, astro_time_t time)
	292	{
	293	astro_state_vector_t state;
	294
	295	state.status = ASTRO_SUCCESS;
	296	state.x = calc.r.x;
	297	state.y = calc.r.y;
	298	state.z = calc.r.z;
	299	state.vx = calc.v.x;
	300	state.vy = calc.v.y;
	301	state.vz = calc.v.z;
	302	state.t = time;
	303
	304	return state;
	305	}
	306
	307	static const double DAYS_PER_TROPICAL_YEAR = 365.24217;
	308	static const double ASEC360 = 1296000.0;
	309	static const double ASEC2RAD = 4.848136811095359935899141e-6;
	310	static const double PI2 = 2.0 * PI;
	311	static const double ARC = 3600.0 * 180.0 / PI; /* arcseconds per radian */
	312	static const double SECONDS_PER_DAY = 24.0 * 3600.0;
	313	static const double SOLAR_DAYS_PER_SIDEREAL_DAY = 0.9972695717592592;
	314	static const double MEAN_SYNODIC_MONTH = 29.530588; /* average number of days for Moon to return to the same phase */
	315	static const double EARTH_ORBITAL_PERIOD = 365.256;
	316	static const double NEPTUNE_ORBITAL_PERIOD = 60189.0;
	317
	318	/*
	319	Degrees of refractive "lift" seen for objects near horizon.
	320	More precisely, the angle below the horizon a point has to be, at sea level,
	321	to appear to be exactly on the horizon.
	322	If the ground plane is higher than sea level, this angle
	323	needs to be corrected for decreased atmospheric density.
	324	*/
	325	static const double REFRACTION_NEAR_HORIZON = 34.0 / 60.0;
	326
	327
	328	#define SUN_RADIUS_AU (SUN_RADIUS_KM / KM_PER_AU)
	329
	330	#define EARTH_MEAN_RADIUS_KM 6371.0 /* mean radius of the Earth's geoid, without atmosphere */
	331	#define EARTH_ATMOSPHERE_KM 88.0 /* effective atmosphere thickness for lunar eclipses. see: https://eclipse.gsfc.nasa.gov/LEcat5/shadow.html */
	332	#define EARTH_ECLIPSE_RADIUS_KM (EARTH_MEAN_RADIUS_KM + EARTH_ATMOSPHERE_KM)
	333	#define EARTH_EQUATORIAL_RADIUS_AU (EARTH_EQUATORIAL_RADIUS_KM / KM_PER_AU)
	334
	335	#define MOON_MEAN_RADIUS_KM 1737.4
	336	#define MOON_EQUATORIAL_RADIUS_AU (MOON_EQUATORIAL_RADIUS_KM / KM_PER_AU)
	337	#define MOON_POLAR_RADIUS_AU (MOON_POLAR_RADIUS_KM / KM_PER_AU)
	338
	339	/* The inclination of the moon's rotation axis to the ecliptic plane, in radians. */
	340	#define MOON_AXIS_INCLINATION_RADIANS (DEG2RAD * 1.543)
	341
	342	static const double ASEC180 = 180.0 * 60.0 * 60.0; /* arcseconds per 180 degrees (or pi radians) */
	343	static const double EARTH_MOON_MASS_RATIO = 81.30056;
	344
	345	/*
	346	Masses of the Sun and planets, used for:
	347	(1) Calculating the Solar System Barycenter
	348	(2) Integrating the movement of Pluto
	349
	350	https://web.archive.org/web/20120220062549/http://iau-comm4.jpl.nasa.gov/de405iom/de405iom.pdf
	351
	352	Page 10 in the above document describes the constants used in the DE405 ephemeris.
	353	The following are GM values (gravity constant * mass) in [au^3 / day^2].
	354	This side-steps issues of not knowing the exact values of G and masses M[i];
	355	the products GM[i] are known extremely accurately.
	356	*/
	357	static const double SUN_GM = 0.2959122082855911e-03;
	358	static const double MERCURY_GM = 0.4912547451450812e-10;
	359	static const double VENUS_GM = 0.7243452486162703e-09;
	360	static const double EARTH_GM = 0.8887692390113509e-09;
	361	static const double MARS_GM = 0.9549535105779258e-10;
	362	static const double JUPITER_GM = 0.2825345909524226e-06;
	363	static const double SATURN_GM = 0.8459715185680659e-07;
	364	static const double URANUS_GM = 0.1292024916781969e-07;
	365	static const double NEPTUNE_GM = 0.1524358900784276e-07;
	366	static const double PLUTO_GM = 0.2188699765425970e-11;
	367
	368	#define MOON_GM (EARTH_GM / EARTH_MOON_MASS_RATIO)
	369
	370	/** @cond DOXYGEN_SKIP */
	371	#define ASTRO_ARRAYSIZE(x) (sizeof(x) / sizeof(x[0]))
	372	#define AU_PER_PARSEC (ASEC180 / PI) /* exact definition of how many AU = one parsec */
	373	#define Y2000_IN_MJD (T0 - MJD_BASIS)
	374	/** @endcond */
	375
	376	static astro_ecliptic_t RotateEquatorialToEcliptic(const double pos[3], double obliq_radians, astro_time_t time);
	377	static int QuadInterp(
	378	double tm, double dt, double fa, double fm, double fb,
	379	double t, double df_dt);
	380
	381	static double LongitudeOffset(double diff)
	382	{
	383	double offset = diff;
	384
	385	while (offset <= -180.0)
	386	offset += 360.0;
	387
	388	while (offset > 180.0)
	389	offset -= 360.0;
	390
	391	return offset;
	392	}
	393
	394	static double NormalizeLongitude(double lon)
	395	{
	396	while (lon < 0.0)
	397	lon += 360.0;
	398
	399	while (lon >= 360.0)
	400	lon -= 360.0;
	401
	402	return lon;
	403	}
	404
	405	/**
	406	* @brief Calculates the length of the given vector.
	407	*
	408	* Calculates the non-negative length of the given vector.
	409	* The length is expressed in the same units as the vector's components,
	410	* usually astronomical units (AU).
	411	*
	412	* @param vector The vector whose length is to be calculated.
	413	* @return The length of the vector.
	414	*/
	415	double Astronomy_VectorLength(astro_vector_t vector)
	416	{
	417	return sqrt(vector.xvector.x + vector.yvector.y + vector.z*vector.z);
	418	}
	419
	420	/**
	421	* @brief Finds the name of a celestial body.
	422	* @param body The celestial body whose name is to be found.
	423	* @return The English-language name of the celestial body, or "" if the body is not valid.
	424	*/
	425	const char *Astronomy_BodyName(astro_body_t body)
	426	{
	427	switch (body)
	428	{
	429	case BODY_MERCURY: return "Mercury";
	430	case BODY_VENUS: return "Venus";
	431	case BODY_EARTH: return "Earth";
	432	case BODY_MARS: return "Mars";
	433	case BODY_JUPITER: return "Jupiter";
	434	case BODY_SATURN: return "Saturn";
	435	case BODY_URANUS: return "Uranus";
	436	case BODY_NEPTUNE: return "Neptune";
	437	case BODY_PLUTO: return "Pluto";
	438	case BODY_SUN: return "Sun";
	439	case BODY_MOON: return "Moon";
	440	case BODY_EMB: return "EMB";
	441	case BODY_SSB: return "SSB";
	442	default: return "";
	443	}
	444	}
	445
	446	/**
	447	* @brief Returns the #astro_body_t value corresponding to the given English name.
	448	* @param name One of the following strings: Sun, Moon, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, Pluto, EMB, SSB.
	449	* @return If `name` is one of the listed strings (case-sensitive), the returned value is the corresponding #astro_body_t value, otherwise it is `BODY_INVALID`.
	450	*/
	451	astro_body_t Astronomy_BodyCode(const char *name)
	452	{
	453	if (name != NULL)
	454	{
	455	if (!strcmp(name, "Mercury")) return BODY_MERCURY;
	456	if (!strcmp(name, "Venus")) return BODY_VENUS;
	457	if (!strcmp(name, "Earth")) return BODY_EARTH;
	458	if (!strcmp(name, "Mars")) return BODY_MARS;
	459	if (!strcmp(name, "Jupiter")) return BODY_JUPITER;
	460	if (!strcmp(name, "Saturn")) return BODY_SATURN;
	461	if (!strcmp(name, "Uranus")) return BODY_URANUS;
	462	if (!strcmp(name, "Neptune")) return BODY_NEPTUNE;
	463	if (!strcmp(name, "Pluto")) return BODY_PLUTO;
	464	if (!strcmp(name, "Sun")) return BODY_SUN;
	465	if (!strcmp(name, "Moon")) return BODY_MOON;
	466	if (!strcmp(name, "EMB")) return BODY_EMB;
	467	if (!strcmp(name, "SSB")) return BODY_SSB;
	468	}
	469	return BODY_INVALID;
	470	}
	471
	472	/**
	473	* @brief Returns 1 for planets that are farther from the Sun than the Earth is, 0 otherwise.
	474	*/
	475	static int IsSuperiorPlanet(astro_body_t body)
	476	{
	477	switch (body)
	478	{
	479	case BODY_MARS:
	480	case BODY_JUPITER:
	481	case BODY_SATURN:
	482	case BODY_URANUS:
	483	case BODY_NEPTUNE:
	484	case BODY_PLUTO:
	485	return 1;
	486
	487	default:
	488	return 0;
	489	}
	490	}
	491
	492	/**
	493	* @brief Returns the average number of days it takes for a planet to orbit the Sun.
	494	* @param body One of the planets: Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, Neptune, or Pluto.
	495	* @return The mean orbital period of the body, or 0.0 if the `body` parameter is not valid.
	496	*/
	497	double Astronomy_PlanetOrbitalPeriod(astro_body_t body)
	498	{
	499	switch (body)
	500	{
	501	case BODY_MERCURY: return 87.969;
	502	case BODY_VENUS: return 224.701;
	503	case BODY_EARTH: return EARTH_ORBITAL_PERIOD;
	504	case BODY_MARS: return 686.980;
	505	case BODY_JUPITER: return 4332.589;
	506	case BODY_SATURN: return 10759.22;
	507	case BODY_URANUS: return 30685.4;
	508	case BODY_NEPTUNE: return NEPTUNE_ORBITAL_PERIOD;
	509	case BODY_PLUTO: return 90560.0;
	510	default: return 0.0; /* invalid body */
	511	}
	512	}
	513
	514	static astro_vector_t VecError(astro_status_t status, astro_time_t time)
	515	{
	516	astro_vector_t vec;
	517	vec.x = vec.y = vec.z = NAN;
	518	vec.t = time;
	519	vec.status = status;
	520	return vec;
	521	}
	522
	523	static astro_state_vector_t StateVecError(astro_status_t status, astro_time_t time)
	524	{
	525	astro_state_vector_t vec;
	526	vec.x = vec.y = vec.z = NAN;
	527	vec.vx = vec.vy = vec.vz = NAN;
	528	vec.t = time;
	529	vec.status = status;
	530	return vec;
	531	}
	532
	533	static astro_spherical_t SphereError(astro_status_t status)
	534	{
	535	astro_spherical_t sphere;
	536	sphere.status = status;
	537	sphere.dist = sphere.lat = sphere.lon = NAN;
	538	return sphere;
	539	}
	540
	541	static astro_time_t TimeError(void)
	542	{
	543	astro_time_t time;
	544	time.tt = time.ut = time.eps = time.psi = time.st = NAN;
	545	return time;
	546	}
	547
	548	static astro_equatorial_t EquError(astro_status_t status)
	549	{
	550	astro_equatorial_t equ;
	551	equ.vec = VecError(status, TimeError());
	552	equ.ra = equ.dec = equ.dist = NAN;
	553	equ.status = status;
	554	return equ;
	555	}
	556
	557	static astro_ecliptic_t EclError(astro_status_t status)
	558	{
	559	astro_ecliptic_t ecl;
	560	ecl.status = status;
	561	ecl.elon = ecl.elat = NAN;
	562	ecl.vec = VecError(status, TimeError());
	563	return ecl;
	564	}
	565
	566	static astro_angle_result_t AngleError(astro_status_t status)
	567	{
	568	astro_angle_result_t result;
	569	result.status = status;
	570	result.angle = NAN;
	571	return result;
	572	}
	573
	574	static astro_func_result_t FuncError(astro_status_t status)
	575	{
	576	astro_func_result_t result;
	577	result.status = status;
	578	result.value = NAN;
	579	return result;
	580	}
	581
	582	static astro_rotation_t RotationErr(astro_status_t status)
	583	{
	584	astro_rotation_t rotation;
	585	int i, j;
	586
	587	rotation.status = status;
	588	for (i=0; i<3; ++i)
	589	for (j=0; j<3; ++j)
	590	rotation.rot[i][j] = NAN;
	591
	592	return rotation;
	593	}
	594
	595	static astro_moon_quarter_t MoonQuarterError(astro_status_t status)
	596	{
	597	astro_moon_quarter_t result;
	598	result.status = status;
	599	result.quarter = -1;
	600	result.time = TimeError();
	601	return result;
	602	}
	603
	604	static astro_elongation_t ElongError(astro_status_t status)
	605	{
	606	astro_elongation_t result;
	607
	608	result.status = status;
	609	result.elongation = NAN;
	610	result.ecliptic_separation = NAN;
	611	result.time = TimeError();
	612	result.visibility = (astro_visibility_t)(-1);
	613
	614	return result;
	615	}
	616
	617	static astro_hour_angle_t HourAngleError(astro_status_t status)
	618	{
	619	astro_hour_angle_t result;
	620
	621	result.status = status;
	622	result.time = TimeError();
	623	result.hor.altitude = result.hor.azimuth = result.hor.dec = result.hor.ra = NAN;
	624
	625	return result;
	626	}
	627
	628	static astro_illum_t IllumError(astro_status_t status)
	629	{
	630	astro_illum_t result;
	631
	632	result.status = status;
	633	result.time = TimeError();
	634	result.mag = NAN;
	635	result.phase_angle = NAN;
	636	result.phase_fraction = NAN;
	637	result.helio_dist = NAN;
	638	result.ring_tilt = NAN;
	639
	640	return result;
	641	}
	642
	643	static astro_apsis_t ApsisError(astro_status_t status)
	644	{
	645	astro_apsis_t result;
	646
	647	result.status = status;
	648	result.time = TimeError();
	649	result.kind = APSIS_INVALID;
	650	result.dist_km = result.dist_au = NAN;
	651
	652	return result;
	653	}
	654
	655	static astro_search_result_t SearchError(astro_status_t status)
	656	{
	657	astro_search_result_t result;
	658	result.time = TimeError();
	659	result.status = status;
	660	return result;
	661	}
	662
	663	static astro_constellation_t ConstelErr(astro_status_t status)
	664	{
	665	astro_constellation_t constel;
	666	constel.status = status;
	667	constel.symbol = constel.name = NULL;
	668	constel.ra_1875 = constel.dec_1875 = NAN;
	669	return constel;
	670	}
	671
	672	static astro_transit_t TransitErr(astro_status_t status)
	673	{
	674	astro_transit_t transit;
	675	transit.status = status;
	676	transit.start = transit.peak = transit.finish = TimeError();
	677	transit.separation = NAN;
	678	return transit;
	679	}
	680
	681	static astro_axis_t AxisErr(astro_status_t status, astro_time_t time)
	682	{
	683	astro_axis_t axis;
	684	axis.status = status;
	685	axis.ra = axis.dec = axis.spin = NAN;
	686	axis.north = VecError(status, time);
	687	return axis;
	688	}
	689
	690	static astro_func_result_t SynodicPeriod(astro_body_t body)
	691	{
	692	double Tp; /* planet's orbital period in days */
	693	astro_func_result_t result;
	694
	695	/* The Earth does not have a synodic period as seen from itself. */
	696	if (body == BODY_EARTH)
	697	return FuncError(ASTRO_EARTH_NOT_ALLOWED);
	698
	699	if (body == BODY_MOON)
	700	{
	701	result.status = ASTRO_SUCCESS;
	702	result.value = MEAN_SYNODIC_MONTH;
	703	return result;
	704	}
	705
	706	Tp = Astronomy_PlanetOrbitalPeriod(body);
	707	if (Tp <= 0.0)
	708	return FuncError(ASTRO_INVALID_BODY);
	709
	710	result.status = ASTRO_SUCCESS;
	711	result.value = fabs(EARTH_ORBITAL_PERIOD / (EARTH_ORBITAL_PERIOD/Tp - 1.0));
	712	return result;
	713	}
	714
	715
	716	/**
	717	* @brief Calculates the angle between two vectors.
	718	*
	719	* Given a pair of vectors, this function returns the angle in degrees
	720	* between the two vectors in 3D space.
	721	* The angle is measured in the plane that contains both vectors.
	722	*
	723	* @param a
	724	* The first vector.
	725	*
	726	* @param b
	727	* The second vector.
	728	*
	729	* @returns
	730	* On success, the `status` field holds `ASTRO_SUCCESS` and `angle` holds
	731	* a number of degrees in the range [0, 180].
	732	* If either vector has a zero magnitude or contains NAN (not a number)
	733	* components, the `status` will hold the error code `ASTRO_BAD_VECTOR`.
	734	*/
	735	astro_angle_result_t Astronomy_AngleBetween(astro_vector_t a, astro_vector_t b)
	736	{
	737	double r, dot;
	738	astro_angle_result_t result;
	739
	740	r = Astronomy_VectorLength(a) * Astronomy_VectorLength(b);
	741	if (r < 1.0e-8 \|\| !isfinite(r))
	742	return AngleError(ASTRO_BAD_VECTOR);
	743
	744	dot = (a.xb.x + a.yb.y + a.z*b.z) / r;
	745
	746	if (dot <= -1.0)
	747	result.angle = 180.0;
	748	else if (dot >= +1.0)
	749	result.angle = 0.0;
	750	else
	751	result.angle = RAD2DEG * acos(dot);
	752
	753	result.status = ASTRO_SUCCESS;
	754	return result;
	755	}
	756
	757	/**
	758	* @brief The default Delta T function used by Astronomy Engine.
	759	*
	760	* Espenak and Meeus use a series of piecewise polynomials to
	761	* approximate DeltaT of the Earth in their "Five Millennium Canon of Solar Eclipses".
	762	* See: https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html
	763	* This is the default Delta T function used by Astronomy Engine.
	764	*
	765	* @param ut
	766	* The floating point number of days since noon UTC on January 1, 2000.
	767	*
	768	* @returns
	769	* The estimated difference TT-UT on the given date, expressed in seconds.
	770	*/
	771	double Astronomy_DeltaT_EspenakMeeus(double ut)
	772	{
	773	double y, u, u2, u3, u4, u5, u6, u7;
	774
	775	/*
	776	Fred Espenak writes about Delta-T generically here:
	777	https://eclipse.gsfc.nasa.gov/SEhelp/deltaT.html
	778	https://eclipse.gsfc.nasa.gov/SEhelp/deltat2004.html
	779
	780	He provides polynomial approximations for distant years here:
	781	https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html
	782
	783	They start with a year value 'y' such that y=2000 corresponds
	784	to the UTC Date 15-January-2000. Convert difference in days
	785	to mean tropical years.
	786	*/
	787
	788	y = 2000 + ((ut - 14) / DAYS_PER_TROPICAL_YEAR);
	789
	790	if (y < -500)
	791	{
	792	u = (y - 1820) / 100;
	793	return -20 + (32 * u*u);
	794	}
	795	if (y < 500)
	796	{
	797	u = y / 100;
	798	u2 = uu; u3 = uu2; u4 = u2u2; u5 = u2u3; u6 = u3*u3;
	799	return 10583.6 - 1014.41u + 33.78311u2 - 5.952053u3 - 0.1798452u4 + 0.022174192u5 + 0.0090316521u6;
	800	}
	801	if (y < 1600)
	802	{
	803	u = (y - 1000) / 100;
	804	u2 = uu; u3 = uu2; u4 = u2u2; u5 = u2u3; u6 = u3*u3;
	805	return 1574.2 - 556.01u + 71.23472u2 + 0.319781u3 - 0.8503463u4 - 0.005050998u5 + 0.0083572073u6;
	806	}
	807	if (y < 1700)
	808	{
	809	u = y - 1600;
	810	u2 = uu; u3 = uu2;
	811	return 120 - 0.9808u - 0.01532u2 + u3/7129.0;
	812	}
	813	if (y < 1800)
	814	{
	815	u = y - 1700;
	816	u2 = uu; u3 = uu2; u4 = u2*u2;
	817	return 8.83 + 0.1603u - 0.0059285u2 + 0.00013336*u3 - u4/1174000;
	818	}
	819	if (y < 1860)
	820	{
	821	u = y - 1800;
	822	u2 = uu; u3 = uu2; u4 = u2u2; u5 = u2u3; u6 = u3u3; u7 = u3u4;
	823	return 13.72 - 0.332447u + 0.0068612u2 + 0.0041116u3 - 0.00037436u4 + 0.0000121272u5 - 0.0000001699u6 + 0.000000000875*u7;
	824	}
	825	if (y < 1900)
	826	{
	827	u = y - 1860;
	828	u2 = uu; u3 = uu2; u4 = u2u2; u5 = u2u3;
	829	return 7.62 + 0.5737u - 0.251754u2 + 0.01680668u3 - 0.0004473624u4 + u5/233174;
	830	}
	831	if (y < 1920)
	832	{
	833	u = y - 1900;
	834	u2 = uu; u3 = uu2; u4 = u2*u2;
	835	return -2.79 + 1.494119u - 0.0598939u2 + 0.0061966u3 - 0.000197u4;
	836	}
	837	if (y < 1941)
	838	{
	839	u = y - 1920;
	840	u2 = uu; u3 = uu2;
	841	return 21.20 + 0.84493u - 0.076100u2 + 0.0020936*u3;
	842	}
	843	if (y < 1961)
	844	{
	845	u = y - 1950;
	846	u2 = uu; u3 = uu2;
	847	return 29.07 + 0.407*u - u2/233 + u3/2547;
	848	}
	849	if (y < 1986)
	850	{
	851	u = y - 1975;
	852	u2 = uu; u3 = uu2;
	853	return 45.45 + 1.067*u - u2/260 - u3/718;
	854	}
	855	if (y < 2005)
	856	{
	857	u = y - 2000;
	858	u2 = uu; u3 = uu2; u4 = u2u2; u5 = u2u3;
	859	return 63.86 + 0.3345u - 0.060374u2 + 0.0017275u3 + 0.000651814u4 + 0.00002373599*u5;
	860	}
	861	if (y < 2050)
	862	{
	863	u = y - 2000;
	864	return 62.92 + 0.32217u + 0.005589u*u;
	865	}
	866	if (y < 2150)
	867	{
	868	u = (y-1820)/100;
	869	return -20 + 32uu - 0.5628*(2150 - y);
	870	}
	871
	872	/* all years after 2150 */
	873	u = (y - 1820) / 100;
	874	return -20 + (32 * u*u);
	875	}
	876
	877	/**
	878	* @brief A Delta T function that approximates the one used by the JPL Horizons tool.
	879	*
	880	* In order to support unit tests based on data generated by the JPL Horizons online
	881	* tool, I had to reverse engineer their Delta T function by generating a table that
	882	* contained it. The main difference between their tool and the Espenak/Meeus function
	883	* is that they stop extrapolating the Earth's deceleration after the year 2017.
	884	*
	885	* @param ut
	886	* The floating point number of days since noon UTC on January 1, 2000.
	887	*
	888	* @returns
	889	* The estimated difference TT-UT on the given date, expressed in seconds.
	890	*/
	891	double Astronomy_DeltaT_JplHorizons(double ut)
	892	{
	893	if (ut > 17.0 * DAYS_PER_TROPICAL_YEAR)
	894	ut = 17.0 * DAYS_PER_TROPICAL_YEAR;
	895
	896	return Astronomy_DeltaT_EspenakMeeus(ut);
	897	}
	898
	899	static astro_deltat_func DeltaTFunc = Astronomy_DeltaT_EspenakMeeus;
	900
	901	/**
	902	* @brief Changes the function Astronomy Engine uses to calculate Delta T.
	903	*
	904	* Most programs should not call this function. It is for advanced use cases only.
	905	* By default, Astronomy Engine uses the function #Astronomy_DeltaT_EspenakMeeus
	906	* to estimate changes in the Earth's rotation rate over time.
	907	* However, for the sake of unit tests that compare calculations against
	908	* external data sources that use alternative models for Delta T,
	909	* it is sometimes useful to replace the Delta T model to match.
	910	* This function allows replacing the Delta T model with any other
	911	* desired model.
	912	*
	913	* @param func
	914	* A pointer to a function to convert UT values to DeltaT values.
	915	*/
	916	void Astronomy_SetDeltaTFunction(astro_deltat_func func)
	917	{
	918	DeltaTFunc = func;
	919	}
	920
	921	static double TerrestrialTime(double ut)
	922	{
	923	return ut + DeltaTFunc(ut)/86400.0;
	924	}
	925
	926	/**
	927	* @brief Converts a J2000 day value to an #astro_time_t value.
	928	*
	929	* This function can be useful for reproducing an #astro_time_t structure
	930	* from its `ut` field only.
	931	*
	932	* @param ut
	933	* The floating point number of days since noon UTC on January 1, 2000.
	934	* This time is based on UTC/UT1 civil time.
	935	* See #Astronomy_TerrestrialTime if you instead want to create
	936	* a time value based on atomic Terrestrial Time (TT).
	937	*
	938	* @returns
	939	* An #astro_time_t value for the given `ut` value.
	940	*/
	941	astro_time_t Astronomy_TimeFromDays(double ut)
	942	{
	943	astro_time_t time;
	944	time.ut = ut;
	945	time.tt = TerrestrialTime(ut);
	946	time.psi = time.eps = time.st = NAN;
	947	return time;
	948	}
	949
	950
	951	/**
	952	* @brief Converts a terrestrial time value into an #astro_time_t value.
	953	*
	954	* This function can be used in rare cases where a time must be based
	955	* on Terrestrial Time (TT) rather than Universal Time (UT).
	956	* Most developers will want to call #Astronomy_TimeFromDays instead of
	957	* this function, because usually time is based on civil time adjusted
	958	* by leap seconds to match the Earth's rotation, rather than the uniformly
	959	* flowing TT used to calculate solar system dynamics. In rare cases
	960	* where the caller already knows TT, this function is provided to create
	961	* an #astro_time_t value that can be passed to Astronomy Engine functions.
	962	*
	963	* @param tt
	964	* The floating point number of days of uniformly flowing
	965	* Terrestrial Time since the J2000 epoch.
	966	*
	967	* @returns
	968	* An #astro_time_t value for the given `tt` value.
	969	*/
	970	astro_time_t Astronomy_TerrestrialTime(double tt)
	971	{
	972	/* Iterate to solve to find the correct ut for a given tt, and create an astro_time_t for that time. */
	973	astro_time_t time = Astronomy_TimeFromDays(tt);
	974	for(;;)
	975	{
	976	double err = tt - time.tt;
	977	if (fabs(err) < 1.0e-12)
	978	return time;
	979	time = Astronomy_AddDays(time, err);
	980	}
	981	}
	982
	983	#if !defined(ASTRONOMY_ENGINE_NO_CURRENT_TIME)
	984	/**
	985	* @brief Returns the computer's current date and time in the form of an #astro_time_t.
	986	*
	987	* Uses the computer's system clock to find the current UTC date and time.
	988	* Converts that date and time to an #astro_time_t value and returns the result.
	989	* Callers can pass this value to other Astronomy Engine functions to calculate
	990	* current observational conditions.
	991	*
	992	* On supported platforms (Linux/Unix, Mac, Windows), the time is measured with
	993	* microsecond resolution.
	994	*
	995	* On unsupported platforms, a compiler error will occur due to lack of
	996	* microsecond resolution support. However, if whole second resolution is good
	997	* enough for your application, you can define the preprocessor symbol
	998	* `ASTRONOMY_ENGINE_WHOLE_SECOND` to use the portable function `time(NULL)`.
	999	* Alternatively, if you do not need to use `Astronomy_CurrentTime`, you can
	1000	* define the preprocessor symbol `ASTRONOMY_ENGINE_NO_CURRENT_TIME` to
	1001	* exclude this function from your code.
	1002	*/
	1003	astro_time_t Astronomy_CurrentTime(void)
	1004	{
	1005	astro_time_t t;
	1006	double sec; /* Seconds since midnight January 1, 1970. */
	1007
	1008	#if defined(__unix__) \|\| defined(__unix) \|\| (defined(__APPLE__) && defined(__MACH__))
	1009	struct timeval tv;
	1010	gettimeofday(&tv, NULL);
	1011	sec = (double)tv.tv_sec + tv.tv_usec/1.0e+6;
	1012	#elif defined(_WIN32)
	1013	FILETIME ft;
	1014	ULARGE_INTEGER large;
	1015	/* Get time in 100-nanosecond units from January 1, 1601. */
	1016	GetSystemTimePreciseAsFileTime(&ft);
	1017	large.u.LowPart = ft.dwLowDateTime;
	1018	large.u.HighPart = ft.dwHighDateTime;
	1019	sec = (large.QuadPart - 116444736000000000ULL) / 1.0e+7;
	1020	#elif defined(ASTRONOMY_ENGINE_WHOLE_SECOND)
	1021	sec = time(NULL);
	1022	#else
	1023	#error Microsecond time resolution is not supported on this platform. Define ASTRONOMY_ENGINE_WHOLE_SECOND to use second resolution instead.
	1024	#endif
	1025
	1026	/* Convert seconds to days, then subtract to get days since noon on January 1, 2000. */
	1027	t.ut = (sec / SECONDS_PER_DAY) - 10957.5;
	1028	t.tt = TerrestrialTime(t.ut);
	1029	t.psi = t.eps = t.st = NAN;
	1030	return t;
	1031	}
	1032	#endif
	1033
	1034	/**
	1035	* @brief Creates an #astro_time_t value from a given calendar date and time.
	1036	*
	1037	* Given a UTC calendar date and time, calculates an #astro_time_t value that can
	1038	* be passed to other Astronomy Engine functions for performing various calculations
	1039	* relating to that date and time.
	1040	*
	1041	* It is the caller's responsibility to ensure that the parameter values are correct.
	1042	* The parameters are not checked for validity,
	1043	* and this function never returns any indication of an error.
	1044	* Invalid values, for example passing in February 31, may cause unexpected return values.
	1045	*
	1046	* @param year The UTC calendar year, e.g. 2019.
	1047	* @param month The UTC calendar month in the range 1..12.
	1048	* @param day The UTC calendar day in the range 1..31.
	1049	* @param hour The UTC hour of the day in the range 0..23.
	1050	* @param minute The UTC minute in the range 0..59.
	1051	* @param second The UTC floating-point second in the range [0, 60).
	1052	*
	1053	* @return An #astro_time_t value that represents the given calendar date and time.
	1054	*/
	1055	astro_time_t Astronomy_MakeTime(int year, int month, int day, int hour, int minute, double second)
	1056	{
	1057	astro_time_t time;
	1058	int64_t y = (int64_t)year;
	1059	int64_t m = (int64_t)month;
	1060	int64_t d = (int64_t)day;
	1061	int64_t f = (14 - m) / 12;
	1062
	1063	/*
	1064	This formula is adapted from NOVAS C 3.1 function julian_date(),
	1065	which in turn comes from Henry F. Fliegel & Thomas C. Van Flendern:
	1066	Communications of the ACM, Vol 11, No 10, October 1968, p. 657.
	1067	See: https://dl.acm.org/doi/pdf/10.1145/364096.364097
	1068
	1069	[Don Cross - 2023-02-25] I modified the formula so that it will
	1070	work correctly with years as far back as -999999.
	1071	*/
	1072	int64_t y2000 = (
	1073	(d - 365972956)
	1074	+ (1461*(y + 1000000 - f))/4
	1075	+ (367(m - 2 + 12f))/12
	1076	- (3*((y + 1000100 - f) / 100))/4
	1077	);
	1078
	1079	time.ut = (y2000 - 0.5) + (hour / 24.0) + (minute / 1440.0) + (second / 86400.0);
	1080	time.tt = TerrestrialTime(time.ut);
	1081	time.psi = time.eps = time.st = NAN;
	1082
	1083	return time;
	1084	}
	1085
	1086	/**
	1087	* @brief Calculates the sum or difference of an #astro_time_t with a specified floating point number of days.
	1088	*
	1089	* Sometimes we need to adjust a given #astro_time_t value by a certain amount of time.
	1090	* This function adds the given real number of days in `days` to the date and time in `time`.
	1091	*
	1092	* More precisely, the result's Universal Time field `ut` is exactly adjusted by `days` and
	1093	* the Terrestrial Time field `tt` is adjusted correctly for the resulting UTC date and time,
	1094	* according to the historical and predictive Delta-T model provided by the
	1095	* [United States Naval Observatory](http://maia.usno.navy.mil/ser7/).
	1096	*
	1097	* The value stored in `time` will not be modified; it is passed by value.
	1098	*
	1099	* @param time A date and time for which to calculate an adjusted date and time.
	1100	* @param days A floating point number of days by which to adjust `time`. May be negative, 0, or positive.
	1101	* @return A date and time that is conceptually equal to `time + days`.
	1102	*/
	1103	astro_time_t Astronomy_AddDays(astro_time_t time, double days)
	1104	{
	1105	/*
	1106	This is slightly wrong, but the error is tiny.
	1107	We really should be adding to TT, not to UT.
	1108	But using TT would require creating an inverse function for DeltaT,
	1109	which would be quite a bit of extra calculation.
	1110	I estimate the error is in practice on the order of 10^(-7)
	1111	times the value of 'days'.
	1112	This is based on a typical drift of 1 second per year between UT and TT.
	1113	*/
	1114
	1115	astro_time_t sum;
	1116
	1117	sum.ut = time.ut + days;
	1118	sum.tt = TerrestrialTime(sum.ut);
	1119	sum.eps = sum.psi = sum.st = NAN;
	1120
	1121	return sum;
	1122	}
	1123
	1124	/**
	1125	* @brief Creates an #astro_time_t value from a given calendar date and time.
	1126	*
	1127	* This function is similar to #Astronomy_MakeTime, only it receives a
	1128	* UTC calendar date and time in the form of an #astro_utc_t structure instead of
	1129	* as separate numeric parameters. Astronomy_TimeFromUtc is the inverse of
	1130	* #Astronomy_UtcFromTime.
	1131	*
	1132	* @param utc The UTC calendar date and time to be converted to #astro_time_t.
	1133	* @return A value that can be used for astronomical calculations for the given date and time.
	1134	*/
	1135	astro_time_t Astronomy_TimeFromUtc(astro_utc_t utc)
	1136	{
	1137	return Astronomy_MakeTime(utc.year, utc.month, utc.day, utc.hour, utc.minute, utc.second);
	1138	}
	1139
	1140	/**
	1141	* @brief Determines the calendar year, month, day, and time from an #astro_time_t value.
	1142	*
	1143	* After calculating the date and time of an astronomical event in the form of
	1144	* an #astro_time_t value, it is often useful to display the result in a human-readable
	1145	* form. This function converts the linear time scales in the `ut` field of #astro_time_t
	1146	* into a calendar date and time: year, month, day, hours, minutes, and seconds, expressed
	1147	* in UTC.
	1148	*
	1149	* @param time The astronomical time value to be converted to calendar date and time.
	1150	* @return A date and time broken out into conventional year, month, day, hour, minute, and second.
	1151	*/
	1152	astro_utc_t Astronomy_UtcFromTime(astro_time_t time)
	1153	{
	1154	/* Adapted from the NOVAS C 3.1 function cal_date() */
	1155	astro_utc_t utc;
	1156	int64_t jd, k, m, n;
	1157	double djd, x;
	1158	const int64_t c = 2500;
	1159
	1160	djd = time.ut + 2451545.5;
	1161	jd = (int64_t)floor(djd);
	1162
	1163	x = 24.0 * fmod(djd, 1.0);
	1164	if (x < 0.0)
	1165	x += 24.0;
	1166	utc.hour = (int)x;
	1167	x = 60.0 * fmod(x, 1.0);
	1168	utc.minute = (int)x;
	1169	utc.second = 60.0 * fmod(x, 1.0);
	1170
	1171	/*
	1172	This is my own adjustment to the NOVAS cal_date logic
	1173	so that it can handle dates much farther back in the past.
	1174	I add c*400 years worth of days at the front,
	1175	then subtract c*400 years at the back,
	1176	which avoids negative values in the formulas that mess up
	1177	the calendar date calculations.
	1178	Any multiple of 400 years has the same number of days,
	1179	because it eliminates all the special cases for leap years.
	1180	*/
	1181	k = jd + (68569 + c*146097);
	1182	n = (4 * k) / 146097;
	1183	k = k - (146097 * n + 3)/4;
	1184	m = (4000 * (k+1)) / 1461001;
	1185	k = k - (1461 * m)/4 + 31;
	1186
	1187	utc.month = (int) ((80 * k) / 2447);
	1188	utc.day = (int) (k - (2447*utc.month)/80);
	1189	k = utc.month / 11;
	1190
	1191	utc.month = (int) (utc.month + 2 - 12*k);
	1192	utc.year = (int) (100 * (n - 49) + m + k - 400*c);
	1193
	1194	return utc;
	1195	}
	1196
	1197
	1198	/**
	1199	* @brief Formats an #astro_time_t value as an ISO 8601 string.
	1200	*
	1201	* Given an #astro_time_t value `time`, formats it as an ISO 8601
	1202	* string to the resolution specified by the `format` parameter.
	1203	* The result is stored in the `text` buffer whose capacity in bytes
	1204	* is specified by `size`.
	1205	*
	1206	* @param time
	1207	* The date and time whose civil time `time.ut` is to be formatted as an ISO 8601 string.
	1208	* If the civil time is outside the year range -999999 to +999999, the function fails
	1209	* and returns `ASTRO_BAD_TIME`. Years prior to 1583 are treated as if they are
	1210	* using the modern Gregorian calendar, even when the Julian calendar was actually in effect.
	1211	* The year before 1 AD, commonly known as 1 BC, is represented by the value 0.
	1212	* The year 2 BC is represented by -1, etc.
	1213	*
	1214	* @param format
	1215	* Specifies the resolution to which the date and time should be formatted,
	1216	* as explained at #astro_time_format_t.
	1217	* If the value of `format` is not recognized, the function fails and
	1218	* returns `ASTRO_INVALID_PARAMETER`.
	1219	*
	1220	* @param text
	1221	* A pointer to a text buffer to receive the output.
	1222	* If `text` is `NULL`, this function returns `ASTRO_INVALID_PARAMETER`.
	1223	* If the function fails for any reason, and `text` is not `NULL`,
	1224	* and `size` is greater than 0, the `text` buffer is set to an empty string.
	1225	*
	1226	* @param size
	1227	* The size in bytes of the buffer pointed to by `text`. The buffer must
	1228	* be large enough to accomodate the output format selected by the
	1229	* `format` parameter, as specified at #astro_time_format_t.
	1230	* If `size` is too small to hold the string as specified by `format`,
	1231	* the `text` buffer is set to `""` (if possible)
	1232	* and the function returns `ASTRO_BUFFER_TOO_SMALL`.
	1233	* A buffer that is `TIME_TEXT_BYTES` (28) bytes or larger is always large enough for this function.
	1234	*
	1235	* @return `ASTRO_SUCCESS` on success; otherwise an error as described in the parameter notes.
	1236	*/
	1237	astro_status_t Astronomy_FormatTime(
	1238	astro_time_t time,
	1239	astro_time_format_t format,
	1240	char *text,
	1241	size_t size)
	1242	{
	1243	int nprinted;
	1244	double rounding;
	1245	size_t min_size;
	1246	astro_utc_t utc;
	1247	char ytext[20]; /* worst case: "+999999" = 8 characters including terminal '\0'. But gcc 12.2 still complains! */
	1248
	1249	if (text == NULL)
	1250	return ASTRO_INVALID_PARAMETER;
	1251
	1252	if (size == 0)
	1253	return ASTRO_BUFFER_TOO_SMALL;
	1254
	1255	text[0] = '\0'; /* initialize to empty string, in case an error occurs */
	1256
	1257	/* Validate 'size' parameter and perform date/time rounding. */
	1258	switch (format)
	1259	{
	1260	case TIME_FORMAT_DAY:
	1261	min_size = 11; /* "2020-12-31" */
	1262	rounding = 0.0; /* no rounding */
	1263	break;
	1264
	1265	case TIME_FORMAT_MINUTE:
	1266	min_size = 18; /* "2020-12-31T15:47Z" */
	1267	rounding = 0.5 / (24.0 * 60.0); /* round to nearest minute */
	1268	break;
	1269
	1270	case TIME_FORMAT_SECOND:
	1271	min_size = 21; /* "2020-12-31T15:47:59Z" */
	1272	rounding = 0.5 / (24.0 * 3600.0); /* round to nearest second */
	1273	break;
	1274
	1275	case TIME_FORMAT_MILLI:
	1276	min_size = 25; /* "2020-12-31T15:47:59.123Z" */
	1277	rounding = 0.5 / (24.0 * 3600000.0); /* round to nearest millisecond */
	1278	break;
	1279
	1280	default:
	1281	return ASTRO_INVALID_PARAMETER;
	1282	}
	1283
	1284	/* Perform rounding. */
	1285	time.ut += rounding;
	1286
	1287	/* Convert linear J2000 days to Gregorian UTC date/time. */
	1288	utc = Astronomy_UtcFromTime(time);
	1289	if (utc.year < -999999 \|\| utc.year > +999999)
	1290	return ASTRO_BAD_TIME;
	1291
	1292	if (utc.year < 0)
	1293	{
	1294	snprintf(ytext, sizeof(ytext), "-%06d", -utc.year);
	1295	min_size += 3; /* '-' prefix and two extra year digits. */
	1296	}
	1297	else if (utc.year <= 9999)
	1298	{
	1299	snprintf(ytext, sizeof(ytext), "%04d", utc.year);
	1300	}
	1301	else
	1302	{
	1303	snprintf(ytext, sizeof(ytext), "+%06d", utc.year);
	1304	min_size += 3; /* '+' prefix and two extra year digits. */
	1305	}
	1306
	1307	/* Check for insufficient buffer size. */
	1308	if (size < min_size)
	1309	return ASTRO_BUFFER_TOO_SMALL;
	1310
	1311	/* Format the string. */
	1312	switch (format)
	1313	{
	1314	case TIME_FORMAT_DAY:
	1315	nprinted = snprintf(text, size, "%s-%02d-%02d",
	1316	ytext, utc.month, utc.day);
	1317	break;
	1318
	1319	case TIME_FORMAT_MINUTE:
	1320	nprinted = snprintf(text, size, "%s-%02d-%02dT%02d:%02dZ",
	1321	ytext, utc.month, utc.day,
	1322	utc.hour, utc.minute);
	1323	break;
	1324
	1325	case TIME_FORMAT_SECOND:
	1326	nprinted = snprintf(text, size, "%s-%02d-%02dT%02d:%02d:%02.0lfZ",
	1327	ytext, utc.month, utc.day,
	1328	utc.hour, utc.minute, floor(utc.second));
	1329	break;
	1330
	1331	case TIME_FORMAT_MILLI:
	1332	nprinted = snprintf(text, size, "%s-%02d-%02dT%02d:%02d:%06.3lfZ",
	1333	ytext, utc.month, utc.day,
	1334	utc.hour, utc.minute, floor(1000.0 * utc.second) / 1000.0);
	1335	break;
	1336
	1337	default:
	1338	/* We should have already failed for any unknown 'format' value. */
	1339	return ASTRO_INTERNAL_ERROR;
	1340	}
	1341
	1342	if (nprinted < 0)
	1343	return ASTRO_INTERNAL_ERROR; /* should not be possible for snprintf to return a negative number */
	1344
	1345	if ((size_t)(1+nprinted) != min_size)
	1346	return ASTRO_INTERNAL_ERROR; /* there must be a bug calculating min_size or formatting the string */
	1347
	1348	return ASTRO_SUCCESS;
	1349	}
	1350
	1351
	1352	/**
	1353	* @brief Creates an observer object that represents a location on or near the surface of the Earth.
	1354	*
	1355	* Some Astronomy Engine functions calculate values pertaining to an observer on the Earth.
	1356	* These functions require a value of type #astro_observer_t that represents the location
	1357	* of such an observer.
	1358	*
	1359	* @param latitude The geographic latitude of the observer in degrees north (positive) or south (negative) of the equator.
	1360	* @param longitude The geographic longitude of the observer in degrees east (positive) or west (negative) of the prime meridian at Greenwich, England.
	1361	* @param height The height of the observer in meters above mean sea level.
	1362	* @return An observer object that can be passed to astronomy functions that require a geographic location.
	1363	*/
	1364	astro_observer_t Astronomy_MakeObserver(double latitude, double longitude, double height)
	1365	{
	1366	astro_observer_t observer;
	1367
	1368	observer.latitude = latitude;
	1369	observer.longitude = longitude;
	1370	observer.height = height;
	1371
	1372	return observer;
	1373	}
	1374
	1375	static void iau2000b(astro_time_t *time)
	1376	{
	1377	/* Truncated and hand-optimized nutation model. */
	1378
	1379	if ((time != NULL) && isnan(time->psi))
	1380	{
	1381	double t, elp, f, d, om, arg, dp, de, sarg, carg;
	1382
	1383	t = time->tt / 36525.0;
	1384	elp = fmod(1287104.79305 + t * 129596581.0481, ASEC360) * ASEC2RAD;
	1385	f = fmod(335779.526232 + t * 1739527262.8478, ASEC360) * ASEC2RAD;
	1386	d = fmod(1072260.70369 + t * 1602961601.2090, ASEC360) * ASEC2RAD;
	1387	om = fmod(450160.398036 - t * 6962890.5431, ASEC360) * ASEC2RAD;
	1388
	1389	sarg = sin(om);
	1390	carg = cos(om);
	1391	dp = (-172064161.0 - 174666.0t)sarg + 33386.0*carg;
	1392	de = (92052331.0 + 9086.0t)carg + 15377.0*sarg;
	1393
	1394	arg = 2.0*(f - d + om);
	1395	sarg = sin(arg);
	1396	carg = cos(arg);
	1397	dp += (-13170906.0 - 1675.0t)sarg - 13696.0*carg;
	1398	de += (5730336.0 - 3015.0t)carg - 4587.0*sarg;
	1399
	1400	arg = 2.0*(f + om);
	1401	sarg = sin(arg);
	1402	carg = cos(arg);
	1403	dp += (-2276413.0 - 234.0t)sarg + 2796.0*carg;
	1404	de += (978459.0 - 485.0t)carg + 1374.0*sarg;
	1405
	1406	arg = 2.0*om;
	1407	sarg = sin(arg);
	1408	carg = cos(arg);
	1409	dp += (2074554.0 + 207.0t)sarg - 698.0*carg;
	1410	de += (-897492.0 + 470.0t)carg - 291.0*sarg;
	1411
	1412	sarg = sin(elp);
	1413	carg = cos(elp);
	1414	dp += (1475877.0 - 3633.0t)sarg + 11817.0*carg;
	1415	de += (73871.0 - 184.0t)carg - 1924.0*sarg;
	1416
	1417	time->psi = -0.000135 + (dp * 1.0e-7);
	1418	time->eps = +0.000388 + (de * 1.0e-7);
	1419	}
	1420	}
	1421
	1422	static double mean_obliq(double tt)
	1423	{
	1424	double t = tt / 36525.0;
	1425	double asec =
	1426	(((( - 0.0000000434 * t
	1427	- 0.000000576 ) * t
	1428	+ 0.00200340 ) * t
	1429	- 0.0001831 ) * t
	1430	- 46.836769 ) * t + 84381.406;
	1431
	1432	return asec / 3600.0;
	1433	}
	1434
	1435	/** @cond DOXYGEN_SKIP */
	1436	typedef struct
	1437	{
	1438	double tt;
	1439	double dpsi;
	1440	double deps;
	1441	double ee;
	1442	double mobl;
	1443	double tobl;
	1444	}
	1445	earth_tilt_t;
	1446	/** @endcond */
	1447
	1448	static earth_tilt_t e_tilt(astro_time_t *time)
	1449	{
	1450	earth_tilt_t et;
	1451
	1452	/* There is no good answer for what to do if time==NULL. Callers must prevent! */
	1453
	1454	iau2000b(time);
	1455	et.dpsi = time->psi;
	1456	et.deps = time->eps;
	1457	et.mobl = mean_obliq(time->tt);
	1458	et.tobl = et.mobl + (et.deps / 3600.0);
	1459	et.tt = time->tt;
	1460	et.ee = et.dpsi * cos(et.mobl * DEG2RAD) / 15.0;
	1461
	1462	return et;
	1463	}
	1464
	1465	static void obl_ecl2equ_vec(double obl, astro_time_t time, const double ecl[3], double equ[3])
	1466	{
	1467	double obl_rad = obl * DEG2RAD;
	1468	double cos_obl = cos(obl_rad);
	1469	double sin_obl = sin(obl_rad);
	1470
	1471	equ[0] = ecl[0];
	1472	equ[1] = ecl[1]cos_obl - ecl[2]sin_obl;
	1473	equ[2] = ecl[1]sin_obl + ecl[2]cos_obl;
	1474	}
	1475
	1476	static void ecl2equ_vec(astro_time_t time, const double ecl[3], double equ[3])
	1477	{
	1478	double obl = mean_obliq(time.tt);
	1479	obl_ecl2equ_vec(obl, time, ecl, equ);
	1480	}
	1481
	1482	static astro_rotation_t precession_rot(astro_time_t time, precess_dir_t dir)
	1483	{
	1484	/*
	1485	dir==INTO_2000: converts mean equator of date (EQM) to J2000 mean equator (EQJ).
	1486	dir==FROM_2000: converts J2000 mean equator (EQJ) to mean equator of date (EQM).
	1487	*/
	1488
	1489	astro_rotation_t rotation;
	1490	double xx, yx, zx, xy, yy, zy, xz, yz, zz;
	1491	double t, psia, omegaa, chia, sa, ca, sb, cb, sc, cc, sd, cd;
	1492	double eps0 = 84381.406;
	1493
	1494	t = time.tt / 36525;
	1495
	1496	psia = (((((- 0.0000000951 * t
	1497	+ 0.000132851 ) * t
	1498	- 0.00114045 ) * t
	1499	- 1.0790069 ) * t
	1500	+ 5038.481507 ) * t);
	1501
	1502	omegaa = (((((+ 0.0000003337 * t
	1503	- 0.000000467 ) * t
	1504	- 0.00772503 ) * t
	1505	+ 0.0512623 ) * t
	1506	- 0.025754 ) * t + eps0);
	1507
	1508	chia = (((((- 0.0000000560 * t
	1509	+ 0.000170663 ) * t
	1510	- 0.00121197 ) * t
	1511	- 2.3814292 ) * t
	1512	+ 10.556403 ) * t);
	1513
	1514	eps0 = eps0 * ASEC2RAD;
	1515	psia = psia * ASEC2RAD;
	1516	omegaa = omegaa * ASEC2RAD;
	1517	chia = chia * ASEC2RAD;
	1518
	1519	sa = sin(eps0);
	1520	ca = cos(eps0);
	1521	sb = sin(-psia);
	1522	cb = cos(-psia);
	1523	sc = sin(-omegaa);
	1524	cc = cos(-omegaa);
	1525	sd = sin(chia);
	1526	cd = cos(chia);
	1527
	1528	xx = cd * cb - sb * sd * cc;
	1529	yx = cd * sb * ca + sd * cc * cb * ca - sa * sd * sc;
	1530	zx = cd * sb * sa + sd * cc * cb * sa + ca * sd * sc;
	1531	xy = -sd * cb - sb * cd * cc;
	1532	yy = -sd * sb * ca + cd * cc * cb * ca - sa * cd * sc;
	1533	zy = -sd * sb * sa + cd * cc * cb * sa + ca * cd * sc;
	1534	xz = sb * sc;
	1535	yz = -sc * cb * ca - sa * cc;
	1536	zz = -sc * cb * sa + cc * ca;
	1537
	1538	if (dir == INTO_2000)
	1539	{
	1540	/* Perform rotation from other epoch to J2000.0. */
	1541	rotation.rot[0][0] = xx;
	1542	rotation.rot[0][1] = yx;
	1543	rotation.rot[0][2] = zx;
	1544	rotation.rot[1][0] = xy;
	1545	rotation.rot[1][1] = yy;
	1546	rotation.rot[1][2] = zy;
	1547	rotation.rot[2][0] = xz;
	1548	rotation.rot[2][1] = yz;
	1549	rotation.rot[2][2] = zz;
	1550	}
	1551	else
	1552	{
	1553	/* Perform rotation from J2000.0 to other epoch. */
	1554	rotation.rot[0][0] = xx;
	1555	rotation.rot[0][1] = xy;
	1556	rotation.rot[0][2] = xz;
	1557	rotation.rot[1][0] = yx;
	1558	rotation.rot[1][1] = yy;
	1559	rotation.rot[1][2] = yz;
	1560	rotation.rot[2][0] = zx;
	1561	rotation.rot[2][1] = zy;
	1562	rotation.rot[2][2] = zz;
	1563	}
	1564
	1565	rotation.status = ASTRO_SUCCESS;
	1566	return rotation;
	1567	}
	1568
	1569
	1570	static void rotate(const double invec[3], const double rot[3][3], double outvec[3])
	1571	{
	1572	outvec[0] = rot[0][0]invec[0] + rot[1][0]invec[1] + rot[2][0]*invec[2];
	1573	outvec[1] = rot[0][1]invec[0] + rot[1][1]invec[1] + rot[2][1]*invec[2];
	1574	outvec[2] = rot[0][2]invec[0] + rot[1][2]invec[1] + rot[2][2]*invec[2];
	1575	}
	1576
	1577	static void precession(
	1578	const double pos1[3],
	1579	astro_time_t time,
	1580	precess_dir_t dir,
	1581	double pos2[3])
	1582	{
	1583	astro_rotation_t r = precession_rot(time, dir);
	1584	rotate(pos1, r.rot, pos2);
	1585	}
	1586
	1587	static void precession_posvel(
	1588	const double pos1[3],
	1589	const double vel1[3],
	1590	astro_time_t time,
	1591	precess_dir_t dir,
	1592	double pos2[3],
	1593	double vel2[3])
	1594	{
	1595	astro_rotation_t r = precession_rot(time, dir);
	1596	rotate(pos1, r.rot, pos2);
	1597	rotate(vel1, r.rot, vel2);
	1598	}
	1599
	1600
	1601	static astro_equatorial_t vector2radec(const double pos[3], astro_time_t time)
	1602	{
	1603	astro_equatorial_t equ;
	1604	double xyproj;
	1605
	1606	/* Copy the cartesian coordinates from the input into the returned structure. */
	1607	equ.vec.status = ASTRO_SUCCESS;
	1608	equ.vec.t = time;
	1609	equ.vec.x = pos[0];
	1610	equ.vec.y = pos[1];
	1611	equ.vec.z = pos[2];
	1612
	1613	/* Calculate spherical coordinates: RA, DEC, distance. */
	1614	xyproj = pos[0]pos[0] + pos[1]pos[1];
	1615	equ.dist = sqrt(xyproj + pos[2]*pos[2]);
	1616	equ.status = ASTRO_SUCCESS;
	1617	if (xyproj == 0.0)
	1618	{
	1619	if (pos[2] == 0.0)
	1620	{
	1621	/* Indeterminate coordinates; pos vector has zero length. */
	1622	equ = EquError(ASTRO_BAD_VECTOR);
	1623	}
	1624	else if (pos[2] < 0)
	1625	{
	1626	equ.ra = 0.0;
	1627	equ.dec = -90.0;
	1628	}
	1629	else
	1630	{
	1631	equ.ra = 0.0;
	1632	equ.dec = +90.0;
	1633	}
	1634	}
	1635	else
	1636	{
	1637	equ.ra = RAD2HOUR * atan2(pos[1], pos[0]);
	1638	if (equ.ra < 0)
	1639	equ.ra += 24.0;
	1640
	1641	equ.dec = RAD2DEG * atan2(pos[2], sqrt(xyproj));
	1642	}
	1643
	1644	return equ;
	1645	}
	1646
	1647
	1648	static astro_rotation_t nutation_rot(astro_time_t *time, precess_dir_t dir)
	1649	{
	1650	/*
	1651	Creates a rotation matrix that adds/removes nutation from
	1652	an equatorial vector of date:
	1653
	1654	The `dir` parameter is a little misleading, but reflects the
	1655	common task of working together with precession_rot() to
	1656	convert mean equator of 2000 to/from true equator of date.
	1657	Here is the actual result of `dir`:
	1658
	1659	dir==INTO_2000: Subtract nutation from true equator of date (EQD)
	1660	to produce mean equator of date (EQM).
	1661
	1662	dir==FROM_2000: Add nutation from mean equator of date (EQM) to
	1663	produce true equator of date (EQD).
	1664	*/
	1665
	1666	astro_rotation_t rotation;
	1667	earth_tilt_t tilt;
	1668	double oblm, oblt, psi, cobm, sobm, cobt, sobt, cpsi, spsi;
	1669	double xx, yx, zx, xy, yy, zy, xz, yz, zz;
	1670
	1671	if (time == NULL)
	1672	return RotationErr(ASTRO_INVALID_PARAMETER);
	1673
	1674	tilt = e_tilt(time);
	1675	oblm = tilt.mobl * DEG2RAD;
	1676	oblt = tilt.tobl * DEG2RAD;
	1677	psi = tilt.dpsi * ASEC2RAD;
	1678	cobm = cos(oblm);
	1679	sobm = sin(oblm);
	1680	cobt = cos(oblt);
	1681	sobt = sin(oblt);
	1682	cpsi = cos(psi);
	1683	spsi = sin(psi);
	1684
	1685	xx = cpsi;
	1686	yx = -spsi * cobm;
	1687	zx = -spsi * sobm;
	1688	xy = spsi * cobt;
	1689	yy = cpsi * cobm * cobt + sobm * sobt;
	1690	zy = cpsi * sobm * cobt - cobm * sobt;
	1691	xz = spsi * sobt;
	1692	yz = cpsi * cobm * sobt - sobm * cobt;
	1693	zz = cpsi * sobm * sobt + cobm * cobt;
	1694
	1695	if (dir == FROM_2000)
	1696	{
	1697	/* convert J2000 to of-date */
	1698	rotation.rot[0][0] = xx;
	1699	rotation.rot[0][1] = xy;
	1700	rotation.rot[0][2] = xz;
	1701	rotation.rot[1][0] = yx;
	1702	rotation.rot[1][1] = yy;
	1703	rotation.rot[1][2] = yz;
	1704	rotation.rot[2][0] = zx;
	1705	rotation.rot[2][1] = zy;
	1706	rotation.rot[2][2] = zz;
	1707	}
	1708	else
	1709	{
	1710	/* convert of-date to J2000 */
	1711	rotation.rot[0][0] = xx;
	1712	rotation.rot[0][1] = yx;
	1713	rotation.rot[0][2] = zx;
	1714	rotation.rot[1][0] = xy;
	1715	rotation.rot[1][1] = yy;
	1716	rotation.rot[1][2] = zy;
	1717	rotation.rot[2][0] = xz;
	1718	rotation.rot[2][1] = yz;
	1719	rotation.rot[2][2] = zz;
	1720	}
	1721
	1722	rotation.status = ASTRO_SUCCESS;
	1723	return rotation;
	1724	}
	1725
	1726	static void nutation(
	1727	const double inpos[3],
	1728	astro_time_t *time,
	1729	precess_dir_t dir,
	1730	double outpos[3])
	1731	{
	1732	astro_rotation_t r = nutation_rot(time, dir);
	1733	rotate(inpos, r.rot, outpos);
	1734	}
	1735
	1736	static void nutation_posvel(
	1737	const double inpos[3],
	1738	const double invel[3],
	1739	astro_time_t *time,
	1740	precess_dir_t dir,
	1741	double outpos[3],
	1742	double outvel[3])
	1743	{
	1744	astro_rotation_t r = nutation_rot(time, dir);
	1745	rotate(inpos, r.rot, outpos);
	1746	rotate(invel, r.rot, outvel);
	1747	}
	1748
	1749	static double era(double ut) /* Earth Rotation Angle */
	1750	{
	1751	double thet1 = 0.7790572732640 + 0.00273781191135448 * ut;
	1752	double thet3 = fmod(ut, 1.0);
	1753	double theta = 360.0 * fmod(thet1 + thet3, 1.0);
	1754	if (theta < 0.0)
	1755	theta += 360.0;
	1756
	1757	return theta;
	1758	}
	1759
	1760	/**
	1761	* @brief Calculates Greenwich Apparent Sidereal Time (GAST).
	1762	*
	1763	* Given a date and time, this function calculates the rotation of the
	1764	* Earth, represented by the equatorial angle of the Greenwich prime meridian
	1765	* with respect to distant stars (not the Sun, which moves relative to background
	1766	* stars by almost one degree per day).
	1767	* This angle is called Greenwich Apparent Sidereal Time (GAST).
	1768	* GAST is measured in sidereal hours in the half-open range [0, 24).
	1769	* When GAST = 0, it means the prime meridian is aligned with the of-date equinox,
	1770	* corrected at that time for precession and nutation of the Earth's axis.
	1771	* In this context, the "equinox" is the direction in space where the Earth's
	1772	* orbital plane (the ecliptic) intersects with the plane of the Earth's equator,
	1773	* at the location on the Earth's orbit of the (seasonal) March equinox.
	1774	* As the Earth rotates, GAST increases from 0 up to 24 sidereal hours,
	1775	* then starts over at 0.
	1776	* To convert to degrees, multiply the return value by 15.
	1777	*
	1778	* @param time
	1779	* The date and time for which to find GAST.
	1780	* The parameter is passed by address because it can be modified by the call:
	1781	* As an optimization, this function caches the sidereal time value in `time`,
	1782	* unless it has already been cached, in which case the cached value is reused.
	1783	* If the `time` pointer is NULL, this function returns a NAN value.
	1784	*
	1785	* @returns {number}
	1786	*/
	1787	double Astronomy_SiderealTime(astro_time_t *time)
	1788	{
	1789	if (time == NULL)
	1790	return NAN;
	1791
	1792	if (isnan(time->st))
	1793	{
	1794	double t = time->tt / 36525.0;
	1795	double eqeq = 15.0 * e_tilt(time).ee; /* Replace with eqeq=0 to get GMST instead of GAST (if we ever need it) */
	1796	double theta = era(time->ut);
	1797	double st = (eqeq + 0.014506 +
	1798	(((( - 0.0000000368 * t
	1799	- 0.000029956 ) * t
	1800	- 0.00000044 ) * t
	1801	+ 1.3915817 ) * t
	1802	+ 4612.156534 ) * t);
	1803
	1804	double gst = fmod(st/3600.0 + theta, 360.0) / 15.0;
	1805	if (gst < 0.0)
	1806	gst += 24.0;
	1807
	1808	time->st = gst;
	1809	}
	1810
	1811	return time->st; /* return sidereal hours in the half-open range [0, 24). */
	1812	}
	1813
	1814	static astro_observer_t inverse_terra(const double ovec[3], double st)
	1815	{
	1816	double x, y, z, p, F, W, D, c, s, c2, s2;
	1817	double lon_deg, lat_deg, lat, radicand, factor, denom, adjust;
	1818	double height_km, stlocl;
	1819	astro_observer_t observer;
	1820	int count;
	1821
	1822	/* Convert from AU to kilometers. */
	1823	x = ovec[0] * KM_PER_AU;
	1824	y = ovec[1] * KM_PER_AU;
	1825	z = ovec[2] * KM_PER_AU;
	1826	p = hypot(x, y);
	1827	if (p < 1.0e-6)
	1828	{
	1829	/* Special case: within 1 millimeter of a pole! */
	1830	/* Use arbitrary longitude, and latitude determined by polarity of z. */
	1831	lon_deg = 0.0;
	1832	lat_deg = (z > 0.0) ? +90.0 : -90.0;
	1833	/* Elevation is calculated directly from z */
	1834	height_km = fabs(z) - EARTH_POLAR_RADIUS_KM;
	1835	}
	1836	else
	1837	{
	1838	stlocl = atan2(y, x);
	1839	/* Calculate exact longitude. */
	1840	lon_deg = RAD2DEGstlocl - (15.0 st);
	1841	/* Normalize longitude to the range (-180, +180]. */
	1842	while (lon_deg <= -180.0)
	1843	lon_deg += 360.0;
	1844	while (lon_deg > +180.0)
	1845	lon_deg -= 360.0;
	1846	/* Numerically solve for exact latitude, using Newton's Method. */
	1847	F = EARTH_FLATTENING * EARTH_FLATTENING;
	1848	/* Start with initial latitude estimate, based on a spherical Earth. */
	1849	lat = atan2(z, p);
	1850	for (count = 0; ; ++count)
	1851	{
	1852	if (count > 10)
	1853	{
	1854	fprintf(stderr, "\nFATAL(inverse_terra): did not converge!\n");
	1855	exit(1);
	1856	}
	1857
	1858	/* Calculate the error function W(lat). */
	1859	/* We try to find the root of W, meaning where the error is 0. */
	1860	c = cos(lat);
	1861	s = sin(lat);
	1862	factor = (F-1)*EARTH_EQUATORIAL_RADIUS_KM;
	1863	c2 = c*c;
	1864	s2 = s*s;
	1865	radicand = c2 + F*s2;
	1866	denom = sqrt(radicand);
	1867	W = (factorsc)/denom - zc + ps;
	1868	if (fabs(W) < 1.0e-8)
	1869	break; /* The error is now negligible. */
	1870	/* Error is still too large. Find the next estimate. */
	1871	/* Calculate D = the derivative of W with respect to lat. */
	1872	D = factor((c2 - s2)/denom - s2c2(F-1)/(factorradicand)) + zs + pc;
	1873	lat -= W/D;
	1874	}
	1875	/* We now have a solution for the latitude in radians. */
	1876	lat_deg = lat * RAD2DEG;
	1877	/* Solve for exact height in meters. */
	1878	/* There are two formulas I can use. Use whichever has the less risky denominator. */
	1879	adjust = EARTH_EQUATORIAL_RADIUS_KM / denom;
	1880	if (fabs(s) > fabs(c))
	1881	height_km = z/s - F*adjust;
	1882	else
	1883	height_km = p/c - adjust;
	1884	}
	1885
	1886	observer.latitude = lat_deg;
	1887	observer.longitude = lon_deg;
	1888	observer.height = 1000.0 * height_km;
	1889	return observer;
	1890	}
	1891
	1892	static void terra(astro_observer_t observer, double st, double pos[3], double vel[3])
	1893	{
	1894	static const double ANGVEL = 7.2921150e-5;
	1895
	1896	double phi = observer.latitude * DEG2RAD;
	1897	double sinphi = sin(phi);
	1898	double cosphi = cos(phi);
	1899	double c = 1.0 / hypot(cosphi, sinphi*EARTH_FLATTENING);
	1900	double s = c * (EARTH_FLATTENING * EARTH_FLATTENING);
	1901	double ht_km = observer.height / 1000.0;
	1902	double ach = EARTH_EQUATORIAL_RADIUS_KM*c + ht_km;
	1903	double ash = EARTH_EQUATORIAL_RADIUS_KM*s + ht_km;
	1904	double stlocl = (15.0st + observer.longitude) DEG2RAD;
	1905	double sinst = sin(stlocl);
	1906	double cosst = cos(stlocl);
	1907
	1908	if (pos != NULL)
	1909	{
	1910	pos[0] = ach * cosphi * cosst / KM_PER_AU;
	1911	pos[1] = ach * cosphi * sinst / KM_PER_AU;
	1912	pos[2] = ash * sinphi / KM_PER_AU;
	1913	}
	1914
	1915	if (vel != NULL)
	1916	{
	1917	vel[0] = -(ANGVEL * 86400.0 / KM_PER_AU) * ach * cosphi * sinst;
	1918	vel[1] = +(ANGVEL * 86400.0 / KM_PER_AU) * ach * cosphi * cosst;
	1919	vel[2] = 0.0;
	1920	}
	1921	}
	1922
	1923	static void geo_pos(astro_time_t *time, astro_observer_t observer, double pos[3])
	1924	{
	1925	double gast;
	1926	double pos1[3], pos2[3];
	1927
	1928	if (time == NULL)
	1929	{
	1930	pos[0] = pos[1] = pos[2] = NAN;
	1931	}
	1932	else
	1933	{
	1934	gast = Astronomy_SiderealTime(time);
	1935	terra(observer, gast, pos1, NULL);
	1936	nutation(pos1, time, INTO_2000, pos2);
	1937	precession(pos2, *time, INTO_2000, pos);
	1938	}
	1939	}
	1940
	1941	static void spin(double angle, const double pos1[3], double vec2[3])
	1942	{
	1943	double angr = angle * DEG2RAD;
	1944	double cosang = cos(angr);
	1945	double sinang = sin(angr);
	1946	vec2[0] = +cosangpos1[0] + sinangpos1[1];
	1947	vec2[1] = -sinangpos1[0] + cosangpos1[1];
	1948	vec2[2] = pos1[2];
	1949	}
	1950
	1951	/------------------ CalcMoon ------------------/
	1952
	1953	/** @cond DOXYGEN_SKIP */
	1954
	1955	#define DECLARE_PASCAL_ARRAY_1(elemtype,name,xmin,xmax) \
	1956	elemtype name[(xmax)-(xmin)+1]
	1957
	1958	#define DECLARE_PASCAL_ARRAY_2(elemtype,name,xmin,xmax,ymin,ymax) \
	1959	elemtype name[(xmax)-(xmin)+1][(ymax)-(ymin)+1]
	1960
	1961	#define ACCESS_PASCAL_ARRAY_1(name,xmin,x) \
	1962	((name)[(x)-(xmin)])
	1963
	1964	#define ACCESS_PASCAL_ARRAY_2(name,xmin,ymin,x,y) \
	1965	((name)[(x)-(xmin)][(y)-(ymin)])
	1966
	1967	typedef struct
	1968	{
	1969	double t;
	1970	double dgam;
	1971	double dlam, n, gam1c, sinpi;
	1972	double l0, l, ls, f, d, s;
	1973	double dl0, dl, dls, df, dd, ds;
	1974	DECLARE_PASCAL_ARRAY_2(double,co,-6,6,1,4); /* ARRAY[-6..6,1..4] OF REAL */
	1975	DECLARE_PASCAL_ARRAY_2(double,si,-6,6,1,4); /* ARRAY[-6..6,1..4] OF REAL */
	1976	}
	1977	MoonContext;
	1978
	1979	#define T (ctx->t)
	1980	#define DGAM (ctx->dgam)
	1981	#define DLAM (ctx->dlam)
	1982	#define N (ctx->n)
	1983	#define GAM1C (ctx->gam1c)
	1984	#define SINPI (ctx->sinpi)
	1985	#define L0 (ctx->l0)
	1986	#define L (ctx->l)
	1987	#define LS (ctx->ls)
	1988	#define F (ctx->f)
	1989	#define D (ctx->d)
	1990	#define S (ctx->s)
	1991	#define DL0 (ctx->dl0)
	1992	#define DL (ctx->dl)
	1993	#define DLS (ctx->dls)
	1994	#define DF (ctx->df)
	1995	#define DD (ctx->dd)
	1996	#define DS (ctx->ds)
	1997	#define CO(x,y) ACCESS_PASCAL_ARRAY_2(ctx->co,-6,1,x,y)
	1998	#define SI(x,y) ACCESS_PASCAL_ARRAY_2(ctx->si,-6,1,x,y)
	1999
	2000	static double Frac(double x)
	2001	{
	2002	return x - floor(x);
	2003	}
	2004
	2005	static void AddThe(
	2006	double c1, double s1, double c2, double s2,
	2007	double c, double s)
	2008	{
	2009	c = c1c2 - s1*s2;
	2010	s = s1c2 + c1*s2;
	2011	}
	2012
	2013	static double Sine(double phi)
	2014	{
	2015	/* sine, of phi in revolutions, not radians */
	2016	return sin(PI2 * phi);
	2017	}
	2018
	2019	static void LongPeriodic(MoonContext *ctx)
	2020	{
	2021	double S1 = Sine(0.19833+0.05611*T);
	2022	double S2 = Sine(0.27869+0.04508*T);
	2023	double S3 = Sine(0.16827-0.36903*T);
	2024	double S4 = Sine(0.34734-5.37261*T);
	2025	double S5 = Sine(0.10498-5.37899*T);
	2026	double S6 = Sine(0.42681-0.41855*T);
	2027	double S7 = Sine(0.14943-5.37511*T);
	2028
	2029	DL0 = 0.84S1+0.31S2+14.27S3+ 7.26S4+ 0.28S5+0.24S6;
	2030	DL = 2.94S1+0.31S2+14.27S3+ 9.34S4+ 1.12S5+0.83S6;
	2031	DLS =-6.40S1 -1.89S6;
	2032	DF = 0.21S1+0.31S2+14.27S3-88.70S4-15.30S5+0.24S6-1.86*S7;
	2033	DD = DL0-DLS;
	2034	DGAM = -3332E-9 * Sine(0.59734-5.37261*T)
	2035	-539E-9 * Sine(0.35498-5.37899*T)
	2036	-64E-9 * Sine(0.39943-5.37511*T);
	2037	}
	2038
	2039	static void Init(MoonContext *ctx)
	2040	{
	2041	int I, J, MAX;
	2042	double T2, ARG, FAC;
	2043
	2044	T2 = T*T;
	2045	DLAM = 0;
	2046	DS = 0;
	2047	GAM1C = 0;
	2048	SINPI = 3422.7000;
	2049	LongPeriodic(ctx);
	2050	L0 = PI2Frac(0.60643382+1336.85522467T-0.00000313*T2) + DL0/ARC;
	2051	L = PI2Frac(0.37489701+1325.55240982T+0.00002565*T2) + DL /ARC;
	2052	LS = PI2Frac(0.99312619+ 99.99735956T-0.00000044*T2) + DLS/ARC;
	2053	F = PI2Frac(0.25909118+1342.22782980T-0.00000892*T2) + DF /ARC;
	2054	D = PI2Frac(0.82736186+1236.85308708T-0.00000397*T2) + DD /ARC;
	2055	for (I=1; I<=4; ++I)
	2056	{
	2057	switch(I)
	2058	{
	2059	case 1: ARG=L; MAX=4; FAC=1.000002208; break;
	2060	case 2: ARG=LS; MAX=3; FAC=0.997504612-0.002495388*T; break;
	2061	case 3: ARG=F; MAX=4; FAC=1.000002708+139.978*DGAM; break;
	2062	default: ARG=D; MAX=6; FAC=1.0; break;
	2063	}
	2064	CO(0,I) = 1.0;
	2065	CO(1,I) = cos(ARG)*FAC;
	2066	SI(0,I) = 0.0;
	2067	SI(1,I) = sin(ARG)*FAC;
	2068	for (J=2; J<=MAX; ++J)
	2069	AddThe(CO(J-1,I), SI(J-1,I), CO(1,I), SI(1,I), &CO(J,I), &SI(J,I));
	2070
	2071	for (J=1; J<=MAX; ++J)
	2072	{
	2073	CO(-J,I) = CO(J,I);
	2074	SI(-J,I) = -SI(J,I);
	2075	}
	2076	}
	2077	}
	2078
	2079	static void Term(const MoonContext ctx, int p, int q, int r, int s, double x, double *y)
	2080	{
	2081	int k;
	2082	DECLARE_PASCAL_ARRAY_1(int, i, 1, 4);
	2083	#define I(n) ACCESS_PASCAL_ARRAY_1(i,1,n)
	2084
	2085	I(1) = p;
	2086	I(2) = q;
	2087	I(3) = r;
	2088	I(4) = s;
	2089	*x = 1.0;
	2090	*y = 0.0;
	2091
	2092	for (k=1; k<=4; ++k)
	2093	if (I(k) != 0.0)
	2094	AddThe(x, y, CO(I(k), k), SI(I(k), k), x, y);
	2095
	2096	#undef I
	2097	}
	2098
	2099	static void AddSol(
	2100	MoonContext *ctx,
	2101	double coeffl,
	2102	double coeffs,
	2103	double coeffg,
	2104	double coeffp,
	2105	int p,
	2106	int q,
	2107	int r,
	2108	int s)
	2109	{
	2110	double x, y;
	2111	Term(ctx, p, q, r, s, &x, &y);
	2112	DLAM += coeffl*y;
	2113	DS += coeffs*y;
	2114	GAM1C += coeffg*x;
	2115	SINPI += coeffp*x;
	2116	}
	2117
	2118	#define ADDN(coeffn,p,q,r,s) ( Term(ctx, (p),(q),(r),(s),&x,&y), (N += (coeffn)*y) )
	2119
	2120	static void SolarN(MoonContext *ctx)
	2121	{
	2122	double x, y;
	2123
	2124	N = 0.0;
	2125	ADDN(-526.069, 0, 0,1,-2);
	2126	ADDN( -3.352, 0, 0,1,-4);
	2127	ADDN( +44.297,+1, 0,1,-2);
	2128	ADDN( -6.000,+1, 0,1,-4);
	2129	ADDN( +20.599,-1, 0,1, 0);
	2130	ADDN( -30.598,-1, 0,1,-2);
	2131	ADDN( -24.649,-2, 0,1, 0);
	2132	ADDN( -2.000,-2, 0,1,-2);
	2133	ADDN( -22.571, 0,+1,1,-2);
	2134	ADDN( +10.985, 0,-1,1,-2);
	2135	}
	2136
	2137	static void Planetary(MoonContext *ctx)
	2138	{
	2139	DLAM +=
	2140	+0.82Sine(0.7736 -62.5512T)+0.31Sine(0.0466 -125.1025T)
	2141	+0.35Sine(0.5785 -25.1042T)+0.66Sine(0.4591+1335.8075T)
	2142	+0.64Sine(0.3130 -91.5680T)+1.14Sine(0.1480+1331.2898T)
	2143	+0.21Sine(0.5918+1056.5859T)+0.44Sine(0.5784+1322.8595T)
	2144	+0.24Sine(0.2275 -5.7374T)+0.28Sine(0.2965 +2.6929T)
	2145	+0.33Sine(0.3132 +6.3368T);
	2146	}
	2147
	2148	int _CalcMoonCount; /* Undocumented global for performance tuning. */
	2149
	2150	static void CalcMoon(
	2151	double centuries_since_j2000,
	2152	double geo_eclip_lon, / (LAMBDA) equinox of date */
	2153	double geo_eclip_lat, / (BETA) equinox of date */
	2154	double distance_au) / (R) */
	2155	{
	2156	double lat_seconds;
	2157	MoonContext context;
	2158	MoonContext ctx = &context; / goofy, but makes macros work inside this function */
	2159
	2160	context.t = centuries_since_j2000;
	2161	Init(ctx);
	2162
	2163	AddSol(ctx, 13.9020, 14.0600, -0.0010, 0.2607, 0, 0, 0, 4);
	2164	AddSol(ctx, 0.4030, -4.0100, 0.3940, 0.0023, 0, 0, 0, 3);
	2165	AddSol(ctx, 2369.9120, 2373.3600, 0.6010, 28.2333, 0, 0, 0, 2);
	2166	AddSol(ctx, -125.1540, -112.7900, -0.7250, -0.9781, 0, 0, 0, 1);
	2167	AddSol(ctx, 1.9790, 6.9800, -0.4450, 0.0433, 1, 0, 0, 4);
	2168	AddSol(ctx, 191.9530, 192.7200, 0.0290, 3.0861, 1, 0, 0, 2);
	2169	AddSol(ctx, -8.4660, -13.5100, 0.4550, -0.1093, 1, 0, 0, 1);
	2170	AddSol(ctx, 22639.5000, 22609.0700, 0.0790, 186.5398, 1, 0, 0, 0);
	2171	AddSol(ctx, 18.6090, 3.5900, -0.0940, 0.0118, 1, 0, 0,-1);
	2172	AddSol(ctx, -4586.4650, -4578.1300, -0.0770, 34.3117, 1, 0, 0,-2);
	2173	AddSol(ctx, 3.2150, 5.4400, 0.1920, -0.0386, 1, 0, 0,-3);
	2174	AddSol(ctx, -38.4280, -38.6400, 0.0010, 0.6008, 1, 0, 0,-4);
	2175	AddSol(ctx, -0.3930, -1.4300, -0.0920, 0.0086, 1, 0, 0,-6);
	2176	AddSol(ctx, -0.2890, -1.5900, 0.1230, -0.0053, 0, 1, 0, 4);
	2177	AddSol(ctx, -24.4200, -25.1000, 0.0400, -0.3000, 0, 1, 0, 2);
	2178	AddSol(ctx, 18.0230, 17.9300, 0.0070, 0.1494, 0, 1, 0, 1);
	2179	AddSol(ctx, -668.1460, -126.9800, -1.3020, -0.3997, 0, 1, 0, 0);
	2180	AddSol(ctx, 0.5600, 0.3200, -0.0010, -0.0037, 0, 1, 0,-1);
	2181	AddSol(ctx, -165.1450, -165.0600, 0.0540, 1.9178, 0, 1, 0,-2);
	2182	AddSol(ctx, -1.8770, -6.4600, -0.4160, 0.0339, 0, 1, 0,-4);
	2183	AddSol(ctx, 0.2130, 1.0200, -0.0740, 0.0054, 2, 0, 0, 4);
	2184	AddSol(ctx, 14.3870, 14.7800, -0.0170, 0.2833, 2, 0, 0, 2);
	2185	AddSol(ctx, -0.5860, -1.2000, 0.0540, -0.0100, 2, 0, 0, 1);
	2186	AddSol(ctx, 769.0160, 767.9600, 0.1070, 10.1657, 2, 0, 0, 0);
	2187	AddSol(ctx, 1.7500, 2.0100, -0.0180, 0.0155, 2, 0, 0,-1);
	2188	AddSol(ctx, -211.6560, -152.5300, 5.6790, -0.3039, 2, 0, 0,-2);
	2189	AddSol(ctx, 1.2250, 0.9100, -0.0300, -0.0088, 2, 0, 0,-3);
	2190	AddSol(ctx, -30.7730, -34.0700, -0.3080, 0.3722, 2, 0, 0,-4);
	2191	AddSol(ctx, -0.5700, -1.4000, -0.0740, 0.0109, 2, 0, 0,-6);
	2192	AddSol(ctx, -2.9210, -11.7500, 0.7870, -0.0484, 1, 1, 0, 2);
	2193	AddSol(ctx, 1.2670, 1.5200, -0.0220, 0.0164, 1, 1, 0, 1);
	2194	AddSol(ctx, -109.6730, -115.1800, 0.4610, -0.9490, 1, 1, 0, 0);
	2195	AddSol(ctx, -205.9620, -182.3600, 2.0560, 1.4437, 1, 1, 0,-2);
	2196	AddSol(ctx, 0.2330, 0.3600, 0.0120, -0.0025, 1, 1, 0,-3);
	2197	AddSol(ctx, -4.3910, -9.6600, -0.4710, 0.0673, 1, 1, 0,-4);
	2198	AddSol(ctx, 0.2830, 1.5300, -0.1110, 0.0060, 1,-1, 0, 4);
	2199	AddSol(ctx, 14.5770, 31.7000, -1.5400, 0.2302, 1,-1, 0, 2);
	2200	AddSol(ctx, 147.6870, 138.7600, 0.6790, 1.1528, 1,-1, 0, 0);
	2201	AddSol(ctx, -1.0890, 0.5500, 0.0210, 0.0000, 1,-1, 0,-1);
	2202	AddSol(ctx, 28.4750, 23.5900, -0.4430, -0.2257, 1,-1, 0,-2);
	2203	AddSol(ctx, -0.2760, -0.3800, -0.0060, -0.0036, 1,-1, 0,-3);
	2204	AddSol(ctx, 0.6360, 2.2700, 0.1460, -0.0102, 1,-1, 0,-4);
	2205	AddSol(ctx, -0.1890, -1.6800, 0.1310, -0.0028, 0, 2, 0, 2);
	2206	AddSol(ctx, -7.4860, -0.6600, -0.0370, -0.0086, 0, 2, 0, 0);
	2207	AddSol(ctx, -8.0960, -16.3500, -0.7400, 0.0918, 0, 2, 0,-2);
	2208	AddSol(ctx, -5.7410, -0.0400, 0.0000, -0.0009, 0, 0, 2, 2);
	2209	AddSol(ctx, 0.2550, 0.0000, 0.0000, 0.0000, 0, 0, 2, 1);
	2210	AddSol(ctx, -411.6080, -0.2000, 0.0000, -0.0124, 0, 0, 2, 0);
	2211	AddSol(ctx, 0.5840, 0.8400, 0.0000, 0.0071, 0, 0, 2,-1);
	2212	AddSol(ctx, -55.1730, -52.1400, 0.0000, -0.1052, 0, 0, 2,-2);
	2213	AddSol(ctx, 0.2540, 0.2500, 0.0000, -0.0017, 0, 0, 2,-3);
	2214	AddSol(ctx, 0.0250, -1.6700, 0.0000, 0.0031, 0, 0, 2,-4);
	2215	AddSol(ctx, 1.0600, 2.9600, -0.1660, 0.0243, 3, 0, 0, 2);
	2216	AddSol(ctx, 36.1240, 50.6400, -1.3000, 0.6215, 3, 0, 0, 0);
	2217	AddSol(ctx, -13.1930, -16.4000, 0.2580, -0.1187, 3, 0, 0,-2);
	2218	AddSol(ctx, -1.1870, -0.7400, 0.0420, 0.0074, 3, 0, 0,-4);
	2219	AddSol(ctx, -0.2930, -0.3100, -0.0020, 0.0046, 3, 0, 0,-6);
	2220	AddSol(ctx, -0.2900, -1.4500, 0.1160, -0.0051, 2, 1, 0, 2);
	2221	AddSol(ctx, -7.6490, -10.5600, 0.2590, -0.1038, 2, 1, 0, 0);
	2222	AddSol(ctx, -8.6270, -7.5900, 0.0780, -0.0192, 2, 1, 0,-2);
	2223	AddSol(ctx, -2.7400, -2.5400, 0.0220, 0.0324, 2, 1, 0,-4);
	2224	AddSol(ctx, 1.1810, 3.3200, -0.2120, 0.0213, 2,-1, 0, 2);
	2225	AddSol(ctx, 9.7030, 11.6700, -0.1510, 0.1268, 2,-1, 0, 0);
	2226	AddSol(ctx, -0.3520, -0.3700, 0.0010, -0.0028, 2,-1, 0,-1);
	2227	AddSol(ctx, -2.4940, -1.1700, -0.0030, -0.0017, 2,-1, 0,-2);
	2228	AddSol(ctx, 0.3600, 0.2000, -0.0120, -0.0043, 2,-1, 0,-4);
	2229	AddSol(ctx, -1.1670, -1.2500, 0.0080, -0.0106, 1, 2, 0, 0);
	2230	AddSol(ctx, -7.4120, -6.1200, 0.1170, 0.0484, 1, 2, 0,-2);
	2231	AddSol(ctx, -0.3110, -0.6500, -0.0320, 0.0044, 1, 2, 0,-4);
	2232	AddSol(ctx, 0.7570, 1.8200, -0.1050, 0.0112, 1,-2, 0, 2);
	2233	AddSol(ctx, 2.5800, 2.3200, 0.0270, 0.0196, 1,-2, 0, 0);
	2234	AddSol(ctx, 2.5330, 2.4000, -0.0140, -0.0212, 1,-2, 0,-2);
	2235	AddSol(ctx, -0.3440, -0.5700, -0.0250, 0.0036, 0, 3, 0,-2);
	2236	AddSol(ctx, -0.9920, -0.0200, 0.0000, 0.0000, 1, 0, 2, 2);
	2237	AddSol(ctx, -45.0990, -0.0200, 0.0000, -0.0010, 1, 0, 2, 0);
	2238	AddSol(ctx, -0.1790, -9.5200, 0.0000, -0.0833, 1, 0, 2,-2);
	2239	AddSol(ctx, -0.3010, -0.3300, 0.0000, 0.0014, 1, 0, 2,-4);
	2240	AddSol(ctx, -6.3820, -3.3700, 0.0000, -0.0481, 1, 0,-2, 2);
	2241	AddSol(ctx, 39.5280, 85.1300, 0.0000, -0.7136, 1, 0,-2, 0);
	2242	AddSol(ctx, 9.3660, 0.7100, 0.0000, -0.0112, 1, 0,-2,-2);
	2243	AddSol(ctx, 0.2020, 0.0200, 0.0000, 0.0000, 1, 0,-2,-4);
	2244	AddSol(ctx, 0.4150, 0.1000, 0.0000, 0.0013, 0, 1, 2, 0);
	2245	AddSol(ctx, -2.1520, -2.2600, 0.0000, -0.0066, 0, 1, 2,-2);
	2246	AddSol(ctx, -1.4400, -1.3000, 0.0000, 0.0014, 0, 1,-2, 2);
	2247	AddSol(ctx, 0.3840, -0.0400, 0.0000, 0.0000, 0, 1,-2,-2);
	2248	AddSol(ctx, 1.9380, 3.6000, -0.1450, 0.0401, 4, 0, 0, 0);
	2249	AddSol(ctx, -0.9520, -1.5800, 0.0520, -0.0130, 4, 0, 0,-2);
	2250	AddSol(ctx, -0.5510, -0.9400, 0.0320, -0.0097, 3, 1, 0, 0);
	2251	AddSol(ctx, -0.4820, -0.5700, 0.0050, -0.0045, 3, 1, 0,-2);
	2252	AddSol(ctx, 0.6810, 0.9600, -0.0260, 0.0115, 3,-1, 0, 0);
	2253	AddSol(ctx, -0.2970, -0.2700, 0.0020, -0.0009, 2, 2, 0,-2);
	2254	AddSol(ctx, 0.2540, 0.2100, -0.0030, 0.0000, 2,-2, 0,-2);
	2255	AddSol(ctx, -0.2500, -0.2200, 0.0040, 0.0014, 1, 3, 0,-2);
	2256	AddSol(ctx, -3.9960, 0.0000, 0.0000, 0.0004, 2, 0, 2, 0);
	2257	AddSol(ctx, 0.5570, -0.7500, 0.0000, -0.0090, 2, 0, 2,-2);
	2258	AddSol(ctx, -0.4590, -0.3800, 0.0000, -0.0053, 2, 0,-2, 2);
	2259	AddSol(ctx, -1.2980, 0.7400, 0.0000, 0.0004, 2, 0,-2, 0);
	2260	AddSol(ctx, 0.5380, 1.1400, 0.0000, -0.0141, 2, 0,-2,-2);
	2261	AddSol(ctx, 0.2630, 0.0200, 0.0000, 0.0000, 1, 1, 2, 0);
	2262	AddSol(ctx, 0.4260, 0.0700, 0.0000, -0.0006, 1, 1,-2,-2);
	2263	AddSol(ctx, -0.3040, 0.0300, 0.0000, 0.0003, 1,-1, 2, 0);
	2264	AddSol(ctx, -0.3720, -0.1900, 0.0000, -0.0027, 1,-1,-2, 2);
	2265	AddSol(ctx, 0.4180, 0.0000, 0.0000, 0.0000, 0, 0, 4, 0);
	2266	AddSol(ctx, -0.3300, -0.0400, 0.0000, 0.0000, 3, 0, 2, 0);
	2267
	2268	SolarN(ctx);
	2269	Planetary(ctx);
	2270	S = F + DS/ARC;
	2271
	2272	lat_seconds = (1.000002708 + 139.978DGAM)(18518.511+1.189+GAM1C)sin(S)-6.24sin(3*S) + N;
	2273
	2274	geo_eclip_lon = PI2 Frac((L0+DLAM/ARC) / PI2);
	2275	geo_eclip_lat = lat_seconds (DEG2RAD / 3600.0);
	2276	distance_au = (ARC EARTH_EQUATORIAL_RADIUS_AU) / (0.999953253 * SINPI);
	2277	++_CalcMoonCount;
	2278	}
	2279
	2280	#undef T
	2281	#undef DGAM
	2282	#undef DLAM
	2283	#undef N
	2284	#undef GAM1C
	2285	#undef SINPI
	2286	#undef L0
	2287	#undef L
	2288	#undef LS
	2289	#undef F
	2290	#undef D
	2291	#undef S
	2292	#undef DL0
	2293	#undef DL
	2294	#undef DLS
	2295	#undef DF
	2296	#undef DD
	2297	#undef DS
	2298	#undef CO
	2299	#undef SI
	2300
	2301	/** @endcond */
	2302
	2303	/**
	2304	* @brief Calculates equatorial geocentric position of the Moon at a given time.
	2305	*
	2306	* Given a time of observation, calculates the Moon's position as a vector.
	2307	* The vector gives the location of the Moon's center relative to the Earth's center
	2308	* with x-, y-, and z-components measured in astronomical units.
	2309	* The coordinates are oriented with respect to the Earth's equator at the J2000 epoch.
	2310	* In Astronomy Engine, this orientation is called EQJ.
	2311	*
	2312	* This algorithm is based on the Nautical Almanac Office's Improved Lunar Ephemeris of 1954,
	2313	* which in turn derives from E. W. Brown's lunar theories from the early twentieth century.
	2314	* It is adapted from Turbo Pascal code from the book
	2315	* [Astronomy on the Personal Computer](https://www.springer.com/us/book/9783540672210)
	2316	* by Montenbruck and Pfleger.
	2317	*
	2318	* To calculate ecliptic spherical coordinates instead, see #Astronomy_EclipticGeoMoon.
	2319	*
	2320	* @param time The date and time for which to calculate the Moon's position.
	2321	* @return The Moon's position as a vector in J2000 Cartesian equatorial (EQJ) coordinates.
	2322	*/
	2323	astro_vector_t Astronomy_GeoMoon(astro_time_t time)
	2324	{
	2325	double geo_eclip_lon, geo_eclip_lat, distance_au;
	2326	double dist_cos_lat;
	2327	astro_vector_t vector;
	2328	double gepos[3];
	2329	double mpos1[3];
	2330	double mpos2[3];
	2331
	2332	CalcMoon(time.tt / 36525.0, &geo_eclip_lon, &geo_eclip_lat, &distance_au);
	2333
	2334	/* Convert geocentric ecliptic spherical coordinates to Cartesian coordinates. */
	2335	dist_cos_lat = distance_au * cos(geo_eclip_lat);
	2336	gepos[0] = dist_cos_lat * cos(geo_eclip_lon);
	2337	gepos[1] = dist_cos_lat * sin(geo_eclip_lon);
	2338	gepos[2] = distance_au * sin(geo_eclip_lat);
	2339
	2340	/* Convert ecliptic coordinates to equatorial coordinates, both in mean equinox of date. */
	2341	ecl2equ_vec(time, gepos, mpos1);
	2342
	2343	/* Convert equatorial coordinates from mean equinox of date to J2000 mean equinox. */
	2344	precession(mpos1, time, INTO_2000, mpos2);
	2345
	2346	vector.status = ASTRO_SUCCESS;
	2347	vector.x = mpos2[0];
	2348	vector.y = mpos2[1];
	2349	vector.z = mpos2[2];
	2350	vector.t = time;
	2351	return vector;
	2352	}
	2353
	2354
	2355	/**
	2356	* @brief Calculates spherical ecliptic geocentric position of the Moon.
	2357	*
	2358	* Given a time of observation, calculates the Moon's geocentric position
	2359	* in ecliptic spherical coordinates. Provides the ecliptic latitude and
	2360	* longitude in degrees, and the geocentric distance in astronomical units (AU).
	2361	*
	2362	* The ecliptic angles are measured in "ECT": relative to the true ecliptic plane and
	2363	* equatorial plane at the specified time. This means the Earth's equator
	2364	* is corrected for precession and nutation, and the plane of the Earth's
	2365	* orbit is corrected for gradual obliquity drift.
	2366	*
	2367	* This algorithm is based on the Nautical Almanac Office's Improved Lunar Ephemeris of 1954,
	2368	* which in turn derives from E. W. Brown's lunar theories from the early twentieth century.
	2369	* It is adapted from Turbo Pascal code from the book
	2370	* [Astronomy on the Personal Computer](https://www.springer.com/us/book/9783540672210)
	2371	* by Montenbruck and Pfleger.
	2372	*
	2373	* To calculate a J2000 mean equator vector instead, use #Astronomy_GeoMoon.
	2374	*
	2375	* @param time The date and time for which to calculate the Moon's position.
	2376	* @return The Moon's position expressed in ecliptic coordinates using the true equinox of date (ECT).
	2377	*/
	2378	astro_spherical_t Astronomy_EclipticGeoMoon(astro_time_t time)
	2379	{
	2380	astro_spherical_t sphere;
	2381	astro_ecliptic_t eclip;
	2382	earth_tilt_t et;
	2383	double dist_cos_lat, ecm[3], eqm[3], eqd[3];
	2384
	2385	/* CalcMoon produces ecliptic coordinates in mean equinox of date (ECM). */
	2386	CalcMoon(time.tt / 36525.0, &sphere.lon, &sphere.lat, &sphere.dist);
	2387
	2388	/* Calculate vector in ecliptic coordinates (ECM). */
	2389	dist_cos_lat = sphere.dist * cos(sphere.lat);
	2390	ecm[0] = dist_cos_lat * cos(sphere.lon);
	2391	ecm[1] = dist_cos_lat * sin(sphere.lon);
	2392	ecm[2] = sphere.dist * sin(sphere.lat);
	2393
	2394	/* Obtain true and mean obliquity angles for the given time. */
	2395	/* This serves to pre-calculate the nutation also, and cache it in `time`. */
	2396	et = e_tilt(&time);
	2397
	2398	/* Convert ecliptic coordinates to equatorial coordinates, both in mean equinox of date. */
	2399	/* In other words, convert ECM to EQM. */
	2400	obl_ecl2equ_vec(et.mobl, time, ecm, eqm);
	2401
	2402	/* Add nutation to convert ECM to true equatorial coordinates of date (EQD). */
	2403	nutation(eqm, &time, FROM_2000, eqd);
	2404
	2405	/* Convert back to ecliptic, this time in true equinox of date (ECT). */
	2406	eclip = RotateEquatorialToEcliptic(eqd, DEG2RAD * et.tobl, time);
	2407
	2408	/* Package the return value. */
	2409	/* CalcMoon() already set sphere.dist to the correct value. */
	2410	sphere.status = eclip.status;
	2411	sphere.lat = eclip.elat;
	2412	sphere.lon = eclip.elon;
	2413	return sphere;
	2414	}
	2415
	2416
	2417	/**
	2418	* @brief Calculates equatorial geocentric position and velocity of the Moon at a given time.
	2419	*
	2420	* Given a time of observation, calculates the Moon's position and velocity vectors.
	2421	* The position and velocity are of the Moon's center relative to the Earth's center.
	2422	* The position (x, y, z) components are expressed in AU (astronomical units).
	2423	* The velocity (vx, vy, vz) components are expressed in AU/day.
	2424	* The coordinates are oriented with respect to the Earth's equator at the J2000 epoch.
	2425	* In Astronomy Engine, this orientation is called EQJ.
	2426	*
	2427	* If you need the Moon's position only, and not its velocity,
	2428	* it is much more efficient to use #Astronomy_GeoMoon instead.
	2429	*
	2430	* @param time The date and time for which to calculate the Moon's position and velocity.
	2431	* @return The Moon's position and velocity vectors in J2000 equatorial coordinates (EQJ).
	2432	*/
	2433	astro_state_vector_t Astronomy_GeoMoonState(astro_time_t time)
	2434	{
	2435	/*
	2436	This is a hack, because trying to figure out how to derive a time
	2437	derivative for CalcMoon() would be extremely painful!
	2438	Calculate just before and just after the given time.
	2439	Average to find position, subtract to find velocity.
	2440	*/
	2441	const double dt = 1.0e-5; /* 0.864 seconds */
	2442	astro_vector_t r1, r2;
	2443	astro_time_t t1, t2;
	2444	astro_state_vector_t s;
	2445
	2446	t1 = Astronomy_AddDays(time, -dt);
	2447	t2 = Astronomy_AddDays(time, +dt);
	2448
	2449	r1 = Astronomy_GeoMoon(t1);
	2450	r2 = Astronomy_GeoMoon(t2);
	2451
	2452	/* The desired position is the average of the two calculated positions. */
	2453	s.x = (r1.x + r2.x) / 2;
	2454	s.y = (r1.y + r2.y) / 2;
	2455	s.z = (r1.z + r2.z) / 2;
	2456
	2457	/* The difference of the position vectors divided by the time span gives the velocity vector. */
	2458	s.vx = (r2.x - r1.x) / (2 * dt);
	2459	s.vy = (r2.y - r1.y) / (2 * dt);
	2460	s.vz = (r2.z - r1.z) / (2 * dt);
	2461	s.t = time;
	2462	s.status = ASTRO_SUCCESS;
	2463
	2464	return s;
	2465	}
	2466
	2467
	2468	/**
	2469	* @brief Calculates the geocentric position and velocity of the Earth/Moon barycenter.
	2470	*
	2471	* Given a time of observation, calculates the geocentric position and velocity vectors
	2472	* of the Earth/Moon barycenter (EMB).
	2473	* The position (x, y, z) components are expressed in AU (astronomical units).
	2474	* The velocity (vx, vy, vz) components are expressed in AU/day.
	2475	* The coordinates are oriented with respect to the Earth's equator at the J2000 epoch.
	2476	* In Astronomy Engine, this orientation is called EQJ.
	2477	*
	2478	* @param time The date and time for which to calculate the EMB vectors.
	2479	* @return The EMB's position and velocity vectors in geocentric J2000 equatorial coordinates.
	2480	*/
	2481	astro_state_vector_t Astronomy_GeoEmbState(astro_time_t time)
	2482	{
	2483	astro_state_vector_t s = Astronomy_GeoMoonState(time);
	2484	const double d = 1.0 + EARTH_MOON_MASS_RATIO;
	2485	s.x /= d;
	2486	s.y /= d;
	2487	s.z /= d;
	2488	s.vx /= d;
	2489	s.vy /= d;
	2490	s.vz /= d;
	2491	return s;
	2492	}
	2493
	2494
	2495	/**
	2496	* @brief Calculates the Moon's libration angles at a given moment in time.
	2497	*
	2498	* Libration is an observed back-and-forth wobble of the portion of the
	2499	* Moon visible from the Earth. It is caused by the imperfect tidal locking
	2500	* of the Moon's fixed rotation rate, compared to its variable angular speed
	2501	* of orbit around the Earth.
	2502	*
	2503	* This function calculates a pair of perpendicular libration angles,
	2504	* one representing rotation of the Moon in ecliptic longitude `elon`, the other
	2505	* in ecliptic latitude `elat`, both relative to the Moon's mean Earth-facing position.
	2506	*
	2507	* This function also returns the geocentric position of the Moon
	2508	* expressed in ecliptic longitude `mlon`, ecliptic latitude `mlat`, the
	2509	* distance `dist_km` between the centers of the Earth and Moon expressed in kilometers,
	2510	* and the apparent angular diameter of the Moon `diam_deg`.
	2511	*
	2512	* @param time The date and time for which to calculate libration angles.
	2513	* @return The Moon's ecliptic position and libration angles as seen from the Earth.
	2514	*/
	2515	astro_libration_t Astronomy_Libration(astro_time_t time)
	2516	{
	2517	astro_libration_t lib;
	2518	double t, t2, t3, t4;
	2519	double f, omega, w, a, ldash, ldash2, bdash, bdash2;
	2520	double k1, k2, m, mdash, d, e, rho, sigma, tau;
	2521	const double sin_I = sin(MOON_AXIS_INCLINATION_RADIANS);
	2522	const double cos_I = cos(MOON_AXIS_INCLINATION_RADIANS);
	2523
	2524	t = time.tt / 36525.0;
	2525	t2 = t * t;
	2526	t3 = t2 * t;
	2527	t4 = t2 * t2;
	2528
	2529	double mlon; /* Moon's ecliptic longitude in radians. */
	2530	double mlat; /* Moon's ecliptic latitude in radians. */
	2531	CalcMoon(t, &mlon, &mlat, &lib.dist_km);
	2532	lib.mlon = RAD2DEG * mlon;
	2533	lib.mlat = RAD2DEG * mlat;
	2534	lib.dist_km *= KM_PER_AU;
	2535	lib.diam_deg = (2.0 * RAD2DEG) * atan(MOON_MEAN_RADIUS_KM / sqrt(lib.dist_kmlib.dist_km - MOON_MEAN_RADIUS_KMMOON_MEAN_RADIUS_KM));
	2536
	2537	/* Moon's argument of latitude in radians. */
	2538	f = DEG2RAD * NormalizeLongitude(93.2720950 + 483202.0175233t - 0.0036539t2 - t3/3526000 + t4/863310000);
	2539
	2540	/* Moon's ascending node's mean longitude in radians. */
	2541	omega = DEG2RAD * NormalizeLongitude(125.0445479 - 1934.1362891t + 0.0020754t2 + t3/467441 - t4/60616000);
	2542
	2543	/* Sun's mean anomaly. */
	2544	m = DEG2RAD * NormalizeLongitude(357.5291092 + 35999.0502909t - 0.0001536t2 + t3/24490000);
	2545
	2546	/* Moon's mean anomaly. */
	2547	mdash = DEG2RAD * NormalizeLongitude(134.9633964 + 477198.8675055t + 0.0087414t2 + t3/69699 - t4/14712000);
	2548
	2549	/* Moon's mean elongation. */
	2550	d = DEG2RAD * NormalizeLongitude(297.8501921 + 445267.1114034t - 0.0018819t2 + t3/545868 - t4/113065000);
	2551
	2552	/* Eccentricity of the Earth's orbit. */
	2553	e = 1.0 - 0.002516t - 0.0000074t2;
	2554
	2555	/* Optical librations */
	2556	w = mlon - omega;
	2557	a = atan2(sin(w)cos(mlat)cos_I - sin(mlat)sin_I, cos(w)cos(mlat));
	2558	ldash = LongitudeOffset(RAD2DEG * (a - f));
	2559	bdash = asin(-sin(w)cos(mlat)sin_I - sin(mlat)*cos_I);
	2560
	2561	/* Physical librations */
	2562	k1 = DEG2RAD(119.75 + 131.849t);
	2563	k2 = DEG2RAD(72.56 + 20.186t);
	2564
	2565	rho = (
	2566	-0.02752*cos(mdash) +
	2567	-0.02245*sin(f) +
	2568	+0.00684cos(mdash - 2f) +
	2569	-0.00293cos(2f) +
	2570	-0.00085cos(2f - 2*d) +
	2571	-0.00054cos(mdash - 2d) +
	2572	-0.00020*sin(mdash + f) +
	2573	-0.00020cos(mdash + 2f) +
	2574	-0.00020*cos(mdash - f) +
	2575	+0.00014cos(mdash + 2f - 2*d)
	2576	);
	2577
	2578	sigma = (
	2579	-0.02816*sin(mdash) +
	2580	+0.02244*cos(f) +
	2581	-0.00682sin(mdash - 2f) +
	2582	-0.00279sin(2f) +
	2583	-0.00083sin(2f - 2*d) +
	2584	+0.00069sin(mdash - 2d) +
	2585	+0.00040*cos(mdash + f) +
	2586	-0.00025sin(2mdash) +
	2587	-0.00023sin(mdash + 2f) +
	2588	+0.00020*cos(mdash - f) +
	2589	+0.00019*sin(mdash - f) +
	2590	+0.00013sin(mdash + 2f - 2*d) +
	2591	-0.00010cos(mdash - 3f)
	2592	);
	2593
	2594	tau = (
	2595	+0.02520esin(m) +
	2596	+0.00473sin(2mdash - 2*f) +
	2597	-0.00467*sin(mdash) +
	2598	+0.00396*sin(k1) +
	2599	+0.00276sin(2mdash - 2*d) +
	2600	+0.00196*sin(omega) +
	2601	-0.00183*cos(mdash - f) +
	2602	+0.00115sin(mdash - 2d) +
	2603	-0.00096*sin(mdash - d) +
	2604	+0.00046sin(2f - 2*d) +
	2605	-0.00039*sin(mdash - f) +
	2606	-0.00032*sin(mdash - m - d) +
	2607	+0.00027sin(2mdash - m - 2*d) +
	2608	+0.00023*sin(k2) +
	2609	-0.00014sin(2d) +
	2610	+0.00014cos(2mdash - 2*f) +
	2611	-0.00012sin(mdash - 2f) +
	2612	-0.00012sin(2mdash) +
	2613	+0.00011sin(2mdash - 2m - 2d)
	2614	);
	2615
	2616	ldash2 = -tau + (rhocos(a) + sigmasin(a))*tan(bdash);
	2617	bdash *= RAD2DEG;
	2618	bdash2 = sigmacos(a) - rhosin(a);
	2619
	2620	lib.elon = ldash + ldash2;
	2621	lib.elat = bdash + bdash2;
	2622
	2623	return lib;
	2624	}
	2625
	2626
	2627	/------------------ VSOP ------------------/
	2628
	2629	/** @cond DOXYGEN_SKIP */
	2630	typedef struct
	2631	{
	2632	double amplitude;
	2633	double phase;
	2634	double frequency;
	2635	}
	2636	vsop_term_t;
	2637
	2638	typedef struct
	2639	{
	2640	int nterms;
	2641	const vsop_term_t *term;
	2642	}
	2643	vsop_series_t;
	2644
	2645	typedef struct
	2646	{
	2647	int nseries;
	2648	const vsop_series_t *series;
	2649	}
	2650	vsop_formula_t;
	2651
	2652	typedef struct
	2653	{
	2654	const vsop_formula_t formula[3];
	2655	}
	2656	vsop_model_t;
	2657
	2658	typedef struct
	2659	{
	2660	double mu;
	2661	double al[2];
	2662	vsop_series_t a;
	2663	vsop_series_t l;
	2664	vsop_series_t z;
	2665	vsop_series_t zeta;
	2666	}
	2667	jupiter_moon_t;
	2668	/** @endcond */
	2669
	2670	static const vsop_term_t vsop_lon_Mercury_0[] =
	2671	{
	2672	{ 4.40250710144, 0.00000000000, 0.00000000000 },
	2673	{ 0.40989414977, 1.48302034195, 26087.90314157420 },
	2674	{ 0.05046294200, 4.47785489551, 52175.80628314840 },
	2675	{ 0.00855346844, 1.16520322459, 78263.70942472259 },
	2676	{ 0.00165590362, 4.11969163423, 104351.61256629678 },
	2677	{ 0.00034561897, 0.77930768443, 130439.51570787099 },
	2678	{ 0.00007583476, 3.71348404924, 156527.41884944518 }
	2679	};
	2680
	2681	static const vsop_term_t vsop_lon_Mercury_1[] =
	2682	{
	2683	{ 26087.90313685529, 0.00000000000, 0.00000000000 },
	2684	{ 0.01131199811, 6.21874197797, 26087.90314157420 },
	2685	{ 0.00292242298, 3.04449355541, 52175.80628314840 },
	2686	{ 0.00075775081, 6.08568821653, 78263.70942472259 },
	2687	{ 0.00019676525, 2.80965111777, 104351.61256629678 }
	2688	};
	2689
	2690	static const vsop_series_t vsop_lon_Mercury[] =
	2691	{
	2692	{ 7, vsop_lon_Mercury_0 },
	2693	{ 5, vsop_lon_Mercury_1 }
	2694	};
	2695
	2696	static const vsop_term_t vsop_lat_Mercury_0[] =
	2697	{
	2698	{ 0.11737528961, 1.98357498767, 26087.90314157420 },
	2699	{ 0.02388076996, 5.03738959686, 52175.80628314840 },
	2700	{ 0.01222839532, 3.14159265359, 0.00000000000 },
	2701	{ 0.00543251810, 1.79644363964, 78263.70942472259 },
	2702	{ 0.00129778770, 4.83232503958, 104351.61256629678 },
	2703	{ 0.00031866927, 1.58088495658, 130439.51570787099 },
	2704	{ 0.00007963301, 4.60972126127, 156527.41884944518 }
	2705	};
	2706
	2707	static const vsop_term_t vsop_lat_Mercury_1[] =
	2708	{
	2709	{ 0.00274646065, 3.95008450011, 26087.90314157420 },
	2710	{ 0.00099737713, 3.14159265359, 0.00000000000 }
	2711	};
	2712
	2713	static const vsop_series_t vsop_lat_Mercury[] =
	2714	{
	2715	{ 7, vsop_lat_Mercury_0 },
	2716	{ 2, vsop_lat_Mercury_1 }
	2717	};
	2718
	2719	static const vsop_term_t vsop_rad_Mercury_0[] =
	2720	{
	2721	{ 0.39528271651, 0.00000000000, 0.00000000000 },
	2722	{ 0.07834131818, 6.19233722598, 26087.90314157420 },
	2723	{ 0.00795525558, 2.95989690104, 52175.80628314840 },
	2724	{ 0.00121281764, 6.01064153797, 78263.70942472259 },
	2725	{ 0.00021921969, 2.77820093972, 104351.61256629678 },
	2726	{ 0.00004354065, 5.82894543774, 130439.51570787099 }
	2727	};
	2728
	2729	static const vsop_term_t vsop_rad_Mercury_1[] =
	2730	{
	2731	{ 0.00217347740, 4.65617158665, 26087.90314157420 },
	2732	{ 0.00044141826, 1.42385544001, 52175.80628314840 }
	2733	};
	2734
	2735	static const vsop_series_t vsop_rad_Mercury[] =
	2736	{
	2737	{ 6, vsop_rad_Mercury_0 },
	2738	{ 2, vsop_rad_Mercury_1 }
	2739	};
	2740
	2741	;
	2742	static const vsop_term_t vsop_lon_Venus_0[] =
	2743	{
	2744	{ 3.17614666774, 0.00000000000, 0.00000000000 },
	2745	{ 0.01353968419, 5.59313319619, 10213.28554621100 },
	2746	{ 0.00089891645, 5.30650047764, 20426.57109242200 },
	2747	{ 0.00005477194, 4.41630661466, 7860.41939243920 },
	2748	{ 0.00003455741, 2.69964447820, 11790.62908865880 },
	2749	{ 0.00002372061, 2.99377542079, 3930.20969621960 },
	2750	{ 0.00001317168, 5.18668228402, 26.29831979980 },
	2751	{ 0.00001664146, 4.25018630147, 1577.34354244780 },
	2752	{ 0.00001438387, 4.15745084182, 9683.59458111640 },
	2753	{ 0.00001200521, 6.15357116043, 30639.85663863300 }
	2754	};
	2755
	2756	static const vsop_term_t vsop_lon_Venus_1[] =
	2757	{
	2758	{ 10213.28554621638, 0.00000000000, 0.00000000000 },
	2759	{ 0.00095617813, 2.46406511110, 10213.28554621100 },
	2760	{ 0.00007787201, 0.62478482220, 20426.57109242200 }
	2761	};
	2762
	2763	static const vsop_series_t vsop_lon_Venus[] =
	2764	{
	2765	{ 10, vsop_lon_Venus_0 },
	2766	{ 3, vsop_lon_Venus_1 }
	2767	};
	2768
	2769	static const vsop_term_t vsop_lat_Venus_0[] =
	2770	{
	2771	{ 0.05923638472, 0.26702775812, 10213.28554621100 },
	2772	{ 0.00040107978, 1.14737178112, 20426.57109242200 },
	2773	{ 0.00032814918, 3.14159265359, 0.00000000000 }
	2774	};
	2775
	2776	static const vsop_term_t vsop_lat_Venus_1[] =
	2777	{
	2778	{ 0.00287821243, 1.88964962838, 10213.28554621100 }
	2779	};
	2780
	2781	static const vsop_series_t vsop_lat_Venus[] =
	2782	{
	2783	{ 3, vsop_lat_Venus_0 },
	2784	{ 1, vsop_lat_Venus_1 }
	2785	};
	2786
	2787	static const vsop_term_t vsop_rad_Venus_0[] =
	2788	{
	2789	{ 0.72334820891, 0.00000000000, 0.00000000000 },
	2790	{ 0.00489824182, 4.02151831717, 10213.28554621100 },
	2791	{ 0.00001658058, 4.90206728031, 20426.57109242200 },
	2792	{ 0.00001378043, 1.12846591367, 11790.62908865880 },
	2793	{ 0.00001632096, 2.84548795207, 7860.41939243920 },
	2794	{ 0.00000498395, 2.58682193892, 9683.59458111640 },
	2795	{ 0.00000221985, 2.01346696541, 19367.18916223280 },
	2796	{ 0.00000237454, 2.55136053886, 15720.83878487840 }
	2797	};
	2798
	2799	static const vsop_term_t vsop_rad_Venus_1[] =
	2800	{
	2801	{ 0.00034551041, 0.89198706276, 10213.28554621100 }
	2802	};
	2803
	2804	static const vsop_series_t vsop_rad_Venus[] =
	2805	{
	2806	{ 8, vsop_rad_Venus_0 },
	2807	{ 1, vsop_rad_Venus_1 }
	2808	};
	2809
	2810	;
	2811	static const vsop_term_t vsop_lon_Earth_0[] =
	2812	{
	2813	{ 1.75347045673, 0.00000000000, 0.00000000000 },
	2814	{ 0.03341656453, 4.66925680415, 6283.07584999140 },
	2815	{ 0.00034894275, 4.62610242189, 12566.15169998280 },
	2816	{ 0.00003417572, 2.82886579754, 3.52311834900 },
	2817	{ 0.00003497056, 2.74411783405, 5753.38488489680 },
	2818	{ 0.00003135899, 3.62767041756, 77713.77146812050 },
	2819	{ 0.00002676218, 4.41808345438, 7860.41939243920 },
	2820	{ 0.00002342691, 6.13516214446, 3930.20969621960 },
	2821	{ 0.00001273165, 2.03709657878, 529.69096509460 },
	2822	{ 0.00001324294, 0.74246341673, 11506.76976979360 },
	2823	{ 0.00000901854, 2.04505446477, 26.29831979980 },
	2824	{ 0.00001199167, 1.10962946234, 1577.34354244780 },
	2825	{ 0.00000857223, 3.50849152283, 398.14900340820 },
	2826	{ 0.00000779786, 1.17882681962, 5223.69391980220 },
	2827	{ 0.00000990250, 5.23268072088, 5884.92684658320 },
	2828	{ 0.00000753141, 2.53339052847, 5507.55323866740 },
	2829	{ 0.00000505267, 4.58292599973, 18849.22754997420 },
	2830	{ 0.00000492392, 4.20505711826, 775.52261132400 },
	2831	{ 0.00000356672, 2.91954114478, 0.06731030280 },
	2832	{ 0.00000284125, 1.89869240932, 796.29800681640 },
	2833	{ 0.00000242879, 0.34481445893, 5486.77784317500 },
	2834	{ 0.00000317087, 5.84901948512, 11790.62908865880 },
	2835	{ 0.00000271112, 0.31486255375, 10977.07880469900 },
	2836	{ 0.00000206217, 4.80646631478, 2544.31441988340 },
	2837	{ 0.00000205478, 1.86953770281, 5573.14280143310 },
	2838	{ 0.00000202318, 2.45767790232, 6069.77675455340 },
	2839	{ 0.00000126225, 1.08295459501, 20.77539549240 },
	2840	{ 0.00000155516, 0.83306084617, 213.29909543800 }
	2841	};
	2842
	2843	static const vsop_term_t vsop_lon_Earth_1[] =
	2844	{
	2845	{ 6283.07584999140, 0.00000000000, 0.00000000000 },
	2846	{ 0.00206058863, 2.67823455808, 6283.07584999140 },
	2847	{ 0.00004303419, 2.63512233481, 12566.15169998280 }
	2848	};
	2849
	2850	static const vsop_term_t vsop_lon_Earth_2[] =
	2851	{
	2852	{ 0.00008721859, 1.07253635559, 6283.07584999140 }
	2853	};
	2854
	2855	static const vsop_series_t vsop_lon_Earth[] =
	2856	{
	2857	{ 28, vsop_lon_Earth_0 },
	2858	{ 3, vsop_lon_Earth_1 },
	2859	{ 1, vsop_lon_Earth_2 }
	2860	};
	2861
	2862	static const vsop_term_t vsop_lat_Earth_1[] =
	2863	{
	2864	{ 0.00227777722, 3.41376620530, 6283.07584999140 },
	2865	{ 0.00003805678, 3.37063423795, 12566.15169998280 }
	2866	};
	2867
	2868	static const vsop_series_t vsop_lat_Earth[] =
	2869	{
	2870	{ 0, NULL },
	2871	{ 2, vsop_lat_Earth_1 }
	2872	};
	2873
	2874	static const vsop_term_t vsop_rad_Earth_0[] =
	2875	{
	2876	{ 1.00013988784, 0.00000000000, 0.00000000000 },
	2877	{ 0.01670699632, 3.09846350258, 6283.07584999140 },
	2878	{ 0.00013956024, 3.05524609456, 12566.15169998280 },
	2879	{ 0.00003083720, 5.19846674381, 77713.77146812050 },
	2880	{ 0.00001628463, 1.17387558054, 5753.38488489680 },
	2881	{ 0.00001575572, 2.84685214877, 7860.41939243920 },
	2882	{ 0.00000924799, 5.45292236722, 11506.76976979360 },
	2883	{ 0.00000542439, 4.56409151453, 3930.20969621960 },
	2884	{ 0.00000472110, 3.66100022149, 5884.92684658320 },
	2885	{ 0.00000085831, 1.27079125277, 161000.68573767410 },
	2886	{ 0.00000057056, 2.01374292245, 83996.84731811189 },
	2887	{ 0.00000055736, 5.24159799170, 71430.69561812909 },
	2888	{ 0.00000174844, 3.01193636733, 18849.22754997420 },
	2889	{ 0.00000243181, 4.27349530790, 11790.62908865880 }
	2890	};
	2891
	2892	static const vsop_term_t vsop_rad_Earth_1[] =
	2893	{
	2894	{ 0.00103018607, 1.10748968172, 6283.07584999140 },
	2895	{ 0.00001721238, 1.06442300386, 12566.15169998280 }
	2896	};
	2897
	2898	static const vsop_term_t vsop_rad_Earth_2[] =
	2899	{
	2900	{ 0.00004359385, 5.78455133808, 6283.07584999140 }
	2901	};
	2902
	2903	static const vsop_series_t vsop_rad_Earth[] =
	2904	{
	2905	{ 14, vsop_rad_Earth_0 },
	2906	{ 2, vsop_rad_Earth_1 },
	2907	{ 1, vsop_rad_Earth_2 }
	2908	};
	2909
	2910	;
	2911	static const vsop_term_t vsop_lon_Mars_0[] =
	2912	{
	2913	{ 6.20347711581, 0.00000000000, 0.00000000000 },
	2914	{ 0.18656368093, 5.05037100270, 3340.61242669980 },
	2915	{ 0.01108216816, 5.40099836344, 6681.22485339960 },
	2916	{ 0.00091798406, 5.75478744667, 10021.83728009940 },
	2917	{ 0.00027744987, 5.97049513147, 3.52311834900 },
	2918	{ 0.00010610235, 2.93958560338, 2281.23049651060 },
	2919	{ 0.00012315897, 0.84956094002, 2810.92146160520 },
	2920	{ 0.00008926784, 4.15697846427, 0.01725365220 },
	2921	{ 0.00008715691, 6.11005153139, 13362.44970679920 },
	2922	{ 0.00006797556, 0.36462229657, 398.14900340820 },
	2923	{ 0.00007774872, 3.33968761376, 5621.84292321040 },
	2924	{ 0.00003575078, 1.66186505710, 2544.31441988340 },
	2925	{ 0.00004161108, 0.22814971327, 2942.46342329160 },
	2926	{ 0.00003075252, 0.85696614132, 191.44826611160 },
	2927	{ 0.00002628117, 0.64806124465, 3337.08930835080 },
	2928	{ 0.00002937546, 6.07893711402, 0.06731030280 },
	2929	{ 0.00002389414, 5.03896442664, 796.29800681640 },
	2930	{ 0.00002579844, 0.02996736156, 3344.13554504880 },
	2931	{ 0.00001528141, 1.14979301996, 6151.53388830500 },
	2932	{ 0.00001798806, 0.65634057445, 529.69096509460 },
	2933	{ 0.00001264357, 3.62275122593, 5092.15195811580 },
	2934	{ 0.00001286228, 3.06796065034, 2146.16541647520 },
	2935	{ 0.00001546404, 2.91579701718, 1751.53953141600 },
	2936	{ 0.00001024902, 3.69334099279, 8962.45534991020 },
	2937	{ 0.00000891566, 0.18293837498, 16703.06213349900 },
	2938	{ 0.00000858759, 2.40093811940, 2914.01423582380 },
	2939	{ 0.00000832715, 2.46418619474, 3340.59517304760 },
	2940	{ 0.00000832720, 4.49495782139, 3340.62968035200 },
	2941	{ 0.00000712902, 3.66335473479, 1059.38193018920 },
	2942	{ 0.00000748723, 3.82248614017, 155.42039943420 },
	2943	{ 0.00000723861, 0.67497311481, 3738.76143010800 },
	2944	{ 0.00000635548, 2.92182225127, 8432.76438481560 },
	2945	{ 0.00000655162, 0.48864064125, 3127.31333126180 },
	2946	{ 0.00000550474, 3.81001042328, 0.98032106820 },
	2947	{ 0.00000552750, 4.47479317037, 1748.01641306700 },
	2948	{ 0.00000425966, 0.55364317304, 6283.07584999140 },
	2949	{ 0.00000415131, 0.49662285038, 213.29909543800 },
	2950	{ 0.00000472167, 3.62547124025, 1194.44701022460 },
	2951	{ 0.00000306551, 0.38052848348, 6684.74797174860 },
	2952	{ 0.00000312141, 0.99853944405, 6677.70173505060 },
	2953	{ 0.00000293198, 4.22131299634, 20.77539549240 },
	2954	{ 0.00000302375, 4.48618007156, 3532.06069281140 },
	2955	{ 0.00000274027, 0.54222167059, 3340.54511639700 },
	2956	{ 0.00000281079, 5.88163521788, 1349.86740965880 },
	2957	{ 0.00000231183, 1.28242156993, 3870.30339179440 },
	2958	{ 0.00000283602, 5.76885434940, 3149.16416058820 },
	2959	{ 0.00000236117, 5.75503217933, 3333.49887969900 },
	2960	{ 0.00000274033, 0.13372524985, 3340.67973700260 },
	2961	{ 0.00000299395, 2.78323740866, 6254.62666252360 }
	2962	};
	2963
	2964	static const vsop_term_t vsop_lon_Mars_1[] =
	2965	{
	2966	{ 3340.61242700512, 0.00000000000, 0.00000000000 },
	2967	{ 0.01457554523, 3.60433733236, 3340.61242669980 },
	2968	{ 0.00168414711, 3.92318567804, 6681.22485339960 },
	2969	{ 0.00020622975, 4.26108844583, 10021.83728009940 },
	2970	{ 0.00003452392, 4.73210393190, 3.52311834900 },
	2971	{ 0.00002586332, 4.60670058555, 13362.44970679920 },
	2972	{ 0.00000841535, 4.45864030426, 2281.23049651060 }
	2973	};
	2974
	2975	static const vsop_term_t vsop_lon_Mars_2[] =
	2976	{
	2977	{ 0.00058152577, 2.04961712429, 3340.61242669980 },
	2978	{ 0.00013459579, 2.45738706163, 6681.22485339960 }
	2979	};
	2980
	2981	static const vsop_series_t vsop_lon_Mars[] =
	2982	{
	2983	{ 49, vsop_lon_Mars_0 },
	2984	{ 7, vsop_lon_Mars_1 },
	2985	{ 2, vsop_lon_Mars_2 }
	2986	};
	2987
	2988	static const vsop_term_t vsop_lat_Mars_0[] =
	2989	{
	2990	{ 0.03197134986, 3.76832042431, 3340.61242669980 },
	2991	{ 0.00298033234, 4.10616996305, 6681.22485339960 },
	2992	{ 0.00289104742, 0.00000000000, 0.00000000000 },
	2993	{ 0.00031365539, 4.44651053090, 10021.83728009940 },
	2994	{ 0.00003484100, 4.78812549260, 13362.44970679920 }
	2995	};
	2996
	2997	static const vsop_term_t vsop_lat_Mars_1[] =
	2998	{
	2999	{ 0.00217310991, 6.04472194776, 3340.61242669980 },
	3000	{ 0.00020976948, 3.14159265359, 0.00000000000 },
	3001	{ 0.00012834709, 1.60810667915, 6681.22485339960 }
	3002	};
	3003
	3004	static const vsop_series_t vsop_lat_Mars[] =
	3005	{
	3006	{ 5, vsop_lat_Mars_0 },
	3007	{ 3, vsop_lat_Mars_1 }
	3008	};
	3009
	3010	static const vsop_term_t vsop_rad_Mars_0[] =
	3011	{
	3012	{ 1.53033488271, 0.00000000000, 0.00000000000 },
	3013	{ 0.14184953160, 3.47971283528, 3340.61242669980 },
	3014	{ 0.00660776362, 3.81783443019, 6681.22485339960 },
	3015	{ 0.00046179117, 4.15595316782, 10021.83728009940 },
	3016	{ 0.00008109733, 5.55958416318, 2810.92146160520 },
	3017	{ 0.00007485318, 1.77239078402, 5621.84292321040 },
	3018	{ 0.00005523191, 1.36436303770, 2281.23049651060 },
	3019	{ 0.00003825160, 4.49407183687, 13362.44970679920 },
	3020	{ 0.00002306537, 0.09081579001, 2544.31441988340 },
	3021	{ 0.00001999396, 5.36059617709, 3337.08930835080 },
	3022	{ 0.00002484394, 4.92545639920, 2942.46342329160 },
	3023	{ 0.00001960195, 4.74249437639, 3344.13554504880 },
	3024	{ 0.00001167119, 2.11260868341, 5092.15195811580 },
	3025	{ 0.00001102816, 5.00908403998, 398.14900340820 },
	3026	{ 0.00000899066, 4.40791133207, 529.69096509460 },
	3027	{ 0.00000992252, 5.83861961952, 6151.53388830500 },
	3028	{ 0.00000807354, 2.10217065501, 1059.38193018920 },
	3029	{ 0.00000797915, 3.44839203899, 796.29800681640 },
	3030	{ 0.00000740975, 1.49906336885, 2146.16541647520 }
	3031	};
	3032
	3033	static const vsop_term_t vsop_rad_Mars_1[] =
	3034	{
	3035	{ 0.01107433345, 2.03250524857, 3340.61242669980 },
	3036	{ 0.00103175887, 2.37071847807, 6681.22485339960 },
	3037	{ 0.00012877200, 0.00000000000, 0.00000000000 },
	3038	{ 0.00010815880, 2.70888095665, 10021.83728009940 }
	3039	};
	3040
	3041	static const vsop_term_t vsop_rad_Mars_2[] =
	3042	{
	3043	{ 0.00044242249, 0.47930604954, 3340.61242669980 },
	3044	{ 0.00008138042, 0.86998389204, 6681.22485339960 }
	3045	};
	3046
	3047	static const vsop_series_t vsop_rad_Mars[] =
	3048	{
	3049	{ 19, vsop_rad_Mars_0 },
	3050	{ 4, vsop_rad_Mars_1 },
	3051	{ 2, vsop_rad_Mars_2 }
	3052	};
	3053
	3054	;
	3055	static const vsop_term_t vsop_lon_Jupiter_0[] =
	3056	{
	3057	{ 0.59954691494, 0.00000000000, 0.00000000000 },
	3058	{ 0.09695898719, 5.06191793158, 529.69096509460 },
	3059	{ 0.00573610142, 1.44406205629, 7.11354700080 },
	3060	{ 0.00306389205, 5.41734730184, 1059.38193018920 },
	3061	{ 0.00097178296, 4.14264726552, 632.78373931320 },
	3062	{ 0.00072903078, 3.64042916389, 522.57741809380 },
	3063	{ 0.00064263975, 3.41145165351, 103.09277421860 },
	3064	{ 0.00039806064, 2.29376740788, 419.48464387520 },
	3065	{ 0.00038857767, 1.27231755835, 316.39186965660 },
	3066	{ 0.00027964629, 1.78454591820, 536.80451209540 },
	3067	{ 0.00013589730, 5.77481040790, 1589.07289528380 },
	3068	{ 0.00008246349, 3.58227925840, 206.18554843720 },
	3069	{ 0.00008768704, 3.63000308199, 949.17560896980 },
	3070	{ 0.00007368042, 5.08101194270, 735.87651353180 },
	3071	{ 0.00006263150, 0.02497628807, 213.29909543800 },
	3072	{ 0.00006114062, 4.51319998626, 1162.47470440780 },
	3073	{ 0.00004905396, 1.32084470588, 110.20632121940 },
	3074	{ 0.00005305285, 1.30671216791, 14.22709400160 },
	3075	{ 0.00005305441, 4.18625634012, 1052.26838318840 },
	3076	{ 0.00004647248, 4.69958103684, 3.93215326310 },
	3077	{ 0.00003045023, 4.31676431084, 426.59819087600 },
	3078	{ 0.00002609999, 1.56667394063, 846.08283475120 },
	3079	{ 0.00002028191, 1.06376530715, 3.18139373770 },
	3080	{ 0.00001764763, 2.14148655117, 1066.49547719000 },
	3081	{ 0.00001722972, 3.88036268267, 1265.56747862640 },
	3082	{ 0.00001920945, 0.97168196472, 639.89728631400 },
	3083	{ 0.00001633223, 3.58201833555, 515.46387109300 },
	3084	{ 0.00001431999, 4.29685556046, 625.67019231240 },
	3085	{ 0.00000973272, 4.09764549134, 95.97922721780 }
	3086	};
	3087
	3088	static const vsop_term_t vsop_lon_Jupiter_1[] =
	3089	{
	3090	{ 529.69096508814, 0.00000000000, 0.00000000000 },
	3091	{ 0.00489503243, 4.22082939470, 529.69096509460 },
	3092	{ 0.00228917222, 6.02646855621, 7.11354700080 },
	3093	{ 0.00030099479, 4.54540782858, 1059.38193018920 },
	3094	{ 0.00020720920, 5.45943156902, 522.57741809380 },
	3095	{ 0.00012103653, 0.16994816098, 536.80451209540 },
	3096	{ 0.00006067987, 4.42422292017, 103.09277421860 },
	3097	{ 0.00005433968, 3.98480737746, 419.48464387520 },
	3098	{ 0.00004237744, 5.89008707199, 14.22709400160 }
	3099	};
	3100
	3101	static const vsop_term_t vsop_lon_Jupiter_2[] =
	3102	{
	3103	{ 0.00047233601, 4.32148536482, 7.11354700080 },
	3104	{ 0.00030649436, 2.92977788700, 529.69096509460 },
	3105	{ 0.00014837605, 3.14159265359, 0.00000000000 }
	3106	};
	3107
	3108	static const vsop_series_t vsop_lon_Jupiter[] =
	3109	{
	3110	{ 29, vsop_lon_Jupiter_0 },
	3111	{ 9, vsop_lon_Jupiter_1 },
	3112	{ 3, vsop_lon_Jupiter_2 }
	3113	};
	3114
	3115	static const vsop_term_t vsop_lat_Jupiter_0[] =
	3116	{
	3117	{ 0.02268615702, 3.55852606721, 529.69096509460 },
	3118	{ 0.00109971634, 3.90809347197, 1059.38193018920 },
	3119	{ 0.00110090358, 0.00000000000, 0.00000000000 },
	3120	{ 0.00008101428, 3.60509572885, 522.57741809380 },
	3121	{ 0.00006043996, 4.25883108339, 1589.07289528380 },
	3122	{ 0.00006437782, 0.30627119215, 536.80451209540 }
	3123	};
	3124
	3125	static const vsop_term_t vsop_lat_Jupiter_1[] =
	3126	{
	3127	{ 0.00078203446, 1.52377859742, 529.69096509460 }
	3128	};
	3129
	3130	static const vsop_series_t vsop_lat_Jupiter[] =
	3131	{
	3132	{ 6, vsop_lat_Jupiter_0 },
	3133	{ 1, vsop_lat_Jupiter_1 }
	3134	};
	3135
	3136	static const vsop_term_t vsop_rad_Jupiter_0[] =
	3137	{
	3138	{ 5.20887429326, 0.00000000000, 0.00000000000 },
	3139	{ 0.25209327119, 3.49108639871, 529.69096509460 },
	3140	{ 0.00610599976, 3.84115365948, 1059.38193018920 },
	3141	{ 0.00282029458, 2.57419881293, 632.78373931320 },
	3142	{ 0.00187647346, 2.07590383214, 522.57741809380 },
	3143	{ 0.00086792905, 0.71001145545, 419.48464387520 },
	3144	{ 0.00072062974, 0.21465724607, 536.80451209540 },
	3145	{ 0.00065517248, 5.97995884790, 316.39186965660 },
	3146	{ 0.00029134542, 1.67759379655, 103.09277421860 },
	3147	{ 0.00030135335, 2.16132003734, 949.17560896980 },
	3148	{ 0.00023453271, 3.54023522184, 735.87651353180 },
	3149	{ 0.00022283743, 4.19362594399, 1589.07289528380 },
	3150	{ 0.00023947298, 0.27458037480, 7.11354700080 },
	3151	{ 0.00013032614, 2.96042965363, 1162.47470440780 },
	3152	{ 0.00009703360, 1.90669633585, 206.18554843720 },
	3153	{ 0.00012749023, 2.71550286592, 1052.26838318840 },
	3154	{ 0.00007057931, 2.18184839926, 1265.56747862640 },
	3155	{ 0.00006137703, 6.26418240033, 846.08283475120 },
	3156	{ 0.00002616976, 2.00994012876, 1581.95934828300 }
	3157	};
	3158
	3159	static const vsop_term_t vsop_rad_Jupiter_1[] =
	3160	{
	3161	{ 0.01271801520, 2.64937512894, 529.69096509460 },
	3162	{ 0.00061661816, 3.00076460387, 1059.38193018920 },
	3163	{ 0.00053443713, 3.89717383175, 522.57741809380 },
	3164	{ 0.00031185171, 4.88276958012, 536.80451209540 },
	3165	{ 0.00041390269, 0.00000000000, 0.00000000000 }
	3166	};
	3167
	3168	static const vsop_series_t vsop_rad_Jupiter[] =
	3169	{
	3170	{ 19, vsop_rad_Jupiter_0 },
	3171	{ 5, vsop_rad_Jupiter_1 }
	3172	};
	3173
	3174	;
	3175	static const vsop_term_t vsop_lon_Saturn_0[] =
	3176	{
	3177	{ 0.87401354025, 0.00000000000, 0.00000000000 },
	3178	{ 0.11107659762, 3.96205090159, 213.29909543800 },
	3179	{ 0.01414150957, 4.58581516874, 7.11354700080 },
	3180	{ 0.00398379389, 0.52112032699, 206.18554843720 },
	3181	{ 0.00350769243, 3.30329907896, 426.59819087600 },
	3182	{ 0.00206816305, 0.24658372002, 103.09277421860 },
	3183	{ 0.00079271300, 3.84007056878, 220.41264243880 },
	3184	{ 0.00023990355, 4.66976924553, 110.20632121940 },
	3185	{ 0.00016573588, 0.43719228296, 419.48464387520 },
	3186	{ 0.00014906995, 5.76903183869, 316.39186965660 },
	3187	{ 0.00015820290, 0.93809155235, 632.78373931320 },
	3188	{ 0.00014609559, 1.56518472000, 3.93215326310 },
	3189	{ 0.00013160301, 4.44891291899, 14.22709400160 },
	3190	{ 0.00015053543, 2.71669915667, 639.89728631400 },
	3191	{ 0.00013005299, 5.98119023644, 11.04570026390 },
	3192	{ 0.00010725067, 3.12939523827, 202.25339517410 },
	3193	{ 0.00005863206, 0.23656938524, 529.69096509460 },
	3194	{ 0.00005227757, 4.20783365759, 3.18139373770 },
	3195	{ 0.00006126317, 1.76328667907, 277.03499374140 },
	3196	{ 0.00005019687, 3.17787728405, 433.71173787680 },
	3197	{ 0.00004592550, 0.61977744975, 199.07200143640 },
	3198	{ 0.00004005867, 2.24479718502, 63.73589830340 },
	3199	{ 0.00002953796, 0.98280366998, 95.97922721780 },
	3200	{ 0.00003873670, 3.22283226966, 138.51749687070 },
	3201	{ 0.00002461186, 2.03163875071, 735.87651353180 },
	3202	{ 0.00003269484, 0.77492638211, 949.17560896980 },
	3203	{ 0.00001758145, 3.26580109940, 522.57741809380 },
	3204	{ 0.00001640172, 5.50504453050, 846.08283475120 },
	3205	{ 0.00001391327, 4.02333150505, 323.50541665740 },
	3206	{ 0.00001580648, 4.37265307169, 309.27832265580 },
	3207	{ 0.00001123498, 2.83726798446, 415.55249061210 },
	3208	{ 0.00001017275, 3.71700135395, 227.52618943960 },
	3209	{ 0.00000848642, 3.19150170830, 209.36694217490 }
	3210	};
	3211
	3212	static const vsop_term_t vsop_lon_Saturn_1[] =
	3213	{
	3214	{ 213.29909521690, 0.00000000000, 0.00000000000 },
	3215	{ 0.01297370862, 1.82834923978, 213.29909543800 },
	3216	{ 0.00564345393, 2.88499717272, 7.11354700080 },
	3217	{ 0.00093734369, 1.06311793502, 426.59819087600 },
	3218	{ 0.00107674962, 2.27769131009, 206.18554843720 },
	3219	{ 0.00040244455, 2.04108104671, 220.41264243880 },
	3220	{ 0.00019941774, 1.27954390470, 103.09277421860 },
	3221	{ 0.00010511678, 2.74880342130, 14.22709400160 },
	3222	{ 0.00006416106, 0.38238295041, 639.89728631400 },
	3223	{ 0.00004848994, 2.43037610229, 419.48464387520 },
	3224	{ 0.00004056892, 2.92133209468, 110.20632121940 },
	3225	{ 0.00003768635, 3.64965330780, 3.93215326310 }
	3226	};
	3227
	3228	static const vsop_term_t vsop_lon_Saturn_2[] =
	3229	{
	3230	{ 0.00116441330, 1.17988132879, 7.11354700080 },
	3231	{ 0.00091841837, 0.07325195840, 213.29909543800 },
	3232	{ 0.00036661728, 0.00000000000, 0.00000000000 },
	3233	{ 0.00015274496, 4.06493179167, 206.18554843720 }
	3234	};
	3235
	3236	static const vsop_series_t vsop_lon_Saturn[] =
	3237	{
	3238	{ 33, vsop_lon_Saturn_0 },
	3239	{ 12, vsop_lon_Saturn_1 },
	3240	{ 4, vsop_lon_Saturn_2 }
	3241	};
	3242
	3243	static const vsop_term_t vsop_lat_Saturn_0[] =
	3244	{
	3245	{ 0.04330678039, 3.60284428399, 213.29909543800 },
	3246	{ 0.00240348302, 2.85238489373, 426.59819087600 },
	3247	{ 0.00084745939, 0.00000000000, 0.00000000000 },
	3248	{ 0.00030863357, 3.48441504555, 220.41264243880 },
	3249	{ 0.00034116062, 0.57297307557, 206.18554843720 },
	3250	{ 0.00014734070, 2.11846596715, 639.89728631400 },
	3251	{ 0.00009916667, 5.79003188904, 419.48464387520 },
	3252	{ 0.00006993564, 4.73604689720, 7.11354700080 },
	3253	{ 0.00004807588, 5.43305312061, 316.39186965660 }
	3254	};
	3255
	3256	static const vsop_term_t vsop_lat_Saturn_1[] =
	3257	{
	3258	{ 0.00198927992, 4.93901017903, 213.29909543800 },
	3259	{ 0.00036947916, 3.14159265359, 0.00000000000 },
	3260	{ 0.00017966989, 0.51979431110, 426.59819087600 }
	3261	};
	3262
	3263	static const vsop_series_t vsop_lat_Saturn[] =
	3264	{
	3265	{ 9, vsop_lat_Saturn_0 },
	3266	{ 3, vsop_lat_Saturn_1 }
	3267	};
	3268
	3269	static const vsop_term_t vsop_rad_Saturn_0[] =
	3270	{
	3271	{ 9.55758135486, 0.00000000000, 0.00000000000 },
	3272	{ 0.52921382865, 2.39226219573, 213.29909543800 },
	3273	{ 0.01873679867, 5.23549604660, 206.18554843720 },
	3274	{ 0.01464663929, 1.64763042902, 426.59819087600 },
	3275	{ 0.00821891141, 5.93520042303, 316.39186965660 },
	3276	{ 0.00547506923, 5.01532618980, 103.09277421860 },
	3277	{ 0.00371684650, 2.27114821115, 220.41264243880 },
	3278	{ 0.00361778765, 3.13904301847, 7.11354700080 },
	3279	{ 0.00140617506, 5.70406606781, 632.78373931320 },
	3280	{ 0.00108974848, 3.29313390175, 110.20632121940 },
	3281	{ 0.00069006962, 5.94099540992, 419.48464387520 },
	3282	{ 0.00061053367, 0.94037691801, 639.89728631400 },
	3283	{ 0.00048913294, 1.55733638681, 202.25339517410 },
	3284	{ 0.00034143772, 0.19519102597, 277.03499374140 },
	3285	{ 0.00032401773, 5.47084567016, 949.17560896980 },
	3286	{ 0.00020936596, 0.46349251129, 735.87651353180 },
	3287	{ 0.00009796004, 5.20477537945, 1265.56747862640 },
	3288	{ 0.00011993338, 5.98050967385, 846.08283475120 },
	3289	{ 0.00020839300, 1.52102476129, 433.71173787680 },
	3290	{ 0.00015298404, 3.05943814940, 529.69096509460 },
	3291	{ 0.00006465823, 0.17732249942, 1052.26838318840 },
	3292	{ 0.00011380257, 1.73105427040, 522.57741809380 },
	3293	{ 0.00003419618, 4.94550542171, 1581.95934828300 }
	3294	};
	3295
	3296	static const vsop_term_t vsop_rad_Saturn_1[] =
	3297	{
	3298	{ 0.06182981340, 0.25843511480, 213.29909543800 },
	3299	{ 0.00506577242, 0.71114625261, 206.18554843720 },
	3300	{ 0.00341394029, 5.79635741658, 426.59819087600 },
	3301	{ 0.00188491195, 0.47215589652, 220.41264243880 },
	3302	{ 0.00186261486, 3.14159265359, 0.00000000000 },
	3303	{ 0.00143891146, 1.40744822888, 7.11354700080 }
	3304	};
	3305
	3306	static const vsop_term_t vsop_rad_Saturn_2[] =
	3307	{
	3308	{ 0.00436902572, 4.78671677509, 213.29909543800 }
	3309	};
	3310
	3311	static const vsop_series_t vsop_rad_Saturn[] =
	3312	{
	3313	{ 23, vsop_rad_Saturn_0 },
	3314	{ 6, vsop_rad_Saturn_1 },
	3315	{ 1, vsop_rad_Saturn_2 }
	3316	};
	3317
	3318	;
	3319	static const vsop_term_t vsop_lon_Uranus_0[] =
	3320	{
	3321	{ 5.48129294297, 0.00000000000, 0.00000000000 },
	3322	{ 0.09260408234, 0.89106421507, 74.78159856730 },
	3323	{ 0.01504247898, 3.62719260920, 1.48447270830 },
	3324	{ 0.00365981674, 1.89962179044, 73.29712585900 },
	3325	{ 0.00272328168, 3.35823706307, 149.56319713460 },
	3326	{ 0.00070328461, 5.39254450063, 63.73589830340 },
	3327	{ 0.00068892678, 6.09292483287, 76.26607127560 },
	3328	{ 0.00061998615, 2.26952066061, 2.96894541660 },
	3329	{ 0.00061950719, 2.85098872691, 11.04570026390 },
	3330	{ 0.00026468770, 3.14152083966, 71.81265315070 },
	3331	{ 0.00025710476, 6.11379840493, 454.90936652730 },
	3332	{ 0.00021078850, 4.36059339067, 148.07872442630 },
	3333	{ 0.00017818647, 1.74436930289, 36.64856292950 },
	3334	{ 0.00014613507, 4.73732166022, 3.93215326310 },
	3335	{ 0.00011162509, 5.82681796350, 224.34479570190 },
	3336	{ 0.00010997910, 0.48865004018, 138.51749687070 },
	3337	{ 0.00009527478, 2.95516862826, 35.16409022120 },
	3338	{ 0.00007545601, 5.23626582400, 109.94568878850 },
	3339	{ 0.00004220241, 3.23328220918, 70.84944530420 },
	3340	{ 0.00004051900, 2.27755017300, 151.04766984290 },
	3341	{ 0.00003354596, 1.06549007380, 4.45341812490 },
	3342	{ 0.00002926718, 4.62903718891, 9.56122755560 },
	3343	{ 0.00003490340, 5.48306144511, 146.59425171800 },
	3344	{ 0.00003144069, 4.75199570434, 77.75054398390 },
	3345	{ 0.00002922333, 5.35235361027, 85.82729883120 },
	3346	{ 0.00002272788, 4.36600400036, 70.32818044240 },
	3347	{ 0.00002051219, 1.51773566586, 0.11187458460 },
	3348	{ 0.00002148602, 0.60745949945, 38.13303563780 },
	3349	{ 0.00001991643, 4.92437588682, 277.03499374140 },
	3350	{ 0.00001376226, 2.04283539351, 65.22037101170 },
	3351	{ 0.00001666902, 3.62744066769, 380.12776796000 },
	3352	{ 0.00001284107, 3.11347961505, 202.25339517410 },
	3353	{ 0.00001150429, 0.93343589092, 3.18139373770 },
	3354	{ 0.00001533221, 2.58594681212, 52.69019803950 },
	3355	{ 0.00001281604, 0.54271272721, 222.86032299360 },
	3356	{ 0.00001372139, 4.19641530878, 111.43016149680 },
	3357	{ 0.00001221029, 0.19900650030, 108.46121608020 },
	3358	{ 0.00000946181, 1.19253165736, 127.47179660680 },
	3359	{ 0.00001150989, 4.17898916639, 33.67961751290 }
	3360	};
	3361
	3362	static const vsop_term_t vsop_lon_Uranus_1[] =
	3363	{
	3364	{ 74.78159860910, 0.00000000000, 0.00000000000 },
	3365	{ 0.00154332863, 5.24158770553, 74.78159856730 },
	3366	{ 0.00024456474, 1.71260334156, 1.48447270830 },
	3367	{ 0.00009258442, 0.42829732350, 11.04570026390 },
	3368	{ 0.00008265977, 1.50218091379, 63.73589830340 },
	3369	{ 0.00009150160, 1.41213765216, 149.56319713460 }
	3370	};
	3371
	3372	static const vsop_series_t vsop_lon_Uranus[] =
	3373	{
	3374	{ 39, vsop_lon_Uranus_0 },
	3375	{ 6, vsop_lon_Uranus_1 }
	3376	};
	3377
	3378	static const vsop_term_t vsop_lat_Uranus_0[] =
	3379	{
	3380	{ 0.01346277648, 2.61877810547, 74.78159856730 },
	3381	{ 0.00062341400, 5.08111189648, 149.56319713460 },
	3382	{ 0.00061601196, 3.14159265359, 0.00000000000 },
	3383	{ 0.00009963722, 1.61603805646, 76.26607127560 },
	3384	{ 0.00009926160, 0.57630380333, 73.29712585900 }
	3385	};
	3386
	3387	static const vsop_term_t vsop_lat_Uranus_1[] =
	3388	{
	3389	{ 0.00034101978, 0.01321929936, 74.78159856730 }
	3390	};
	3391
	3392	static const vsop_series_t vsop_lat_Uranus[] =
	3393	{
	3394	{ 5, vsop_lat_Uranus_0 },
	3395	{ 1, vsop_lat_Uranus_1 }
	3396	};
	3397
	3398	static const vsop_term_t vsop_rad_Uranus_0[] =
	3399	{
	3400	{ 19.21264847206, 0.00000000000, 0.00000000000 },
	3401	{ 0.88784984413, 5.60377527014, 74.78159856730 },
	3402	{ 0.03440836062, 0.32836099706, 73.29712585900 },
	3403	{ 0.02055653860, 1.78295159330, 149.56319713460 },
	3404	{ 0.00649322410, 4.52247285911, 76.26607127560 },
	3405	{ 0.00602247865, 3.86003823674, 63.73589830340 },
	3406	{ 0.00496404167, 1.40139935333, 454.90936652730 },
	3407	{ 0.00338525369, 1.58002770318, 138.51749687070 },
	3408	{ 0.00243509114, 1.57086606044, 71.81265315070 },
	3409	{ 0.00190522303, 1.99809394714, 1.48447270830 },
	3410	{ 0.00161858838, 2.79137786799, 148.07872442630 },
	3411	{ 0.00143706183, 1.38368544947, 11.04570026390 },
	3412	{ 0.00093192405, 0.17437220467, 36.64856292950 },
	3413	{ 0.00071424548, 4.24509236074, 224.34479570190 },
	3414	{ 0.00089806014, 3.66105364565, 109.94568878850 },
	3415	{ 0.00039009723, 1.66971401684, 70.84944530420 },
	3416	{ 0.00046677296, 1.39976401694, 35.16409022120 },
	3417	{ 0.00039025624, 3.36234773834, 277.03499374140 },
	3418	{ 0.00036755274, 3.88649278513, 146.59425171800 },
	3419	{ 0.00030348723, 0.70100838798, 151.04766984290 },
	3420	{ 0.00029156413, 3.18056336700, 77.75054398390 },
	3421	{ 0.00022637073, 0.72518687029, 529.69096509460 },
	3422	{ 0.00011959076, 1.75043392140, 984.60033162190 },
	3423	{ 0.00025620756, 5.25656086672, 380.12776796000 }
	3424	};
	3425
	3426	static const vsop_term_t vsop_rad_Uranus_1[] =
	3427	{
	3428	{ 0.01479896629, 3.67205697578, 74.78159856730 }
	3429	};
	3430
	3431	static const vsop_series_t vsop_rad_Uranus[] =
	3432	{
	3433	{ 24, vsop_rad_Uranus_0 },
	3434	{ 1, vsop_rad_Uranus_1 }
	3435	};
	3436
	3437	;
	3438	static const vsop_term_t vsop_lon_Neptune_0[] =
	3439	{
	3440	{ 5.31188633046, 0.00000000000, 0.00000000000 },
	3441	{ 0.01798475530, 2.90101273890, 38.13303563780 },
	3442	{ 0.01019727652, 0.48580922867, 1.48447270830 },
	3443	{ 0.00124531845, 4.83008090676, 36.64856292950 },
	3444	{ 0.00042064466, 5.41054993053, 2.96894541660 },
	3445	{ 0.00037714584, 6.09221808686, 35.16409022120 },
	3446	{ 0.00033784738, 1.24488874087, 76.26607127560 },
	3447	{ 0.00016482741, 0.00007727998, 491.55792945680 },
	3448	{ 0.00009198584, 4.93747051954, 39.61750834610 },
	3449	{ 0.00008994250, 0.27462171806, 175.16605980020 }
	3450	};
	3451
	3452	static const vsop_term_t vsop_lon_Neptune_1[] =
	3453	{
	3454	{ 38.13303563957, 0.00000000000, 0.00000000000 },
	3455	{ 0.00016604172, 4.86323329249, 1.48447270830 },
	3456	{ 0.00015744045, 2.27887427527, 38.13303563780 }
	3457	};
	3458
	3459	static const vsop_series_t vsop_lon_Neptune[] =
	3460	{
	3461	{ 10, vsop_lon_Neptune_0 },
	3462	{ 3, vsop_lon_Neptune_1 }
	3463	};
	3464
	3465	static const vsop_term_t vsop_lat_Neptune_0[] =
	3466	{
	3467	{ 0.03088622933, 1.44104372644, 38.13303563780 },
	3468	{ 0.00027780087, 5.91271884599, 76.26607127560 },
	3469	{ 0.00027623609, 0.00000000000, 0.00000000000 },
	3470	{ 0.00015355489, 2.52123799551, 36.64856292950 },
	3471	{ 0.00015448133, 3.50877079215, 39.61750834610 }
	3472	};
	3473
	3474	static const vsop_series_t vsop_lat_Neptune[] =
	3475	{
	3476	{ 5, vsop_lat_Neptune_0 }
	3477	};
	3478
	3479	static const vsop_term_t vsop_rad_Neptune_0[] =
	3480	{
	3481	{ 30.07013205828, 0.00000000000, 0.00000000000 },
	3482	{ 0.27062259632, 1.32999459377, 38.13303563780 },
	3483	{ 0.01691764014, 3.25186135653, 36.64856292950 },
	3484	{ 0.00807830553, 5.18592878704, 1.48447270830 },
	3485	{ 0.00537760510, 4.52113935896, 35.16409022120 },
	3486	{ 0.00495725141, 1.57105641650, 491.55792945680 },
	3487	{ 0.00274571975, 1.84552258866, 175.16605980020 },
	3488	{ 0.00012012320, 1.92059384991, 1021.24889455140 },
	3489	{ 0.00121801746, 5.79754470298, 76.26607127560 },
	3490	{ 0.00100896068, 0.37702724930, 73.29712585900 },
	3491	{ 0.00135134092, 3.37220609835, 39.61750834610 },
	3492	{ 0.00007571796, 1.07149207335, 388.46515523820 }
	3493	};
	3494
	3495	static const vsop_series_t vsop_rad_Neptune[] =
	3496	{
	3497	{ 12, vsop_rad_Neptune_0 }
	3498	};
	3499
	3500	;
	3501
	3502	/** @cond DOXYGEN_SKIP */
	3503	#define VSOPFORMULA(x) { ASTRO_ARRAYSIZE(x), x }
	3504	/** @endcond */
	3505
	3506	static const vsop_model_t vsop[] =
	3507	{
	3508	{ { VSOPFORMULA(vsop_lon_Mercury), VSOPFORMULA(vsop_lat_Mercury), VSOPFORMULA(vsop_rad_Mercury) } },
	3509	{ { VSOPFORMULA(vsop_lon_Venus), VSOPFORMULA(vsop_lat_Venus), VSOPFORMULA(vsop_rad_Venus) } },
	3510	{ { VSOPFORMULA(vsop_lon_Earth), VSOPFORMULA(vsop_lat_Earth), VSOPFORMULA(vsop_rad_Earth) } },
	3511	{ { VSOPFORMULA(vsop_lon_Mars), VSOPFORMULA(vsop_lat_Mars), VSOPFORMULA(vsop_rad_Mars) } },
	3512	{ { VSOPFORMULA(vsop_lon_Jupiter), VSOPFORMULA(vsop_lat_Jupiter), VSOPFORMULA(vsop_rad_Jupiter) } },
	3513	{ { VSOPFORMULA(vsop_lon_Saturn), VSOPFORMULA(vsop_lat_Saturn), VSOPFORMULA(vsop_rad_Saturn) } },
	3514	{ { VSOPFORMULA(vsop_lon_Uranus), VSOPFORMULA(vsop_lat_Uranus), VSOPFORMULA(vsop_rad_Uranus) } },
	3515	{ { VSOPFORMULA(vsop_lon_Neptune), VSOPFORMULA(vsop_lat_Neptune), VSOPFORMULA(vsop_rad_Neptune) } }
	3516	};
	3517
	3518	/** @cond DOXYGEN_SKIP */
	3519	#define CalcEarth(time) CalcVsop(&vsop[BODY_EARTH], (time))
	3520	#define LON_INDEX 0
	3521	#define LAT_INDEX 1
	3522	#define RAD_INDEX 2
	3523	/** @endcond */
	3524
	3525	static void VsopCoords(const vsop_model_t *model, double t, double sphere[3])
	3526	{
	3527	int k, s, i;
	3528	double incr;
	3529
	3530	for (k=0; k < 3; ++k)
	3531	{
	3532	double tpower = 1.0;
	3533	const vsop_formula_t *formula = &model->formula[k];
	3534	sphere[k] = 0.0;
	3535	for (s=0; s < formula->nseries; ++s)
	3536	{
	3537	double sum = 0.0;
	3538	const vsop_series_t *series = &formula->series[s];
	3539	for (i=0; i < series->nterms; ++i)
	3540	{
	3541	const vsop_term_t *term = &series->term[i];
	3542	sum += term->amplitude * cos(term->phase + (t * term->frequency));
	3543	}
	3544	incr = tpower * sum;
	3545	if (k == LON_INDEX)
	3546	incr = fmod(incr, PI2); /* improve precision for longitudes, which can be hundreds of radians */
	3547	sphere[k] += incr;
	3548	tpower *= t;
	3549	}
	3550	}
	3551	}
	3552
	3553
	3554	static terse_vector_t VsopRotate(const double ecl[3])
	3555	{
	3556	terse_vector_t equ;
	3557
	3558	/*
	3559	X +1.000000000000 +0.000000440360 -0.000000190919 X
	3560	Y = -0.000000479966 +0.917482137087 -0.397776982902 Y
	3561	Z FK5 0.000000000000 +0.397776982902 +0.917482137087 Z VSOP87A
	3562	*/
	3563
	3564	equ.x = ecl[0] + 0.000000440360ecl[1] - 0.000000190919ecl[2];
	3565	equ.y = -0.000000479966ecl[0] + 0.917482137087ecl[1] - 0.397776982902*ecl[2];
	3566	equ.z = 0.397776982902ecl[1] + 0.917482137087ecl[2];
	3567
	3568	return equ;
	3569	}
	3570
	3571
	3572	static void VsopSphereToRect(double lon, double lat, double radius, double pos[3])
	3573	{
	3574	double r_coslat = radius * cos(lat);
	3575	double coslon = cos(lon);
	3576	double sinlon = sin(lon);
	3577	pos[0] = r_coslat * coslon;
	3578	pos[1] = r_coslat * sinlon;
	3579	pos[2] = radius * sin(lat);
	3580	}
	3581
	3582	static const double DAYS_PER_MILLENNIUM = 365250.0;
	3583
	3584
	3585	static astro_vector_t CalcVsop(const vsop_model_t *model, astro_time_t time)
	3586	{
	3587	double t = time.tt / DAYS_PER_MILLENNIUM;
	3588	double sphere[3]; /* lon, lat, rad */
	3589	double eclip[3];
	3590	astro_vector_t vector;
	3591	terse_vector_t pos;
	3592
	3593	/* Calculate the VSOP "B" trigonometric series to obtain ecliptic spherical coordinates. */
	3594	VsopCoords(model, t, sphere);
	3595
	3596	/* Convert ecliptic spherical coordinates to ecliptic Cartesian coordinates. */
	3597	VsopSphereToRect(sphere[LON_INDEX], sphere[LAT_INDEX], sphere[RAD_INDEX], eclip);
	3598
	3599	/* Convert ecliptic Cartesian coordinates to equatorial Cartesian coordinates. */
	3600	pos = VsopRotate(eclip);
	3601
	3602	/* Package the position as astro_vector_t. */
	3603	vector.status = ASTRO_SUCCESS;
	3604	vector.t = time;
	3605	vector.x = pos.x;
	3606	vector.y = pos.y;
	3607	vector.z = pos.z;
	3608
	3609	return vector;
	3610	}
	3611
	3612
	3613	static void VsopDeriv(const vsop_model_t *model, double t, double deriv[3])
	3614	{
	3615	int k, s, i;
	3616
	3617	for (k=0; k < 3; ++k)
	3618	{
	3619	double tpower = 1.0; /* t^s */
	3620	double dpower = 0.0; /* t^(s-1) */
	3621	const vsop_formula_t *formula = &model->formula[k];
	3622	deriv[k] = 0.0;
	3623	for (s=0; s < formula->nseries; ++s)
	3624	{
	3625	double sin_sum = 0.0;
	3626	double cos_sum = 0.0;
	3627	const vsop_series_t *series = &formula->series[s];
	3628	for (i=0; i < series->nterms; ++i)
	3629	{
	3630	const vsop_term_t *term = &series->term[i];
	3631	double angle = term->phase + (t * term->frequency);
	3632	sin_sum += term->amplitude * term->frequency * sin(angle);
	3633	if (s > 0)
	3634	cos_sum += term->amplitude * cos(angle);
	3635	}
	3636	deriv[k] += (s * dpower * cos_sum) - (tpower * sin_sum);
	3637	dpower = tpower;
	3638	tpower *= t;
	3639	}
	3640	}
	3641	}
	3642
	3643
	3644	static body_state_t CalcVsopPosVel(const vsop_model_t *model, double tt)
	3645	{
	3646	body_state_t state;
	3647	double t = tt / DAYS_PER_MILLENNIUM;
	3648	double sphere[3]; /* lon, lat, r */
	3649	double deriv[3]; /* d(lon)/dt, d(lat)/dt, dr/dt */
	3650	double eclip[3];
	3651	double dr_dt, dlat_dt, dlon_dt;
	3652	double r, coslat, coslon, sinlat, sinlon;
	3653
	3654	state.tt = tt;
	3655	VsopCoords(model, t, sphere);
	3656	VsopSphereToRect(sphere[LON_INDEX], sphere[LAT_INDEX], sphere[RAD_INDEX], eclip);
	3657	state.r = VsopRotate(eclip);
	3658
	3659	VsopDeriv(model, t, deriv);
	3660
	3661	/* Use spherical coords and spherical derivatives to calculate */
	3662	/* the velocity vector in rectangular coordinates. */
	3663
	3664	/* Calculate mnemonic variables to help keep the math straight. */
	3665	coslon = cos(sphere[LON_INDEX]);
	3666	sinlon = sin(sphere[LON_INDEX]);
	3667	coslat = cos(sphere[LAT_INDEX]);
	3668	sinlat = sin(sphere[LAT_INDEX]);
	3669	r = sphere[RAD_INDEX];
	3670	dlon_dt = deriv[LON_INDEX];
	3671	dlat_dt = deriv[LAT_INDEX];
	3672	dr_dt = deriv[RAD_INDEX];
	3673
	3674	/* vx = dx/dt */
	3675	eclip[0] = (dr_dt * coslat * coslon) - (r * sinlat * coslon * dlat_dt) - (r * coslat * sinlon * dlon_dt);
	3676
	3677	/* vy = dy/dt */
	3678	eclip[1] = (dr_dt * coslat * sinlon) - (r * sinlat * sinlon * dlat_dt) + (r * coslat * coslon * dlon_dt);
	3679
	3680	/* vz = dz/dt */
	3681	eclip[2] = (dr_dt * sinlat) + (r * coslat * dlat_dt);
	3682
	3683	/* Rotate the velocity vector from ecliptic to equatorial coordinates. */
	3684	state.v = VsopRotate(eclip);
	3685
	3686	/* Convert speed units from [AU/millennium] to [AU/day]. */
	3687	VecScale(&state.v, 1 / DAYS_PER_MILLENNIUM);
	3688
	3689	return state;
	3690	}
	3691
	3692
	3693	static double VsopHelioDistance(const vsop_model_t *model, astro_time_t time)
	3694	{
	3695	int s, i;
	3696	double t = time.tt / DAYS_PER_MILLENNIUM;
	3697	double distance = 0.0;
	3698	double tpower = 1.0;
	3699	const vsop_formula_t formula = &model->formula[2]; / [2] is the distance part of the formula */
	3700
	3701	/*
	3702	The caller only wants to know the distance between the planet and the Sun.
	3703	So we only need to calculate the radial component of the spherical coordinates.
	3704	*/
	3705
	3706	for (s=0; s < formula->nseries; ++s)
	3707	{
	3708	double sum = 0.0;
	3709	const vsop_series_t *series = &formula->series[s];
	3710	for (i=0; i < series->nterms; ++i)
	3711	{
	3712	const vsop_term_t *term = &series->term[i];
	3713	sum += term->amplitude * cos(term->phase + (t * term->frequency));
	3714	}
	3715	distance += tpower * sum;
	3716	tpower *= t;
	3717	}
	3718
	3719	return distance;
	3720	}
	3721
	3722
	3723	static void AdjustBarycenter(astro_vector_t *ssb, astro_time_t time, astro_body_t body, double planet_gm)
	3724	{
	3725	astro_vector_t planet;
	3726	double shift;
	3727
	3728	shift = planet_gm / (planet_gm + SUN_GM);
	3729	planet = CalcVsop(&vsop[body], time);
	3730	ssb->x += shift * planet.x;
	3731	ssb->y += shift * planet.y;
	3732	ssb->z += shift * planet.z;
	3733	}
	3734
	3735
	3736	static astro_vector_t CalcSolarSystemBarycenter(astro_time_t time)
	3737	{
	3738	astro_vector_t ssb;
	3739
	3740	ssb.status = ASTRO_SUCCESS;
	3741	ssb.t = time;
	3742	ssb.x = ssb.y = ssb.z = 0.0;
	3743
	3744	AdjustBarycenter(&ssb, time, BODY_JUPITER, JUPITER_GM);
	3745	AdjustBarycenter(&ssb, time, BODY_SATURN, SATURN_GM);
	3746	AdjustBarycenter(&ssb, time, BODY_URANUS, URANUS_GM);
	3747	AdjustBarycenter(&ssb, time, BODY_NEPTUNE, NEPTUNE_GM);
	3748
	3749	return ssb;
	3750	}
	3751
	3752	/------------------ begin general gravity simulator ------------------/
	3753
	3754	static terse_vector_t UpdatePosition(double dt, terse_vector_t r, terse_vector_t v, terse_vector_t a)
	3755	{
	3756	r.x += (v.x + a.xdt/2) dt;
	3757	r.y += (v.y + a.ydt/2) dt;
	3758	r.z += (v.z + a.zdt/2) dt;
	3759	return r;
	3760	}
	3761
	3762
	3763	static terse_vector_t UpdateVelocity(double dt, terse_vector_t v, terse_vector_t a)
	3764	{
	3765	v.x += dt * a.x;
	3766	v.y += dt * a.y;
	3767	v.z += dt * a.z;
	3768	return v;
	3769	}
	3770
	3771
	3772	static body_state_t AdjustBarycenterPosVel(body_state_t *ssb, double tt, astro_body_t body, double planet_gm)
	3773	{
	3774	body_state_t planet;
	3775	double shift;
	3776
	3777	/*
	3778	This function does 2 important things:
	3779	1. Adjusts 'ssb' by the effect of one major body on the Solar System Barycenter.
	3780	2, Returns the heliocentric position of that major body.
	3781	*/
	3782
	3783	shift = planet_gm / (planet_gm + SUN_GM);
	3784	planet = CalcVsopPosVel(&vsop[body], tt);
	3785	VecIncr(&ssb->r, VecMul(shift, planet.r));
	3786	VecIncr(&ssb->v, VecMul(shift, planet.v));
	3787
	3788	return planet;
	3789	}
	3790
	3791
	3792	static void MajorBodyBary(major_bodies_t *bary, double tt)
	3793	{
	3794	/* Initialize the Sun's position as a zero vector, then adjust it from pulls from the planets. */
	3795	bary->Sun.tt = tt;
	3796	bary->Sun.r = VecZero;
	3797	bary->Sun.v = VecZero;
	3798
	3799	/* Calculate heliocentric planet positions and SSB. */
	3800	bary->Jupiter = AdjustBarycenterPosVel(&bary->Sun, tt, BODY_JUPITER, JUPITER_GM);
	3801	bary->Saturn = AdjustBarycenterPosVel(&bary->Sun, tt, BODY_SATURN, SATURN_GM);
	3802	bary->Uranus = AdjustBarycenterPosVel(&bary->Sun, tt, BODY_URANUS, URANUS_GM);
	3803	bary->Neptune = AdjustBarycenterPosVel(&bary->Sun, tt, BODY_NEPTUNE, NEPTUNE_GM);
	3804
	3805	/* Convert planet [pos, vel] from heliocentric to barycentric. */
	3806	VecDecr(&bary->Jupiter.r, bary->Sun.r); VecDecr(&bary->Jupiter.v, bary->Sun.v);
	3807	VecDecr(&bary->Saturn.r, bary->Sun.r); VecDecr(&bary->Saturn.v, bary->Sun.v);
	3808	VecDecr(&bary->Uranus.r, bary->Sun.r); VecDecr(&bary->Uranus.v, bary->Sun.v);
	3809	VecDecr(&bary->Neptune.r, bary->Sun.r); VecDecr(&bary->Neptune.v, bary->Sun.v);
	3810
	3811	/* Convert heliocentric SSB to barycentric Sun. */
	3812	VecScale(&bary->Sun.r, -1.0);
	3813	VecScale(&bary->Sun.v, -1.0);
	3814	}
	3815
	3816
	3817	static void AddAcceleration(terse_vector_t *acc, terse_vector_t small_pos, double gm, terse_vector_t major_pos)
	3818	{
	3819	double dx, dy, dz, r2, pull;
	3820
	3821	dx = major_pos.x - small_pos.x;
	3822	dy = major_pos.y - small_pos.y;
	3823	dz = major_pos.z - small_pos.z;
	3824
	3825	r2 = dxdx + dydy + dz*dz;
	3826	pull = gm / (r2 * sqrt(r2));
	3827
	3828	acc->x += dx * pull;
	3829	acc->y += dy * pull;
	3830	acc->z += dz * pull;
	3831	}
	3832
	3833
	3834	static terse_vector_t SmallBodyAcceleration(terse_vector_t small_pos, const major_bodies_t *bary)
	3835	{
	3836	terse_vector_t acc = VecZero;
	3837
	3838	/* Use barycentric coordinates of the Sun and major planets to calculate gravitational accelerations. */
	3839	AddAcceleration(&acc, small_pos, SUN_GM, bary->Sun.r);
	3840	AddAcceleration(&acc, small_pos, JUPITER_GM, bary->Jupiter.r);
	3841	AddAcceleration(&acc, small_pos, SATURN_GM, bary->Saturn.r);
	3842	AddAcceleration(&acc, small_pos, URANUS_GM, bary->Uranus.r);
	3843	AddAcceleration(&acc, small_pos, NEPTUNE_GM, bary->Neptune.r);
	3844
	3845	return acc;
	3846	}
	3847
	3848
	3849	body_grav_calc_t GravSim( /* out: [pos, vel, acc] of the simulated body at time tt2 */
	3850	major_bodies_t bary2, / temp: work area for major body barycentric state */
	3851	double tt2, /* in: a target time to be calculated (either before or after tt1) */
	3852	const body_grav_calc_t calc1) / in: [pos, vel, acc] of the simulated body at time tt1 */
	3853	{
	3854	body_grav_calc_t calc2;
	3855	terse_vector_t approx_pos;
	3856	terse_vector_t acc;
	3857	const double dt = tt2 - calc1->tt;
	3858
	3859	/* Calculate where the major bodies (Sun, Jupiter...Neptune) will be at the next time step. */
	3860	MajorBodyBary(bary2, tt2);
	3861
	3862	/* Estimate position of small body as if current acceleration applies across the whole time interval. */
	3863	/* approx_pos = pos1 + vel1dt + (1/2)accdt^2 */
	3864	approx_pos = UpdatePosition(dt, calc1->r, calc1->v, calc1->a);
	3865
	3866	/* Calculate acceleration experienced by small body at approximate next location. */
	3867	acc = SmallBodyAcceleration(approx_pos, bary2);
	3868
	3869	/* Calculate the average acceleration of the endpoints. */
	3870	/* This becomes our estimate of the mean effective acceleration over the whole interval. */
	3871	acc = VecMean(acc, calc1->a);
	3872
	3873	/* Refine the estimates of [pos, vel, acc] at tt2 using the mean acceleration. */
	3874	calc2.r = UpdatePosition(dt, calc1->r, calc1->v, acc);
	3875	calc2.v = UpdateVelocity(dt, calc1->v, acc);
	3876	calc2.a = SmallBodyAcceleration(calc2.r, bary2);
	3877	calc2.tt = tt2;
	3878	return calc2;
	3879	}
	3880
	3881
	3882	static body_grav_calc_t GravFromState(major_bodies_t bary, const body_state_t state)
	3883	{
	3884	body_grav_calc_t calc;
	3885
	3886	MajorBodyBary(bary, state->tt);
	3887
	3888	calc.tt = state->tt;
	3889	calc.r = VecAdd(state->r, bary->Sun.r); /* convert heliocentric to barycentric */
	3890	calc.v = VecAdd(state->v, bary->Sun.v); /* convert heliocentric to barycentric */
	3891	calc.a = SmallBodyAcceleration(calc.r, bary);
	3892
	3893	return calc;
	3894	}
	3895
	3896
	3897	static void CalcSolarSystem(astro_grav_sim_t *sim)
	3898	{
	3899	int body;
	3900	double tt = sim->curr->time.tt;
	3901	body_state_t *grav = sim->curr->gravitators;
	3902	body_state_t *sun = &grav[BODY_SUN];
	3903
	3904	/* Initialize the Sun's position/velocity as zero vectors, then adjust from pulls from the planets. */
	3905	sun->tt = tt;
	3906	sun->r = VecZero;
	3907	sun->v = VecZero;
	3908
	3909	/* Calculate the position of each planet, and adjust the SSB position accordingly. */
	3910	grav[BODY_MERCURY] = AdjustBarycenterPosVel(sun, tt, BODY_MERCURY, MERCURY_GM);
	3911	grav[BODY_VENUS ] = AdjustBarycenterPosVel(sun, tt, BODY_VENUS, VENUS_GM);
	3912	grav[BODY_EARTH ] = AdjustBarycenterPosVel(sun, tt, BODY_EARTH, EARTH_GM + MOON_GM);
	3913	grav[BODY_MARS ] = AdjustBarycenterPosVel(sun, tt, BODY_MARS, MARS_GM);
	3914	grav[BODY_JUPITER] = AdjustBarycenterPosVel(sun, tt, BODY_JUPITER, JUPITER_GM);
	3915	grav[BODY_SATURN ] = AdjustBarycenterPosVel(sun, tt, BODY_SATURN, SATURN_GM);
	3916	grav[BODY_URANUS ] = AdjustBarycenterPosVel(sun, tt, BODY_URANUS, URANUS_GM);
	3917	grav[BODY_NEPTUNE] = AdjustBarycenterPosVel(sun, tt, BODY_NEPTUNE, NEPTUNE_GM);
	3918
	3919	/* Convert planet state vectors from heliocentric to barycentric. */
	3920	for (body = BODY_MERCURY; body <= BODY_NEPTUNE; ++body)
	3921	{
	3922	VecDecr(&grav[body].r, sun->r);
	3923	VecDecr(&grav[body].v, sun->v);
	3924	}
	3925
	3926	/* Convert heliocentric SSB to barycentric Sun. */
	3927	VecScale(&sun->r, -1.0);
	3928	VecScale(&sun->v, -1.0);
	3929	}
	3930
	3931
	3932	static void CalcBodyAccelerations(astro_grav_sim_t *sim)
	3933	{
	3934	int i;
	3935	const body_state_t *grav = sim->curr->gravitators;
	3936
	3937	/* Calculate the gravitational acceleration experienced by the simulated bodies. */
	3938	for (i = 0; i < sim->numBodies; ++i)
	3939	{
	3940	body_grav_calc_t *calc = &sim->curr->bodies[i];
	3941
	3942	calc->a = VecZero;
	3943
	3944	AddAcceleration(&calc->a, calc->r, SUN_GM, grav[BODY_SUN ].r);
	3945	AddAcceleration(&calc->a, calc->r, MERCURY_GM, grav[BODY_MERCURY].r);
	3946	AddAcceleration(&calc->a, calc->r, VENUS_GM, grav[BODY_VENUS ].r);
	3947	AddAcceleration(&calc->a, calc->r, EARTH_GM + MOON_GM, grav[BODY_EARTH ].r);
	3948	AddAcceleration(&calc->a, calc->r, MARS_GM, grav[BODY_MARS ].r);
	3949	AddAcceleration(&calc->a, calc->r, JUPITER_GM, grav[BODY_JUPITER].r);
	3950	AddAcceleration(&calc->a, calc->r, SATURN_GM, grav[BODY_SATURN ].r);
	3951	AddAcceleration(&calc->a, calc->r, URANUS_GM, grav[BODY_URANUS ].r);
	3952	AddAcceleration(&calc->a, calc->r, NEPTUNE_GM, grav[BODY_NEPTUNE].r);
	3953	}
	3954	}
	3955
	3956
	3957	static body_state_t GravSimBodyStatePtr(astro_grav_sim_t sim, astro_body_t body)
	3958	{
	3959	/*
	3960	Return a pointer to the place where we cache the barycentric
	3961	state of the given body, or NULL if this body is not one
	3962	that we use for calculating gravitational interactions.
	3963	*/
	3964
	3965	if ((body == BODY_SUN) \|\| (body >= BODY_MERCURY && body <= BODY_NEPTUNE))
	3966	return &sim->curr->gravitators[body];
	3967
	3968	return NULL;
	3969	}
	3970
	3971
	3972	static astro_state_vector_t GravSimOriginState(astro_grav_sim_t *sim)
	3973	{
	3974	body_state_t *optr;
	3975	astro_time_t time = sim->curr->time;
	3976
	3977	if (sim->originBody == BODY_SSB)
	3978	{
	3979	/* The barycentric state of the SSB is zero, by definition. */
	3980	astro_state_vector_t state;
	3981	state.status = ASTRO_SUCCESS;
	3982	state.t = time;
	3983	state.x = 0.0;
	3984	state.y = 0.0;
	3985	state.z = 0.0;
	3986	state.vx = 0.0;
	3987	state.vy = 0.0;
	3988	state.vz = 0.0;
	3989	return state;
	3990	}
	3991
	3992	optr = GravSimBodyStatePtr(sim, sim->originBody);
	3993	if (optr != NULL)
	3994	return ExportState(*optr, time);
	3995
	3996	/* We only support the VSOP bodies, for efficiency. */
	3997	return StateVecError(ASTRO_INVALID_BODY, time);
	3998	}
	3999
	4000
	4001	static void GravSimDuplicate(astro_grav_sim_t *sim)
	4002	{
	4003	/* Copy the current state into the previous state, so that both become the same moment in time. */
	4004	sim->prev->time = sim->curr->time;
	4005	memcpy(sim->prev->gravitators, sim->curr->gravitators, sizeof(sim->prev->gravitators));
	4006	memcpy(sim->prev->bodies, sim->curr->bodies, ((size_t)sim->numBodies) * sizeof(sim->prev->bodies[0]));
	4007	}
	4008
	4009
	4010	/**
	4011	* @brief Allocate and initialize a gravity step simulator.
	4012	*
	4013	* Prepares to simulate a series of incremental time steps,
	4014	* simulating the movement of zero or more small bodies through the Solar System
	4015	* acting under gravitational attraction from the Sun and planets.
	4016	*
	4017	* After calling this function, you can call #Astronomy_GravSimUpdate
	4018	* as many times as desired to advance the simulation by small time steps.
	4019	*
	4020	* If this function succeeds (returns `ASTRO_SUCCESS`), `sim`
	4021	* will be set to a dynamically allocated object. The caller is
	4022	* then responsible for eventually calling #Astronomy_GravSimFree
	4023	* to release the memory.
	4024	*
	4025	* @param simOut
	4026	* The address of a pointer to store the newly allocated simulation object.
	4027	* The type #astro_grav_sim_t is an opaque type, so its internal structure is not documented.
	4028	*
	4029	* @param originBody
	4030	* Specifies the origin of the reference frame.
	4031	* All position vectors and velocity vectors will use `originBody`
	4032	* as the origin of the coordinate system.
	4033	* This origin applies to all the input vectors provided in the
	4034	* `bodyStateArray` parameter of this function, along with all
	4035	* output vectors returned by #Astronomy_GravSimUpdate.
	4036	* Most callers will want to provide one of the following:
	4037	* `BODY_SUN` for heliocentric coordinates,
	4038	* `BODY_SSB` for solar system barycentric coordinates,
	4039	* or `BODY_EARTH` for geocentric coordinates. Note that the
	4040	* gravity simulator does not correct for light travel time;
	4041	* all state vectors are tied to a Newtonian "instantaneous" time.
	4042	*
	4043	* @param time
	4044	* The initial time at which to start the simulation.
	4045	*
	4046	* @param numBodies
	4047	* The number of small bodies to be simulated. This may be any non-negative integer.
	4048	*
	4049	* @param bodyStateArray
	4050	* An array of initial state vectors (positions and velocities) of the small bodies to be simulated.
	4051	* The caller must know the positions and velocities of the small bodies at an initial moment in time.
	4052	* Their positions and velocities are expressed with respect to `originBody`, using J2000 mean equator orientation (EQJ).
	4053	* Positions are expressed in astronomical units (AU). Velocities are expressed in AU/day.
	4054	* All the times embedded within the state vectors must be exactly equal to `time`,
	4055	* or this function will fail with the error `ASTRO_INCONSISTENT_TIMES`.
	4056	*
	4057	* @return
	4058	* `ASTRO_SUCCESS` on success, with `sim` set to a non-NULL value. Otherwise an error code with `sim` set to NULL.
	4059	*/
	4060	astro_status_t Astronomy_GravSimInit(
	4061	astro_grav_sim_t **simOut,
	4062	astro_body_t originBody,
	4063	astro_time_t time,
	4064	int numBodies,
	4065	const astro_state_vector_t *bodyStateArray)
	4066	{
	4067	astro_grav_sim_t *sim;
	4068	astro_status_t status;
	4069	body_grav_calc_t *array;
	4070	int i;
	4071
	4072	/* Validate parameters before attempting to allocate memory. */
	4073
	4074	if (simOut == NULL)
	4075	return ASTRO_INVALID_PARAMETER;
	4076
	4077	*simOut = NULL;
	4078
	4079	if (numBodies < 0)
	4080	return ASTRO_INVALID_PARAMETER;
	4081
	4082	if (numBodies > 0 && bodyStateArray == NULL)
	4083	return ASTRO_INVALID_PARAMETER;
	4084
	4085	if (originBody < BODY_MERCURY \|\| originBody > BODY_SSB)
	4086	return ASTRO_INVALID_BODY;
	4087
	4088	/* Verify that all the state vectors are valid and have matching times. */
	4089	for (i = 0; i < numBodies; ++i)
	4090	{
	4091	if (bodyStateArray[i].status != ASTRO_SUCCESS)
	4092	return ASTRO_INVALID_PARAMETER;
	4093
	4094	if (bodyStateArray[i].t.tt != time.tt)
	4095	return ASTRO_INCONSISTENT_TIMES;
	4096	}
	4097
	4098	simOut = sim = (astro_grav_sim_t ) calloc(1, sizeof(astro_grav_sim_t));
	4099	if (sim == NULL)
	4100	return ASTRO_OUT_OF_MEMORY;
	4101
	4102	sim->originBody = originBody;
	4103	sim->numBodies = numBodies;
	4104	sim->prev = &(sim->endpoint[0]);
	4105	sim->curr = &(sim->endpoint[1]);
	4106	sim->curr->time = time;
	4107
	4108	if (numBodies > 0)
	4109	{
	4110	sim->prev->bodies = (body_grav_calc_t *) calloc(numBodies, sizeof(body_grav_calc_t));
	4111	sim->curr->bodies = (body_grav_calc_t *) calloc(numBodies, sizeof(body_grav_calc_t));
	4112	if (sim->prev->bodies == NULL \|\| sim->curr->bodies == NULL)
	4113	{
	4114	status = ASTRO_OUT_OF_MEMORY;
	4115	goto fail;
	4116	}
	4117	}
	4118
	4119	/* Remember the initial states of all the bodies as "current". */
	4120	/* Convert from the public type astro_state_t to our internal type body_grav_calc_t. */
	4121	array = sim->curr->bodies;
	4122	for (i = 0; i < numBodies; ++i)
	4123	{
	4124	array[i].tt = bodyStateArray[i].t.tt;
	4125	array[i].r.x = bodyStateArray[i].x;
	4126	array[i].r.y = bodyStateArray[i].y;
	4127	array[i].r.z = bodyStateArray[i].z;
	4128	array[i].v.x = bodyStateArray[i].vx;
	4129	array[i].v.y = bodyStateArray[i].vy;
	4130	array[i].v.z = bodyStateArray[i].vz;
	4131	}
	4132
	4133	/* Calculate the state of the Sun and planets. */
	4134	CalcSolarSystem(sim);
	4135
	4136	/*
	4137	We need to do all the physics calculations in barycentric coordinates.
	4138	But the caller can provide the input vectors with respect to any body.
	4139	Correct the input body state vectors for the specified coordinate origin.
	4140	*/
	4141	if (originBody != BODY_SSB)
	4142	{
	4143	/* Determine the barycentric state of the origin body. */
	4144	astro_state_vector_t originState = GravSimOriginState(sim);
	4145	if (originState.status != ASTRO_SUCCESS)
	4146	{
	4147	status = originState.status;
	4148	goto fail;
	4149	}
	4150
	4151	/* Add barycentric origin to origin-centric body to obtain barycentric body. */
	4152	for (i = 0; i < numBodies; ++i)
	4153	{
	4154	array[i].r.x += originState.x;
	4155	array[i].r.y += originState.y;
	4156	array[i].r.z += originState.z;
	4157	array[i].v.x += originState.vx;
	4158	array[i].v.y += originState.vy;
	4159	array[i].v.z += originState.vz;
	4160	}
	4161	}
	4162
	4163	/* Calculate the net acceleration experienced by the small bodies. */
	4164	CalcBodyAccelerations(sim);
	4165
	4166	/* To prepare for a possible swap operation, duplicate the current state into the previous state. */
	4167	GravSimDuplicate(sim);
	4168
	4169	return ASTRO_SUCCESS;
	4170
	4171	fail:
	4172	Astronomy_GravSimFree(sim);
	4173	*simOut = NULL;
	4174	return status;
	4175	}
	4176
	4177
	4178	/**
	4179	* @brief Advances a gravity simulation by a small time step.
	4180	*
	4181	* @param sim
	4182	* A simulation object that was created by a prior call to #Astronomy_GravSimInit.
	4183	*
	4184	* @param time
	4185	* A time that is a small increment away from the current simulation time.
	4186	* It is up to the developer to figure out an appropriate time increment.
	4187	* Depending on the trajectories, a smaller or larger increment
	4188	* may be needed for the desired accuracy. Some experimentation may be needed.
	4189	* Generally, bodies that stay in the outer Solar System and move slowly can
	4190	* use larger time steps. Bodies that pass into the inner Solar System and
	4191	* move faster will need a smaller time step to maintain accuracy.
	4192	* The `time` value may be after or before the current simulation time
	4193	* to move forward or backward in time.
	4194	*
	4195	* @param numBodies
	4196	* The number of bodies whose state vectors are to be updated.
	4197	* This is the number of elements in the `bodyStateArray`.
	4198	* This parameter is passed as a sanity check, and must be equal
	4199	* to the value passed to #Astronomy_GravSimInit when `sim` was created.
	4200	*
	4201	* @param bodyStateArray
	4202	* An array big enough to hold `numBodies` state vectors, to receive
	4203	* the updated positions and velocities of the simulated small bodies.
	4204	* Alternatively, `bodyStateArray` may be NULL if the output of this
	4205	* simulation step is not needed. This makes the call slightly faster.
	4206	*
	4207	* @return
	4208	* `ASTRO_SUCCESS` if the calculation was successful.
	4209	* Otherwise, an error code if something went wrong, in which case
	4210	* the simulation should be considered "broken". This means there
	4211	* is no reliable output in `bodyStateArray` and that no more calculations
	4212	* can be performed with `sim`.
	4213	*/
	4214	astro_status_t Astronomy_GravSimUpdate(
	4215	astro_grav_sim_t *sim,
	4216	astro_time_t time,
	4217	int numBodies,
	4218	astro_state_vector_t *bodyStateArray)
	4219	{
	4220	terse_vector_t acc;
	4221	double dt; /* terrestrial time increment */
	4222	int i;
	4223
	4224	/*
	4225	The caller's understanding of the number of bodies must match the actual
	4226	array size in `sim`, or we risk corrupting/accessing invalid memory.
	4227	*/
	4228	if (numBodies != sim->numBodies)
	4229	return ASTRO_INVALID_PARAMETER;
	4230
	4231	dt = time.tt - sim->curr->time.tt;
	4232
	4233	if (dt == 0.0)
	4234	{
	4235	/*
	4236	Special case: the time has not changed, so skip the usual physics calculations.
	4237	This allows a way for the caller to query the current state if desired.
	4238	It is also necessary to avoid dividing by `dt` if `dt` is zero.
	4239	To prepare for a possible swap operation, duplicate the current state into the previous state.
	4240	*/
	4241	GravSimDuplicate(sim);
	4242	}
	4243	else
	4244	{
	4245	/* Swap the current state and the previous state. Then calculate the new current state. */
	4246	Astronomy_GravSimSwap(sim);
	4247
	4248	/* Update the current time. This is the only place we have a full (tt,ut) pair. */
	4249	/* All of the Newtonian dynamics are calculated using tt only. */
	4250	sim->curr->time = time;
	4251
	4252	/* Now that sim->time is set, it is safe to call `CalcSolarSystem`. */
	4253	CalcSolarSystem(sim);
	4254
	4255	for (i = 0; i < numBodies; ++i)
	4256	{
	4257	/*
	4258	Estimate the positions of the small bodies as if their
	4259	current accelerations apply across the whole time interval.
	4260	approx_pos = pos1 + vel1dt + (1/2)accdt^2
	4261	*/
	4262	const body_grav_calc_t *prev = &sim->prev->bodies[i];
	4263	sim->curr->bodies[i].r = UpdatePosition(dt, prev->r, prev->v, prev->a);
	4264	}
	4265
	4266	/*
	4267	Calculate the acceleration experienced by the small bodies
	4268	at their respective approximate next locations.
	4269	*/
	4270	CalcBodyAccelerations(sim);
	4271
	4272	for (i = 0; i < numBodies; ++i)
	4273	{
	4274	const body_grav_calc_t *prev = &sim->prev->bodies[i];
	4275	body_grav_calc_t *curr = &sim->curr->bodies[i];
	4276
	4277	/*
	4278	Calculate the average of the acceleration vectors
	4279	experienced by the previous body positions and
	4280	their estimated next positions.
	4281	These become estimates of the mean effective accelerations over the whole interval.
	4282	*/
	4283	acc = VecMean(prev->a, curr->a);
	4284
	4285	/*
	4286	Refine the estimates of position and velocity at the next time step,
	4287	using the mean acceleration as a better approximation of the
	4288	continuously changing acceleration acting on each body.
	4289	*/
	4290	curr->tt = time.tt;
	4291	curr->r = UpdatePosition(dt, prev->r, prev->v, acc);
	4292	curr->v = UpdateVelocity(dt, prev->v, acc);
	4293	}
	4294
	4295	/*
	4296	Re-calculate accelerations experienced by each body.
	4297	These will be needed for the next simulation step (if any).
	4298	Also, they will be potentially useful if some day we add
	4299	a function to query the acceleration vectors for the bodies.
	4300	*/
	4301	CalcBodyAccelerations(sim);
	4302	}
	4303
	4304	/*
	4305	Translate our internal calculations of body positions
	4306	and velocities into state vectors that the caller can understand.
	4307	But if the output buffer `bodyStateArray` is NULL, it means
	4308	the caller wanted us to update the simulation state without
	4309	returning any output.
	4310	*/
	4311	if (bodyStateArray != NULL)
	4312	{
	4313	for (i = 0; i < numBodies; ++i)
	4314	bodyStateArray[i] = ExportGravCalc(sim->curr->bodies[i], time);
	4315
	4316	if (sim->originBody != BODY_SSB)
	4317	{
	4318	/* Determine the barycentric state of the origin body. */
	4319	astro_state_vector_t originState = GravSimOriginState(sim);
	4320	if (originState.status != ASTRO_SUCCESS)
	4321	return originState.status;
	4322
	4323	/* Subtract vectors to convert barycentric states to origin-centric states. */
	4324	for (i = 0; i < numBodies; ++i)
	4325	{
	4326	bodyStateArray[i].x -= originState.x;
	4327	bodyStateArray[i].y -= originState.y;
	4328	bodyStateArray[i].z -= originState.z;
	4329	bodyStateArray[i].vx -= originState.vx;
	4330	bodyStateArray[i].vy -= originState.vy;
	4331	bodyStateArray[i].vz -= originState.vz;
	4332	}
	4333	}
	4334	}
	4335
	4336	return ASTRO_SUCCESS;
	4337	}
	4338
	4339
	4340	/**
	4341	* @brief Get the position and velocity of a Solar System body included in the simulation.
	4342	*
	4343	* In order to simulate the movement of small bodies through the Solar System,
	4344	* the simulator needs to calculate the state vectors for the Sun and planets.
	4345	*
	4346	* If an application wants to know the positions of one or more of the planets
	4347	* in addition to the small bodies, this function provides a way to obtain
	4348	* their state vectors. This is provided for the sake of efficiency, to avoid
	4349	* redundant calculations.
	4350	*
	4351	* @param sim
	4352	* A gravity simulator object created by a successful call to #Astronomy_GravSimInit.
	4353	*
	4354	* @param body
	4355	* The Sun, Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, or Neptune.
	4356	*
	4357	* @return
	4358	* If the given body is part of the set of calculated bodies
	4359	* (Sun and planets), returns the current time step's state
	4360	* vector for that body, expressed in the coordinate system
	4361	* that was specified by the `originBody` parameter to #Astronomy_GravSimInit.
	4362	* Success is indicated by the returned structure's `status` field holding
	4363	* `ASTRO_SUCCESS`. Any other `status` value indicates an error, meaning
	4364	* the returned state vector is invalid.
	4365	*/
	4366	astro_state_vector_t Astronomy_GravSimBodyState(
	4367	astro_grav_sim_t *sim,
	4368	astro_body_t body)
	4369	{
	4370	astro_state_vector_t state;
	4371	body_state_t *bptr;
	4372
	4373	bptr = GravSimBodyStatePtr(sim, body);
	4374	if (bptr == NULL)
	4375	return StateVecError(ASTRO_INVALID_BODY, sim->curr->time);
	4376
	4377	state = GravSimOriginState(sim);
	4378	if (state.status != ASTRO_SUCCESS)
	4379	return state;
	4380
	4381	/*
	4382	Subtract the origin's state from the body's barycentric
	4383	state to get the body in the desired reference frame.
	4384	state.t and state.status are already initialized correctly.
	4385	*/
	4386
	4387	state.x = bptr->r.x - state.x;
	4388	state.y = bptr->r.y - state.y;
	4389	state.z = bptr->r.z - state.z;
	4390	state.vx = bptr->v.x - state.vx;
	4391	state.vy = bptr->v.y - state.vy;
	4392	state.vz = bptr->v.z - state.vz;
	4393
	4394	return state;
	4395	}
	4396
	4397
	4398	/**
	4399	* @brief Exchange the current time step with the previous time step.
	4400	*
	4401	* Sometimes it is helpful to "explore" various times near a given
	4402	* simulation time step, while repeatedly returning to the original
	4403	* time step. For example, when backdating a position for light travel
	4404	* time, the caller may wish to repeatedly try different amounts of
	4405	* backdating. When the backdating solver has converged, the caller
	4406	* wants to leave the simulation in its original state.
	4407	*
	4408	* This function allows a single "undo" of a simulation, and does so
	4409	* very efficiently.
	4410	*
	4411	* Usually this function will be called immediately after a matching
	4412	* call to #Astronomy_GravSimUpdate. It has the effect of rolling
	4413	* back the most recent update. If called twice in a row, it reverts
	4414	* the swap and thus has no net effect.
	4415	*
	4416	* #Astronomy_GravSimInit initializes the current state and previous
	4417	* state to be identical. Both states represent the `time` parameter that was
	4418	* passed into the initializer. Therefore, `Astronomy_GravSimSwap` will
	4419	* have no effect from the caller's point of view when passed a simulator
	4420	* that has not yet been updated by a call to #Astronomy_GravSimUpdate.
	4421	*
	4422	* @param sim
	4423	* A gravity simulator object that was created by a prior call to #Astronomy_GravSimInit.
	4424	*/
	4425	void Astronomy_GravSimSwap(astro_grav_sim_t *sim)
	4426	{
	4427	gravsim_endpoint_t *swap = sim->prev;
	4428	sim->prev = sim->curr;
	4429	sim->curr = swap;
	4430	}
	4431
	4432
	4433	/**
	4434	* @brief Returns the time of the current simulation step.
	4435	*
	4436	* @param sim
	4437	* A gravity simulator object that was created by a prior call to #Astronomy_GravSimInit.
	4438	*/
	4439	astro_time_t Astronomy_GravSimTime(const astro_grav_sim_t *sim)
	4440	{
	4441	return sim->curr->time;
	4442	}
	4443
	4444
	4445	/**
	4446	* @brief Returns the number of small bodies represented in this simulation.
	4447	*
	4448	* When a simulation is created by a call to #Astronomy_GravSimInit,
	4449	* the caller specifies the number of small bodies.
	4450	* This function returns that same number, which may be convenient for a caller,
	4451	* so that it does not need to track the body count separately.
	4452	*
	4453	* @param sim
	4454	* A gravity simulator object that was created by a prior call to #Astronomy_GravSimInit.
	4455	*/
	4456	int Astronomy_GravSimNumBodies(const astro_grav_sim_t *sim)
	4457	{
	4458	return sim->numBodies;
	4459	}
	4460
	4461
	4462	/**
	4463	* @brief Returns the body whose center is the coordinate origin that small bodies are referenced to.
	4464	*
	4465	* When a simulation is created by a call to #Astronomy_GravSimInit,
	4466	* the caller specifies an `originBody` to indicate the coordinate origin
	4467	* used to represent the small bodies being simulated.
	4468	* This function returns that same #astro_body_t value.
	4469	*
	4470	* @param sim
	4471	* A gravity simulator object that was created by a prior call to #Astronomy_GravSimInit.
	4472	*/
	4473	astro_body_t Astronomy_GravSimOrigin(const astro_grav_sim_t *sim)
	4474	{
	4475	return sim->originBody;
	4476	}
	4477
	4478
	4479	/**
	4480	* @brief Releases memory allocated to a gravity simulator object.
	4481	*
	4482	* To avoid memory leaks, any successful call to #Astronomy_GravSimInit
	4483	* must be paired with a matching call to `Astronomy_GravSimFree`.
	4484	*
	4485	* @param sim
	4486	* A gravity simulator object that was created by a prior call to #Astronomy_GravSimInit.
	4487	*/
	4488	void Astronomy_GravSimFree(astro_grav_sim_t *sim)
	4489	{
	4490	if (sim != NULL)
	4491	{
	4492	free(sim->endpoint[0].bodies);
	4493	free(sim->endpoint[1].bodies);
	4494	free(sim);
	4495	}
	4496	}
	4497
	4498
	4499	/------------------ begin Pluto integrator ------------------/
	4500
	4501	static const body_state_t PlutoStateTable[] =
	4502	{
	4503	{ -730000.0, {-26.118207232108, -14.376168177825, 3.384402515299}, { 1.6339372163656e-03, -2.7861699588508e-03, -1.3585880229445e-03} }
	4504	, { -700800.0, { 41.974905202127, -0.448502952929, -12.770351505989}, { 7.3458569351457e-04, 2.2785014891658e-03, 4.8619778602049e-04} }
	4505	, { -671600.0, { 14.706930780744, 44.269110540027, 9.353698474772}, {-2.1000147999800e-03, 2.2295915939915e-04, 7.0143443551414e-04} }
	4506	, { -642400.0, {-29.441003929957, -6.430161530570, 6.858481011305}, { 8.4495803960544e-04, -3.0783914758711e-03, -1.2106305981192e-03} }
	4507	, { -613200.0, { 39.444396946234, -6.557989760571, -13.913760296463}, { 1.1480029005873e-03, 2.2400006880665e-03, 3.5168075922288e-04} }
	4508	, { -584000.0, { 20.230380950700, 43.266966657189, 7.382966091923}, {-1.9754081700585e-03, 5.3457141292226e-04, 7.5929169129793e-04} }
	4509	, { -554800.0, {-30.658325364620, 2.093818874552, 9.880531138071}, { 6.1010603013347e-05, -3.1326500935382e-03, -9.9346125151067e-04} }
	4510	, { -525600.0, { 35.737703251673, -12.587706024764, -14.677847247563}, { 1.5802939375649e-03, 2.1347678412429e-03, 1.9074436384343e-04} }
	4511	, { -496400.0, { 25.466295188546, 41.367478338417, 5.216476873382}, {-1.8054401046468e-03, 8.3283083599510e-04, 8.0260156912107e-04} }
	4512	, { -467200.0, {-29.847174904071, 10.636426313081, 12.297904180106}, {-6.3257063052907e-04, -2.9969577578221e-03, -7.4476074151596e-04} }
	4513	, { -438000.0, { 30.774692107687, -18.236637015304, -14.945535879896}, { 2.0113162005465e-03, 1.9353827024189e-03, -2.0937793168297e-06} }
	4514	, { -408800.0, { 30.243153324028, 38.656267888503, 2.938501750218}, {-1.6052508674468e-03, 1.1183495337525e-03, 8.3333973416824e-04} }
	4515	, { -379600.0, {-27.288984772533, 18.643162147874, 14.023633623329}, {-1.1856388898191e-03, -2.7170609282181e-03, -4.9015526126399e-04} }
	4516	, { -350400.0, { 24.519605196774, -23.245756064727, -14.626862367368}, { 2.4322321483154e-03, 1.6062008146048e-03, -2.3369181613312e-04} }
	4517	, { -321200.0, { 34.505274805875, 35.125338586954, 0.557361475637}, {-1.3824391637782e-03, 1.3833397561817e-03, 8.4823598806262e-04} }
	4518	, { -292000.0, {-23.275363915119, 25.818514298769, 15.055381588598}, {-1.6062295460975e-03, -2.3395961498533e-03, -2.4377362639479e-04} }
	4519	, { -262800.0, { 17.050384798092, -27.180376290126, -13.608963321694}, { 2.8175521080578e-03, 1.1358749093955e-03, -4.9548725258825e-04} }
	4520	, { -233600.0, { 38.093671910285, 30.880588383337, -1.843688067413}, {-1.1317697153459e-03, 1.6128814698472e-03, 8.4177586176055e-04} }
	4521	, { -204400.0, {-18.197852930878, 31.932869934309, 15.438294826279}, {-1.9117272501813e-03, -1.9146495909842e-03, -1.9657304369835e-05} }
	4522	, { -175200.0, { 8.528924039997, -29.618422200048, -11.805400994258}, { 3.1034370787005e-03, 5.1393633292430e-04, -7.7293066202546e-04} }
	4523	, { -146000.0, { 40.946857258640, 25.904973592021, -4.256336240499}, {-8.3652705194051e-04, 1.8129497136404e-03, 8.1564228273060e-04} }
	4524	, { -116800.0, {-12.326958895325, 36.881883446292, 15.217158258711}, {-2.1166103705038e-03, -1.4814420035990e-03, 1.7401209844705e-04} }
	4525	, { -87600.0, { -0.633258375909, -30.018759794709, -9.171932874950}, { 3.2016994581737e-03, -2.5279858672148e-04, -1.0411088271861e-03} }
	4526	, { -58400.0, { 42.936048423883, 20.344685584452, -6.588027007912}, {-5.0525450073192e-04, 1.9910074335507e-03, 7.7440196540269e-04} }
	4527	, { -29200.0, { -5.975910552974, 40.611809958460, 14.470131723673}, {-2.2184202156107e-03, -1.0562361130164e-03, 3.3652250216211e-04} }
	4528	, { 0.0, { -9.875369580774, -27.978926224737, -5.753711824704}, { 3.0287533248818e-03, -1.1276087003636e-03, -1.2651326732361e-03} }
	4529	, { 29200.0, { 43.958831986165, 14.214147973292, -8.808306227163}, {-1.4717608981871e-04, 2.1404187242141e-03, 7.1486567806614e-04} }
	4530	, { 58400.0, { 0.678136763520, 43.094461639362, 13.243238780721}, {-2.2358226110718e-03, -6.3233636090933e-04, 4.7664798895648e-04} }
	4531	, { 87600.0, {-18.282602096834, -23.305039586660, -1.766620508028}, { 2.5567245263557e-03, -1.9902940754171e-03, -1.3943491701082e-03} }
	4532	, { 116800.0, { 43.873338744526, 7.700705617215, -10.814273666425}, { 2.3174803055677e-04, 2.2402163127924e-03, 6.2988756452032e-04} }
	4533	, { 146000.0, { 7.392949027906, 44.382678951534, 11.629500214854}, {-2.1932815453830e-03, -2.1751799585364e-04, 5.9556516201114e-04} }
	4534	, { 175200.0, {-24.981690229261, -16.204012851426, 2.466457544298}, { 1.8193989149580e-03, -2.6765419531201e-03, -1.3848283502247e-03} }
	4535	, { 204400.0, { 42.530187039511, 0.845935508021, -12.554907527683}, { 6.5059779150669e-04, 2.2725657282262e-03, 5.1133743202822e-04} }
	4536	, { 233600.0, { 13.999526486822, 44.462363044894, 9.669418486465}, {-2.1079296569252e-03, 1.7533423831993e-04, 6.9128485798076e-04} }
	4537	, { 262800.0, {-29.184024803031, -7.371243995762, 6.493275957928}, { 9.3581363109681e-04, -3.0610357109184e-03, -1.2364201089345e-03} }
	4538	, { 292000.0, { 39.831980671753, -6.078405766765, -13.909815358656}, { 1.1117769689167e-03, 2.2362097830152e-03, 3.6230548231153e-04} }
	4539	, { 321200.0, { 20.294955108476, 43.417190420251, 7.450091985932}, {-1.9742157451535e-03, 5.3102050468554e-04, 7.5938408813008e-04} }
	4540	, { 350400.0, {-30.669992302160, 2.318743558955, 9.973480913858}, { 4.5605107450676e-05, -3.1308219926928e-03, -9.9066533301924e-04} }
	4541	, { 379600.0, { 35.626122155983, -12.897647509224, -14.777586508444}, { 1.6015684949743e-03, 2.1171931182284e-03, 1.8002516202204e-04} }
	4542	, { 408800.0, { 26.133186148561, 41.232139187599, 5.006401326220}, {-1.7857704419579e-03, 8.6046232702817e-04, 8.0614690298954e-04} }
	4543	, { 438000.0, {-29.576740229230, 11.863535943587, 12.631323039872}, {-7.2292830060955e-04, -2.9587820140709e-03, -7.0824296450300e-04} }
	4544	, { 467200.0, { 29.910805787391, -19.159019294000, -15.013363865194}, { 2.0871080437997e-03, 1.8848372554514e-03, -3.8528655083926e-05} }
	4545	, { 496400.0, { 31.375957451819, 38.050372720763, 2.433138343754}, {-1.5546055556611e-03, 1.1699815465629e-03, 8.3565439266001e-04} }
	4546	, { 525600.0, {-26.360071336928, 20.662505904952, 14.414696258958}, {-1.3142373118349e-03, -2.6236647854842e-03, -4.2542017598193e-04} }
	4547	, { 554800.0, { 22.599441488648, -24.508879898306, -14.484045731468}, { 2.5454108304806e-03, 1.4917058755191e-03, -3.0243665086079e-04} }
	4548	, { 584000.0, { 35.877864013014, 33.894226366071, -0.224524636277}, {-1.2941245730845e-03, 1.4560427668319e-03, 8.4762160640137e-04} }
	4549	, { 613200.0, {-21.538149762417, 28.204068269761, 15.321973799534}, {-1.7312117409010e-03, -2.1939631314577e-03, -1.6316913275180e-04} }
	4550	, { 642400.0, { 13.971521374415, -28.339941764789, -13.083792871886}, { 2.9334630526035e-03, 9.1860931752944e-04, -5.9939422488627e-04} }
	4551	, { 671600.0, { 39.526942044143, 28.939897360110, -2.872799527539}, {-1.0068481658095e-03, 1.7021132888090e-03, 8.3578230511981e-04} }
	4552	, { 700800.0, {-15.576200701394, 34.399412961275, 15.466033737854}, {-2.0098814612884e-03, -1.7191109825989e-03, 7.0414782780416e-05} }
	4553	, { 730000.0, { 4.243252837090, -30.118201690825, -10.707441231349}, { 3.1725847067411e-03, 1.6098461202270e-04, -9.0672150593868e-04} }
	4554	};
	4555
	4556	/* FIXFIXFIX - Using a global is not thread-safe. Either add thread-locks or change API to accept a cache pointer. */
	4557	static body_segment_t *pluto_cache[PLUTO_NUM_STATES-1];
	4558
	4559
	4560	static int ClampIndex(double frac, int nsteps)
	4561	{
	4562	int index = (int) floor(frac);
	4563	if (index < 0)
	4564	return 0;
	4565	if (index >= nsteps)
	4566	return nsteps-1;
	4567	return index;
	4568	}
	4569
	4570
	4571	static astro_status_t GetSegment(int seg_index, body_segment_t cache[], double tt)
	4572	{
	4573	int i;
	4574	body_segment_t reverse;
	4575	body_segment_t *seg;
	4576	major_bodies_t bary;
	4577	double step_tt, ramp;
	4578
	4579	if (tt < PlutoStateTable[0].tt \|\| tt > PlutoStateTable[PLUTO_NUM_STATES-1].tt)
	4580	{
	4581	/* We don't bother calculating a segment. Let the caller crawl backward/forward to this time. */
	4582	*seg_index = -1;
	4583	return ASTRO_SUCCESS;
	4584	}
	4585
	4586	/* See if we have a segment that straddles the requested time. */
	4587	/* If so, return it. Otherwise, calculate it and return it. */
	4588
	4589	*seg_index = ClampIndex((tt - PlutoStateTable[0].tt) / PLUTO_TIME_STEP, PLUTO_NUM_STATES-1);
	4590	if (cache[*seg_index] == NULL)
	4591	{
	4592	/* Allocate memory for the segment (about 11K each). */
	4593	seg = cache[seg_index] = (body_segment_t ) calloc(1, sizeof(body_segment_t));
	4594	if (seg == NULL)
	4595	return ASTRO_OUT_OF_MEMORY;
	4596
	4597	/* Calculate the segment. */
	4598	/* Pick the pair of bracketing body states to fill the segment. */
	4599
	4600	/* Each endpoint is exact. */
	4601	seg->step[0] = GravFromState(&bary, &PlutoStateTable[*seg_index]);
	4602	seg->step[PLUTO_NSTEPS-1] = GravFromState(&bary, &PlutoStateTable[*seg_index + 1]);
	4603
	4604	/* Simulate forwards from the lower time bound. */
	4605	step_tt = seg->step[0].tt;
	4606	for (i=1; i < PLUTO_NSTEPS-1; ++i)
	4607	seg->step[i] = GravSim(&bary, step_tt += PLUTO_DT, &seg->step[i-1]);
	4608
	4609	/* Simulate backwards from the upper time bound. */
	4610	step_tt = seg->step[PLUTO_NSTEPS-1].tt;
	4611	reverse.step[PLUTO_NSTEPS-1] = seg->step[PLUTO_NSTEPS-1];
	4612	for (i=PLUTO_NSTEPS-2; i > 0; --i)
	4613	reverse.step[i] = GravSim(&bary, step_tt -= PLUTO_DT, &reverse.step[i+1]);
	4614
	4615	/* Fade-mix the two series so that there are no discontinuities. */
	4616	for (i=PLUTO_NSTEPS-2; i > 0; --i)
	4617	{
	4618	ramp = (double)i / (PLUTO_NSTEPS-1);
	4619	seg->step[i].r = VecRamp(seg->step[i].r, reverse.step[i].r, ramp);
	4620	seg->step[i].v = VecRamp(seg->step[i].v, reverse.step[i].v, ramp);
	4621	seg->step[i].a = VecRamp(seg->step[i].a, reverse.step[i].a, ramp);
	4622	}
	4623	}
	4624
	4625	return ASTRO_SUCCESS;
	4626	}
	4627
	4628
	4629	static body_grav_calc_t CalcPlutoOneWay(major_bodies_t bary, const body_state_t init_state, double target_tt, double dt)
	4630	{
	4631	body_grav_calc_t calc;
	4632	int i, n;
	4633
	4634	calc = GravFromState(bary, init_state);
	4635	n = (int) ceil((target_tt - calc.tt) / dt);
	4636	for (i=0; i < n; ++i)
	4637	calc = GravSim(bary, (i+1 == n) ? target_tt : (calc.tt + dt), &calc);
	4638
	4639	return calc;
	4640	}
	4641
	4642
	4643	static astro_status_t CalcPluto(body_state_t *bstate, astro_time_t time, int helio)
	4644	{
	4645	terse_vector_t acc, ra, rb, va, vb;
	4646	major_bodies_t bary;
	4647	const body_segment_t *seg;
	4648	int seg_index, left;
	4649	const body_grav_calc_t *s1;
	4650	const body_grav_calc_t *s2;
	4651	body_grav_calc_t calc;
	4652	astro_status_t status;
	4653	double ramp;
	4654
	4655	memset(bstate, 0, sizeof(body_state_t));
	4656	bstate->tt = time.tt;
	4657
	4658	status = GetSegment(&seg_index, pluto_cache, time.tt);
	4659	if (status != ASTRO_SUCCESS)
	4660	return status;
	4661
	4662	if (seg_index < 0)
	4663	{
	4664	/* The target time is outside the year range 0000..4000. */
	4665	/* Calculate it by crawling backward from 0000 or forward from 4000. */
	4666	/* FIXFIXFIX - This is super slow. Could optimize this with extra caching if needed. */
	4667	if (time.tt < PlutoStateTable[0].tt)
	4668	calc = CalcPlutoOneWay(&bary, &PlutoStateTable[0], time.tt, -PLUTO_DT);
	4669	else
	4670	calc = CalcPlutoOneWay(&bary, &PlutoStateTable[PLUTO_NUM_STATES-1], time.tt, +PLUTO_DT);
	4671
	4672	bstate->r = calc.r;
	4673	bstate->v = calc.v;
	4674	}
	4675	else
	4676	{
	4677	seg = pluto_cache[seg_index];
	4678	left = ClampIndex((time.tt - seg->step[0].tt) / PLUTO_DT, PLUTO_NSTEPS-1);
	4679	s1 = &seg->step[left];
	4680	s2 = &seg->step[left+1];
	4681
	4682	/* Find mean acceleration vector over the interval. */
	4683	acc = VecMean(s1->a, s2->a);
	4684
	4685	/* Use Newtonian mechanics to extrapolate away from t1 in the positive time direction. */
	4686	ra = UpdatePosition(time.tt - s1->tt, s1->r, s1->v, acc);
	4687	va = UpdateVelocity(time.tt - s1->tt, s1->v, acc);
	4688
	4689	/* Use Newtonian mechanics to extrapolate away from t2 in the negative time direction. */
	4690	rb = UpdatePosition(time.tt - s2->tt, s2->r, s2->v, acc);
	4691	vb = UpdateVelocity(time.tt - s2->tt, s2->v, acc);
	4692
	4693	/* Use fade in/out idea to blend the two position estimates. */
	4694	ramp = (time.tt - s1->tt)/PLUTO_DT;
	4695	bstate->r = VecRamp(ra, rb, ramp);
	4696	bstate->v = VecRamp(va, vb, ramp);
	4697
	4698	if (helio)
	4699	MajorBodyBary(&bary, time.tt);
	4700	}
	4701
	4702	if (helio)
	4703	{
	4704	/* Convert barycentric coordinates back to heliocentric coordinates. */
	4705	VecDecr(&bstate->r, bary.Sun.r);
	4706	VecDecr(&bstate->v, bary.Sun.v);
	4707	}
	4708
	4709	return ASTRO_SUCCESS;
	4710	}
	4711
	4712	/------------------ end Pluto integrator ------------------/
	4713
	4714
	4715	/---------------------- begin Jupiter moons ----------------------/
	4716
	4717	static const astro_rotation_t Rotation_JUP_EQJ =
	4718	{
	4719	ASTRO_SUCCESS,
	4720	{
	4721	{ 9.99432765338654e-01, -3.36771074697641e-02, 0.00000000000000e+00 },
	4722	{ 3.03959428906285e-02, 9.02057912352809e-01, 4.30543388542295e-01 },
	4723	{ -1.44994559663353e-02, -4.30299169409101e-01, 9.02569881273754e-01 }
	4724	}
	4725	};
	4726
	4727	static const vsop_term_t jm_Io_a[] =
	4728	{
	4729	{ 0.0028210960212903, 0.0000000000000000e+00, 0.0000000000000000e+00 }
	4730	};
	4731
	4732	static const vsop_term_t jm_Io_l[] =
	4733	{
	4734	{ -0.0001925258348666, 4.9369589722644998e+00, 1.3584836583050000e-02 },
	4735	{ -0.0000970803596076, 4.3188796477322002e+00, 1.3034138432430000e-02 },
	4736	{ -0.0000898817416500, 1.9080016428616999e+00, 3.0506486715799999e-03 },
	4737	{ -0.0000553101050262, 1.4936156681568999e+00, 1.2938928911549999e-02 }
	4738	};
	4739
	4740	static const vsop_term_t jm_Io_z[] =
	4741	{
	4742	{ 0.0041510849668155, 4.0899396355450000e+00, -1.2906864146660001e-02 },
	4743	{ 0.0006260521444113, 1.4461888986270000e+00, 3.5515522949801999e+00 },
	4744	{ 0.0000352747346169, 2.1256287034577999e+00, 1.2727416566999999e-04 }
	4745	};
	4746
	4747	static const vsop_term_t jm_Io_zeta[] =
	4748	{
	4749	{ 0.0003142172466014, 2.7964219722923001e+00, -2.3150960980000000e-03 },
	4750	{ 0.0000904169207946, 1.0477061879627001e+00, -5.6920638196000003e-04 }
	4751	};
	4752
	4753	static const vsop_term_t jm_Europa_a[] =
	4754	{
	4755	{ 0.0044871037804314, 0.0000000000000000e+00, 0.0000000000000000e+00 },
	4756	{ 0.0000004324367498, 1.8196456062910000e+00, 1.7822295777568000e+00 }
	4757	};
	4758
	4759	static const vsop_term_t jm_Europa_l[] =
	4760	{
	4761	{ 0.0008576433172936, 4.3188693178264002e+00, 1.3034138308049999e-02 },
	4762	{ 0.0004549582875086, 1.4936531751079001e+00, 1.2938928819619999e-02 },
	4763	{ 0.0003248939825174, 1.8196494533458001e+00, 1.7822295777568000e+00 },
	4764	{ -0.0003074250079334, 4.9377037005910998e+00, 1.3584832867240000e-02 },
	4765	{ 0.0001982386144784, 1.9079869054759999e+00, 3.0510121286900001e-03 },
	4766	{ 0.0001834063551804, 2.1402853388529000e+00, 1.4500978933800000e-03 },
	4767	{ -0.0001434383188452, 5.6222140366630002e+00, 8.9111478887838003e-01 },
	4768	{ -0.0000771939140944, 4.3002724372349999e+00, 2.6733443704265998e+00 }
	4769	};
	4770
	4771	static const vsop_term_t jm_Europa_z[] =
	4772	{
	4773	{ -0.0093589104136341, 4.0899396509038999e+00, -1.2906864146660001e-02 },
	4774	{ 0.0002988994545555, 5.9097265185595003e+00, 1.7693227079461999e+00 },
	4775	{ 0.0002139036390350, 2.1256289300016000e+00, 1.2727418406999999e-04 },
	4776	{ 0.0001980963564781, 2.7435168292649998e+00, 6.7797343008999997e-04 },
	4777	{ 0.0001210388158965, 5.5839943711203004e+00, 3.2056614899999997e-05 },
	4778	{ 0.0000837042048393, 1.6094538368039000e+00, -9.0402165808846002e-01 },
	4779	{ 0.0000823525166369, 1.4461887708689001e+00, 3.5515522949801999e+00 }
	4780	};
	4781
	4782	static const vsop_term_t jm_Europa_zeta[] =
	4783	{
	4784	{ 0.0040404917832303, 1.0477063169425000e+00, -5.6920640539999997e-04 },
	4785	{ 0.0002200421034564, 3.3368857864364001e+00, -1.2491307306999999e-04 },
	4786	{ 0.0001662544744719, 2.4134862374710999e+00, 0.0000000000000000e+00 },
	4787	{ 0.0000590282470983, 5.9719930968366004e+00, -3.0561602250000000e-05 }
	4788	};
	4789
	4790	static const vsop_term_t jm_Ganymede_a[] =
	4791	{
	4792	{ 0.0071566594572575, 0.0000000000000000e+00, 0.0000000000000000e+00 },
	4793	{ 0.0000013930299110, 1.1586745884981000e+00, 2.6733443704265998e+00 }
	4794	};
	4795
	4796	static const vsop_term_t jm_Ganymede_l[] =
	4797	{
	4798	{ 0.0002310797886226, 2.1402987195941998e+00, 1.4500978438400001e-03 },
	4799	{ -0.0001828635964118, 4.3188672736968003e+00, 1.3034138282630000e-02 },
	4800	{ 0.0001512378778204, 4.9373102372298003e+00, 1.3584834812520000e-02 },
	4801	{ -0.0001163720969778, 4.3002659861490002e+00, 2.6733443704265998e+00 },
	4802	{ -0.0000955478069846, 1.4936612842567001e+00, 1.2938928798570001e-02 },
	4803	{ 0.0000815246854464, 5.6222137132535002e+00, 8.9111478887838003e-01 },
	4804	{ -0.0000801219679602, 1.2995922951532000e+00, 1.0034433456728999e+00 },
	4805	{ -0.0000607017260182, 6.4978769669238001e-01, 5.0172167043264004e-01 }
	4806	};
	4807
	4808	static const vsop_term_t jm_Ganymede_z[] =
	4809	{
	4810	{ 0.0014289811307319, 2.1256295942738999e+00, 1.2727413029000001e-04 },
	4811	{ 0.0007710931226760, 5.5836330003496002e+00, 3.2064341100000001e-05 },
	4812	{ 0.0005925911780766, 4.0899396636447998e+00, -1.2906864146660001e-02 },
	4813	{ 0.0002045597496146, 5.2713683670371996e+00, -1.2523544076106000e-01 },
	4814	{ 0.0001785118648258, 2.8743156721063001e-01, 8.7820792442520001e-01 },
	4815	{ 0.0001131999784893, 1.4462127277818000e+00, 3.5515522949801999e+00 },
	4816	{ -0.0000658778169210, 2.2702423990985001e+00, -1.7951364394536999e+00 },
	4817	{ 0.0000497058888328, 5.9096792204858000e+00, 1.7693227129285001e+00 }
	4818	};
	4819
	4820	static const vsop_term_t jm_Ganymede_zeta[] =
	4821	{
	4822	{ 0.0015932721570848, 3.3368862796665000e+00, -1.2491307058000000e-04 },
	4823	{ 0.0008533093128905, 2.4133881688166001e+00, 0.0000000000000000e+00 },
	4824	{ 0.0003513347911037, 5.9720789850126996e+00, -3.0561017709999999e-05 },
	4825	{ -0.0001441929255483, 1.0477061764435001e+00, -5.6920632124000004e-04 }
	4826	};
	4827
	4828	static const vsop_term_t jm_Callisto_a[] =
	4829	{
	4830	{ 0.0125879701715314, 0.0000000000000000e+00, 0.0000000000000000e+00 },
	4831	{ 0.0000035952049470, 6.4965776007116005e-01, 5.0172168165034003e-01 },
	4832	{ 0.0000027580210652, 1.8084235781510001e+00, 3.1750660413359002e+00 }
	4833	};
	4834
	4835	static const vsop_term_t jm_Callisto_l[] =
	4836	{
	4837	{ 0.0005586040123824, 2.1404207189814999e+00, 1.4500979323100001e-03 },
	4838	{ -0.0003805813868176, 2.7358844897852999e+00, 2.9729650620000000e-05 },
	4839	{ 0.0002205152863262, 6.4979652596399995e-01, 5.0172167243580001e-01 },
	4840	{ 0.0001877895151158, 1.8084787604004999e+00, 3.1750660413359002e+00 },
	4841	{ 0.0000766916975242, 6.2720114319754998e+00, 1.3928364636651001e+00 },
	4842	{ 0.0000747056855106, 1.2995916202344000e+00, 1.0034433456728999e+00 }
	4843	};
	4844
	4845	static const vsop_term_t jm_Callisto_z[] =
	4846	{
	4847	{ 0.0073755808467977, 5.5836071576083999e+00, 3.2065099140000001e-05 },
	4848	{ 0.0002065924169942, 5.9209831565786004e+00, 3.7648624194703001e-01 },
	4849	{ 0.0001589869764021, 2.8744006242622999e-01, 8.7820792442520001e-01 },
	4850	{ -0.0001561131605348, 2.1257397865089001e+00, 1.2727441285000001e-04 },
	4851	{ 0.0001486043380971, 1.4462134301023000e+00, 3.5515522949801999e+00 },
	4852	{ 0.0000635073108731, 5.9096803285953996e+00, 1.7693227129285001e+00 },
	4853	{ 0.0000599351698525, 4.1125517584797997e+00, -2.7985797954588998e+00 },
	4854	{ 0.0000540660842731, 5.5390350845569003e+00, 2.8683408228299999e-03 },
	4855	{ -0.0000489596900866, 4.6218149483337996e+00, -6.2695712529518999e-01 }
	4856	};
	4857
	4858	static const vsop_term_t jm_Callisto_zeta[] =
	4859	{
	4860	{ 0.0038422977898495, 2.4133922085556998e+00, 0.0000000000000000e+00 },
	4861	{ 0.0022453891791894, 5.9721736773277003e+00, -3.0561255249999997e-05 },
	4862	{ -0.0002604479450559, 3.3368746306408998e+00, -1.2491309972000001e-04 },
	4863	{ 0.0000332112143230, 5.5604137742336999e+00, 2.9003768850700000e-03 }
	4864	};
	4865
	4866	static const jupiter_moon_t JupiterMoonModel[] =
	4867	{
	4868	{ 2.8248942843381399e-07, { 1.4462132960212239e+00, 3.5515522861824000e+00 }
	4869	, { 1, jm_Io_a }
	4870	, { 4, jm_Io_l }
	4871	, { 3, jm_Io_z }
	4872	, { 2, jm_Io_zeta } },
	4873
	4874	{ 2.8248327439289299e-07, { -3.7352634374713622e-01, 1.7693227111234699e+00 }
	4875	, { 2, jm_Europa_a }
	4876	, { 8, jm_Europa_l }
	4877	, { 7, jm_Europa_z }
	4878	, { 4, jm_Europa_zeta } },
	4879
	4880	{ 2.8249818418472298e-07, { 2.8740893911433479e-01, 8.7820792358932798e-01 }
	4881	, { 2, jm_Ganymede_a }
	4882	, { 8, jm_Ganymede_l }
	4883	, { 8, jm_Ganymede_z }
	4884	, { 4, jm_Ganymede_zeta } },
	4885
	4886	{ 2.8249214488990899e-07, { -3.6203412913757038e-01, 3.7648623343382798e-01 }
	4887	, { 3, jm_Callisto_a }
	4888	, { 6, jm_Callisto_l }
	4889	, { 9, jm_Callisto_z }
	4890	, { 4, jm_Callisto_zeta } }
	4891	};
	4892
	4893	static astro_state_vector_t JupiterMoon_elem2pv(astro_time_t time, double mu, const double elem[6])
	4894	{
	4895	/* Translation of FORTRAN subroutine ELEM2PV from: */
	4896	/* https://ftp.imcce.fr/pub/ephem/satel/galilean/L1/L1.2/ */
	4897	astro_state_vector_t state;
	4898	double EE, DE, CE, SE, DLE, RSAM1, ASR, PHI, PSI, X1, Y1, VX1, VY1, F2, P2, Q2, PQ;
	4899
	4900	const double A = elem[0];
	4901	const double AL = elem[1];
	4902	const double K = elem[2];
	4903	const double H = elem[3];
	4904	const double Q = elem[4];
	4905	const double P = elem[5];
	4906
	4907	const double AN = sqrt(mu / (AAA));
	4908
	4909	EE = AL + Ksin(AL) - Hcos(AL);
	4910	do
	4911	{
	4912	CE = cos(EE);
	4913	SE = sin(EE);
	4914	DE = (AL - EE + KSE - HCE) / (1.0 - KCE - HSE);
	4915	EE += DE;
	4916	}
	4917	while (fabs(DE) >= 1.0e-12);
	4918
	4919	CE = cos(EE);
	4920	SE = sin(EE);
	4921	DLE = HCE - KSE;
	4922	RSAM1 = -KCE - HSE;
	4923	ASR = 1.0/(1.0 + RSAM1);
	4924	PHI = sqrt(1.0 - KK - HH);
	4925	PSI = 1.0/(1.0 + PHI);
	4926	X1 = A(CE - K - PSIH*DLE);
	4927	Y1 = A(SE - H + PSIK*DLE);
	4928	VX1 = ANASRA(-SE - PSIH*RSAM1);
	4929	VY1 = ANASRA(+CE + PSIK*RSAM1);
	4930	F2 = 2.0sqrt(1.0 - QQ - P*P);
	4931	P2 = 1.0 - 2.0PP;
	4932	Q2 = 1.0 - 2.0QQ;
	4933	PQ = 2.0PQ;
	4934
	4935	state.x = X1P2 + Y1PQ;
	4936	state.y = X1PQ + Y1Q2;
	4937	state.z = (QY1 - X1P)*F2;
	4938
	4939	state.vx = VX1P2 + VY1PQ;
	4940	state.vy = VX1PQ + VY1Q2;
	4941	state.vz = (QVY1 - VX1P)*F2;
	4942
	4943	state.t = time;
	4944	state.status = ASTRO_SUCCESS;
	4945	return state;
	4946	}
	4947
	4948	static astro_state_vector_t CalcJupiterMoon(astro_time_t time, int mindex)
	4949	{
	4950	/* This is a translation of FORTRAN code by Duriez, Lainey, and Vienne: */
	4951	/* https://ftp.imcce.fr/pub/ephem/satel/galilean/L1/L1.2/ */
	4952
	4953	astro_state_vector_t state;
	4954	int k;
	4955	double arg;
	4956	double elem[6];
	4957	const jupiter_moon_t *m = &JupiterMoonModel[mindex];
	4958	const double t = time.tt + 18262.5; /* t = time since 1950-01-01T00:00:00Z */
	4959
	4960	/* Calculate 6 orbital elements at the given time t. */
	4961
	4962	elem[0] = 0.0;
	4963	for (k = 0; k < m->a.nterms; ++k)
	4964	{
	4965	arg = m->a.term[k].phase + (t * m->a.term[k].frequency);
	4966	elem[0] += m->a.term[k].amplitude * cos(arg);
	4967	}
	4968
	4969	elem[1] = m->al[0] + (t * m->al[1]);
	4970	for (k = 0; k < m->l.nterms; ++k)
	4971	{
	4972	arg = m->l.term[k].phase + (t * m->l.term[k].frequency);
	4973	elem[1] += m->l.term[k].amplitude * sin(arg);
	4974	}
	4975	elem[1] = fmod(elem[1], PI2);
	4976	if (elem[1] < 0.0)
	4977	elem[1] += PI2;
	4978
	4979	elem[2] = elem[3] = 0.0;
	4980	for (k = 0; k < m->z.nterms; ++k)
	4981	{
	4982	arg = m->z.term[k].phase + (t * m->z.term[k].frequency);
	4983	elem[2] += m->z.term[k].amplitude * cos(arg);
	4984	elem[3] += m->z.term[k].amplitude * sin(arg);
	4985	}
	4986
	4987	elem[4] = elem[5] = 0.0;
	4988	for (k = 0; k < m->zeta.nterms; ++k)
	4989	{
	4990	arg = m->zeta.term[k].phase + (t * m->zeta.term[k].frequency);
	4991	elem[4] += m->zeta.term[k].amplitude * cos(arg);
	4992	elem[5] += m->zeta.term[k].amplitude * sin(arg);
	4993	}
	4994
	4995	/* Convert the oribital elements into position vectors in the Jupiter equatorial system (JUP). */
	4996	state = JupiterMoon_elem2pv(time, m->mu, elem);
	4997
	4998	/* Re-orient position and velocity vectors from Jupiter-equatorial (JUP) to Earth-equatorial in J2000 (EQJ). */
	4999	return Astronomy_RotateState(Rotation_JUP_EQJ, state);
	5000	}
	5001
	5002
	5003	/**
	5004	* @brief Calculates jovicentric positions and velocities of Jupiter's largest 4 moons.
	5005	*
	5006	* Calculates position and velocity vectors for Jupiter's moons
	5007	* Io, Europa, Ganymede, and Callisto, at the given date and time.
	5008	* The vectors are jovicentric (relative to the center of Jupiter).
	5009	* Their orientation is the Earth's equatorial system at the J2000 epoch (EQJ).
	5010	* The position components are expressed in astronomical units (AU), and the
	5011	* velocity components are in AU/day.
	5012	*
	5013	* To convert to heliocentric position vectors, call #Astronomy_HelioVector
	5014	* with `BODY_JUPITER` to get Jupiter's heliocentric position, then
	5015	* add the jovicentric positions.
	5016	*
	5017	* Likewise, you can call #Astronomy_GeoVector
	5018	* with `BODY_JUPITER` to convert to geocentric positions.
	5019	* However, you will have to manually correct for light travel time
	5020	* from the Jupiter system to Earth to figure out what time to pass
	5021	* to `Astronomy_JupiterMoons` to get an accurate picture
	5022	* of how Jupiter and its moons look from Earth.
	5023	*
	5024	* @param time The date and time for which to calculate the position vectors.
	5025	* @return Position vectors of Jupiter's largest 4 moons, as described above.
	5026	*/
	5027	astro_jupiter_moons_t Astronomy_JupiterMoons(astro_time_t time)
	5028	{
	5029	astro_jupiter_moons_t jm;
	5030
	5031	jm.io = CalcJupiterMoon(time, 0);
	5032	jm.europa = CalcJupiterMoon(time, 1);
	5033	jm.ganymede = CalcJupiterMoon(time, 2);
	5034	jm.callisto = CalcJupiterMoon(time, 3);
	5035
	5036	return jm;
	5037	}
	5038
	5039	/---------------------- end Jupiter moons ----------------------/
	5040
	5041
	5042	/**
	5043	* @brief Calculates heliocentric Cartesian coordinates of a body in the J2000 equatorial system.
	5044	*
	5045	* This function calculates the position of the given celestial body as a vector,
	5046	* using the center of the Sun as the origin. The result is expressed as a Cartesian
	5047	* vector in the J2000 equatorial system: the coordinates are based on the mean equator
	5048	* of the Earth at noon UTC on 1 January 2000.
	5049	*
	5050	* The position is not corrected for light travel time or aberration.
	5051	* This is different from the behavior of #Astronomy_GeoVector.
	5052	*
	5053	* If given an invalid value for `body`, this function will fail. The caller should always check
	5054	* the `status` field inside the returned #astro_vector_t for `ASTRO_SUCCESS` (success)
	5055	* or any other value (failure) before trusting the resulting vector.
	5056	*
	5057	* @param body
	5058	* A body for which to calculate a heliocentric position: the Sun, Moon, any of the planets,
	5059	* the Solar System Barycenter (SSB), or the Earth Moon Barycenter (EMB).
	5060	* Can also be a star defined by #Astronomy_DefineStar.
	5061	* @param time The date and time for which to calculate the position.
	5062	* @return A heliocentric position vector of the center of the given body.
	5063	*/
	5064	astro_vector_t Astronomy_HelioVector(astro_body_t body, astro_time_t time)
	5065	{
	5066	astro_vector_t vector, earth;
	5067	body_state_t bstate;
	5068	stardef_t *star;
	5069
	5070	star = UserDefinedStar(body);
	5071	if (star != NULL)
	5072	{
	5073	astro_spherical_t sphere;
	5074	sphere.lat = star->dec;
	5075	sphere.lon = 15.0 * star->ra;
	5076	sphere.dist = star->dist;
	5077	sphere.status = ASTRO_SUCCESS;
	5078	return Astronomy_VectorFromSphere(sphere, time);
	5079	}
	5080
	5081	switch (body)
	5082	{
	5083	case BODY_SUN:
	5084	vector.status = ASTRO_SUCCESS;
	5085	vector.x = 0.0;
	5086	vector.y = 0.0;
	5087	vector.z = 0.0;
	5088	vector.t = time;
	5089	return vector;
	5090
	5091	case BODY_MERCURY:
	5092	case BODY_VENUS:
	5093	case BODY_EARTH:
	5094	case BODY_MARS:
	5095	case BODY_JUPITER:
	5096	case BODY_SATURN:
	5097	case BODY_URANUS:
	5098	case BODY_NEPTUNE:
	5099	return CalcVsop(&vsop[body], time);
	5100
	5101	case BODY_PLUTO:
	5102	vector.t = time;
	5103	vector.status = CalcPluto(&bstate, time, 1);
	5104	if (vector.status != ASTRO_SUCCESS)
	5105	{
	5106	vector.x = vector.y = vector.z = NAN;
	5107	}
	5108	else
	5109	{
	5110	vector.x = bstate.r.x;
	5111	vector.y = bstate.r.y;
	5112	vector.z = bstate.r.z;
	5113	}
	5114	return vector;
	5115
	5116	case BODY_MOON:
	5117	vector = Astronomy_GeoMoon(time);
	5118	earth = CalcEarth(time);
	5119	vector.x += earth.x;
	5120	vector.y += earth.y;
	5121	vector.z += earth.z;
	5122	return vector;
	5123
	5124	case BODY_EMB:
	5125	vector = Astronomy_GeoMoon(time);
	5126	earth = CalcEarth(time);
	5127	vector.x = earth.x + (vector.x / (1.0 + EARTH_MOON_MASS_RATIO));
	5128	vector.y = earth.y + (vector.y / (1.0 + EARTH_MOON_MASS_RATIO));
	5129	vector.z = earth.z + (vector.z / (1.0 + EARTH_MOON_MASS_RATIO));
	5130	return vector;
	5131
	5132	case BODY_SSB:
	5133	return CalcSolarSystemBarycenter(time);
	5134
	5135	default:
	5136	return VecError(ASTRO_INVALID_BODY, time);
	5137	}
	5138	}
	5139
	5140	/**
	5141	* @brief Calculates the distance from a body to the Sun at a given time.
	5142	*
	5143	* Given a date and time, this function calculates the distance between
	5144	* the center of `body` and the center of the Sun.
	5145	* For the planets Mercury through Neptune, this function is significantly
	5146	* more efficient than calling #Astronomy_HelioVector followed by #Astronomy_VectorLength.
	5147	*
	5148	* @param body
	5149	* A body for which to calculate a heliocentric distance:
	5150	* the Sun, Moon, any of the planets, or a user-defined star.
	5151	*
	5152	* @param time
	5153	* The date and time for which to calculate the heliocentric distance.
	5154	*
	5155	* @return
	5156	* If successful, an #astro_func_result_t structure whose `status` is `ASTRO_SUCCESS`
	5157	* and whose `value` holds the heliocentric distance in AU.
	5158	* Otherwise, `status` reports an error condition.
	5159	*/
	5160	astro_func_result_t Astronomy_HelioDistance(astro_body_t body, astro_time_t time)
	5161	{
	5162	astro_vector_t vector;
	5163	astro_func_result_t result;
	5164	stardef_t *star;
	5165
	5166	star = UserDefinedStar(body);
	5167	if (star != NULL)
	5168	{
	5169	result.status = ASTRO_SUCCESS;
	5170	result.value = star->dist;
	5171	return result;
	5172	}
	5173
	5174	switch (body)
	5175	{
	5176	case BODY_SUN:
	5177	result.status = ASTRO_SUCCESS;
	5178	result.value = 0.0;
	5179	return result;
	5180
	5181	case BODY_MERCURY:
	5182	case BODY_VENUS:
	5183	case BODY_EARTH:
	5184	case BODY_MARS:
	5185	case BODY_JUPITER:
	5186	case BODY_SATURN:
	5187	case BODY_URANUS:
	5188	case BODY_NEPTUNE:
	5189	result.status = ASTRO_SUCCESS;
	5190	result.value = VsopHelioDistance(&vsop[body], time);
	5191	return result;
	5192
	5193	default:
	5194	/* For non-VSOP objects, fall back to taking the length of the heliocentric vector. */
	5195	vector = Astronomy_HelioVector(body, time);
	5196	if (vector.status != ASTRO_SUCCESS)
	5197	return FuncError(vector.status);
	5198	result.status = ASTRO_SUCCESS;
	5199	result.value = Astronomy_VectorLength(vector);
	5200	return result;
	5201	}
	5202	}
	5203
	5204
	5205	/**
	5206	* @brief Solve for light travel time of a vector function.
	5207	*
	5208	* When observing a distant object, for example Jupiter as seen from Earth,
	5209	* the amount of time it takes for light to travel from the object to the
	5210	* observer can significantly affect the object's apparent position.
	5211	* This function is a generic solver that figures out how long in the
	5212	* past light must have left the observed object to reach the observer
	5213	* at the specified observation time. It uses a context/function pair
	5214	* as a generic interface that expresses an arbitrary position vector
	5215	* as a function of time.
	5216	*
	5217	* This function repeatedly calls `func`, passing `context` and a series of time
	5218	* estimates in the past. Then `func` must return a relative position vector between
	5219	* the observer and the target. `Astronomy_CorrectLightTravel` keeps calling
	5220	* `func` with more and more refined estimates of the time light must have
	5221	* left the target to arrive at the observer.
	5222	*
	5223	* For common use cases, it is simpler to use #Astronomy_BackdatePosition
	5224	* for calculating the light travel time correction of one body observing another body.
	5225	*
	5226	* For geocentric calculations, #Astronomy_GeoVector also backdates the returned
	5227	* position vector for light travel time, only it returns the observation time in
	5228	* the returned vector's `t` field rather than the backdated time.
	5229	*
	5230	* @param context Holds any parameters needed by `func`.
	5231	* @param func Pointer to a function that returns a relative position vector as a function of time.
	5232	* @param time The observation time for which to solve for light travel delay.
	5233	* @return
	5234	* The position vector returned by `func` at the solved backdated time.
	5235	* On success, the vector will hold `ASTRO_SUCCESS` in its `status` field,
	5236	* the backdated time in its `t` field, along with the apparent relative position.
	5237	* If an error occurs, `status` will hold an error code and the remaining fields
	5238	* should be ignored.
	5239	*/
	5240	astro_vector_t Astronomy_CorrectLightTravel(
	5241	void *context,
	5242	astro_position_func_t func,
	5243	astro_time_t time)
	5244	{
	5245	int iter;
	5246	astro_time_t ltime, ltime2;
	5247	astro_vector_t pos;
	5248	double distance, dt;
	5249
	5250	ltime = time;
	5251	for (iter = 0; iter < 10; ++iter)
	5252	{
	5253	pos = func(context, ltime);
	5254	if (pos.status != ASTRO_SUCCESS)
	5255	return pos;
	5256
	5257	distance = Astronomy_VectorLength(pos);
	5258
	5259	/*
	5260	This solver does not support more than one light-day of distance,
	5261	because that would cause convergence problems and inaccurate
	5262	values for stellar aberration angles.
	5263	*/
	5264	if (distance > C_AUDAY)
	5265	return VecError(ASTRO_INVALID_PARAMETER, time);
	5266
	5267	ltime2 = Astronomy_AddDays(time, -distance/C_AUDAY);
	5268	dt = fabs(ltime2.tt - ltime.tt);
	5269	if (dt < 1.0e-9) /* 86.4 microseconds */
	5270	return pos;
	5271
	5272	ltime = ltime2;
	5273	}
	5274	return VecError(ASTRO_NO_CONVERGE, time); /* light travel time solver did not converge */
	5275	}
	5276
	5277
	5278	/** @cond DOXYGEN_SKIP */
	5279	typedef struct
	5280	{
	5281	astro_body_t observerBody;
	5282	astro_body_t targetBody;
	5283	astro_aberration_t aberration;
	5284	astro_vector_t observerPos; /* used only when aberration == NO_ABERRATION */
	5285	}
	5286	backdate_context_t;
	5287	/** @endcond */
	5288
	5289
	5290	static astro_vector_t BodyPosition(void *context, astro_time_t time)
	5291	{
	5292	const backdate_context_t b = (const backdate_context_t )context;
	5293	astro_vector_t observerPos, pos;
	5294
	5295	if (b->aberration == NO_ABERRATION)
	5296	{
	5297	/* No aberration, so use the pre-calculated initial position of the observer body. */
	5298	observerPos = b->observerPos;
	5299	}
	5300	else
	5301	{
	5302	/*
	5303	The following discussion is worded with the observer body being the Earth,
	5304	which is often the case. However, the same reasoning applies to any observer body
	5305	without loss of generality.
	5306
	5307	To include aberration, make a good first-order approximation
	5308	by backdating the Earth's position also.
	5309	This is confusing, but it works for objects within the Solar System
	5310	because the distance the Earth moves in that small amount of light
	5311	travel time (a few minutes to a few hours) is well approximated
	5312	by a line segment that substends the angle seen from the remote
	5313	body viewing Earth. That angle is pretty close to the aberration
	5314	angle of the moving Earth viewing the remote body.
	5315	In other words, both of the following approximate the aberration angle:
	5316	(transverse distance Earth moves) / (distance to body)
	5317	(transverse speed of Earth) / (speed of light).
	5318	*/
	5319	observerPos = Astronomy_HelioVector(b->observerBody, time);
	5320	}
	5321
	5322	if (observerPos.status != ASTRO_SUCCESS)
	5323	return observerPos;
	5324
	5325	pos = Astronomy_HelioVector(b->targetBody, time);
	5326	if (pos.status == ASTRO_SUCCESS)
	5327	{
	5328	/* Convert heliocentric body position to observer-centric position. */
	5329	pos.x -= observerPos.x;
	5330	pos.y -= observerPos.y;
	5331	pos.z -= observerPos.z;
	5332	}
	5333	return pos;
	5334	}
	5335
	5336
	5337	/**
	5338	* @brief Solve for light travel time correction of apparent position.
	5339	*
	5340	* When observing a distant object, for example Jupiter as seen from Earth,
	5341	* the amount of time it takes for light to travel from the object to the
	5342	* observer can significantly affect the object's apparent position.
	5343	*
	5344	* This function solves the light travel time correction for the apparent
	5345	* relative position vector of a target body as seen by an observer body
	5346	* at a given observation time.
	5347	*
	5348	* For geocentric calculations, #Astronomy_GeoVector also includes light
	5349	* travel time correction, but the time `t` embedded in its returned vector
	5350	* refers to the observation time, not the backdated time that light left
	5351	* the observed body. Thus `Astronomy_BackdatePosition` provides direct
	5352	* access to the light departure time for callers that need it.
	5353	*
	5354	* For a more generalized light travel correction solver, see #Astronomy_CorrectLightTravel.
	5355	*
	5356	* @param time The time of observation.
	5357	* @param observerBody The body to be used as the observation location.
	5358	* @param targetBody The body to be observed.
	5359	* @param aberration `ABERRATION` to correct for aberration, or `NO_ABERRATION` to leave uncorrected.
	5360	*
	5361	* @return
	5362	* On success, the position vector at the solved backdated time.
	5363	* The returned vector will hold `ASTRO_SUCCESS` in its `status` field,
	5364	* the backdated time in its `t` field, along with the apparent relative position.
	5365	* If an error occurs, `status` will hold an error code and the remaining fields should be ignored.
	5366	*/
	5367	astro_vector_t Astronomy_BackdatePosition(
	5368	astro_time_t time,
	5369	astro_body_t observerBody,
	5370	astro_body_t targetBody,
	5371	astro_aberration_t aberration)
	5372	{
	5373	if (UserDefinedStar(targetBody))
	5374	{
	5375	/*
	5376	This is a user-defined star, which must be treated as a special case.
	5377	First, we assume its heliocentric position does not change with time.
	5378	Second, we assume its heliocentric position has already been corrected
	5379	for light-travel time, its coordinates given as it appears on Earth at the present.
	5380	Therefore, no backdating is applied.
	5381	*/
	5382	astro_vector_t ovec, tvec, vec;
	5383	double rx, ry, rz, s;
	5384	astro_state_vector_t ostate;
	5385
	5386	tvec = Astronomy_HelioVector(targetBody, time);
	5387	if (tvec.status != ASTRO_SUCCESS)
	5388	return tvec;
	5389
	5390	switch (aberration)
	5391	{
	5392	case NO_ABERRATION:
	5393	/* Return the star's position as seen from the observer. */
	5394	ovec = Astronomy_HelioVector(observerBody, time);
	5395	if (ovec.status != ASTRO_SUCCESS)
	5396	return ovec;
	5397	vec.x = tvec.x - ovec.x;
	5398	vec.y = tvec.y - ovec.y;
	5399	vec.z = tvec.z - ovec.z;
	5400	vec.t = time;
	5401	vec.status = ASTRO_SUCCESS;
	5402	return vec;
	5403
	5404	case ABERRATION:
	5405	/*
	5406	(Observer velocity) - (light vector) = (Aberration-corrected direction to target body).
	5407	Note that this is an approximation, because technically the light vector should
	5408	be measured in barycentric coordinates, not heliocentric. The error is very small.
	5409	*/
	5410	ostate = Astronomy_HelioState(observerBody, time);
	5411	if (ostate.status != ASTRO_SUCCESS)
	5412	return VecError(ostate.status, time);
	5413
	5414	rx = tvec.x - ostate.x;
	5415	ry = tvec.y - ostate.y;
	5416	rz = tvec.z - ostate.z;
	5417	s = C_AUDAY / sqrt(rxrx + ryry + rz*rz);
	5418
	5419	vec.x = rx + ostate.vx/s;
	5420	vec.y = ry + ostate.vy/s;
	5421	vec.z = rz + ostate.vz/s;
	5422	vec.t = time;
	5423	vec.status = ASTRO_SUCCESS;
	5424	return vec;
	5425
	5426	default:
	5427	return VecError(ASTRO_INVALID_PARAMETER, time);
	5428	}
	5429	}
	5430	else
	5431	{
	5432	backdate_context_t context;
	5433
	5434	context.observerBody = observerBody;
	5435	context.targetBody = targetBody;
	5436	context.aberration = aberration;
	5437	switch (aberration)
	5438	{
	5439	case NO_ABERRATION:
	5440	/* Without aberration, we need the observer body position at the observation time only. */
	5441	/* For efficiency, calculate it once and hold onto it, so `BodyPosition` can keep using it. */
	5442	context.observerPos = Astronomy_HelioVector(observerBody, time);
	5443	break;
	5444
	5445	case ABERRATION:
	5446	/* With aberration, `BackdatePosition` will calculate the observer body state at different times. */
	5447	/* Therefore, do not waste time calculating it at the observation time. */
	5448	/* Initialize the memory with an explicitly invalid value. */
	5449	context.observerPos = VecError(ASTRO_NOT_INITIALIZED, time);
	5450	break;
	5451
	5452	default:
	5453	return VecError(ASTRO_INVALID_PARAMETER, time);
	5454	}
	5455
	5456	return Astronomy_CorrectLightTravel(&context, BodyPosition, time);
	5457	}
	5458	}
	5459
	5460
	5461	/**
	5462	* @brief Calculates geocentric Cartesian coordinates of a body in the J2000 equatorial system.
	5463	*
	5464	* This function calculates the position of the given celestial body as a vector,
	5465	* using the center of the Earth as the origin. The result is expressed as a Cartesian
	5466	* vector in the J2000 equatorial system: the coordinates are based on the mean equator
	5467	* of the Earth at noon UTC on 1 January 2000.
	5468	*
	5469	* If given an invalid value for `body`, this function will fail. The caller should always check
	5470	* the `status` field inside the returned #astro_vector_t for `ASTRO_SUCCESS` (success)
	5471	* or any other value (failure) before trusting the resulting vector.
	5472	*
	5473	* Unlike #Astronomy_HelioVector, this function corrects for light travel time.
	5474	* This means the position of the body is "back-dated" by the amount of time it takes
	5475	* light to travel from that body to an observer on the Earth.
	5476	*
	5477	* Also, the position can optionally be corrected for
	5478	* [aberration](https://en.wikipedia.org/wiki/Aberration_of_light), an effect
	5479	* causing the apparent direction of the body to be shifted due to transverse
	5480	* movement of the Earth with respect to the rays of light coming from that body.
	5481	*
	5482	* @param body
	5483	* A body for which to calculate a heliocentric position: the Sun, Moon, or any of the planets.
	5484	* Can also be a star defined by #Astronomy_DefineStar.
	5485	* @param time The date and time for which to calculate the position.
	5486	* @param aberration `ABERRATION` to correct for aberration, or `NO_ABERRATION` to leave uncorrected.
	5487	* @return A geocentric position vector of the center of the given body.
	5488	*/
	5489	astro_vector_t Astronomy_GeoVector(astro_body_t body, astro_time_t time, astro_aberration_t aberration)
	5490	{
	5491	astro_vector_t vector;
	5492
	5493	switch (body)
	5494	{
	5495	case BODY_EARTH:
	5496	/* The Earth's geocentric coordinates are always (0,0,0). */
	5497	vector.status = ASTRO_SUCCESS;
	5498	vector.x = 0.0;
	5499	vector.y = 0.0;
	5500	vector.z = 0.0;
	5501	break;
	5502
	5503	case BODY_MOON:
	5504	/* The moon is so close, aberration and light travel time don't matter. */
	5505	vector = Astronomy_GeoMoon(time);
	5506	break;
	5507
	5508	default:
	5509	/* For all other bodies, apply light travel time correction. */
	5510	vector = Astronomy_BackdatePosition(time, BODY_EARTH, body, aberration);
	5511	break;
	5512	}
	5513
	5514	vector.t = time; /* tricky: return the observation time, not the backdated time */
	5515	return vector;
	5516	}
	5517
	5518
	5519	/**
	5520	* @brief Calculates barycentric position and velocity vectors for the given body.
	5521	*
	5522	* Given a body and a time, calculates the barycentric position and velocity
	5523	* vectors for the center of that body at that time.
	5524	* The vectors are expressed in J2000 mean equator coordinates (EQJ).
	5525	*
	5526	* @param body
	5527	* The celestial body whose barycentric state vector is to be calculated.
	5528	* Supported values are `BODY_SUN`, `BODY_MOON`, `BODY_EMB`, `BODY_SSB`, and all planets:
	5529	* `BODY_MERCURY`, `BODY_VENUS`, `BODY_EARTH`, `BODY_MARS`, `BODY_JUPITER`,
	5530	* `BODY_SATURN`, `BODY_URANUS`, `BODY_NEPTUNE`, `BODY_PLUTO`.
	5531	* @param time
	5532	* The date and time for which to calculate position and velocity.
	5533	* @return
	5534	* A structure that contains barycentric position and velocity vectors.
	5535	*/
	5536	astro_state_vector_t Astronomy_BaryState(astro_body_t body, astro_time_t time)
	5537	{
	5538	astro_state_vector_t state;
	5539	major_bodies_t bary;
	5540	body_state_t planet, earth;
	5541
	5542	if (body == BODY_SSB)
	5543	{
	5544	/* Trivial case: the solar system barycenter itself. */
	5545	state.status = ASTRO_SUCCESS;
	5546	state.x = state.y = state.z = 0.0;
	5547	state.vx = state.vy = state.vz = 0.0;
	5548	state.t = time;
	5549	return state;
	5550	}
	5551
	5552	if (body == BODY_PLUTO)
	5553	{
	5554	astro_status_t status = CalcPluto(&planet, time, 0);
	5555	if (status != ASTRO_SUCCESS)
	5556	return StateVecError(status, time);
	5557	return ExportState(planet, time);
	5558	}
	5559
	5560	MajorBodyBary(&bary, time.tt);
	5561
	5562	switch (body)
	5563	{
	5564	/* If the caller is asking for one of the major bodies, we can immediately return the answer. */
	5565	case BODY_SUN: return ExportState(bary.Sun, time);
	5566	case BODY_JUPITER: return ExportState(bary.Jupiter, time);
	5567	case BODY_SATURN: return ExportState(bary.Saturn, time);
	5568	case BODY_URANUS: return ExportState(bary.Uranus, time);
	5569	case BODY_NEPTUNE: return ExportState(bary.Neptune, time);
	5570
	5571	/* Handle the remaining VSOP bodies: Mercury, Venus, Earth, Mars. */
	5572	case BODY_MERCURY:
	5573	case BODY_VENUS:
	5574	case BODY_EARTH:
	5575	case BODY_MARS:
	5576	planet = CalcVsopPosVel(&vsop[body], time.tt);
	5577	/* BarySun + HelioBody = BaryBody */
	5578	state.x = bary.Sun.r.x + planet.r.x;
	5579	state.y = bary.Sun.r.y + planet.r.y;
	5580	state.z = bary.Sun.r.z + planet.r.z;
	5581	state.vx = bary.Sun.v.x + planet.v.x;
	5582	state.vy = bary.Sun.v.y + planet.v.y;
	5583	state.vz = bary.Sun.v.z + planet.v.z;
	5584	state.t = time;
	5585	state.status = ASTRO_SUCCESS;
	5586	return state;
	5587
	5588	case BODY_MOON:
	5589	case BODY_EMB:
	5590	earth = CalcVsopPosVel(&vsop[BODY_EARTH], time.tt);
	5591	if (body == BODY_MOON)
	5592	state = Astronomy_GeoMoonState(time);
	5593	else
	5594	state = Astronomy_GeoEmbState(time);
	5595	state.x += bary.Sun.r.x + earth.r.x;
	5596	state.y += bary.Sun.r.y + earth.r.y;
	5597	state.z += bary.Sun.r.z + earth.r.z;
	5598	state.vx += bary.Sun.v.x + earth.v.x;
	5599	state.vy += bary.Sun.v.y + earth.v.y;
	5600	state.vz += bary.Sun.v.z + earth.v.z;
	5601	return state;
	5602
	5603	default:
	5604	return StateVecError(ASTRO_INVALID_BODY, time);
	5605	}
	5606	}
	5607
	5608
	5609	/**
	5610	* @brief Calculates heliocentric position and velocity vectors for the given body.
	5611	*
	5612	* Given a body and a time, calculates the position and velocity
	5613	* vectors for the center of that body at that time, relative to the center of the Sun.
	5614	* The vectors are expressed in J2000 mean equator coordinates (EQJ).
	5615	* If you need the position vector only, it is more efficient to call #Astronomy_HelioVector.
	5616	* The Sun's center is a non-inertial frame of reference. In other words, the Sun
	5617	* experiences acceleration due to gravitational forces, mostly from the larger
	5618	* planets (Jupiter, Saturn, Uranus, and Neptune). If you want to calculate momentum,
	5619	* kinetic energy, or other quantities that require a non-accelerating frame
	5620	* of reference, consider using #Astronomy_BaryState instead.
	5621	*
	5622	* @param body
	5623	* The celestial body whose heliocentric state vector is to be calculated.
	5624	* Supported values are `BODY_SUN`, `BODY_MOON`, `BODY_EMB`, `BODY_SSB`, and all planets:
	5625	* `BODY_MERCURY`, `BODY_VENUS`, `BODY_EARTH`, `BODY_MARS`, `BODY_JUPITER`,
	5626	* `BODY_SATURN`, `BODY_URANUS`, `BODY_NEPTUNE`, `BODY_PLUTO`.
	5627	* Also allowed to be a user-defined star created by #Astronomy_DefineStar.
	5628	* @param time
	5629	* The date and time for which to calculate position and velocity.
	5630	* @return
	5631	* A structure that contains heliocentric position and velocity vectors.
	5632	*/
	5633	astro_state_vector_t Astronomy_HelioState(astro_body_t body, astro_time_t time)
	5634	{
	5635	astro_status_t status;
	5636	astro_state_vector_t state;
	5637	major_bodies_t bary;
	5638	body_state_t planet, earth;
	5639
	5640	if (UserDefinedStar(body))
	5641	{
	5642	astro_vector_t vec = Astronomy_HelioVector(body, time);
	5643	state.x = vec.x;
	5644	state.y = vec.y;
	5645	state.z = vec.z;
	5646	state.vx = state.vy = state.vz = 0.0;
	5647	state.t = time;
	5648	state.status = vec.status;
	5649	return state;
	5650	}
	5651
	5652	switch (body)
	5653	{
	5654	case BODY_SUN:
	5655	/* Trivial case: the Sun is the origin of the heliocentric frame. */
	5656	state.status = ASTRO_SUCCESS;
	5657	state.x = state.y = state.z = 0.0;
	5658	state.vx = state.vy = state.vz = 0.0;
	5659	state.t = time;
	5660	return state;
	5661
	5662	case BODY_SSB:
	5663	/* Calculate the barycentric Sun. Then the negative of that is the heliocentric SSB. */
	5664	MajorBodyBary(&bary, time.tt);
	5665	state.x = -bary.Sun.r.x;
	5666	state.y = -bary.Sun.r.y;
	5667	state.z = -bary.Sun.r.z;
	5668	state.vx = -bary.Sun.v.x;
	5669	state.vy = -bary.Sun.v.y;
	5670	state.vz = -bary.Sun.v.z;
	5671	state.t = time;
	5672	state.status = ASTRO_SUCCESS;
	5673	return state;
	5674
	5675	case BODY_MERCURY:
	5676	case BODY_VENUS:
	5677	case BODY_EARTH:
	5678	case BODY_MARS:
	5679	case BODY_JUPITER:
	5680	case BODY_SATURN:
	5681	case BODY_URANUS:
	5682	case BODY_NEPTUNE:
	5683	/* Planets included in the VSOP87 model. */
	5684	planet = CalcVsopPosVel(&vsop[body], time.tt);
	5685	return ExportState(planet, time);
	5686
	5687	case BODY_PLUTO:
	5688	status = CalcPluto(&planet, time, 1);
	5689	if (status != ASTRO_SUCCESS)
	5690	return StateVecError(status, time);
	5691	return ExportState(planet, time);
	5692
	5693	case BODY_MOON:
	5694	case BODY_EMB:
	5695	earth = CalcVsopPosVel(&vsop[BODY_EARTH], time.tt);
	5696	if (body == BODY_MOON)
	5697	state = Astronomy_GeoMoonState(time);
	5698	else
	5699	state = Astronomy_GeoEmbState(time);
	5700	state.x += earth.r.x;
	5701	state.y += earth.r.y;
	5702	state.z += earth.r.z;
	5703	state.vx += earth.v.x;
	5704	state.vy += earth.v.y;
	5705	state.vz += earth.v.z;
	5706	return state;
	5707
	5708	default:
	5709	return StateVecError(ASTRO_INVALID_BODY, time);
	5710	}
	5711	}
	5712
	5713
	5714	/**
	5715	* @brief Returns the product of mass and universal gravitational constant of a Solar System body.
	5716	*
	5717	* For problems involving the gravitational interactions of Solar System bodies,
	5718	* it is helpful to know the product GM, where G = the universal gravitational constant
	5719	* and M = the mass of the body. In practice, GM is known to a higher precision than
	5720	* either G or M alone, and thus using the product results in the most accurate results.
	5721	* This function returns the product GM in the units au^3/day^2, or 0 for invalid bodies.
	5722	* The values come from page 10 of a
	5723	* [JPL memorandum regarding the DE405/LE405 ephemeris](https://web.archive.org/web/20120220062549/http://iau-comm4.jpl.nasa.gov/de405iom/de405iom.pdf).
	5724	*
	5725	* @param body The body for which to find the GM product.
	5726	* @return The mass product of the given body in au^3/day^2.
	5727	*/
	5728	double Astronomy_MassProduct(astro_body_t body)
	5729	{
	5730	switch (body)
	5731	{
	5732	case BODY_SUN: return SUN_GM;
	5733	case BODY_MERCURY: return MERCURY_GM;
	5734	case BODY_VENUS: return VENUS_GM;
	5735	case BODY_EARTH: return EARTH_GM;
	5736	case BODY_MOON: return MOON_GM;
	5737	case BODY_EMB: return EARTH_GM + MOON_GM;
	5738	case BODY_MARS: return MARS_GM;
	5739	case BODY_JUPITER: return JUPITER_GM;
	5740	case BODY_SATURN: return SATURN_GM;
	5741	case BODY_URANUS: return URANUS_GM;
	5742	case BODY_NEPTUNE: return NEPTUNE_GM;
	5743	case BODY_PLUTO: return PLUTO_GM;
	5744	default: return 0.0; /* invalid body */
	5745	}
	5746	}
	5747
	5748
	5749	/**
	5750	* @brief Calculates one of the 5 Lagrange points for a pair of co-orbiting bodies.
	5751	*
	5752	* Given a more massive "major" body and a much less massive "minor" body,
	5753	* calculates one of the five Lagrange points in relation to the minor body's
	5754	* orbit around the major body. The parameter `point` is an integer that
	5755	* selects the Lagrange point as follows:
	5756	*
	5757	* 1 = the Lagrange point between the major body and minor body.
	5758	* 2 = the Lagrange point on the far side of the minor body.
	5759	* 3 = the Lagrange point on the far side of the major body.
	5760	* 4 = the Lagrange point 60 degrees ahead of the minor body's orbital position.
	5761	* 5 = the Lagrange point 60 degrees behind the minor body's orbital position.
	5762	*
	5763	* The function returns the state vector for the selected Lagrange point
	5764	* in J2000 mean equator coordinates (EQJ), with respect to the center of the
	5765	* major body.
	5766	*
	5767	* To calculate Sun/Earth Lagrange points, pass in `BODY_SUN` for `major_body`
	5768	* and `BODY_EMB` (Earth/Moon barycenter) for `minor_body`.
	5769	* For Lagrange points of the Sun and any other planet, pass in that planet
	5770	* (e.g. `BODY_JUPITER`) for `minor_body`.
	5771	* To calculate Earth/Moon Lagrange points, pass in `BODY_EARTH` and `BODY_MOON`
	5772	* for the major and minor bodies respectively.
	5773	*
	5774	* In some cases, it may be more efficient to call #Astronomy_LagrangePointFast,
	5775	* especially when the state vectors have already been calculated, or are needed
	5776	* for some other purpose.
	5777	*
	5778	* @param point A value 1..5 that selects which of the Lagrange points to calculate.
	5779	* @param time The time at which the Lagrange point is to be calculated.
	5780	* @param major_body The more massive of the co-orbiting bodies: `BODY_SUN` or `BODY_EARTH`.
	5781	* @param minor_body The less massive of the co-orbiting bodies. See main remarks.
	5782	* @return The position and velocity of the selected Lagrange point with respect to the major body's center.
	5783	*/
	5784	astro_state_vector_t Astronomy_LagrangePoint(
	5785	int point,
	5786	astro_time_t time,
	5787	astro_body_t major_body,
	5788	astro_body_t minor_body)
	5789	{
	5790	astro_state_vector_t major_state, minor_state;
	5791	double major_mass, minor_mass;
	5792
	5793	major_mass = Astronomy_MassProduct(major_body);
	5794	if (major_mass <= 0.0)
	5795	return StateVecError(ASTRO_INVALID_BODY, time);
	5796
	5797	minor_mass = Astronomy_MassProduct(minor_body);
	5798	if (minor_mass <= 0.0)
	5799	return StateVecError(ASTRO_INVALID_BODY, time);
	5800
	5801	/* Calculate the state vectors for the major and minor bodies. */
	5802	if (major_body == BODY_EARTH && minor_body == BODY_MOON)
	5803	{
	5804	/* Use geocentric calculations for more precision. */
	5805
	5806	/* The Earth's geocentric state is trivial. */
	5807	major_state.status = ASTRO_SUCCESS;
	5808	major_state.t = time;
	5809	major_state.x = major_state.y = major_state.z = 0.0;
	5810	major_state.vx = major_state.vy = major_state.vz = 0.0;
	5811
	5812	minor_state = Astronomy_GeoMoonState(time);
	5813	if (minor_state.status != ASTRO_SUCCESS)
	5814	return minor_state;
	5815	}
	5816	else
	5817	{
	5818	major_state = Astronomy_HelioState(major_body, time);
	5819	if (major_state.status != ASTRO_SUCCESS)
	5820	return major_state;
	5821
	5822	minor_state = Astronomy_HelioState(minor_body, time);
	5823	if (minor_state.status != ASTRO_SUCCESS)
	5824	return minor_state;
	5825	}
	5826
	5827	return Astronomy_LagrangePointFast(
	5828	point,
	5829	major_state,
	5830	major_mass,
	5831	minor_state,
	5832	minor_mass
	5833	);
	5834	}
	5835
	5836
	5837	/**
	5838	* @brief Calculates one of the 5 Lagrange points from body masses and state vectors.
	5839	*
	5840	* Given a more massive "major" body and a much less massive "minor" body,
	5841	* calculates one of the five Lagrange points in relation to the minor body's
	5842	* orbit around the major body. The parameter `point` is an integer that
	5843	* selects the Lagrange point as follows:
	5844	*
	5845	* 1 = the Lagrange point between the major body and minor body.
	5846	* 2 = the Lagrange point on the far side of the minor body.
	5847	* 3 = the Lagrange point on the far side of the major body.
	5848	* 4 = the Lagrange point 60 degrees ahead of the minor body's orbital position.
	5849	* 5 = the Lagrange point 60 degrees behind the minor body's orbital position.
	5850	*
	5851	* The caller passes in the state vector and mass for both bodies.
	5852	* The state vectors can be in any orientation and frame of reference.
	5853	* The body masses are expressed as GM products, where G = the universal
	5854	* gravitation constant and M = the body's mass. Thus the units for
	5855	* `major_mass` and `minor_mass` must be au^3/day^2.
	5856	* Use #Astronomy_MassProduct to obtain GM values for various solar system bodies.
	5857	*
	5858	* The function returns the state vector for the selected Lagrange point
	5859	* using the same orientation as the state vector parameters `major_state` and `minor_state`,
	5860	* and the position and velocity components are with respect to the major body's center.
	5861	*
	5862	* Consider calling #Astronomy_LagrangePoint, instead of this function, for simpler usage in most cases.
	5863	*
	5864	* @param point A value 1..5 that selects which of the Lagrange points to calculate.
	5865	* @param major_state The state vector of the major (more massive) of the pair of bodies.
	5866	* @param major_mass The mass product GM of the major body.
	5867	* @param minor_state The state vector of the minor (less massive) of the pair of bodies.
	5868	* @param minor_mass The mass product GM of the minor body.
	5869	* @return The position and velocity of the selected Lagrange point with respect to the major body's center.
	5870	*/
	5871	astro_state_vector_t Astronomy_LagrangePointFast(
	5872	int point,
	5873	astro_state_vector_t major_state,
	5874	double major_mass,
	5875	astro_state_vector_t minor_state,
	5876	double minor_mass)
	5877	{
	5878	const double cos_60 = 0.5;
	5879	const double sin_60 = 0.8660254037844386; /* sqrt(3) / 2 */
	5880	double scale, dx, dy, dz;
	5881	double vx, vy, vz;
	5882	double R2, R, r1, r2, x, deltax, dr1, dr2, numer1, numer2, omega2, accel, deriv;
	5883	astro_state_vector_t p;
	5884
	5885	if (point < 1 \|\| point > 5)
	5886	return StateVecError(ASTRO_INVALID_PARAMETER, major_state.t);
	5887
	5888	if (major_state.status != ASTRO_SUCCESS \|\| minor_state.status != ASTRO_SUCCESS)
	5889	return StateVecError(ASTRO_INVALID_PARAMETER, major_state.t);
	5890
	5891	if (!isfinite(major_mass) \|\| major_mass <= 0.0)
	5892	return StateVecError(ASTRO_INVALID_PARAMETER, major_state.t);
	5893
	5894	if (!isfinite(minor_mass) \|\| minor_mass <= 0.0)
	5895	return StateVecError(ASTRO_INVALID_PARAMETER, major_state.t);
	5896
	5897	/* Find the relative position vector <dx, dy, dz>. */
	5898	dx = minor_state.x - major_state.x;
	5899	dy = minor_state.y - major_state.y;
	5900	dz = minor_state.z - major_state.z;
	5901	R2 = (dxdx + dydy + dz*dz);
	5902
	5903	/* R = Total distance between the bodies. */
	5904	R = sqrt(R2);
	5905
	5906	/* Find the velocity vector <vx, vy, vz>. */
	5907	vx = minor_state.vx - major_state.vx;
	5908	vy = minor_state.vy - major_state.vy;
	5909	vz = minor_state.vz - major_state.vz;
	5910
	5911	if (point == 4 \|\| point == 5)
	5912	{
	5913	double nx, ny, nz;
	5914	double ux, uy, uz, U;
	5915	double Dx, Dy, Dz;
	5916	double Ux, Uy, Uz;
	5917	double vert, vrad, vtan;
	5918
	5919	/*
	5920	For L4 and L5, we need to find points 60 degrees away from the
	5921	line connecting the two bodies and in the instantaneous orbital plane.
	5922	Define the instantaneous orbital plane as the unique plane that contains
	5923	both the relative position vector and the relative velocity vector.
	5924	*/
	5925
	5926	/* Take the cross product of position and velocity to find a normal vector <nx, ny, nz>. */
	5927	nx = dyvz - dzvy;
	5928	ny = dzvx - dxvz;
	5929	nz = dxvy - dyvx;
	5930
	5931	/* Take the cross product normalposition to get a tangential vector <ux, uy, uz>. /
	5932	ux = nydz - nzdy;
	5933	uy = nzdx - nxdz;
	5934	uz = nxdy - nydx;
	5935
	5936	/* Convert the tangential direction vector to a unit vector. */
	5937	U = sqrt(uxux + uyuy + uz*uz);
	5938	ux /= U;
	5939	uy /= U;
	5940	uz /= U;
	5941
	5942	/* Convert the relative position vector into a unit vector. */
	5943	dx /= R;
	5944	dy /= R;
	5945	dz /= R;
	5946
	5947	/* Now we have two perpendicular unit vectors in the orbital plane: 'd' and 'u'. */
	5948
	5949	/* Create new unit vectors rotated (+/-)60 degrees from the radius/tangent directions. */
	5950	vert = (point == 4) ? +sin_60 : -sin_60;
	5951
	5952	/* Rotated radial vector */
	5953	Dx = cos_60dx + vertux;
	5954	Dy = cos_60dy + vertuy;
	5955	Dz = cos_60dz + vertuz;
	5956
	5957	/* Rotated tangent vector */
	5958	Ux = cos_60ux - vertdx;
	5959	Uy = cos_60uy - vertdy;
	5960	Uz = cos_60uz - vertdz;
	5961
	5962	/* Calculate L4/L5 positions relative to the major body. */
	5963	p.x = R * Dx;
	5964	p.y = R * Dy;
	5965	p.z = R * Dz;
	5966
	5967	/* Use dot products to find radial and tangential components of the relative velocity. */
	5968	vrad = vxdx + vydy + vz*dz;
	5969	vtan = vxux + vyuy + vz*uz;
	5970
	5971	/* Calculate L4/L5 velocities. */
	5972	p.vx = vradDx + vtanUx;
	5973	p.vy = vradDy + vtanUy;
	5974	p.vz = vradDz + vtanUz;
	5975	}
	5976	else
	5977	{
	5978	/*
	5979	Calculate the distances of each body from their mutual barycenter.
	5980	r1 = negative distance of major mass from barycenter (e.g. Sun to the left of barycenter)
	5981	r2 = positive distance of minor mass from barycenter (e.g. Earth to the right of barycenter)
	5982	*/
	5983	r1 = -R * (minor_mass / (major_mass + minor_mass));
	5984	r2 = +R * (major_mass / (major_mass + minor_mass));
	5985
	5986	/* Calculate the square of the angular orbital speed in [rad^2 / day^2]. */
	5987	omega2 = (major_mass + minor_mass) / (R2*R);
	5988
	5989	/*
	5990	Use Newton's Method to numerically solve for the location where
	5991	outward centrifugal acceleration in the rotating frame of reference
	5992	is equal to net inward gravitational acceleration.
	5993	First derive a good initial guess based on approximate analysis.
	5994	*/
	5995	if (point == 1 \|\| point == 2)
	5996	{
	5997	scale = (major_mass / (major_mass + minor_mass)) * cbrt(minor_mass / (3.0 * major_mass));
	5998	numer1 = -major_mass; /* The major mass is to the left of L1 and L2 */
	5999	if (point == 1)
	6000	{
	6001	scale = 1.0 - scale;
	6002	numer2 = +minor_mass; /* The minor mass is to the right of L1. */
	6003	}
	6004	else
	6005	{
	6006	scale = 1.0 + scale;
	6007	numer2 = -minor_mass; /* The minor mass is to the left of L2. */
	6008	}
	6009	}
	6010	else /* point == 3 */
	6011	{
	6012	scale = ((7.0/12.0)*minor_mass - major_mass) / (minor_mass + major_mass);
	6013	numer1 = +major_mass; /* major mass is to the right of L3. */
	6014	numer2 = +minor_mass; /* minor mass is to the right of L3. */
	6015	}
	6016
	6017	/* Iterate Newton's Method until it converges. */
	6018	x = R*scale - r1;
	6019	do
	6020	{
	6021	dr1 = x - r1;
	6022	dr2 = x - r2;
	6023	accel = omega2x + numer1/(dr1dr1) + numer2/(dr2*dr2);
	6024	deriv = omega2 - 2numer1/(dr1dr1dr1) - 2numer2/(dr2dr2dr2);
	6025	deltax = accel/deriv;
	6026	x -= deltax;
	6027	}
	6028	while (fabs(deltax/R) > 1.0e-14);
	6029	scale = (x - r1) / R;
	6030
	6031	p.x = scale * dx;
	6032	p.y = scale * dy;
	6033	p.z = scale * dz;
	6034	p.vx = scale * vx;
	6035	p.vy = scale * vy;
	6036	p.vz = scale * vz;
	6037	}
	6038	p.t = major_state.t;
	6039	p.status = ASTRO_SUCCESS;
	6040	return p;
	6041	}
	6042
	6043
	6044	/**
	6045	* @brief Calculates equatorial coordinates of a celestial body as seen by an observer on the Earth's surface.
	6046	*
	6047	* Calculates topocentric equatorial coordinates in one of two different systems:
	6048	* J2000 or true-equator-of-date, depending on the value of the `equdate` parameter.
	6049	* Equatorial coordinates include right ascension, declination, and distance in astronomical units.
	6050	*
	6051	* This function corrects for light travel time: it adjusts the apparent location
	6052	* of the observed body based on how long it takes for light to travel from the body to the Earth.
	6053	*
	6054	* This function corrects for topocentric parallax, meaning that it adjusts for the
	6055	* angular shift depending on where the observer is located on the Earth. This is most
	6056	* significant for the Moon, because it is so close to the Earth. However, parallax corection
	6057	* has a small effect on the apparent positions of other bodies.
	6058	*
	6059	* Correction for aberration is optional, using the `aberration` parameter.
	6060	*
	6061	* @param body The celestial body to be observed. Not allowed to be `BODY_EARTH`.
	6062	* @param time The date and time at which the observation takes place.
	6063	* @param observer A location on or near the surface of the Earth.
	6064	* @param equdate Selects the date of the Earth's equator in which to express the equatorial coordinates.
	6065	* @param aberration Selects whether or not to correct for aberration.
	6066	* @return Topocentric equatorial coordinates of the celestial body.
	6067	*/
	6068	astro_equatorial_t Astronomy_Equator(
	6069	astro_body_t body,
	6070	astro_time_t *time,
	6071	astro_observer_t observer,
	6072	astro_equator_date_t equdate,
	6073	astro_aberration_t aberration)
	6074	{
	6075	astro_equatorial_t equ;
	6076	astro_vector_t gc;
	6077	double gc_observer[3];
	6078	double j2000[3];
	6079	double temp[3];
	6080	double datevect[3];
	6081
	6082	if (time == NULL)
	6083	return EquError(ASTRO_INVALID_PARAMETER);
	6084
	6085	/* Calculate the geocentric location of the observer. */
	6086	geo_pos(time, observer, gc_observer);
	6087
	6088	/* Calculate the geocentric location of the body. */
	6089	gc = Astronomy_GeoVector(body, *time, aberration);
	6090	if (gc.status != ASTRO_SUCCESS)
	6091	return EquError(gc.status);
	6092
	6093	/* Convert geocentric coordinates to topocentric coordinates. */
	6094	j2000[0] = gc.x - gc_observer[0];
	6095	j2000[1] = gc.y - gc_observer[1];
	6096	j2000[2] = gc.z - gc_observer[2];
	6097
	6098	switch (equdate)
	6099	{
	6100	case EQUATOR_OF_DATE:
	6101	precession(j2000, *time, FROM_2000, temp);
	6102	nutation(temp, time, FROM_2000, datevect);
	6103	equ = vector2radec(datevect, *time);
	6104	return equ;
	6105
	6106	case EQUATOR_J2000:
	6107	equ = vector2radec(j2000, *time);
	6108	return equ;
	6109
	6110	default:
	6111	return EquError(ASTRO_INVALID_PARAMETER);
	6112	}
	6113	}
	6114
	6115	/**
	6116	* @brief Calculates geocentric equatorial coordinates of an observer on the surface of the Earth.
	6117	*
	6118	* This function calculates a vector from the center of the Earth to
	6119	* a point on or near the surface of the Earth, expressed in equatorial
	6120	* coordinates. It takes into account the rotation of the Earth at the given
	6121	* time, along with the given latitude, longitude, and elevation of the observer.
	6122	*
	6123	* The caller may pass a value in `equdate` to select either `EQUATOR_J2000`
	6124	* for using J2000 coordinates, or `EQUATOR_OF_DATE` for using coordinates relative
	6125	* to the Earth's equator at the specified time.
	6126	*
	6127	* The returned vector has components expressed in astronomical units (AU).
	6128	* To convert to kilometers, multiply the `x`, `y`, and `z` values by
	6129	* the constant value #KM_PER_AU.
	6130	*
	6131	* The inverse of this function is also available: #Astronomy_VectorObserver.
	6132	*
	6133	* @param time
	6134	* The date and time for which to calculate the observer's position vector.
	6135	*
	6136	* @param observer
	6137	* The geographic location of a point on or near the surface of the Earth.
	6138	*
	6139	* @param equdate
	6140	* Selects the date of the Earth's equator in which to express the equatorial coordinates.
	6141	* The caller may select `EQUATOR_J2000` to use the orientation of the Earth's equator
	6142	* at noon UTC on January 1, 2000, in which case this function corrects for precession
	6143	* and nutation of the Earth as it was at the moment specified by the `time` parameter.
	6144	* Or the caller may select `EQUATOR_OF_DATE` to use the Earth's equator at `time`
	6145	* as the orientation.
	6146	*
	6147	* @return
	6148	* If successful, the returned vector holds `ASTRO_SUCCESS` in its `status` field,
	6149	* and is an equatorial vector from the center of the Earth to the specified location
	6150	* on (or near) the Earth's surface. Otherwise, `status` holds an error code.
	6151	*/
	6152	astro_vector_t Astronomy_ObserverVector(
	6153	astro_time_t *time,
	6154	astro_observer_t observer,
	6155	astro_equator_date_t equdate)
	6156	{
	6157	astro_vector_t vec;
	6158	double gast, pos[3], temp[3];
	6159
	6160	if (time == NULL)
	6161	return VecError(ASTRO_INVALID_PARAMETER, TimeError());
	6162
	6163	gast = Astronomy_SiderealTime(time);
	6164	terra(observer, gast, pos, NULL);
	6165
	6166	switch (equdate)
	6167	{
	6168	case EQUATOR_OF_DATE:
	6169	/* 'pos' already contains equator-of-date coordinates. */
	6170	break;
	6171
	6172	case EQUATOR_J2000:
	6173	/* Convert 'pos' from equator-of-date to J2000. */
	6174	nutation(pos, time, INTO_2000, temp);
	6175	precession(temp, *time, INTO_2000, pos);
	6176	break;
	6177
	6178	default:
	6179	/* This is not a valid value of the 'equdate' parameter. */
	6180	return VecError(ASTRO_INVALID_PARAMETER, *time);
	6181	}
	6182
	6183	vec.x = pos[0];
	6184	vec.y = pos[1];
	6185	vec.z = pos[2];
	6186	vec.t = *time;
	6187	vec.status = ASTRO_SUCCESS;
	6188	return vec;
	6189	}
	6190
	6191
	6192	/**
	6193	* @brief Calculates geocentric equatorial position and velocity of an observer on the surface of the Earth.
	6194	*
	6195	* This function calculates position and velocity vectors of an observer
	6196	* on or near the surface of the Earth, expressed in equatorial
	6197	* coordinates. It takes into account the rotation of the Earth at the given
	6198	* time, along with the given latitude, longitude, and elevation of the observer.
	6199	*
	6200	* The caller may pass a value in `equdate` to select either `EQUATOR_J2000`
	6201	* for using J2000 coordinates, or `EQUATOR_OF_DATE` for using coordinates relative
	6202	* to the Earth's equator at the specified time.
	6203	*
	6204	* The returned position vector has components expressed in astronomical units (AU).
	6205	* To convert to kilometers, multiply the `x`, `y`, and `z` values by
	6206	* the constant value #KM_PER_AU.
	6207	*
	6208	* The returned velocity vector is measured in AU/day.
	6209	*
	6210	* If you need the position only, and not the velocity, #Astronomy_ObserverVector
	6211	* is slightly more efficient than this function.
	6212	*
	6213	* @param time
	6214	* The date and time for which to calculate the observer's geocentric state vector.
	6215	*
	6216	* @param observer
	6217	* The geographic location of a point on or near the surface of the Earth.
	6218	*
	6219	* @param equdate
	6220	* Selects the date of the Earth's equator in which to express the equatorial coordinates.
	6221	* The caller may select `EQUATOR_J2000` to use the orientation of the Earth's equator
	6222	* at noon UTC on January 1, 2000, in which case this function corrects for precession
	6223	* and nutation of the Earth as it was at the moment specified by the `time` parameter.
	6224	* Or the caller may select `EQUATOR_OF_DATE` to use the Earth's equator at `time`
	6225	* as the orientation.
	6226	*
	6227	* @return
	6228	* If successful, the returned state vector holds `ASTRO_SUCCESS` in its `status` field,
	6229	* and the position (x, y, z) and velocity (vx, vy, vz) vectors are valid.
	6230	* Otherwise, `status` holds an error code.
	6231	*/
	6232	astro_state_vector_t Astronomy_ObserverState(
	6233	astro_time_t *time,
	6234	astro_observer_t observer,
	6235	astro_equator_date_t equdate)
	6236	{
	6237	astro_state_vector_t state;
	6238	double gast, pos[3], vel[3], postemp[3], veltemp[3];
	6239
	6240	if (time == NULL)
	6241	return StateVecError(ASTRO_INVALID_PARAMETER, TimeError());
	6242
	6243	gast = Astronomy_SiderealTime(time);
	6244	terra(observer, gast, pos, vel);
	6245
	6246	switch (equdate)
	6247	{
	6248	case EQUATOR_OF_DATE:
	6249	/* 'pos' and 'vel' already contain equator-of-date coordinates. */
	6250	break;
	6251
	6252	case EQUATOR_J2000:
	6253	/* Convert 'pos' from equator-of-date to J2000. */
	6254	nutation_posvel(pos, vel, time, INTO_2000, postemp, veltemp);
	6255	precession_posvel(postemp, veltemp, *time, INTO_2000, pos, vel);
	6256	break;
	6257
	6258	default:
	6259	/* This is not a valid value of the 'equdate' parameter. */
	6260	return StateVecError(ASTRO_INVALID_PARAMETER, *time);
	6261	}
	6262
	6263	state.x = pos[0];
	6264	state.y = pos[1];
	6265	state.z = pos[2];
	6266	state.vx = vel[0];
	6267	state.vy = vel[1];
	6268	state.vz = vel[2];
	6269	state.t = *time;
	6270	state.status = ASTRO_SUCCESS;
	6271	return state;
	6272	}
	6273
	6274
	6275	/**
	6276	* @brief Calculates the geographic location corresponding to an equatorial vector.
	6277	*
	6278	* This is the inverse function of #Astronomy_ObserverVector.
	6279	* Given a geocentric equatorial vector, it returns the geographic
	6280	* latitude, longitude, and elevation for that vector.
	6281	*
	6282	* @param vector
	6283	* The geocentric equatorial position vector for which to find geographic coordinates.
	6284	* The components are expressed in Astronomical Units (AU).
	6285	* You can calculate AU by dividing kilometers by the constant #KM_PER_AU.
	6286	* The time `vector.t` determines the Earth's rotation. The caller must set `vector.t` to a valid time.
	6287	* The vector is passed by reference (using a pointer) so that nutation calculations
	6288	* can be cached inside `vector.t` as an optimization.
	6289	*
	6290	* @param equdate
	6291	* Selects the date of the Earth's equator in which `vector` is expressed.
	6292	* The caller may select `EQUATOR_J2000` to use the orientation of the Earth's equator
	6293	* at noon UTC on January 1, 2000, in which case this function corrects for precession
	6294	* and nutation of the Earth as it was at the moment specified by `vector.t`.
	6295	* Or the caller may select `EQUATOR_OF_DATE` to use the Earth's equator at `vector.t`
	6296	* as the orientation.
	6297	*
	6298	* @return
	6299	* The geographic latitude, longitude, and elevation above sea level
	6300	* that corresponds to the given equatorial vector.
	6301	*/
	6302	astro_observer_t Astronomy_VectorObserver(
	6303	astro_vector_t *vector,
	6304	astro_equator_date_t equdate)
	6305	{
	6306	double gast;
	6307	double pos1[3];
	6308	double pos2[3];
	6309
	6310	gast = Astronomy_SiderealTime(&vector->t);
	6311	pos1[0] = vector->x;
	6312	pos1[1] = vector->y;
	6313	pos1[2] = vector->z;
	6314	if (equdate == EQUATOR_J2000)
	6315	{
	6316	precession(pos1, vector->t, FROM_2000, pos2);
	6317	nutation(pos2, &vector->t, FROM_2000, pos1);
	6318	}
	6319	return inverse_terra(pos1, gast);
	6320	}
	6321
	6322
	6323	/**
	6324	* @brief Calculates the gravitational acceleration experienced by an observer on the Earth.
	6325	*
	6326	* This function implements the WGS 84 Ellipsoidal Gravity Formula.
	6327	* The result is a combination of inward gravitational acceleration
	6328	* with outward centrifugal acceleration, as experienced by an observer
	6329	* in the Earth's rotating frame of reference.
	6330	* The resulting value increases toward the Earth's poles and decreases
	6331	* toward the equator, consistent with changes of the weight measured
	6332	* by a spring scale of a fixed mass moved to different latitudes and heights
	6333	* on the Earth.
	6334	*
	6335	* @param latitude
	6336	* The latitude of the observer in degrees north or south of the equator.
	6337	* By formula symmetry, positive latitudes give the same answer as negative
	6338	* latitudes, so the sign does not matter.
	6339	*
	6340	* @param height
	6341	* The height above the sea level geoid in meters.
	6342	* No range checking is done; however, accuracy is only valid in the
	6343	* range 0 to 100000 meters.
	6344	*
	6345	* @return
	6346	* The effective gravitational acceleration expressed in meters per second squared [m/s^2].
	6347	*/
	6348	double Astronomy_ObserverGravity(double latitude, double height)
	6349	{
	6350	double s = sin(latitude * DEG2RAD);
	6351	double s2 = s*s;
	6352	double g0 = 9.7803253359 * (1.0 + 0.00193185265241s2) / sqrt(1.0 - 0.00669437999013s2);
	6353	return g0 * (1.0 - (3.15704e-07 - 2.10269e-09s2)height + 7.37452e-14heightheight);
	6354	}
	6355
	6356
	6357	/**
	6358	* @brief Calculates the apparent location of a body relative to the local horizon of an observer on the Earth.
	6359	*
	6360	* Given a date and time, the geographic location of an observer on the Earth, and
	6361	* equatorial coordinates (right ascension and declination) of a celestial body,
	6362	* this function returns horizontal coordinates (azimuth and altitude angles) for the body
	6363	* relative to the horizon at the geographic location.
	6364	*
	6365	* The right ascension `ra` and declination `dec` passed in must be equator of date
	6366	* coordinates, based on the Earth's true equator at the date and time of the observation.
	6367	* Otherwise the resulting horizontal coordinates will be inaccurate.
	6368	* Equator of date coordinates can be obtained by calling #Astronomy_Equator, passing in
	6369	* `EQUATOR_OF_DATE` as its `equdate` parameter. It is also recommended to enable
	6370	* aberration correction by passing in `ABERRATION` as the `aberration` parameter.
	6371	*
	6372	* This function optionally corrects for atmospheric refraction.
	6373	* For most uses, it is recommended to pass `REFRACTION_NORMAL` in the `refraction` parameter to
	6374	* correct for optical lensing of the Earth's atmosphere that causes objects
	6375	* to appear somewhat higher above the horizon than they actually are.
	6376	* However, callers may choose to avoid this correction by passing in `REFRACTION_NONE`.
	6377	* If refraction correction is enabled, the azimuth, altitude, right ascension, and declination
	6378	* in the #astro_horizon_t structure returned by this function will all be corrected for refraction.
	6379	* If refraction is disabled, none of these four coordinates will be corrected; in that case,
	6380	* the right ascension and declination in the returned structure will be numerically identical
	6381	* to the respective `ra` and `dec` values passed in.
	6382	*
	6383	* @param time
	6384	* The date and time of the observation.
	6385	*
	6386	* @param observer
	6387	* The geographic location of the observer.
	6388	*
	6389	* @param ra
	6390	* The right ascension of the body in sidereal hours.
	6391	* See function remarks for more details.
	6392	*
	6393	* @param dec
	6394	* The declination of the body in degrees. See function remarks for more details.
	6395	*
	6396	* @param refraction
	6397	* Selects whether to correct for atmospheric refraction, and if so, which model to use.
	6398	* The recommended value for most uses is `REFRACTION_NORMAL`.
	6399	* See function remarks for more details.
	6400	*
	6401	* @return
	6402	* The body's apparent horizontal coordinates and equatorial coordinates, both optionally corrected for refraction.
	6403	*/
	6404	astro_horizon_t Astronomy_Horizon(
	6405	astro_time_t *time,
	6406	astro_observer_t observer,
	6407	double ra,
	6408	double dec,
	6409	astro_refraction_t refraction)
	6410	{
	6411	astro_horizon_t hor;
	6412	double latrad, lonrad, decrad, rarad;
	6413	double uze[3], une[3], uwe[3];
	6414	double uz[3], un[3], uw[3];
	6415	double p[3], pz, pn, pw, proj;
	6416	double az, zd;
	6417	double spin_angle;
	6418
	6419	if (time == NULL)
	6420	{
	6421	/* The best we can do is return an invalid state. */
	6422	/* It would break external dependencies to expect them to check for errors. */
	6423	hor.altitude = NAN;
	6424	hor.azimuth = NAN;
	6425	hor.ra = NAN;
	6426	hor.dec = NAN;
	6427	return hor;
	6428	}
	6429
	6430	latrad = observer.latitude * DEG2RAD;
	6431	lonrad = observer.longitude * DEG2RAD;
	6432	decrad = dec * DEG2RAD;
	6433	rarad = ra * HOUR2RAD;
	6434
	6435	double sinlat = sin(latrad);
	6436	double coslat = cos(latrad);
	6437	double sinlon = sin(lonrad);
	6438	double coslon = cos(lonrad);
	6439	double sindc = sin(decrad);
	6440	double cosdc = cos(decrad);
	6441	double sinra = sin(rarad);
	6442	double cosra = cos(rarad);
	6443
	6444	/*
	6445	Calculate three mutually perpendicular unit vectors
	6446	in equatorial coordinates: uze, une, uwe.
	6447
	6448	uze = The direction of the observer's local zenith (straight up).
	6449	une = The direction toward due north on the observer's horizon.
	6450	uwe = The direction toward due west on the observer's horizon.
	6451
	6452	HOWEVER, these are uncorrected for the Earth's rotation due to the time of day.
	6453
	6454	The components of these 3 vectors are as follows:
	6455	[0] = x = direction from center of Earth toward 0 degrees longitude (the prime meridian) on equator.
	6456	[1] = y = direction from center of Earth toward 90 degrees west longitude on equator.
	6457	[2] = z = direction from center of Earth toward the north pole.
	6458	*/
	6459
	6460	uze[0] = coslat * coslon;
	6461	uze[1] = coslat * sinlon;
	6462	uze[2] = sinlat;
	6463
	6464	une[0] = -sinlat * coslon;
	6465	une[1] = -sinlat * sinlon;
	6466	une[2] = coslat;
	6467
	6468	uwe[0] = sinlon;
	6469	uwe[1] = -coslon;
	6470	uwe[2] = 0.0;
	6471
	6472	/*
	6473	Correct the vectors uze, une, uwe for the Earth's rotation by calculating
	6474	sidereal time. Call spin() for each uncorrected vector to rotate about
	6475	the Earth's axis to yield corrected unit vectors uz, un, uw.
	6476	Multiply sidereal hours by -15 to convert to degrees and flip eastward
	6477	rotation of the Earth to westward apparent movement of objects with time.
	6478	*/
	6479
	6480	spin_angle = -15.0 * Astronomy_SiderealTime(time);
	6481	spin(spin_angle, uze, uz);
	6482	spin(spin_angle, une, un);
	6483	spin(spin_angle, uwe, uw);
	6484
	6485	/*
	6486	Convert angular equatorial coordinates (RA, DEC) to
	6487	cartesian equatorial coordinates in 'p', using the
	6488	same orientation system as uze, une, uwe.
	6489	*/
	6490
	6491	p[0] = cosdc * cosra;
	6492	p[1] = cosdc * sinra;
	6493	p[2] = sindc;
	6494
	6495	/*
	6496	Use dot products of p with the zenith, north, and west
	6497	vectors to obtain the cartesian coordinates of the body in
	6498	the observer's horizontal orientation system.
	6499
	6500	pn = north component [-1, +1]
	6501	pw = west component [-1, +1]
	6502	pz = zenith component [-1, +1]
	6503	*/
	6504
	6505	pn = p[0]un[0] + p[1]un[1] + p[2]*un[2];
	6506	pw = p[0]uw[0] + p[1]uw[1] + p[2]*uw[2];
	6507	pz = p[0]uz[0] + p[1]uz[1] + p[2]*uz[2];
	6508
	6509	/* proj is the "shadow" of the body vector along the observer's flat ground. */
	6510	proj = hypot(pn, pw);
	6511	if (proj > 0.0)
	6512	{
	6513	/* If the body is not exactly straight up/down, it has an azimuth. */
	6514	/* Invert the angle to produce degrees eastward from north. */
	6515	az = -atan2(pw, pn) * RAD2DEG;
	6516	if (az < 0.0)
	6517	az += 360;
	6518	}
	6519	else
	6520	{
	6521	/* The body is straight up/down, so it does not have an azimuth. */
	6522	/* Report an arbitrary but reasonable value. */
	6523	az = 0.0;
	6524	}
	6525
	6526	/* zd = the angle of the body away from the observer's zenith, in degrees. */
	6527	zd = atan2(proj, pz) * RAD2DEG;
	6528	hor.ra = ra;
	6529	hor.dec = dec;
	6530
	6531	if (refraction == REFRACTION_NORMAL \|\| refraction == REFRACTION_JPLHOR)
	6532	{
	6533	double zd0, refr;
	6534
	6535	zd0 = zd;
	6536	refr = Astronomy_Refraction(refraction, 90.0 - zd);
	6537	zd -= refr;
	6538
	6539	if (refr > 0.0 && zd > 3.0e-4)
	6540	{
	6541	int j;
	6542	double sinzd = sin(zd * DEG2RAD);
	6543	double coszd = cos(zd * DEG2RAD);
	6544	double sinzd0 = sin(zd0 * DEG2RAD);
	6545	double coszd0 = cos(zd0 * DEG2RAD);
	6546	double pr[3];
	6547
	6548	for (j=0; j<3; ++j)
	6549	pr[j] = ((p[j] - coszd0 * uz[j]) / sinzd0)sinzd + uz[j]coszd;
	6550
	6551	proj = hypot(pr[0], pr[1]);
	6552	if (proj > 0)
	6553	{
	6554	hor.ra = RAD2HOUR * atan2(pr[1], pr[0]);
	6555	if (hor.ra < 0.0)
	6556	hor.ra += 24.0;
	6557	}
	6558	else
	6559	{
	6560	hor.ra = 0.0;
	6561	}
	6562	hor.dec = RAD2DEG * atan2(pr[2], proj);
	6563	}
	6564	}
	6565
	6566	hor.azimuth = az;
	6567	hor.altitude = 90.0 - zd;
	6568	return hor;
	6569	}
	6570
	6571	/**
	6572	* @brief Calculates geocentric ecliptic coordinates for the Sun.
	6573	*
	6574	* This function calculates the position of the Sun as seen from the Earth.
	6575	* The returned value includes both Cartesian and spherical coordinates.
	6576	* The x-coordinate and longitude values in the returned structure are based
	6577	* on the true equinox of date: one of two points in the sky where the instantaneous
	6578	* plane of the Earth's equator at the given date and time (the equatorial plane)
	6579	* intersects with the plane of the Earth's orbit around the Sun (the ecliptic plane).
	6580	* By convention, the apparent location of the Sun at the March equinox is chosen
	6581	* as the longitude origin and x-axis direction, instead of the one for September.
	6582	*
	6583	* `Astronomy_SunPosition` corrects for precession and nutation of the Earth's axis
	6584	* in order to obtain the exact equatorial plane at the given time.
	6585	*
	6586	* This function can be used for calculating changes of seasons: equinoxes and solstices.
	6587	* In fact, the function #Astronomy_Seasons does use this function for that purpose.
	6588	*
	6589	* @param time
	6590	* The date and time for which to calculate the Sun's position.
	6591	*
	6592	* @return
	6593	* The ecliptic coordinates of the Sun using the Earth's true equator of date.
	6594	*/
	6595	astro_ecliptic_t Astronomy_SunPosition(astro_time_t time)
	6596	{
	6597	astro_time_t adjusted_time;
	6598	astro_vector_t earth2000;
	6599	double sun2000[3];
	6600	double stemp[3];
	6601	double sun_ofdate[3];
	6602	double true_obliq;
	6603
	6604	/* Correct for light travel time from the Sun. */
	6605	/* Otherwise season calculations (equinox, solstice) will all be early by about 8 minutes! */
	6606	adjusted_time = Astronomy_AddDays(time, -1.0 / C_AUDAY);
	6607
	6608	earth2000 = CalcEarth(adjusted_time);
	6609	if (earth2000.status != ASTRO_SUCCESS)
	6610	return EclError(earth2000.status);
	6611
	6612	/* Convert heliocentric location of Earth to geocentric location of Sun. */
	6613	sun2000[0] = -earth2000.x;
	6614	sun2000[1] = -earth2000.y;
	6615	sun2000[2] = -earth2000.z;
	6616
	6617	/* Convert to equatorial Cartesian coordinates of date. */
	6618	precession(sun2000, adjusted_time, FROM_2000, stemp);
	6619	nutation(stemp, &adjusted_time, FROM_2000, sun_ofdate);
	6620
	6621	/* Convert equatorial coordinates to ecliptic coordinates. */
	6622	true_obliq = DEG2RAD * e_tilt(&adjusted_time).tobl;
	6623	return RotateEquatorialToEcliptic(sun_ofdate, true_obliq, time);
	6624	}
	6625
	6626	/**
	6627	* @brief Converts a J2000 mean equator (EQJ) vector to a true ecliptic of date (ETC) vector and angles.
	6628	*
	6629	* Given coordinates relative to the Earth's equator at J2000 (the instant of noon UTC
	6630	* on 1 January 2000), this function converts those coordinates to true ecliptic coordinates
	6631	* that are relative to the plane of the Earth's orbit around the Sun on that date.
	6632	*
	6633	* @param eqj
	6634	* Equatorial coordinates in the EQJ frame of reference.
	6635	* You can call #Astronomy_GeoVector to obtain suitable equatorial coordinates.
	6636	*
	6637	* @return
	6638	* Spherical and vector coordinates expressed in true ecliptic coordinates of date (ECT).
	6639	*/
	6640	astro_ecliptic_t Astronomy_Ecliptic(astro_vector_t eqj)
	6641	{
	6642	earth_tilt_t et;
	6643	double eqj_pos[3];
	6644	double mean_pos[3];
	6645	double eqd_pos[3];
	6646
	6647	if (eqj.status != ASTRO_SUCCESS)
	6648	return EclError(eqj.status);
	6649
	6650	/* Calculate nutation and obliquity for this time. */
	6651	/* As an optimization, the nutation angles are cached in `time`, */
	6652	/* and reused below when the `nutation` function is called. */
	6653	et = e_tilt(&eqj.t);
	6654
	6655	/* Convert mean J2000 equator (EQJ) to true equator of date (EQD). */
	6656	eqj_pos[0] = eqj.x;
	6657	eqj_pos[1] = eqj.y;
	6658	eqj_pos[2] = eqj.z;
	6659	precession(eqj_pos, eqj.t, FROM_2000, mean_pos);
	6660	nutation(mean_pos, &eqj.t, FROM_2000, eqd_pos);
	6661
	6662	/* Rotate from EQD to true ecliptic of date (ECT). */
	6663	return RotateEquatorialToEcliptic(eqd_pos, et.tobl * DEG2RAD, eqj.t);
	6664	}
	6665
	6666	/**
	6667	* @brief Calculates heliocentric ecliptic longitude of a body.
	6668	*
	6669	* This function calculates the angle around the plane of the Earth's orbit
	6670	* of a celestial body, as seen from the center of the Sun.
	6671	* The angle is measured prograde (in the direction of the Earth's orbit around the Sun)
	6672	* in degrees from the true equinox of date. The ecliptic longitude is always in the range [0, 360).
	6673	*
	6674	* @param body
	6675	* A body other than the Sun.
	6676	*
	6677	* @param time
	6678	* The date and time at which the body's ecliptic longitude is to be calculated.
	6679	*
	6680	* @return
	6681	* On success, returns a structure whose `status` is `ASTRO_SUCCESS` and whose
	6682	* `angle` holds the ecliptic longitude in degrees.
	6683	* On failure, `status` holds a value other than `ASTRO_SUCCESS`.
	6684	*/
	6685	astro_angle_result_t Astronomy_EclipticLongitude(astro_body_t body, astro_time_t time)
	6686	{
	6687	astro_vector_t hv;
	6688	astro_ecliptic_t eclip;
	6689	astro_angle_result_t result;
	6690
	6691	if (body == BODY_SUN)
	6692	return AngleError(ASTRO_INVALID_BODY); /* cannot calculate heliocentric longitude of the Sun */
	6693
	6694	hv = Astronomy_HelioVector(body, time);
	6695	eclip = Astronomy_Ecliptic(hv); /* checks for errors in hv, so we don't have to here */
	6696	if (eclip.status != ASTRO_SUCCESS)
	6697	return AngleError(eclip.status);
	6698
	6699	result.angle = eclip.elon;
	6700	result.status = ASTRO_SUCCESS;
	6701	return result;
	6702	}
	6703
	6704	static astro_ecliptic_t RotateEquatorialToEcliptic(const double pos[3], double obliq_radians, astro_time_t time)
	6705	{
	6706	astro_ecliptic_t ecl;
	6707	double cos_ob, sin_ob;
	6708	double xyproj;
	6709
	6710	cos_ob = cos(obliq_radians);
	6711	sin_ob = sin(obliq_radians);
	6712
	6713	ecl.vec.status = ASTRO_SUCCESS;
	6714	ecl.vec.t = time;
	6715	ecl.vec.x = +pos[0];
	6716	ecl.vec.y = +pos[1]cos_ob + pos[2]sin_ob;
	6717	ecl.vec.z = -pos[1]sin_ob + pos[2]cos_ob;
	6718
	6719	xyproj = hypot(ecl.vec.x, ecl.vec.y);
	6720	if (xyproj > 0.0)
	6721	{
	6722	ecl.elon = RAD2DEG * atan2(ecl.vec.y, ecl.vec.x);
	6723	if (ecl.elon < 0.0)
	6724	ecl.elon += 360.0;
	6725	}
	6726	else
	6727	ecl.elon = 0.0;
	6728
	6729	ecl.elat = RAD2DEG * atan2(ecl.vec.z, xyproj);
	6730	ecl.status = ASTRO_SUCCESS;
	6731	return ecl;
	6732	}
	6733
	6734	static astro_func_result_t sun_offset(void *context, astro_time_t time)
	6735	{
	6736	astro_func_result_t result;
	6737	double targetLon = ((double )context);
	6738	astro_ecliptic_t ecl = Astronomy_SunPosition(time);
	6739	if (ecl.status != ASTRO_SUCCESS)
	6740	return FuncError(ecl.status);
	6741	result.value = LongitudeOffset(ecl.elon - targetLon);
	6742	result.status = ASTRO_SUCCESS;
	6743	return result;
	6744	}
	6745
	6746	/**
	6747	* @brief
	6748	* Searches for the time when the Sun reaches an apparent ecliptic longitude as seen from the Earth.
	6749	*
	6750	* This function finds the moment in time, if any exists in the given time window,
	6751	* that the center of the Sun reaches a specific ecliptic longitude as seen from the center of the Earth.
	6752	*
	6753	* This function can be used to determine equinoxes and solstices.
	6754	* However, it is usually more convenient and efficient to call #Astronomy_Seasons
	6755	* to calculate all equinoxes and solstices for a given calendar year.
	6756	*
	6757	* The function searches the window of time specified by `startTime` and `startTime+limitDays`.
	6758	* The search will return an error if the Sun never reaches the longitude `targetLon` or
	6759	* if the window is so large that the longitude ranges more than 180 degrees within it.
	6760	* It is recommended to keep the window smaller than 10 days when possible.
	6761	*
	6762	* @param targetLon
	6763	* The desired ecliptic longitude in degrees, relative to the true equinox of date.
	6764	* This may be any value in the range [0, 360), although certain values have
	6765	* conventional meanings:
	6766	* 0 = March equinox, 90 = June solstice, 180 = September equinox, 270 = December solstice.
	6767	*
	6768	* @param startTime
	6769	* The date and time for starting the search for the desired longitude event.
	6770	*
	6771	* @param limitDays
	6772	* The real-valued number of days, which when added to `startTime`, limits the
	6773	* range of time over which the search looks.
	6774	* It is recommended to keep this value between 1 and 10 days.
	6775	* See function remarks for more details.
	6776	*
	6777	* @return
	6778	* If successful, the `status` field in the returned structure will contain `ASTRO_SUCCESS`
	6779	* and the `time` field will contain the date and time the Sun reaches the target longitude.
	6780	* Any other value indicates an error.
	6781	* See remarks in #Astronomy_Search (which this function calls) for more information about possible error codes.
	6782	*/
	6783	astro_search_result_t Astronomy_SearchSunLongitude(
	6784	double targetLon,
	6785	astro_time_t startTime,
	6786	double limitDays)
	6787	{
	6788	astro_time_t t2 = Astronomy_AddDays(startTime, limitDays);
	6789	return Astronomy_Search(sun_offset, &targetLon, startTime, t2, 0.01);
	6790	}
	6791
	6792	/** @cond DOXYGEN_SKIP */
	6793	#define CALLFUNC(f,t) \
	6794	do { \
	6795	funcres = func(context, (t)); \
	6796	if (funcres.status != ASTRO_SUCCESS) return SearchError(funcres.status); \
	6797	(f) = funcres.value; \
	6798	} while(0)
	6799	/** @endcond */
	6800
	6801	/**
	6802	* @brief Searches for a time at which a function's value increases through zero.
	6803	*
	6804	* Certain astronomy calculations involve finding a time when an event occurs.
	6805	* Often such events can be defined as the root of a function:
	6806	* the time at which the function's value becomes zero.
	6807	*
	6808	* `Astronomy_Search` finds the ascending root of a function: the time at which
	6809	* the function's value becomes zero while having a positive slope. That is, as time increases,
	6810	* the function transitions from a negative value, through zero at a specific moment,
	6811	* to a positive value later. The goal of the search is to find that specific moment.
	6812	*
	6813	* The search function is specified by two parameters: `func` and `context`.
	6814	* The `func` parameter is a pointer to the function itself, which accepts a time
	6815	* and a context containing any other arguments needed to evaluate the function.
	6816	* The `context` parameter supplies that context for the given search.
	6817	* As an example, a caller may wish to find the moment a celestial body reaches a certain
	6818	* ecliptic longitude. In that case, the caller might create a structure that contains
	6819	* an #astro_body_t member to specify the body and a `double` to hold the target longitude.
	6820	* The function would cast the pointer `context` passed in as a pointer to that structure type.
	6821	* It could subtract the target longitude from the actual longitude at a given time;
	6822	* thus the difference would equal zero at the moment in time the planet reaches the
	6823	* desired longitude.
	6824	*
	6825	* The `func` returns an #astro_func_result_t structure every time it is called.
	6826	* If the returned structure has a value of `status` other than `ASTRO_SUCCESS`,
	6827	* the search immediately fails and reports that same error code in the `status`
	6828	* returned by `Astronomy_Search`. Otherwise, `status` is `ASTRO_SUCCESS` and
	6829	* `value` is the value of the function, and the search proceeds until it either
	6830	* finds the ascending root or fails for some reason.
	6831	*
	6832	* The search calls `func` repeatedly to rapidly narrow in on any ascending
	6833	* root within the time window specified by `t1` and `t2`. The search never
	6834	* reports a solution outside this time window.
	6835	*
	6836	* `Astronomy_Search` uses a combination of bisection and quadratic interpolation
	6837	* to minimize the number of function calls. However, it is critical that the
	6838	* supplied time window be small enough that there cannot be more than one root
	6839	* (ascedning or descending) within it; otherwise the search can fail.
	6840	* Beyond that, it helps to make the time window as small as possible, ideally
	6841	* such that the function itself resembles a smooth parabolic curve within that window.
	6842	*
	6843	* If an ascending root is not found, or more than one root
	6844	* (ascending and/or descending) exists within the window `t1`..`t2`,
	6845	* the search will fail with status code `ASTRO_SEARCH_FAILURE`.
	6846	*
	6847	* If the search does not converge within 20 iterations, it will fail
	6848	* with status code `ASTRO_NO_CONVERGE`.
	6849	*
	6850	* @param func
	6851	* The function for which to find the time of an ascending root.
	6852	* See function remarks for more details.
	6853	*
	6854	* @param context
	6855	* Any ancillary data needed by the function `func` to calculate a value.
	6856	* The data type varies depending on the function passed in.
	6857	* For example, the function may involve a specific celestial body that
	6858	* must be specified somehow.
	6859	*
	6860	* @param t1
	6861	* The lower time bound of the search window.
	6862	* See function remarks for more details.
	6863	*
	6864	* @param t2
	6865	* The upper time bound of the search window.
	6866	* See function remarks for more details.
	6867	*
	6868	* @param dt_tolerance_seconds
	6869	* Specifies an amount of time in seconds within which a bounded ascending root
	6870	* is considered accurate enough to stop. A typical value is 1 second.
	6871	*
	6872	* @return
	6873	* If successful, the returned structure has `status` equal to `ASTRO_SUCCESS`
	6874	* and `time` set to a value within `dt_tolerance_seconds` of an ascending root.
	6875	* On success, the `time` value will always be in the inclusive range [`t1`, `t2`].
	6876	* If the search fails, `status` will be set to a value other than `ASTRO_SUCCESS`.
	6877	* See function remarks for more details.
	6878	*/
	6879	astro_search_result_t Astronomy_Search(
	6880	astro_search_func_t func,
	6881	void *context,
	6882	astro_time_t t1,
	6883	astro_time_t t2,
	6884	double dt_tolerance_seconds)
	6885	{
	6886	astro_search_result_t result;
	6887	astro_time_t tmid;
	6888	astro_time_t tq;
	6889	astro_func_result_t funcres;
	6890	double f1, f2, fmid=0.0, fq, dt_days, dt, dt_guess;
	6891	double q_ut, q_df_dt;
	6892	const int iter_limit = 20;
	6893	int iter = 0;
	6894	int calc_fmid = 1;
	6895
	6896	dt_days = fabs(dt_tolerance_seconds / SECONDS_PER_DAY);
	6897	CALLFUNC(f1, t1);
	6898	CALLFUNC(f2, t2);
	6899
	6900	for(;;)
	6901	{
	6902	if (++iter > iter_limit)
	6903	return SearchError(ASTRO_NO_CONVERGE);
	6904
	6905	dt = (t2.tt - t1.tt) / 2.0;
	6906	tmid = Astronomy_AddDays(t1, dt);
	6907	if (fabs(dt) < dt_days)
	6908	{
	6909	/* We are close enough to the event to stop the search. */
	6910	result.time = tmid;
	6911	result.status = ASTRO_SUCCESS;
	6912	return result;
	6913	}
	6914
	6915	if (calc_fmid)
	6916	CALLFUNC(fmid, tmid);
	6917	else
	6918	calc_fmid = 1; /* we already have the correct value of fmid from the previous loop */
	6919
	6920	/* Quadratic interpolation: */
	6921	/* Try to find a parabola that passes through the 3 points we have sampled: */
	6922	/* (t1,f1), (tmid,fmid), (t2,f2) */
	6923
	6924	if (QuadInterp(tmid.ut, t2.ut - tmid.ut, f1, fmid, f2, &q_ut, &q_df_dt))
	6925	{
	6926	tq = Astronomy_TimeFromDays(q_ut);
	6927	CALLFUNC(fq, tq);
	6928	if (q_df_dt != 0.0)
	6929	{
	6930	dt_guess = fabs(fq / q_df_dt);
	6931	if (dt_guess < dt_days)
	6932	{
	6933	/* The estimated time error is small enough that we can quit now. */
	6934	result.time = tq;
	6935	result.status = ASTRO_SUCCESS;
	6936	return result;
	6937	}
	6938
	6939	/* Try guessing a tighter boundary with the interpolated root at the center. */
	6940	dt_guess *= 1.2;
	6941	if (dt_guess < dt/10.0)
	6942	{
	6943	astro_time_t tleft = Astronomy_AddDays(tq, -dt_guess);
	6944	astro_time_t tright = Astronomy_AddDays(tq, +dt_guess);
	6945	if ((tleft.ut - t1.ut)*(tleft.ut - t2.ut) < 0)
	6946	{
	6947	if ((tright.ut - t1.ut)*(tright.ut - t2.ut) < 0)
	6948	{
	6949	double fleft, fright;
	6950	CALLFUNC(fleft, tleft);
	6951	CALLFUNC(fright, tright);
	6952	if (fleft<0.0 && fright>=0.0)
	6953	{
	6954	f1 = fleft;
	6955	f2 = fright;
	6956	t1 = tleft;
	6957	t2 = tright;
	6958	fmid = fq;
	6959	calc_fmid = 0; /* save a little work -- no need to re-calculate fmid next time around the loop */
	6960	continue;
	6961	}
	6962	}
	6963	}
	6964	}
	6965	}
	6966	}
	6967
	6968	/* After quadratic interpolation attempt. */
	6969	/* Now just divide the region in two parts and pick whichever one appears to contain a root. */
	6970	if (f1 < 0.0 && fmid >= 0.0)
	6971	{
	6972	t2 = tmid;
	6973	f2 = fmid;
	6974	continue;
	6975	}
	6976
	6977	if (fmid < 0.0 && f2 >= 0.0)
	6978	{
	6979	t1 = tmid;
	6980	f1 = fmid;
	6981	continue;
	6982	}
	6983
	6984	/* Either there is no ascending zero-crossing in this range */
	6985	/* or the search window is too wide (more than one zero-crossing). */
	6986	return SearchError(ASTRO_SEARCH_FAILURE);
	6987	}
	6988	}
	6989
	6990	static int QuadInterp(
	6991	double tm, double dt, double fa, double fm, double fb,
	6992	double out_t, double out_df_dt)
	6993	{
	6994	double Q, R, S;
	6995	double x, u, ru, x1, x2;
	6996
	6997	Q = (fb + fa)/2.0 - fm;
	6998	R = (fb - fa)/2.0;
	6999	S = fm;
	7000
	7001	if (Q == 0.0)
	7002	{
	7003	/* This is a line, not a parabola. */
	7004	if (R == 0.0)
	7005	return 0; /* This is a HORIZONTAL line... can't make progress! */
	7006	x = -S / R;
	7007	if (x < -1.0 \|\| x > +1.0)
	7008	return 0; /* out of bounds */
	7009	}
	7010	else
	7011	{
	7012	/* This really is a parabola. Find roots x1, x2. */
	7013	u = RR - 4Q*S;
	7014	if (u <= 0.0)
	7015	return 0; /* can't solve if imaginary, or if vertex of parabola is tangent. */
	7016
	7017	ru = sqrt(u);
	7018	x1 = (-R + ru) / (2.0 * Q);
	7019	x2 = (-R - ru) / (2.0 * Q);
	7020	if (-1.0 <= x1 && x1 <= +1.0)
	7021	{
	7022	if (-1.0 <= x2 && x2 <= +1.0)
	7023	return 0; /* two roots are within bounds; we require a unique zero-crossing. */
	7024	x = x1;
	7025	}
	7026	else if (-1.0 <= x2 && x2 <= +1.0)
	7027	x = x2;
	7028	else
	7029	return 0; /* neither root is within bounds */
	7030	}
	7031
	7032	out_t = tm + xdt;
	7033	out_df_dt = (2Q*x + R) / dt;
	7034	return 1; /* success */
	7035	}
	7036
	7037	static astro_status_t FindSeasonChange(double targetLon, int year, int month, int day, astro_time_t *time)
	7038	{
	7039	astro_time_t startTime;
	7040	astro_search_result_t result;
	7041
	7042	startTime = Astronomy_MakeTime(year, month, day, 0, 0, 0.0);
	7043	result = Astronomy_SearchSunLongitude(targetLon, startTime, 20.0);
	7044	*time = result.time;
	7045	return result.status;
	7046	}
	7047
	7048	/**
	7049	* @brief Finds both equinoxes and both solstices for a given calendar year.
	7050	*
	7051	* The changes of seasons are defined by solstices and equinoxes.
	7052	* Given a calendar year number, this function calculates the
	7053	* March and September equinoxes and the June and December solstices.
	7054	*
	7055	* The equinoxes are the moments twice each year when the plane of the
	7056	* Earth's equator passes through the center of the Sun. In other words,
	7057	* the Sun's declination is zero at both equinoxes.
	7058	* The March equinox defines the beginning of spring in the northern hemisphere
	7059	* and the beginning of autumn in the southern hemisphere.
	7060	* The September equinox defines the beginning of autumn in the northern hemisphere
	7061	* and the beginning of spring in the southern hemisphere.
	7062	*
	7063	* The solstices are the moments twice each year when one of the Earth's poles
	7064	* is most tilted toward the Sun. More precisely, the Sun's declination reaches
	7065	* its minimum value at the December solstice, which defines the beginning of
	7066	* winter in the northern hemisphere and the beginning of summer in the southern
	7067	* hemisphere. The Sun's declination reaches its maximum value at the June solstice,
	7068	* which defines the beginning of summer in the northern hemisphere and the beginning
	7069	* of winter in the southern hemisphere.
	7070	*
	7071	* @param year
	7072	* The calendar year number for which to calculate equinoxes and solstices.
	7073	* The value may be any integer, but only the years 1800 through 2100 have been
	7074	* validated for accuracy: unit testing against data from the
	7075	* United States Naval Observatory confirms that all equinoxes and solstices
	7076	* for that range of years are within 2 minutes of the correct time.
	7077	*
	7078	* @return
	7079	* The times of the four seasonal changes in the given calendar year.
	7080	* This function should always succeed. However, to be safe, callers
	7081	* should check the `status` field of the returned structure to make sure
	7082	* it contains `ASTRO_SUCCESS`. Any failures indicate a bug in the algorithm
	7083	* and should be [reported as an issue](https://github.com/cosinekitty/astronomy/issues).
	7084	*/
	7085	astro_seasons_t Astronomy_Seasons(int year)
	7086	{
	7087	astro_seasons_t seasons;
	7088	astro_status_t status;
	7089
	7090	seasons.status = ASTRO_SUCCESS;
	7091
	7092	/*
	7093	https://github.com/cosinekitty/astronomy/issues/187
	7094	Solstices and equinoxes drift over long spans of time,
	7095	due to precession of the Earth's axis.
	7096	Therefore, we have to search a wider range of time than
	7097	one might expect. It turns out this has very little
	7098	effect on efficiency, thanks to the quick convergence
	7099	of quadratic interpolation inside Astronomy_Search().
	7100	*/
	7101
	7102	status = FindSeasonChange( 0, year, 3, 10, &seasons.mar_equinox);
	7103	if (status != ASTRO_SUCCESS) seasons.status = status;
	7104
	7105	status = FindSeasonChange( 90, year, 6, 10, &seasons.jun_solstice);
	7106	if (status != ASTRO_SUCCESS) seasons.status = status;
	7107
	7108	status = FindSeasonChange(180, year, 9, 10, &seasons.sep_equinox);
	7109	if (status != ASTRO_SUCCESS) seasons.status = status;
	7110
	7111	status = FindSeasonChange(270, year, 12, 10, &seasons.dec_solstice);
	7112	if (status != ASTRO_SUCCESS) seasons.status = status;
	7113
	7114	return seasons;
	7115	}
	7116
	7117	/**
	7118	* @brief Returns the angle between the given body and the Sun, as seen from the Earth.
	7119	*
	7120	* This function calculates the angular separation between the given body and the Sun,
	7121	* as seen from the center of the Earth. This angle is helpful for determining how
	7122	* easy it is to see the body away from the glare of the Sun.
	7123	*
	7124	* @param body
	7125	* The celestial body whose angle from the Sun is to be measured.
	7126	* Not allowed to be `BODY_EARTH`.
	7127	*
	7128	* @param time
	7129	* The time at which the observation is made.
	7130	*
	7131	* @return
	7132	* If successful, the returned structure contains `ASTRO_SUCCESS` in the `status` field
	7133	* and `angle` holds the angle in degrees between the Sun and the specified body as
	7134	* seen from the center of the Earth.
	7135	* If an error occurs, the `status` field contains a value other than `ASTRO_SUCCESS`
	7136	* that indicates the error condition.
	7137	*/
	7138	astro_angle_result_t Astronomy_AngleFromSun(astro_body_t body, astro_time_t time)
	7139	{
	7140	astro_vector_t sv, bv;
	7141
	7142	if (body == BODY_EARTH)
	7143	return AngleError(ASTRO_EARTH_NOT_ALLOWED);
	7144
	7145	sv = Astronomy_GeoVector(BODY_SUN, time, ABERRATION);
	7146	if (sv.status != ASTRO_SUCCESS)
	7147	return AngleError(sv.status);
	7148
	7149	bv = Astronomy_GeoVector(body, time, ABERRATION);
	7150	if (bv.status != ASTRO_SUCCESS)
	7151	return AngleError(bv.status);
	7152
	7153	return Astronomy_AngleBetween(sv, bv);
	7154	}
	7155
	7156	/**
	7157	* @brief
	7158	* Determines visibility of a celestial body relative to the Sun, as seen from the Earth.
	7159	*
	7160	* This function returns an #astro_elongation_t structure, which provides the following
	7161	* information about the given celestial body at the given time:
	7162	*
	7163	* - `visibility` is an enumerated type that specifies whether the body is more easily seen
	7164	* in the morning before sunrise, or in the evening after sunset.
	7165	*
	7166	* - `elongation` is the angle in degrees between two vectors: one from the center of the Earth to the
	7167	* center of the Sun, the other from the center of the Earth to the center of the specified body.
	7168	* This angle indicates how far away the body is from the glare of the Sun.
	7169	* The elongation angle is always in the range [0, 180].
	7170	*
	7171	* - `ecliptic_separation` is the absolute value of the difference between the body's ecliptic longitude
	7172	* and the Sun's ecliptic longitude, both as seen from the center of the Earth. This angle measures
	7173	* around the plane of the Earth's orbit, and ignores how far above or below that plane the body is.
	7174	* The ecliptic separation is measured in degrees and is always in the range [0, 180].
	7175	*
	7176	* @param body
	7177	* The celestial body whose visibility is to be calculated.
	7178	*
	7179	* @param time
	7180	* The date and time of the observation.
	7181	*
	7182	* @return
	7183	* If successful, the `status` field in the returned structure contains `ASTRO_SUCCESS`
	7184	* and all the other fields in the structure are valid. On failure, `status` contains
	7185	* some other value as an error code and the other fields contain invalid values.
	7186	*/
	7187	astro_elongation_t Astronomy_Elongation(astro_body_t body, astro_time_t time)
	7188	{
	7189	astro_elongation_t result;
	7190	astro_angle_result_t angres;
	7191
	7192	angres = Astronomy_PairLongitude(body, BODY_SUN, time);
	7193	if (angres.status != ASTRO_SUCCESS)
	7194	return ElongError(angres.status);
	7195
	7196	if (angres.angle > 180.0)
	7197	{
	7198	result.visibility = VISIBLE_MORNING;
	7199	result.ecliptic_separation = 360.0 - angres.angle;
	7200	}
	7201	else
	7202	{
	7203	result.visibility = VISIBLE_EVENING;
	7204	result.ecliptic_separation = angres.angle;
	7205	}
	7206
	7207	angres = Astronomy_AngleFromSun(body, time);
	7208	if (angres.status != ASTRO_SUCCESS)
	7209	return ElongError(angres.status);
	7210
	7211	result.elongation = angres.angle;
	7212	result.time = time;
	7213	result.status = ASTRO_SUCCESS;
	7214
	7215	return result;
	7216	}
	7217
	7218	static astro_func_result_t neg_elong_slope(void *context, astro_time_t time)
	7219	{
	7220	static const double dt = 0.1;
	7221	astro_angle_result_t e1, e2;
	7222	astro_func_result_t result;
	7223	astro_body_t body = ((astro_body_t )context);
	7224	astro_time_t t1 = Astronomy_AddDays(time, -dt/2.0);
	7225	astro_time_t t2 = Astronomy_AddDays(time, +dt/2.0);
	7226
	7227	e1 = Astronomy_AngleFromSun(body, t1);
	7228	if (e1.status != ASTRO_SUCCESS)
	7229	return FuncError(e1.status);
	7230
	7231	e2 = Astronomy_AngleFromSun(body, t2);
	7232	if (e2.status)
	7233	return FuncError(e2.status);
	7234
	7235	result.value = (e1.angle - e2.angle)/dt;
	7236	result.status = ASTRO_SUCCESS;
	7237	return result;
	7238	}
	7239
	7240	/**
	7241	* @brief
	7242	* Finds a date and time when Mercury or Venus reaches its maximum angle from the Sun as seen from the Earth.
	7243	*
	7244	* Mercury and Venus are are often difficult to observe because they are closer to the Sun than the Earth is.
	7245	* Mercury especially is almost always impossible to see because it gets lost in the Sun's glare.
	7246	* The best opportunities for spotting Mercury, and the best opportunities for viewing Venus through
	7247	* a telescope without atmospheric interference, are when these planets reach maximum elongation.
	7248	* These are events where the planets reach the maximum angle from the Sun as seen from the Earth.
	7249	*
	7250	* This function solves for those times, reporting the next maximum elongation event's date and time,
	7251	* the elongation value itself, the relative longitude with the Sun, and whether the planet is best
	7252	* observed in the morning or evening. See #Astronomy_Elongation for more details about the returned structure.
	7253	*
	7254	* @param body
	7255	* Either `BODY_MERCURY` or `BODY_VENUS`. Any other value will fail with the error `ASTRO_INVALID_BODY`.
	7256	* To find the best viewing opportunites for planets farther from the Sun than the Earth is (Mars through Pluto)
	7257	* use #Astronomy_SearchRelativeLongitude to find the next opposition event.
	7258	*
	7259	* @param startTime
	7260	* The date and time at which to begin the search. The maximum elongation event found will always
	7261	* be the first one that occurs after this date and time.
	7262	*
	7263	* @return
	7264	* If successful, the `status` field of the returned structure will be `ASTRO_SUCCESS`
	7265	* and the other structure fields will be valid. Otherwise, `status` will contain
	7266	* some other value indicating an error.
	7267	*/
	7268	astro_elongation_t Astronomy_SearchMaxElongation(astro_body_t body, astro_time_t startTime)
	7269	{
	7270	double s1, s2;
	7271	int iter;
	7272	astro_angle_result_t plon, elon;
	7273	astro_time_t t_start;
	7274	double rlon, rlon_lo, rlon_hi, adjust_days;
	7275	astro_func_result_t syn;
	7276	astro_search_result_t search1, search2, searchx;
	7277	astro_time_t t1, t2;
	7278	astro_func_result_t m1, m2;
	7279
	7280	/* Determine the range of relative longitudes within which maximum elongation can occur for this planet. */
	7281	switch (body)
	7282	{
	7283	case BODY_MERCURY:
	7284	s1 = 50.0;
	7285	s2 = 85.0;
	7286	break;
	7287
	7288	case BODY_VENUS:
	7289	s1 = 40.0;
	7290	s2 = 50.0;
	7291	break;
	7292
	7293	default:
	7294	/* SearchMaxElongation works for Mercury and Venus only. */
	7295	return ElongError(ASTRO_INVALID_BODY);
	7296	}
	7297
	7298	syn = SynodicPeriod(body);
	7299	if (syn.status != ASTRO_SUCCESS)
	7300	return ElongError(syn.status);
	7301
	7302	iter = 0;
	7303	while (++iter <= 2)
	7304	{
	7305	plon = Astronomy_EclipticLongitude(body, startTime);
	7306	if (plon.status != ASTRO_SUCCESS)
	7307	return ElongError(plon.status);
	7308
	7309	elon = Astronomy_EclipticLongitude(BODY_EARTH, startTime);
	7310	if (elon.status != ASTRO_SUCCESS)
	7311	return ElongError(elon.status);
	7312
	7313	rlon = LongitudeOffset(plon.angle - elon.angle); /* clamp to (-180, +180] */
	7314
	7315	/* The slope function is not well-behaved when rlon is near 0 degrees or 180 degrees */
	7316	/* because there is a cusp there that causes a discontinuity in the derivative. */
	7317	/* So we need to guard against searching near such times. */
	7318	if (rlon >= -s1 && rlon < +s1)
	7319	{
	7320	/* Seek to the window [+s1, +s2]. */
	7321	adjust_days = 0.0;
	7322	/* Search forward for the time t1 when rel lon = +s1. */
	7323	rlon_lo = +s1;
	7324	/* Search forward for the time t2 when rel lon = +s2. */
	7325	rlon_hi = +s2;
	7326	}
	7327	else if (rlon > +s2 \|\| rlon < -s2)
	7328	{
	7329	/* Seek to the next search window at [-s2, -s1]. */
	7330	adjust_days = 0.0;
	7331	/* Search forward for the time t1 when rel lon = -s2. */
	7332	rlon_lo = -s2;
	7333	/* Search forward for the time t2 when rel lon = -s1. */
	7334	rlon_hi = -s1;
	7335	}
	7336	else if (rlon >= 0.0)
	7337	{
	7338	/* rlon must be in the middle of the window [+s1, +s2]. */
	7339	/* Search BACKWARD for the time t1 when rel lon = +s1. */
	7340	adjust_days = -syn.value / 4.0;
	7341	rlon_lo = +s1;
	7342	rlon_hi = +s2;
	7343	/* Search forward from t1 to find t2 such that rel lon = +s2. */
	7344	}
	7345	else
	7346	{
	7347	/* rlon must be in the middle of the window [-s2, -s1]. */
	7348	/* Search BACKWARD for the time t1 when rel lon = -s2. */
	7349	adjust_days = -syn.value / 4.0;
	7350	rlon_lo = -s2;
	7351	/* Search forward from t1 to find t2 such that rel lon = -s1. */
	7352	rlon_hi = -s1;
	7353	}
	7354
	7355	t_start = Astronomy_AddDays(startTime, adjust_days);
	7356
	7357	search1 = Astronomy_SearchRelativeLongitude(body, rlon_lo, t_start);
	7358	if (search1.status != ASTRO_SUCCESS)
	7359	return ElongError(search1.status);
	7360	t1 = search1.time;
	7361
	7362	search2 = Astronomy_SearchRelativeLongitude(body, rlon_hi, t1);
	7363	if (search2.status != ASTRO_SUCCESS)
	7364	return ElongError(search2.status);
	7365	t2 = search2.time;
	7366
	7367	/* Now we have a time range [t1,t2] that brackets a maximum elongation event. */
	7368	/* Confirm the bracketing. */
	7369	m1 = neg_elong_slope(&body, t1);
	7370	if (m1.status != ASTRO_SUCCESS)
	7371	return ElongError(m1.status);
	7372
	7373	if (m1.value >= 0)
	7374	return ElongError(ASTRO_INTERNAL_ERROR); /* there is a bug in the bracketing algorithm! */
	7375
	7376	m2 = neg_elong_slope(&body, t2);
	7377	if (m2.status != ASTRO_SUCCESS)
	7378	return ElongError(m2.status);
	7379
	7380	if (m2.value <= 0)
	7381	return ElongError(ASTRO_INTERNAL_ERROR); /* there is a bug in the bracketing algorithm! */
	7382
	7383	/* Use the generic search algorithm to home in on where the slope crosses from negative to positive. */
	7384	searchx = Astronomy_Search(neg_elong_slope, &body, t1, t2, 10.0);
	7385	if (searchx.status != ASTRO_SUCCESS)
	7386	return ElongError(searchx.status);
	7387
	7388	if (searchx.time.tt >= startTime.tt)
	7389	return Astronomy_Elongation(body, searchx.time);
	7390
	7391	/* This event is in the past (earlier than startTime). */
	7392	/* We need to search forward from t2 to find the next possible window. */
	7393	/* We never need to search more than twice. */
	7394	startTime = Astronomy_AddDays(t2, 1.0);
	7395	}
	7396
	7397	return ElongError(ASTRO_SEARCH_FAILURE);
	7398	}
	7399
	7400
	7401	/**
	7402	* @brief Returns one body's ecliptic longitude with respect to another, as seen from the Earth.
	7403	*
	7404	* This function determines where one body appears around the ecliptic plane
	7405	* (the plane of the Earth's orbit around the Sun) as seen from the Earth,
	7406	* relative to the another body's apparent position.
	7407	* The function returns an angle in the half-open range [0, 360) degrees.
	7408	* The value is the ecliptic longitude of `body1` relative to the ecliptic
	7409	* longitude of `body2`.
	7410	*
	7411	* The angle is 0 when the two bodies are at the same ecliptic longitude
	7412	* as seen from the Earth. The angle increases in the prograde direction
	7413	* (the direction that the planets orbit the Sun and the Moon orbits the Earth).
	7414	*
	7415	* When the angle is 180 degrees, it means the two bodies appear on opposite sides
	7416	* of the sky for an Earthly observer.
	7417	*
	7418	* Neither `body1` nor `body2` is allowed to be `BODY_EARTH`.
	7419	* If this happens, the function fails with the error code `ASTRO_EARTH_NOT_ALLOWED`.
	7420	*
	7421	* @param body1
	7422	* The first body, whose longitude is to be found relative to the second body.
	7423	*
	7424	* @param body2
	7425	* The second body, relative to which the longitude of the first body is to be found.
	7426	*
	7427	* @param time
	7428	* The date and time of the observation.
	7429	*
	7430	* @return
	7431	* On success, the `status` field in the returned structure holds `ASTRO_SUCCESS` and
	7432	* the `angle` field holds a value in the range [0, 360).
	7433	* On failure, the `status` field contains some other value indicating an error condition.
	7434	*/
	7435	astro_angle_result_t Astronomy_PairLongitude(
	7436	astro_body_t body1,
	7437	astro_body_t body2,
	7438	astro_time_t time)
	7439	{
	7440	astro_vector_t vector1, vector2;
	7441	astro_ecliptic_t eclip1, eclip2;
	7442	astro_angle_result_t result;
	7443
	7444	if (body1 == BODY_EARTH \|\| body2 == BODY_EARTH)
	7445	return AngleError(ASTRO_EARTH_NOT_ALLOWED);
	7446
	7447	vector1 = Astronomy_GeoVector(body1, time, NO_ABERRATION);
	7448	eclip1 = Astronomy_Ecliptic(vector1); /* checks for errors in vector1 */
	7449	if (eclip1.status != ASTRO_SUCCESS)
	7450	return AngleError(eclip1.status);
	7451
	7452	vector2 = Astronomy_GeoVector(body2, time, NO_ABERRATION);
	7453	eclip2 = Astronomy_Ecliptic(vector2); /* checks for errors in vector2 */
	7454	if (eclip2.status != ASTRO_SUCCESS)
	7455	return AngleError(eclip2.status);
	7456
	7457	result.status = ASTRO_SUCCESS;
	7458	result.angle = NormalizeLongitude(eclip1.elon - eclip2.elon);
	7459	return result;
	7460	}
	7461
	7462
	7463	/**
	7464	* @brief
	7465	* Returns the Moon's phase as an angle from 0 to 360 degrees.
	7466	*
	7467	* This function determines the phase of the Moon using its apparent
	7468	* ecliptic longitude relative to the Sun, as seen from the center of the Earth.
	7469	* Certain values of the angle have conventional definitions:
	7470	*
	7471	* - 0 = new moon
	7472	* - 90 = first quarter
	7473	* - 180 = full moon
	7474	* - 270 = third quarter
	7475	*
	7476	* @param time
	7477	* The date and time of the observation.
	7478	*
	7479	* @return
	7480	* On success, the function returns the angle as described in the function remarks
	7481	* in the `angle` field and `ASTRO_SUCCESS` in the `status` field.
	7482	* The function should always succeed, but it is a good idea for callers to check
	7483	* the `status` field in the returned structure.
	7484	* Any other value in `status` indicates a failure that should be
	7485	* [reported as an issue](https://github.com/cosinekitty/astronomy/issues).
	7486	*/
	7487	astro_angle_result_t Astronomy_MoonPhase(astro_time_t time)
	7488	{
	7489	return Astronomy_PairLongitude(BODY_MOON, BODY_SUN, time);
	7490	}
	7491
	7492	static astro_func_result_t moon_offset(void *context, astro_time_t time)
	7493	{
	7494	astro_func_result_t result;
	7495	double targetLon = ((double )context);
	7496	astro_angle_result_t angres = Astronomy_MoonPhase(time);
	7497	if (angres.status != ASTRO_SUCCESS)
	7498	return FuncError(angres.status);
	7499	result.value = LongitudeOffset(angres.angle - targetLon);
	7500	result.status = ASTRO_SUCCESS;
	7501	return result;
	7502	}
	7503
	7504	/**
	7505	* @brief
	7506	* Searches for the time that the Moon reaches a specified phase.
	7507	*
	7508	* Lunar phases are conventionally defined in terms of the Moon's geocentric ecliptic
	7509	* longitude with respect to the Sun's geocentric ecliptic longitude.
	7510	* When the Moon and the Sun have the same longitude, that is defined as a new moon.
	7511	* When their longitudes are 180 degrees apart, that is defined as a full moon.
	7512	*
	7513	* This function searches for any value of the lunar phase expressed as an
	7514	* angle in degrees in the range [0, 360).
	7515	*
	7516	* If you want to iterate through lunar quarters (new moon, first quarter, full moon, third quarter)
	7517	* it is much easier to call the functions #Astronomy_SearchMoonQuarter and #Astronomy_NextMoonQuarter.
	7518	* This function is useful for finding general phase angles outside those four quarters.
	7519	*
	7520	* @param targetLon
	7521	* The difference in geocentric longitude between the Sun and Moon
	7522	* that specifies the lunar phase being sought. This can be any value
	7523	* in the range [0, 360). Certain values have conventional names:
	7524	* 0 = new moon, 90 = first quarter, 180 = full moon, 270 = third quarter.
	7525	*
	7526	* @param startTime
	7527	* The beginning of the time window in which to search for the Moon reaching the specified phase.
	7528	*
	7529	* @param limitDays
	7530	* The number of days away from `startTime` that limits the time window for the search.
	7531	* If the value is negative, the search is performed into the past from `startTime`.
	7532	* Otherwise, the search is performed into the future from `startTime`.
	7533	*
	7534	* @return
	7535	* On success, the `status` field in the returned structure holds `ASTRO_SUCCESS` and
	7536	* the `time` field holds the date and time when the Moon reaches the target longitude.
	7537	* On failure, `status` holds some other value as an error code.
	7538	* One possible error code is `ASTRO_NO_MOON_QUARTER` if `startTime` and `limitDays`
	7539	* do not enclose the desired event. See remarks in #Astronomy_Search for other possible
	7540	* error codes.
	7541	*/
	7542	astro_search_result_t Astronomy_SearchMoonPhase(double targetLon, astro_time_t startTime, double limitDays)
	7543	{
	7544	/*
	7545	To avoid discontinuities in the moon_offset function causing problems,
	7546	we need to approximate when that function will next return 0.
	7547	We probe it with the start time and take advantage of the fact
	7548	that every lunar phase repeats roughly every 29.5 days.
	7549	There is a surprising uncertainty in the quarter timing,
	7550	due to the eccentricity of the moon's orbit.
	7551	I have seen more than 0.9 days away from the simple prediction.
	7552	To be safe, we take the predicted time of the event and search
	7553	+/-1.5 days around it (a 3-day wide window).
	7554	Return ASTRO_NO_MOON_QUARTER if the final result goes beyond limitDays after startTime.
	7555	*/
	7556	const double uncertainty = 1.5;
	7557	astro_func_result_t funcres;
	7558	double ya, est_dt, dt1, dt2;
	7559	astro_time_t t1, t2;
	7560
	7561	funcres = moon_offset(&targetLon, startTime);
	7562	if (funcres.status != ASTRO_SUCCESS)
	7563	return SearchError(funcres.status);
	7564
	7565	ya = funcres.value;
	7566	if (limitDays < 0.0)
	7567	{
	7568	/* Search backward in time. */
	7569	if (ya < 0.0) ya += 360.0;
	7570	est_dt = -(MEAN_SYNODIC_MONTH * ya) / 360.0;
	7571	dt1 = est_dt - uncertainty;
	7572	dt2 = est_dt + uncertainty;
	7573	if (dt2 < limitDays)
	7574	return SearchError(ASTRO_NO_MOON_QUARTER); /* not possible for moon phase to occur within specified window (too short) */
	7575	if (dt1 < limitDays)
	7576	dt1 = limitDays;
	7577	}
	7578	else
	7579	{
	7580	/* Search forward in time. */
	7581	if (ya > 0.0) ya -= 360.0;
	7582	est_dt = -(MEAN_SYNODIC_MONTH * ya) / 360.0;
	7583	dt1 = est_dt - uncertainty;
	7584	dt2 = est_dt + uncertainty;
	7585	if (dt1 > limitDays)
	7586	return SearchError(ASTRO_NO_MOON_QUARTER); /* not possible for moon phase to occur within specified window (too short) */
	7587	if (dt2 > limitDays)
	7588	dt2 = limitDays;
	7589	}
	7590	t1 = Astronomy_AddDays(startTime, dt1);
	7591	t2 = Astronomy_AddDays(startTime, dt2);
	7592	return Astronomy_Search(moon_offset, &targetLon, t1, t2, 0.1);
	7593	}
	7594
	7595	/**
	7596	* @brief
	7597	* Finds the first lunar quarter after the specified date and time.
	7598	*
	7599	* A lunar quarter is one of the following four lunar phase events:
	7600	* new moon, first quarter, full moon, third quarter.
	7601	* This function finds the lunar quarter that happens soonest
	7602	* after the specified date and time.
	7603	*
	7604	* To continue iterating through consecutive lunar quarters, call this function once,
	7605	* followed by calls to #Astronomy_NextMoonQuarter as many times as desired.
	7606	*
	7607	* @param startTime
	7608	* The date and time at which to start the search.
	7609	*
	7610	* @return
	7611	* This function should always succeed, indicated by the `status` field
	7612	* in the returned structure holding `ASTRO_SUCCESS`. Any other value indicates
	7613	* an internal error, which should be [reported as an issue](https://github.com/cosinekitty/astronomy/issues).
	7614	* To be safe, calling code should always check the `status` field for errors.
	7615	*/
	7616	astro_moon_quarter_t Astronomy_SearchMoonQuarter(astro_time_t startTime)
	7617	{
	7618	astro_moon_quarter_t mq;
	7619	astro_angle_result_t angres;
	7620	astro_search_result_t srchres;
	7621
	7622	/* Determine what the next quarter phase will be. */
	7623	angres = Astronomy_MoonPhase(startTime);
	7624	if (angres.status != ASTRO_SUCCESS)
	7625	return MoonQuarterError(angres.status);
	7626
	7627	mq.quarter = (1 + (int)floor(angres.angle / 90.0)) % 4;
	7628	srchres = Astronomy_SearchMoonPhase(90.0 * mq.quarter, startTime, 10.0);
	7629	if (srchres.status != ASTRO_SUCCESS)
	7630	return MoonQuarterError(srchres.status);
	7631
	7632	mq.status = ASTRO_SUCCESS;
	7633	mq.time = srchres.time;
	7634	return mq;
	7635	}
	7636
	7637	/**
	7638	* @brief
	7639	* Continues searching for lunar quarters from a previous search.
	7640	*
	7641	* After calling #Astronomy_SearchMoonQuarter, this function can be called
	7642	* one or more times to continue finding consecutive lunar quarters.
	7643	* This function finds the next consecutive moon quarter event after the one passed in as the parameter `mq`.
	7644	*
	7645	* @param mq
	7646	* A value returned by a prior call to #Astronomy_SearchMoonQuarter or #Astronomy_NextMoonQuarter.
	7647	*
	7648	* @return
	7649	* If `mq` is valid, this function should always succeed, indicated by the `status` field
	7650	* in the returned structure holding `ASTRO_SUCCESS`. Any other value indicates
	7651	* an internal error, which (after confirming that `mq` is valid) should be
	7652	* [reported as an issue](https://github.com/cosinekitty/astronomy/issues).
	7653	* To be safe, calling code should always check the `status` field for errors.
	7654	*/
	7655	astro_moon_quarter_t Astronomy_NextMoonQuarter(astro_moon_quarter_t mq)
	7656	{
	7657	astro_time_t time;
	7658	astro_moon_quarter_t next_mq;
	7659
	7660	if (mq.status != ASTRO_SUCCESS)
	7661	return MoonQuarterError(ASTRO_INVALID_PARAMETER);
	7662
	7663	/* Skip 6 days past the previous found moon quarter to find the next one. */
	7664	/* This is less than the minimum possible increment. */
	7665	/* So far I have seen the interval well contained by the range (6.5, 8.3) days. */
	7666
	7667	time = Astronomy_AddDays(mq.time, 6.0);
	7668	next_mq = Astronomy_SearchMoonQuarter(time);
	7669	if (next_mq.status == ASTRO_SUCCESS)
	7670	{
	7671	/* Verify that we found the expected moon quarter. */
	7672	if (next_mq.quarter != (1 + mq.quarter) % 4)
	7673	return MoonQuarterError(ASTRO_WRONG_MOON_QUARTER); /* internal error! we found the wrong moon quarter */
	7674	}
	7675	return next_mq;
	7676	}
	7677
	7678	static astro_func_result_t rlon_offset(astro_body_t body, astro_time_t time, int direction, double targetRelLon)
	7679	{
	7680	astro_func_result_t result;
	7681	astro_angle_result_t plon, elon;
	7682	double diff;
	7683
	7684	plon = Astronomy_EclipticLongitude(body, time);
	7685	if (plon.status != ASTRO_SUCCESS)
	7686	return FuncError(plon.status);
	7687
	7688	elon = Astronomy_EclipticLongitude(BODY_EARTH, time);
	7689	if (elon.status != ASTRO_SUCCESS)
	7690	return FuncError(elon.status);
	7691
	7692	diff = direction * (elon.angle - plon.angle);
	7693	result.value = LongitudeOffset(diff - targetRelLon);
	7694	result.status = ASTRO_SUCCESS;
	7695	return result;
	7696	}
	7697
	7698	/**
	7699	* @brief
	7700	* Searches for the time when the Earth and another planet are separated by a specified angle
	7701	* in ecliptic longitude, as seen from the Sun.
	7702	*
	7703	* A relative longitude is the angle between two bodies measured in the plane of the Earth's orbit
	7704	* (the ecliptic plane). The distance of the bodies above or below the ecliptic plane is ignored.
	7705	* If you imagine the shadow of the body cast onto the ecliptic plane, and the angle measured around
	7706	* that plane from one body to the other in the direction the planets orbit the Sun, you will get an
	7707	* angle somewhere between 0 and 360 degrees. This is the relative longitude.
	7708	*
	7709	* Given a planet other than the Earth in `body` and a time to start the search in `startTime`,
	7710	* this function searches for the next time that the relative longitude measured from the planet
	7711	* to the Earth is `targetRelLon`.
	7712	*
	7713	* Certain astronomical events are defined in terms of relative longitude between the Earth and another planet:
	7714	*
	7715	* - When the relative longitude is 0 degrees, it means both planets are in the same direction from the Sun.
	7716	* For planets that orbit closer to the Sun (Mercury and Venus), this is known as inferior conjunction,
	7717	* a time when the other planet becomes very difficult to see because of being lost in the Sun's glare.
	7718	* (The only exception is in the rare event of a transit, when we see the silhouette of the planet passing
	7719	* between the Earth and the Sun.)
	7720	*
	7721	* - When the relative longitude is 0 degrees and the other planet orbits farther from the Sun,
	7722	* this is known as opposition. Opposition is when the planet is closest to the Earth, and
	7723	* also when it is visible for most of the night, so it is considered the best time to observe the planet.
	7724	*
	7725	* - When the relative longitude is 180 degrees, it means the other planet is on the opposite side of the Sun
	7726	* from the Earth. This is called superior conjunction. Like inferior conjunction, the planet is
	7727	* very difficult to see from the Earth. Superior conjunction is possible for any planet other than the Earth.
	7728	*
	7729	* @param body
	7730	* A planet other than the Earth. If `body` is not a planet other than the Earth, an error occurs.
	7731	*
	7732	* @param targetRelLon
	7733	* The desired relative longitude, expressed in degrees. Must be in the range [0, 360).
	7734	*
	7735	* @param startTime
	7736	* The date and time at which to begin the search.
	7737	*
	7738	* @return
	7739	* If successful, the `status` field in the returned structure will contain `ASTRO_SUCCESS`
	7740	* and `time` will hold the date and time of the relative longitude event.
	7741	* Otherwise `status` will hold some other value that indicates an error condition.
	7742	*/
	7743	astro_search_result_t Astronomy_SearchRelativeLongitude(astro_body_t body, double targetRelLon, astro_time_t startTime)
	7744	{
	7745	astro_search_result_t result;
	7746	astro_func_result_t syn;
	7747	astro_func_result_t error_angle;
	7748	double prev_angle;
	7749	astro_time_t time;
	7750	int iter, direction;
	7751
	7752	if (body == BODY_EARTH)
	7753	return SearchError(ASTRO_EARTH_NOT_ALLOWED);
	7754
	7755	if (body == BODY_MOON \|\| body == BODY_SUN)
	7756	return SearchError(ASTRO_INVALID_BODY);
	7757
	7758	syn = SynodicPeriod(body);
	7759	if (syn.status != ASTRO_SUCCESS)
	7760	return SearchError(syn.status);
	7761
	7762	direction = IsSuperiorPlanet(body) ? +1 : -1;
	7763
	7764	/* Iterate until we converge on the desired event. */
	7765	/* Calculate the error angle, which will be a negative number of degrees, */
	7766	/* meaning we are "behind" the target relative longitude. */
	7767
	7768	error_angle = rlon_offset(body, startTime, direction, targetRelLon);
	7769	if (error_angle.status != ASTRO_SUCCESS)
	7770	return SearchError(error_angle.status);
	7771
	7772	if (error_angle.value > 0)
	7773	error_angle.value -= 360; /* force searching forward in time */
	7774
	7775	time = startTime;
	7776	for (iter = 0; iter < 100; ++iter)
	7777	{
	7778	/* Estimate how many days in the future (positive) or past (negative) */
	7779	/* we have to go to get closer to the target relative longitude. */
	7780	double day_adjust = (-error_angle.value/360.0) * syn.value;
	7781	time = Astronomy_AddDays(time, day_adjust);
	7782	if (fabs(day_adjust) * SECONDS_PER_DAY < 1.0)
	7783	{
	7784	result.time = time;
	7785	result.status = ASTRO_SUCCESS;
	7786	return result;
	7787	}
	7788
	7789	prev_angle = error_angle.value;
	7790	error_angle = rlon_offset(body, time, direction, targetRelLon);
	7791	if (error_angle.status != ASTRO_SUCCESS)
	7792	return SearchError(error_angle.status);
	7793
	7794	if (fabs(prev_angle) < 30.0 && (prev_angle != error_angle.value))
	7795	{
	7796	/* Improve convergence for Mercury/Mars (eccentric orbits) */
	7797	/* by adjusting the synodic period to more closely match the */
	7798	/* variable speed of both planets in this part of their respective orbits. */
	7799	double ratio = prev_angle / (prev_angle - error_angle.value);
	7800	if (ratio > 0.5 && ratio < 2.0)
	7801	syn.value *= ratio;
	7802	}
	7803	}
	7804
	7805	return SearchError(ASTRO_NO_CONVERGE);
	7806	}
	7807
	7808	/**
	7809	* @brief Searches for the time when the center of a body reaches a specified hour angle as seen by an observer on the Earth.
	7810	*
	7811	* The hour angle of a celestial body indicates its position in the sky with respect
	7812	* to the Earth's rotation. The hour angle depends on the location of the observer on the Earth.
	7813	* The hour angle is 0 when the body's center reaches its highest angle above the horizon in a given day.
	7814	* The hour angle increases by 1 unit for every sidereal hour that passes after that point, up
	7815	* to 24 sidereal hours when it reaches the highest point again. So the hour angle indicates
	7816	* the number of hours that have passed since the most recent time that the body has culminated,
	7817	* or reached its highest point.
	7818	*
	7819	* This function searches for the next or previous time a celestial body reaches the given hour angle
	7820	* relative to the date and time specified by `startTime`.
	7821	* To find when a body culminates, pass 0 for `hourAngle`.
	7822	* To find when a body reaches its lowest point in the sky, pass 12 for `hourAngle`.
	7823	*
	7824	* Note that, especially close to the Earth's poles, a body as seen on a given day
	7825	* may always be above the horizon or always below the horizon, so the caller cannot
	7826	* assume that a culminating object is visible nor that an object is below the horizon
	7827	* at its minimum altitude.
	7828	*
	7829	* On success, the function reports the date and time, along with the horizontal coordinates
	7830	* of the body at that time, as seen by the given observer.
	7831	*
	7832	* @param body
	7833	* The Sun, Moon, any planet other than the Earth,
	7834	* or a user-defined star that was created by a call to #Astronomy_DefineStar.
	7835	*
	7836	* @param observer
	7837	* Indicates a location on or near the surface of the Earth where the observer is located.
	7838	* Call #Astronomy_MakeObserver to create an observer structure.
	7839	*
	7840	* @param hourAngle
	7841	* An hour angle value in the range [0, 24) indicating the number of sidereal hours after the
	7842	* body's most recent culmination.
	7843	*
	7844	* @param startTime
	7845	* The date and time at which to start the search.
	7846	*
	7847	* @param direction
	7848	* The direction in time to perform the search: a positive value
	7849	* searches forward in time, a negative value searches backward in time.
	7850	* The function will fail with `ASTRO_INVALID_PARAMETER` if `direction` is zero.
	7851	*
	7852	* @return
	7853	* If successful, the `status` field in the returned structure holds `ASTRO_SUCCESS`
	7854	* and the other structure fields are valid. Otherwise, `status` holds some other value
	7855	* that indicates an error condition.
	7856	*/
	7857	astro_hour_angle_t Astronomy_SearchHourAngleEx(
	7858	astro_body_t body,
	7859	astro_observer_t observer,
	7860	double hourAngle,
	7861	astro_time_t startTime,
	7862	int direction)
	7863	{
	7864	int iter = 0;
	7865	astro_time_t time;
	7866	astro_equatorial_t ofdate;
	7867	astro_hour_angle_t result;
	7868	double delta_sidereal_hours, delta_days, gast;
	7869
	7870	if (body == BODY_EARTH)
	7871	return HourAngleError(ASTRO_EARTH_NOT_ALLOWED);
	7872
	7873	if (hourAngle < 0.0 \|\| hourAngle >= 24.0)
	7874	return HourAngleError(ASTRO_INVALID_PARAMETER);
	7875
	7876	if (direction == 0)
	7877	return HourAngleError(ASTRO_INVALID_PARAMETER);
	7878
	7879	time = startTime;
	7880	for(;;)
	7881	{
	7882	++iter;
	7883
	7884	/* Calculate Greenwich Apparent Sidereal Time (GAST) at the given time. */
	7885	gast = Astronomy_SiderealTime(&time);
	7886
	7887	/* Obtain equatorial coordinates of date for the body. */
	7888	ofdate = Astronomy_Equator(body, &time, observer, EQUATOR_OF_DATE, ABERRATION);
	7889	if (ofdate.status != ASTRO_SUCCESS)
	7890	return HourAngleError(ofdate.status);
	7891
	7892	/* Calculate the adjustment needed in sidereal time */
	7893	/* to bring the hour angle to the desired value. */
	7894
	7895	delta_sidereal_hours = fmod((hourAngle + ofdate.ra - observer.longitude/15) - gast, 24.0);
	7896	if (iter == 1)
	7897	{
	7898	/* On the first iteration, always search the requested time direction. */
	7899	if (direction > 0)
	7900	{
	7901	/* Search forward in time. */
	7902	if (delta_sidereal_hours < 0.0)
	7903	delta_sidereal_hours += 24.0;
	7904	}
	7905	else
	7906	{
	7907	/* Search backward in time. */
	7908	if (delta_sidereal_hours > 0.0)
	7909	delta_sidereal_hours -= 24.0;
	7910	}
	7911	}
	7912	else
	7913	{
	7914	/* On subsequent iterations, we make the smallest possible adjustment, */
	7915	/* either forward or backward in time. */
	7916	if (delta_sidereal_hours < -12.0)
	7917	delta_sidereal_hours += 24.0;
	7918	else if (delta_sidereal_hours > +12.0)
	7919	delta_sidereal_hours -= 24.0;
	7920	}
	7921
	7922	/* If the error is tolerable (less than 0.1 seconds), the search has succeeded. */
	7923	if (fabs(delta_sidereal_hours) * 3600.0 < 0.1)
	7924	{
	7925	result.hor = Astronomy_Horizon(&time, observer, ofdate.ra, ofdate.dec, REFRACTION_NORMAL);
	7926	result.time = time;
	7927	result.status = ASTRO_SUCCESS;
	7928	return result;
	7929	}
	7930
	7931	/* We need to loop another time to get more accuracy. */
	7932	/* Update the terrestrial time (in solar days) adjusting by sidereal time (sidereal hours). */
	7933	delta_days = (delta_sidereal_hours / 24.0) * SOLAR_DAYS_PER_SIDEREAL_DAY;
	7934	time = Astronomy_AddDays(time, delta_days);
	7935	}
	7936	}
	7937
	7938
	7939	/**
	7940	* @brief Finds the hour angle of a body for a given observer and time.
	7941	*
	7942	* The hour angle of a celestial body indicates its position in the sky with respect
	7943	* to the Earth's rotation. The hour angle depends on the location of the observer on the Earth.
	7944	* The hour angle is 0 when the body's center reaches its highest angle above the horizon in a given day.
	7945	* The hour angle increases by 1 unit for every sidereal hour that passes after that point, up
	7946	* to 24 sidereal hours when it reaches the highest point again. So the hour angle indicates
	7947	* the number of hours that have passed since the most recent time that the body has culminated,
	7948	* or reached its highest point.
	7949	*
	7950	* @param body
	7951	* The body whose observed hour angle is to be found.
	7952	*
	7953	* @param time
	7954	* The time of the observation.
	7955	*
	7956	* @param observer
	7957	* The geographic location where the observation takes place.
	7958	*
	7959	* @return astro_func_result_t
	7960	* If successful, the `status` field in the returned structure holds `ASTRO_SUCCESS`
	7961	* and `value` holds the hour angle in the half-open range [0, 24).
	7962	* Otherwise, `status` is an error code that indicates failure.
	7963	*/
	7964	astro_func_result_t Astronomy_HourAngle(astro_body_t body, astro_time_t *time, astro_observer_t observer)
	7965	{
	7966	astro_func_result_t result;
	7967	astro_equatorial_t ofdate;
	7968	double gast;
	7969
	7970	if (time == NULL)
	7971	return FuncError(ASTRO_INVALID_PARAMETER);
	7972
	7973	/* Calculate Greenwich Apparent Sidereal Time (GAST) at the given time. */
	7974	gast = Astronomy_SiderealTime(time);
	7975
	7976	/* Obtain equatorial coordinates of date for the body. */
	7977	ofdate = Astronomy_Equator(body, time, observer, EQUATOR_OF_DATE, ABERRATION);
	7978	if (ofdate.status != ASTRO_SUCCESS)
	7979	return FuncError(ofdate.status);
	7980
	7981	result.value = fmod(observer.longitude/15 + gast - ofdate.ra, 24.0);
	7982	if (result.value < 0.0)
	7983	result.value += 24.0;
	7984	result.status = ASTRO_SUCCESS;
	7985
	7986	return result;
	7987	}
	7988
	7989
	7990	/** @cond DOXYGEN_SKIP */
	7991
	7992	typedef struct
	7993	{
	7994	astro_body_t body;
	7995	int direction; // search option: +1 = rise, -1 = set
	7996	astro_observer_t observer;
	7997	double body_radius_au;
	7998	double target_altitude;
	7999	}
	8000	context_altitude_t;
	8001
	8002	static const double RISE_SET_DT = 0.42; /* 10.08 hours: Nyquist-safe for 22-hour period. */
	8003
	8004	typedef struct
	8005	{
	8006	astro_status_t status;
	8007	astro_time_t tx;
	8008	astro_time_t ty;
	8009	double ax;
	8010	double ay;
	8011	}
	8012	ascent_t;
	8013
	8014	int _AltitudeDiffCallCount;
	8015	int _FindAscentMaxRecursionDepth;
	8016
	8017	/** @endcond */
	8018
	8019	static astro_func_result_t altitude_diff(void *context, astro_time_t time)
	8020	{
	8021	astro_func_result_t result;
	8022	astro_equatorial_t ofdate;
	8023	astro_horizon_t hor;
	8024	double altitude;
	8025	const context_altitude_t p = (const context_altitude_t )context;
	8026
	8027	++_AltitudeDiffCallCount; /* for internal performance testing */
	8028
	8029	ofdate = Astronomy_Equator(p->body, &time, p->observer, EQUATOR_OF_DATE, ABERRATION);
	8030	if (ofdate.status != ASTRO_SUCCESS)
	8031	return FuncError(ofdate.status);
	8032
	8033	hor = Astronomy_Horizon(&time, p->observer, ofdate.ra, ofdate.dec, REFRACTION_NONE);
	8034	altitude = hor.altitude + RAD2DEG*asin(p->body_radius_au / ofdate.dist);
	8035	result.value = p->direction*(altitude - p->target_altitude);
	8036	result.status = ASTRO_SUCCESS;
	8037	return result;
	8038	}
	8039
	8040
	8041	static ascent_t AscentError(astro_status_t status)
	8042	{
	8043	ascent_t ascent;
	8044	ascent.ax = ascent.ay = NAN;
	8045	ascent.tx = ascent.ty = TimeError();
	8046	ascent.status = status;
	8047	return ascent;
	8048	}
	8049
	8050
	8051	static ascent_t FindAscent(
	8052	int depth,
	8053	context_altitude_t *context,
	8054	double max_deriv_alt,
	8055	astro_time_t t1,
	8056	astro_time_t t2,
	8057	double a1,
	8058	double a2)
	8059	{
	8060	ascent_t ascent;
	8061	double da, dt, abs_a1, abs_a2;
	8062	astro_time_t tm;
	8063	astro_func_result_t alt;
	8064
	8065	/* For internal performance testing. */
	8066	if (depth > _FindAscentMaxRecursionDepth)
	8067	_FindAscentMaxRecursionDepth = depth;
	8068
	8069	/* See if we can find any time interval where the altitude-diff function */
	8070	/* rises from non-positive to positive. */
	8071	/* Return ASTRO_SUCCESS if we do, ASTRO_SEARCH_FAILURE if we don't, or some other status for error cases. */
	8072
	8073	if (a1 < 0.0 && a2 >= 0.0)
	8074	{
	8075	/* Trivial success case: the endpoints already rise through zero. */
	8076	ascent.status = ASTRO_SUCCESS;
	8077	ascent.tx = t1;
	8078	ascent.ty = t2;
	8079	ascent.ax = a1;
	8080	ascent.ay = a2;
	8081	return ascent;
	8082	}
	8083
	8084	if (a1 >= 0.0 && a2 < 0.0)
	8085	{
	8086	/* Trivial failure case: Assume Nyquist condition prevents an ascent. */
	8087	return AscentError(ASTRO_SEARCH_FAILURE);
	8088	}
	8089
	8090	if (depth > 17)
	8091	{
	8092	/*
	8093	Safety valve: do not allow unlimited recursion.
	8094	This should never happen if the rest of the logic is working correctly,
	8095	so fail the whole search if it does happen. It's a bug!
	8096	*/
	8097	return AscentError(ASTRO_NO_CONVERGE);
	8098	}
	8099
	8100	/*
	8101	Both altitudes are on the same side of zero: both are negative, or both are non-negative.
	8102	There could be a convex "hill" or a concave "valley" that passes through zero.
	8103	In polar regions sometimes there is a rise/set or set/rise pair within minutes of each other.
	8104	For example, the Moon can be below the horizon, then the very top of it becomes
	8105	visible (moonrise) for a few minutes, then it moves sideways and down below
	8106	the horizon again (moonset). We want to catch these cases.
	8107	However, for efficiency and practicality concerns, because the rise/set search itself
	8108	has a 0.1 second threshold, we do not worry about rise/set pairs that are less than
	8109	one second apart. These are marginal cases that are rendered highly uncertain
	8110	anyway, due to unpredictable atmospheric refraction conditions (air temperature and pressure).
	8111	*/
	8112	dt = (t2.ut - t1.ut) / 2;
	8113	if (dt * SECONDS_PER_DAY < 1.0)
	8114	return AscentError(ASTRO_SEARCH_FAILURE);
	8115
	8116	/* Is it possible to reach zero from the altitude that is closer to zero? */
	8117	abs_a1 = fabs(a1);
	8118	abs_a2 = fabs(a2);
	8119	da = (abs_a1 < abs_a2) ? abs_a1 : abs_a2;
	8120
	8121	/*
	8122	Without loss of generality, assume \|a1\| <= \|a2\|.
	8123	(Reverse the argument in the case \|a2\| < \|a1\|.)
	8124	Imagine you have to "drive" from a1 to 0, then back to a2.
	8125	You can't go faster than max_deriv_alt. If you can't reach 0 in half the time,
	8126	you certainly don't have time to reach 0, turn around, and still make your way
	8127	back up to a2 (which is at least as far from 0 than a1 is) in the time interval dt.
	8128	Therefore, the time threshold is half the time interval, or dt/2.
	8129	*/
	8130	if (da > max_deriv_alt*(dt / 2))
	8131	{
	8132	/* Prune: the altitude cannot change fast enough to reach zero. */
	8133	return AscentError(ASTRO_SEARCH_FAILURE);
	8134	}
	8135
	8136	/* Bisect the time interval and evaluate the altitude at the midpoint. */
	8137	tm = Astronomy_TimeFromDays((t1.ut + t2.ut)/2);
	8138	alt = altitude_diff(context, tm);
	8139	if (alt.status != ASTRO_SUCCESS)
	8140	return AscentError(ASTRO_SEARCH_FAILURE);
	8141
	8142	/* Recurse to the left interval. */
	8143	ascent = FindAscent(1+depth, context, max_deriv_alt, t1, tm, a1, alt.value);
	8144	if (ascent.status == ASTRO_SEARCH_FAILURE)
	8145	{
	8146	/* Recurse to the right interval. */
	8147	ascent = FindAscent(1+depth, context, max_deriv_alt, tm, t2, alt.value, a2);
	8148	}
	8149
	8150	return ascent;
	8151	}
	8152
	8153
	8154	static astro_func_result_t MaxAltitudeSlope(astro_body_t body, double latitude)
	8155	{
	8156	astro_func_result_t result;
	8157	double deriv_ra, deriv_dec, latrad;
	8158
	8159	if (!isfinite(latitude) \|\| latitude < -90.0 \|\| latitude > +90.0)
	8160	{
	8161	result.value = NAN;
	8162	result.status = ASTRO_INVALID_PARAMETER;
	8163	return result;
	8164	}
	8165
	8166	/*
	8167	Calculate the maximum possible rate that this body's altitude
	8168	could change [degrees/day] as seen by this observer.
	8169	First use experimentally determined extreme bounds for this body
	8170	of how much topocentric RA and DEC can ever change per rate of time.
	8171	We need minimum possible d(RA)/dt, and maximum possible magnitude of d(DEC)/dt.
	8172	Conservatively, we round d(RA)/dt down, d(DEC)/dt up.
	8173	Then calculate the resulting maximum possible altitude change rate.
	8174	*/
	8175
	8176	switch (body)
	8177	{
	8178	case BODY_MOON:
	8179	deriv_ra = +4.5;
	8180	deriv_dec = +8.2;
	8181	break;
	8182
	8183	case BODY_SUN:
	8184	deriv_ra = +0.8;
	8185	deriv_dec = +0.5;
	8186	break;
	8187
	8188	case BODY_MERCURY:
	8189	deriv_ra = -1.6;
	8190	deriv_dec = +1.0;
	8191	break;
	8192
	8193	case BODY_VENUS:
	8194	deriv_ra = -0.8;
	8195	deriv_dec = +0.6;
	8196	break;
	8197
	8198	case BODY_MARS:
	8199	deriv_ra = -0.5;
	8200	deriv_dec = +0.4;
	8201	break;
	8202
	8203	case BODY_JUPITER:
	8204	case BODY_SATURN:
	8205	case BODY_URANUS:
	8206	case BODY_NEPTUNE:
	8207	case BODY_PLUTO:
	8208	deriv_ra = -0.2;
	8209	deriv_dec = +0.2;
	8210	break;
	8211
	8212	case BODY_EARTH:
	8213	result.value = NAN;
	8214	result.status = ASTRO_EARTH_NOT_ALLOWED;
	8215	return result;
	8216
	8217	default:
	8218	if (UserDefinedStar(body))
	8219	{
	8220	/*
	8221	The minimum allowed heliocentric distance of a user-defined star
	8222	is one light-year. This can cause a tiny amount of parallax (about 0.001 degrees).
	8223	Also, including stellar aberration (22 arcsec = 0.006 degrees), we provide a
	8224	generous safety buffer of 0.008 degrees.
	8225	*/
	8226	deriv_ra = -0.008;
	8227	deriv_dec = +0.008;
	8228	break;
	8229	}
	8230	result.value = NAN;
	8231	result.status = ASTRO_INVALID_BODY;
	8232	return result;
	8233	}
	8234
	8235	latrad = DEG2RAD * latitude;
	8236	result.value = fabs(((360.0 / SOLAR_DAYS_PER_SIDEREAL_DAY) - deriv_ra)cos(latrad)) + fabs(deriv_decsin(latrad));
	8237	result.status = isfinite(result.value) ? ASTRO_SUCCESS : ASTRO_INTERNAL_ERROR;
	8238	return result;
	8239	}
	8240
	8241
	8242	static astro_search_result_t InternalSearchAltitude(
	8243	astro_body_t body,
	8244	astro_observer_t observer,
	8245	astro_direction_t direction,
	8246	astro_time_t startTime,
	8247	double limitDays,
	8248	double bodyRadiusAu,
	8249	double targetAltitude)
	8250	{
	8251	astro_search_result_t search_result;
	8252	astro_func_result_t func_result;
	8253	context_altitude_t context;
	8254	ascent_t ascent;
	8255	astro_time_t t1, t2;
	8256	double a1, a2, max_deriv_alt;
	8257
	8258	if (!isfinite(targetAltitude) \|\| targetAltitude < -90.0 \|\| targetAltitude > +90.0)
	8259	return SearchError(ASTRO_INVALID_PARAMETER);
	8260
	8261	func_result = MaxAltitudeSlope(body, observer.latitude);
	8262	if (func_result.status != ASTRO_SUCCESS)
	8263	return SearchError(func_result.status);
	8264	max_deriv_alt = func_result.value;
	8265
	8266	context.body = body;
	8267	context.direction = (int)direction;
	8268	context.observer = observer;
	8269	context.body_radius_au = bodyRadiusAu;
	8270	context.target_altitude = targetAltitude;
	8271
	8272	/* We allow searching forward or backward in time. */
	8273	/* But we want to keep t1 < t2, so we need a few if/else statements. */
	8274	t1 = t2 = startTime;
	8275	func_result = altitude_diff(&context, t2);
	8276	if (func_result.status != ASTRO_SUCCESS)
	8277	return SearchError(func_result.status);
	8278	a1 = a2 = func_result.value;
	8279
	8280	for(;;)
	8281	{
	8282	if (limitDays < 0.0)
	8283	{
	8284	t1 = Astronomy_AddDays(t2, -RISE_SET_DT);
	8285	func_result = altitude_diff(&context, t1);
	8286	if (func_result.status != ASTRO_SUCCESS)
	8287	return SearchError(func_result.status);
	8288	a1 = func_result.value;
	8289	}
	8290	else
	8291	{
	8292	t2 = Astronomy_AddDays(t1, +RISE_SET_DT);
	8293	func_result = altitude_diff(&context, t2);
	8294	if (func_result.status != ASTRO_SUCCESS)
	8295	return SearchError(func_result.status);
	8296	a2 = func_result.value;
	8297	}
	8298
	8299	ascent = FindAscent(0, &context, max_deriv_alt, t1, t2, a1, a2);
	8300	if (ascent.status == ASTRO_SUCCESS)
	8301	{
	8302	/* We found a time interval [t1, t2] that contains an alt-diff */
	8303	/* rising from negative a1 to non-negative a2. */
	8304	/* Search for the time where the root occurs. */
	8305	search_result = Astronomy_Search(altitude_diff, &context, ascent.tx, ascent.ty, 0.1);
	8306	if (search_result.status == ASTRO_SUCCESS)
	8307	{
	8308	/* Now that we have a solution, we have to check whether it goes outside the time bounds. */
	8309	if (limitDays < 0.0)
	8310	{
	8311	if (search_result.time.ut < startTime.ut + limitDays)
	8312	return SearchError(ASTRO_SEARCH_FAILURE);
	8313	}
	8314	else
	8315	{
	8316	if (search_result.time.ut > startTime.ut + limitDays)
	8317	return SearchError(ASTRO_SEARCH_FAILURE);
	8318	}
	8319	return search_result; /* success! */
	8320	}
	8321
	8322	/* The search should have succeeded. Something is wrong with FindAscent! */
	8323	return SearchError(ASTRO_INTERNAL_ERROR);
	8324	}
	8325	else if (ascent.status == ASTRO_SEARCH_FAILURE)
	8326	{
	8327	/* There is no ascent in this interval, so keep searching. */
	8328	}
	8329	else
	8330	{
	8331	/* An unexpected error occurred. Fail the search. */
	8332	return SearchError(ascent.status);
	8333	}
	8334
	8335	if (limitDays < 0.0)
	8336	{
	8337	if (t1.ut < startTime.ut + limitDays)
	8338	return SearchError(ASTRO_SEARCH_FAILURE);
	8339	t2 = t1;
	8340	a2 = a1;
	8341	}
	8342	else
	8343	{
	8344	if (t2.ut > startTime.ut + limitDays)
	8345	return SearchError(ASTRO_SEARCH_FAILURE);
	8346	t1 = t2;
	8347	a1 = a2;
	8348	}
	8349	}
	8350	}
	8351
	8352
	8353	/**
	8354	* @brief Calculates U.S. Standard Atmosphere (1976) variables as a function of elevation.
	8355	*
	8356	* This function calculates idealized values of pressure, temperature, and density
	8357	* using the U.S. Standard Atmosphere (1976) model.
	8358	*
	8359	* See:
	8360	* https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml
	8361	* https://ntrs.nasa.gov/api/citations/19770009539/downloads/19770009539.pdf
	8362	* https://www.ngdc.noaa.gov/stp/space-weather/online-publications/miscellaneous/us-standard-atmosphere-1976/us-standard-atmosphere_st76-1562_noaa.pdf
	8363	*
	8364	* @param elevationMeters
	8365	* The elevation above sea level at which to calculate atmospheric variables.
	8366	* The value must be at least -500 to +100000, or the function will
	8367	* fail with status `ASTRO_INVALID_PARAMETER`.
	8368	*
	8369	* @return astro_atmosphere_tp0
	8370	*/
	8371	astro_atmosphere_t Astronomy_Atmosphere(double elevationMeters)
	8372	{
	8373	astro_atmosphere_t atmos;
	8374	const double P0 = 101325.0; /* pressure at sea level [pascals] */
	8375	const double T0 = 288.15; /* temperature at sea level [kelvins] */
	8376	const double T1 = 216.65; /* temperature between 20 km and 32 km [kelvins] */
	8377
	8378	/*
	8379	Formulas for air temperature and pressure at a height of `h` meters
	8380	were found at:
	8381	https://hbcp.chemnetbase.com/faces/documents/14_12/14_12_0001.xhtml
	8382
	8383	These in turn come from:
	8384	1. COESA, U.S. Standard Atmosphere, 1976, U.S. Government Printing Office, Washington, DC, 1976.
	8385	2. Jursa, A. S., Ed., Handbook of Geophysics and the Space Environment, Air Force Geophysics Laboratory, 1985.
	8386	*/
	8387
	8388	if (!isfinite(elevationMeters) \|\| elevationMeters < -500.0 \|\| elevationMeters > 100000.0)
	8389	{
	8390	/* Invalid elevation. */
	8391	atmos.status = ASTRO_INVALID_PARAMETER;
	8392	atmos.pressure = atmos.temperature = atmos.density = NAN;
	8393	}
	8394	else
	8395	{
	8396	if (elevationMeters <= 11000.0)
	8397	{
	8398	atmos.temperature = T0 - 0.0065*elevationMeters;
	8399	atmos.pressure = P0 * pow(T0 / atmos.temperature, -5.25577);
	8400	}
	8401	else if (elevationMeters <= 20000.0)
	8402	{
	8403	atmos.temperature = T1;
	8404	atmos.pressure = 22632.0 * exp(-0.00015768832 * (elevationMeters - 11000.0));
	8405	}
	8406	else
	8407	{
	8408	atmos.temperature = T1 + 0.001*(elevationMeters - 20000.0);
	8409	atmos.pressure = 5474.87 * pow(T1 / atmos.temperature, 34.16319);
	8410	}
	8411	/* The density is calculated relative to the sea level value. */
	8412	/* Using the ideal gas law PV=nRT, we deduce that density is proportional to P/T. */
	8413	atmos.density = (atmos.pressure / atmos.temperature) / (P0 / T0);
	8414	atmos.status = ASTRO_SUCCESS;
	8415	}
	8416
	8417	return atmos;
	8418	}
	8419
	8420
	8421	static double HorizonDipAngle(
	8422	astro_observer_t observer,
	8423	double metersAboveGround)
	8424	{
	8425	double phi, sinphi, cosphi, c, s, ht_km, ach, ash, radius_m;
	8426	double k, dip;
	8427
	8428	/* Calculate the effective radius of the Earth at ground level below the observer. */
	8429	/* Correct for the Earth's oblateness. */
	8430	phi = observer.latitude * DEG2RAD;
	8431	sinphi = sin(phi);
	8432	cosphi = cos(phi);
	8433	c = 1.0 / hypot(cosphi, sinphi*EARTH_FLATTENING);
	8434	s = c * (EARTH_FLATTENING * EARTH_FLATTENING);
	8435	ht_km = (observer.height - metersAboveGround) / 1000.0; /* height of ground above sea level */
	8436	ach = EARTH_EQUATORIAL_RADIUS_KM*c + ht_km;
	8437	ash = EARTH_EQUATORIAL_RADIUS_KM*s + ht_km;
	8438	radius_m = 1000.0 * hypot(achcosphi, ashsinphi);
	8439
	8440	/*
	8441	Correct refraction of a ray of light traveling tangent to the Earth's surface.
	8442	Based on: https://www.largeformatphotography.info/sunmooncalc/SMCalc.js
	8443	which in turn derives from:
	8444	Sweer, John. 1938. The Path of a Ray of Light Tangent to the Surface of the Earth.
	8445	Journal of the Optical Society of America 28 (September):327-329.
	8446	*/
	8447
	8448	/* k = refraction index */
	8449	k = 0.175 * pow(1.0 - (6.5e-3/283.15)(observer.height - (2.0/3.0)metersAboveGround), 3.256);
	8450
	8451	/* Calculate how far below the observer's horizontal plane the observed horizon dips. */
	8452	dip = RAD2DEG * -(sqrt(2(1 - k)metersAboveGround / radius_m) / (1 - k));
	8453	return dip;
	8454	}
	8455
	8456
	8457
	8458	/**
	8459	* @brief Searches for the next time a celestial body rises or sets as seen by an observer on the Earth.
	8460	*
	8461	* This function finds the next rise or set time of the Sun, Moon, or planet other than the Earth.
	8462	* Rise time is when the body first starts to be visible above the horizon.
	8463	* For example, sunrise is the moment that the top of the Sun first appears to peek above the horizon.
	8464	* Set time is the moment when the body appears to vanish below the horizon.
	8465	* Therefore, this function adjusts for the apparent angular radius of the observed body
	8466	* (significant only for the Sun and Moon).
	8467	*
	8468	* This function corrects for a typical value of atmospheric refraction, which causes celestial
	8469	* bodies to appear higher above the horizon than they would if the Earth had no atmosphere.
	8470	* Astronomy Engine uses a correction of 34 arcminutes. Real-world refraction varies based
	8471	* on air temperature, pressure, and humidity; such weather-based conditions are outside
	8472	* the scope of Astronomy Engine.
	8473	*
	8474	* Note that rise or set may not occur in every 24 hour period.
	8475	* For example, near the Earth's poles, there are long periods of time where
	8476	* the Sun stays below the horizon, never rising.
	8477	* Also, it is possible for the Moon to rise just before midnight but not set during the subsequent 24-hour day.
	8478	* This is because the Moon sets nearly an hour later each day due to orbiting the Earth a
	8479	* significant amount during each rotation of the Earth.
	8480	* Therefore callers must not assume that the function will always succeed.
	8481	*
	8482	* @param body
	8483	* The Sun, Moon, any planet other than the Earth,
	8484	* or a user-defined star that was created by a call to #Astronomy_DefineStar.
	8485	*
	8486	* @param observer
	8487	* The location where observation takes place.
	8488	* You can create an observer structure by calling #Astronomy_MakeObserver.
	8489	*
	8490	* @param direction
	8491	* Either `DIRECTION_RISE` to find a rise time or `DIRECTION_SET` to find a set time.
	8492	*
	8493	* @param startTime
	8494	* The date and time at which to start the search.
	8495	*
	8496	* @param limitDays
	8497	* Limits how many days to search for a rise or set time, and defines
	8498	* the direction in time to search. When `limitDays` is positive, the
	8499	* search is performed into the future, after `startTime`.
	8500	* When negative, the search is performed into the past, before `startTime`.
	8501	* To limit a rise or set time to the same day, you can use a value of 1 day.
	8502	* In cases where you want to find the next rise or set time no matter how far
	8503	* in the future (for example, for an observer near the south pole), you can
	8504	* pass in a larger value like 365.
	8505	*
	8506	* @param metersAboveGround
	8507	* Usually the observer is located at ground level. Then this parameter
	8508	* should be zero. But if the observer is significantly higher than ground
	8509	* level, for example in an airplane, this parameter should be a positive
	8510	* number indicating how far above the ground the observer is.
	8511	* An error occurs if `metersAboveGround` is negative.
	8512	*
	8513	* @return
	8514	* On success, the `status` field in the returned structure contains `ASTRO_SUCCESS`
	8515	* and the `time` field contains the date and time of the rise or set time as requested.
	8516	* If the `status` field contains `ASTRO_SEARCH_FAILURE`, it means the rise or set
	8517	* event does not occur within `limitDays` days of `startTime`. This is a normal condition,
	8518	* not an error. Any other value of `status` indicates an error of some kind.
	8519	*/
	8520	astro_search_result_t Astronomy_SearchRiseSetEx(
	8521	astro_body_t body,
	8522	astro_observer_t observer,
	8523	astro_direction_t direction,
	8524	astro_time_t startTime,
	8525	double limitDays,
	8526	double metersAboveGround)
	8527	{
	8528	double altitude, dip;
	8529	double body_radius_au;
	8530	astro_atmosphere_t atmos;
	8531
	8532	if (!isfinite(metersAboveGround) \|\| (metersAboveGround < 0.0))
	8533	return SearchError(ASTRO_INVALID_PARAMETER);
	8534
	8535	switch (body)
	8536	{
	8537	case BODY_SUN: body_radius_au = SUN_RADIUS_AU; break;
	8538	case BODY_MOON: body_radius_au = MOON_EQUATORIAL_RADIUS_AU; break;
	8539	default: body_radius_au = 0.0; break;
	8540	}
	8541
	8542	/* Calculate atmospheric density at ground level. */
	8543	atmos = Astronomy_Atmosphere(observer.height - metersAboveGround);
	8544	if (atmos.status != ASTRO_SUCCESS)
	8545	return SearchError(atmos.status);
	8546
	8547	/* Calculate the apparent angular dip of the horizon. */
	8548	dip = HorizonDipAngle(observer, metersAboveGround);
	8549
	8550	/* Correct refraction for objects near the horizon, using atmospheric density at the ground. */
	8551	altitude = dip - (REFRACTION_NEAR_HORIZON * atmos.density);
	8552
	8553	/* Search for the top of the body crossing the corrected altitude angle. */
	8554	return InternalSearchAltitude(body, observer, direction, startTime, limitDays, body_radius_au, altitude);
	8555	}
	8556
	8557
	8558	/**
	8559	* @brief Finds the next time the center of a body passes through a given altitude.
	8560	*
	8561	* Finds when the center of the given body ascends or descends through a given
	8562	* altitude angle, as seen by an observer at the specified location on the Earth.
	8563	* By using the appropriate combination of `direction` and `altitude` parameters,
	8564	* this function can be used to find when civil, nautical, or astronomical twilight
	8565	* begins (dawn) or ends (dusk).
	8566	*
	8567	* Civil dawn begins before sunrise when the Sun ascends through 6 degrees below
	8568	* the horizon. To find civil dawn, pass `DIRECTION_RISE` for `direction` and -6 for `altitude`.
	8569	*
	8570	* Civil dusk ends after sunset when the Sun descends through 6 degrees below the horizon.
	8571	* To find civil dusk, pass `DIRECTION_SET` for `direction` and -6 for `altitude`.
	8572	*
	8573	* Nautical twilight is similar to civil twilight, only the `altitude` value should be -12 degrees.
	8574	*
	8575	* Astronomical twilight uses -18 degrees as the `altitude` value.
	8576	*
	8577	* By convention for twilight time calculations, the altitude is not corrected for
	8578	* atmospheric refraction. This is because the target altitudes are below the horizon,
	8579	* and refraction is not directly observable.
	8580	*
	8581	* `Astronomy_SearchAltitude` is not intended to find rise/set times of a body for two reasons:
	8582	* (1) Rise/set times of the Sun or Moon are defined by their topmost visible portion, not their centers.
	8583	* (2) Rise/set times are affected significantly by atmospheric refraction.
	8584	* Therefore, it is better to use #Astronomy_SearchRiseSetEx to find rise/set times, which
	8585	* corrects for both of these considerations.
	8586	*
	8587	* `Astronomy_SearchAltitude` will not work reliably for altitudes at or near the body's
	8588	* maximum or minimum altitudes. To find the time a body reaches minimum or maximum altitude
	8589	* angles, use #Astronomy_SearchHourAngleEx.
	8590	*
	8591	* @param body
	8592	* The Sun, Moon, any planet other than the Earth,
	8593	* or a user-defined star that was created by a call to #Astronomy_DefineStar.
	8594	*
	8595	* @param observer
	8596	* The location where observation takes place.
	8597	* You can create an observer structure by calling #Astronomy_MakeObserver.
	8598	*
	8599	* @param direction
	8600	* Either `DIRECTION_RISE` to find when the body ascends through the altitude,
	8601	* or `DIRECTION_SET` for when the body descends through the altitude.
	8602	*
	8603	* @param startTime
	8604	* The date and time at which to start the search.
	8605	*
	8606	* @param limitDays
	8607	* Limits how many days to search for the body reaching the altitude angle,
	8608	* and defines the direction in time to search. When `limitDays` is positive, the
	8609	* search is performed into the future, after `startTime`.
	8610	* When negative, the search is performed into the past, before `startTime`.
	8611	* To limit the search to the same day, you can use a value of 1 day.
	8612	* In cases where you want to find the altitude event no matter how far
	8613	* in the future (for example, for an observer near the south pole), you can
	8614	* pass in a larger value like 365.
	8615	*
	8616	* @param altitude
	8617	* The desired altitude angle of the body's center above (positive)
	8618	* or below (negative) the observer's local horizon, expressed in degrees.
	8619	* Must be in the range [-90, +90].
	8620	*
	8621	* @return
	8622	* On success, the `status` field in the returned structure contains `ASTRO_SUCCESS`
	8623	* and the `time` field contains the date and time of the requested altitude event.
	8624	* If the `status` field contains `ASTRO_SEARCH_FAILURE`, it means the altitude
	8625	* event does not occur within `limitDays` days of `startTime`. This is a normal condition,
	8626	* not an error. Any other value of `status` indicates an error of some kind.
	8627	*/
	8628	astro_search_result_t Astronomy_SearchAltitude(
	8629	astro_body_t body,
	8630	astro_observer_t observer,
	8631	astro_direction_t direction,
	8632	astro_time_t startTime,
	8633	double limitDays,
	8634	double altitude)
	8635	{
	8636	return InternalSearchAltitude(body, observer, direction, startTime, limitDays, 0.0, altitude);
	8637	}
	8638
	8639
	8640	static double MoonMagnitude(double phase, double helio_dist, double geo_dist)
	8641	{
	8642	/* https://astronomy.stackexchange.com/questions/10246/is-there-a-simple-analytical-formula-for-the-lunar-phase-brightness-curve */
	8643	double rad = phase * DEG2RAD;
	8644	double rad2 = rad * rad;
	8645	double rad4 = rad2 * rad2;
	8646	double mag = -12.717 + 1.49fabs(rad) + 0.0431rad4;
	8647	double moon_mean_distance_au = 385000.6 / KM_PER_AU;
	8648	double geo_au = geo_dist / moon_mean_distance_au;
	8649	mag += 5log10(helio_dist geo_au);
	8650	return mag;
	8651	}
	8652
	8653	static astro_status_t SaturnMagnitude(
	8654	double phase,
	8655	double helio_dist,
	8656	double geo_dist,
	8657	astro_vector_t gc,
	8658	astro_time_t time,
	8659	double *mag,
	8660	double *ring_tilt)
	8661	{
	8662	astro_ecliptic_t eclip;
	8663	double ir, Nr, lat, lon, tilt, sin_tilt;
	8664
	8665	mag = ring_tilt = NAN;
	8666
	8667	/* Based on formulas by Paul Schlyter found here: */
	8668	/* http://www.stjarnhimlen.se/comp/ppcomp.html#15 */
	8669
	8670	/* We must handle Saturn's rings as a major component of its visual magnitude. */
	8671	/* Find geocentric ecliptic coordinates of Saturn. */
	8672	eclip = Astronomy_Ecliptic(gc);
	8673	if (eclip.status != ASTRO_SUCCESS)
	8674	return eclip.status;
	8675
	8676	ir = DEG2RAD * 28.06; /* tilt of Saturn's rings to the ecliptic, in radians */
	8677	Nr = DEG2RAD * (169.51 + (3.82e-5 * time.tt)); /* ascending node of Saturn's rings, in radians */
	8678
	8679	/* Find tilt of Saturn's rings, as seen from Earth. */
	8680	lat = DEG2RAD * eclip.elat;
	8681	lon = DEG2RAD * eclip.elon;
	8682	tilt = asin(sin(lat)cos(ir) - cos(lat)sin(ir)*sin(lon-Nr));
	8683	sin_tilt = sin(fabs(tilt));
	8684
	8685	mag = -9.0 + 0.044phase;
	8686	mag += sin_tilt(-2.6 + 1.2*sin_tilt);
	8687	mag += 5.0 log10(helio_dist * geo_dist);
	8688
	8689	ring_tilt = RAD2DEG tilt;
	8690
	8691	return ASTRO_SUCCESS;
	8692	}
	8693
	8694	static astro_status_t VisualMagnitude(
	8695	astro_body_t body,
	8696	double phase,
	8697	double helio_dist,
	8698	double geo_dist,
	8699	double *mag)
	8700	{
	8701	/* For Mercury and Venus, see: https://iopscience.iop.org/article/10.1086/430212 */
	8702	double c0, c1=0, c2=0, c3=0, x;
	8703	*mag = NAN;
	8704	switch (body)
	8705	{
	8706	case BODY_MERCURY: c0 = -0.60, c1 = +4.98, c2 = -4.88, c3 = +3.02; break;
	8707	case BODY_VENUS:
	8708	if (phase < 163.6)
	8709	c0 = -4.47, c1 = +1.03, c2 = +0.57, c3 = +0.13;
	8710	else
	8711	c0 = 0.98, c1 = -1.02;
	8712	break;
	8713	case BODY_MARS: c0 = -1.52, c1 = +1.60; break;
	8714	case BODY_JUPITER: c0 = -9.40, c1 = +0.50; break;
	8715	case BODY_URANUS: c0 = -7.19, c1 = +0.25; break;
	8716	case BODY_NEPTUNE: c0 = -6.87; break;
	8717	case BODY_PLUTO: c0 = -1.00, c1 = +4.00; break;
	8718	default: return ASTRO_INVALID_BODY;
	8719	}
	8720
	8721	x = phase / 100;
	8722	mag = c0 + x(c1 + x(c2 + xc3));
	8723	mag += 5.0 log10(helio_dist * geo_dist);
	8724	return ASTRO_SUCCESS;
	8725	}
	8726
	8727	/**
	8728	* @brief
	8729	* Finds visual magnitude, phase angle, and other illumination information about a celestial body.
	8730	*
	8731	* This function calculates information about how bright a celestial body appears from the Earth,
	8732	* reported as visual magnitude, which is a smaller (or even negative) number for brighter objects
	8733	* and a larger number for dimmer objects.
	8734	*
	8735	* For bodies other than the Sun, it reports a phase angle, which is the angle in degrees between
	8736	* the Sun and the Earth, as seen from the center of the body. Phase angle indicates what fraction
	8737	* of the body appears illuminated as seen from the Earth. For example, when the phase angle is
	8738	* near zero, it means the body appears "full" as seen from the Earth. A phase angle approaching
	8739	* 180 degrees means the body appears as a thin crescent as seen from the Earth. A phase angle
	8740	* of 90 degrees means the body appears "half full".
	8741	* For the Sun, the phase angle is always reported as 0; the Sun emits light rather than reflecting it,
	8742	* so it doesn't have a phase angle.
	8743	*
	8744	* When the body is Saturn, the returned structure contains a field `ring_tilt` that holds
	8745	* the tilt angle in degrees of Saturn's rings as seen from the Earth. A value of 0 means
	8746	* the rings appear edge-on, and are thus nearly invisible from the Earth. The `ring_tilt` holds
	8747	* 0 for all bodies other than Saturn.
	8748	*
	8749	* @param body
	8750	* The Sun, Moon, or any planet other than the Earth.
	8751	*
	8752	* @param time
	8753	* The date and time of the observation.
	8754	*
	8755	* @return
	8756	* On success, the `status` field of the return structure holds `ASTRO_SUCCESS`
	8757	* and the other structure fields are valid.
	8758	* Any other value indicates an error, in which case the remaining structure fields are not valid.
	8759	*/
	8760	astro_illum_t Astronomy_Illumination(astro_body_t body, astro_time_t time)
	8761	{
	8762	astro_vector_t earth; /* vector from Sun to Earth */
	8763	astro_vector_t hc; /* vector from Sun to body */
	8764	astro_vector_t gc; /* vector from Earth to body */
	8765	double mag; /* visual magnitude */
	8766	astro_angle_result_t phase; /* phase angle in degrees between Earth and Sun as seen from body */
	8767	double helio_dist; /* distance from Sun to body */
	8768	double geo_dist; /* distance from Earth to body */
	8769	double ring_tilt = 0.0; /* Saturn's ring tilt (0 for all other bodies) */
	8770	astro_illum_t illum;
	8771	astro_status_t status;
	8772
	8773	if (body == BODY_EARTH)
	8774	return IllumError(ASTRO_EARTH_NOT_ALLOWED);
	8775
	8776	earth = CalcEarth(time);
	8777	if (earth.status != ASTRO_SUCCESS)
	8778	return IllumError(earth.status);
	8779
	8780	if (body == BODY_SUN)
	8781	{
	8782	gc.status = ASTRO_SUCCESS;
	8783	gc.t = time;
	8784	gc.x = -earth.x;
	8785	gc.y = -earth.y;
	8786	gc.z = -earth.z;
	8787
	8788	hc.status = ASTRO_SUCCESS;
	8789	hc.t = time;
	8790	hc.x = 0.0;
	8791	hc.y = 0.0;
	8792	hc.z = 0.0;
	8793
	8794	/* The Sun emits light instead of reflecting it, */
	8795	/* so we report a placeholder phase angle of 0. */
	8796	phase.status = ASTRO_SUCCESS;
	8797	phase.angle = 0.0;
	8798	}
	8799	else
	8800	{
	8801	if (body == BODY_MOON)
	8802	{
	8803	/* For extra numeric precision, use geocentric Moon formula directly. */
	8804	gc = Astronomy_GeoMoon(time);
	8805	if (gc.status != ASTRO_SUCCESS)
	8806	return IllumError(gc.status);
	8807
	8808	hc.status = ASTRO_SUCCESS;
	8809	hc.t = time;
	8810	hc.x = earth.x + gc.x;
	8811	hc.y = earth.y + gc.y;
	8812	hc.z = earth.z + gc.z;
	8813	}
	8814	else
	8815	{
	8816	/* For planets, the heliocentric vector is more direct to calculate. */
	8817	hc = Astronomy_HelioVector(body, time);
	8818	if (hc.status != ASTRO_SUCCESS)
	8819	return IllumError(hc.status);
	8820
	8821	gc.status = ASTRO_SUCCESS;
	8822	gc.t = time;
	8823	gc.x = hc.x - earth.x;
	8824	gc.y = hc.y - earth.y;
	8825	gc.z = hc.z - earth.z;
	8826	}
	8827
	8828	phase = Astronomy_AngleBetween(gc, hc);
	8829	if (phase.status != ASTRO_SUCCESS)
	8830	return IllumError(phase.status);
	8831	}
	8832
	8833	geo_dist = Astronomy_VectorLength(gc);
	8834	helio_dist = Astronomy_VectorLength(hc);
	8835
	8836	switch (body)
	8837	{
	8838	case BODY_SUN:
	8839	mag = -0.17 + 5.0*log10(geo_dist / AU_PER_PARSEC);
	8840	break;
	8841
	8842	case BODY_MOON:
	8843	mag = MoonMagnitude(phase.angle, helio_dist, geo_dist);
	8844	break;
	8845
	8846	case BODY_SATURN:
	8847	status = SaturnMagnitude(phase.angle, helio_dist, geo_dist, gc, time, &mag, &ring_tilt);
	8848	if (status != ASTRO_SUCCESS)
	8849	return IllumError(status);
	8850	break;
	8851
	8852	default:
	8853	status = VisualMagnitude(body, phase.angle, helio_dist, geo_dist, &mag);
	8854	if (status != ASTRO_SUCCESS)
	8855	return IllumError(status);
	8856	break;
	8857	}
	8858
	8859	illum.status = ASTRO_SUCCESS;
	8860	illum.time = time;
	8861	illum.mag = mag;
	8862	illum.phase_angle = phase.angle;
	8863	illum.phase_fraction = (1.0 + cos(DEG2RAD * phase.angle)) / 2.0;
	8864	illum.helio_dist = helio_dist;
	8865	illum.ring_tilt = ring_tilt;
	8866
	8867	return illum;
	8868	}
	8869
	8870	static astro_func_result_t mag_slope(void *context, astro_time_t time)
	8871	{
	8872	/*
	8873	The Search() function finds a transition from negative to positive values.
	8874	The derivative of magnitude y with respect to time t (dy/dt)
	8875	is negative as an object gets brighter, because the magnitude numbers
	8876	get smaller. At peak magnitude dy/dt = 0, then as the object gets dimmer,
	8877	dy/dt > 0.
	8878	*/
	8879	static const double dt = 0.01;
	8880	astro_illum_t y1, y2;
	8881	astro_body_t body = ((astro_body_t )context);
	8882	astro_time_t t1 = Astronomy_AddDays(time, -dt/2);
	8883	astro_time_t t2 = Astronomy_AddDays(time, +dt/2);
	8884	astro_func_result_t result;
	8885
	8886	y1 = Astronomy_Illumination(body, t1);
	8887	if (y1.status != ASTRO_SUCCESS)
	8888	return FuncError(y1.status);
	8889
	8890	y2 = Astronomy_Illumination(body, t2);
	8891	if (y2.status != ASTRO_SUCCESS)
	8892	return FuncError(y2.status);
	8893
	8894	result.value = (y2.mag - y1.mag) / dt;
	8895	result.status = ASTRO_SUCCESS;
	8896	return result;
	8897	}
	8898
	8899	/**
	8900	* @brief
	8901	* Searches for the date and time Venus will next appear brightest as seen from the Earth.
	8902	*
	8903	* This function searches for the date and time Venus appears brightest as seen from the Earth.
	8904	* Currently only Venus is supported for the `body` parameter, though this could change in the future.
	8905	* Mercury's peak magnitude occurs at superior conjunction, when it is virtually impossible to see from the Earth,
	8906	* so peak magnitude events have little practical value for that planet.
	8907	* Planets other than Venus and Mercury reach peak magnitude at opposition, which can
	8908	* be found using #Astronomy_SearchRelativeLongitude.
	8909	* The Moon reaches peak magnitude at full moon, which can be found using
	8910	* #Astronomy_SearchMoonQuarter or #Astronomy_SearchMoonPhase.
	8911	* The Sun reaches peak magnitude at perihelion, which occurs each year in January.
	8912	* However, the difference is minor and has little practical value.
	8913	*
	8914	* @param body
	8915	* Currently only `BODY_VENUS` is allowed. Any other value results in the error `ASTRO_INVALID_BODY`.
	8916	* See function remarks for more details.
	8917	*
	8918	* @param startTime
	8919	* The date and time to start searching for the next peak magnitude event.
	8920	*
	8921	* @return
	8922	* See documentation about the return value from #Astronomy_Illumination.
	8923	*/
	8924	astro_illum_t Astronomy_SearchPeakMagnitude(astro_body_t body, astro_time_t startTime)
	8925	{
	8926	/* s1 and s2 are relative longitudes within which peak magnitude of Venus can occur. */
	8927	static const double s1 = 10.0;
	8928	static const double s2 = 30.0;
	8929	int iter;
	8930	astro_angle_result_t plon, elon;
	8931	astro_search_result_t t1, t2, tx;
	8932	astro_func_result_t syn, m1, m2;
	8933	astro_time_t t_start;
	8934	double rlon, rlon_lo, rlon_hi, adjust_days;
	8935
	8936	if (body != BODY_VENUS)
	8937	return IllumError(ASTRO_INVALID_BODY);
	8938
	8939	iter = 0;
	8940	while (++iter <= 2)
	8941	{
	8942	/* Find current heliocentric relative longitude between the */
	8943	/* inferior planet and the Earth. */
	8944	plon = Astronomy_EclipticLongitude(body, startTime);
	8945	if (plon.status != ASTRO_SUCCESS)
	8946	return IllumError(plon.status);
	8947
	8948	elon = Astronomy_EclipticLongitude(BODY_EARTH, startTime);
	8949	if (elon.status != ASTRO_SUCCESS)
	8950	return IllumError(elon.status);
	8951
	8952	rlon = LongitudeOffset(plon.angle - elon.angle); /* clamp to (-180, +180]. */
	8953
	8954	/* The slope function is not well-behaved when rlon is near 0 degrees or 180 degrees */
	8955	/* because there is a cusp there that causes a discontinuity in the derivative. */
	8956	/* So we need to guard against searching near such times. */
	8957
	8958	if (rlon >= -s1 && rlon < +s1)
	8959	{
	8960	/* Seek to the window [+s1, +s2]. */
	8961	adjust_days = 0.0;
	8962	/* Search forward for the time t1 when rel lon = +s1. */
	8963	rlon_lo = +s1;
	8964	/* Search forward for the time t2 when rel lon = +s2. */
	8965	rlon_hi = +s2;
	8966	}
	8967	else if (rlon >= +s2 \|\| rlon < -s2)
	8968	{
	8969	/* Seek to the next search window at [-s2, -s1]. */
	8970	adjust_days = 0.0;
	8971	/* Search forward for the time t1 when rel lon = -s2. */
	8972	rlon_lo = -s2;
	8973	/* Search forward for the time t2 when rel lon = -s1. */
	8974	rlon_hi = -s1;
	8975	}
	8976	else if (rlon >= 0)
	8977	{
	8978	/* rlon must be in the middle of the window [+s1, +s2]. */
	8979	/* Search BACKWARD for the time t1 when rel lon = +s1. */
	8980	syn = SynodicPeriod(body);
	8981	if (syn.status != ASTRO_SUCCESS)
	8982	return IllumError(syn.status);
	8983	adjust_days = -syn.value / 4;
	8984	rlon_lo = +s1;
	8985	/* Search forward from t1 to find t2 such that rel lon = +s2. */
	8986	rlon_hi = +s2;
	8987	}
	8988	else
	8989	{
	8990	/* rlon must be in the middle of the window [-s2, -s1]. */
	8991	/* Search BACKWARD for the time t1 when rel lon = -s2. */
	8992	syn = SynodicPeriod(body);
	8993	if (syn.status != ASTRO_SUCCESS)
	8994	return IllumError(syn.status);
	8995	adjust_days = -syn.value / 4;
	8996	rlon_lo = -s2;
	8997	/* Search forward from t1 to find t2 such that rel lon = -s1. */
	8998	rlon_hi = -s1;
	8999	}
	9000	t_start = Astronomy_AddDays(startTime, adjust_days);
	9001	t1 = Astronomy_SearchRelativeLongitude(body, rlon_lo, t_start);
	9002	if (t1.status != ASTRO_SUCCESS)
	9003	return IllumError(t1.status);
	9004	t2 = Astronomy_SearchRelativeLongitude(body, rlon_hi, t1.time);
	9005	if (t2.status != ASTRO_SUCCESS)
	9006	return IllumError(t2.status);
	9007
	9008	/* Now we have a time range [t1,t2] that brackets a maximum magnitude event. */
	9009	/* Confirm the bracketing. */
	9010	m1 = mag_slope(&body, t1.time);
	9011	if (m1.status != ASTRO_SUCCESS)
	9012	return IllumError(m1.status);
	9013	if (m1.value >= 0.0)
	9014	return IllumError(ASTRO_INTERNAL_ERROR); /* should never happen! */
	9015
	9016	m2 = mag_slope(&body, t2.time);
	9017	if (m2.status != ASTRO_SUCCESS)
	9018	return IllumError(m2.status);
	9019	if (m2.value <= 0.0)
	9020	return IllumError(ASTRO_INTERNAL_ERROR); /* should never happen! */
	9021
	9022	/* Use the generic search algorithm to home in on where the slope crosses from negative to positive. */
	9023	tx = Astronomy_Search(mag_slope, &body, t1.time, t2.time, 10.0);
	9024	if (tx.status != ASTRO_SUCCESS)
	9025	return IllumError(tx.status);
	9026
	9027	if (tx.time.tt >= startTime.tt)
	9028	return Astronomy_Illumination(body, tx.time);
	9029
	9030	/* This event is in the past (earlier than startTime). */
	9031	/* We need to search forward from t2 to find the next possible window. */
	9032	/* We never need to search more than twice. */
	9033	startTime = Astronomy_AddDays(t2.time, 1.0);
	9034	}
	9035
	9036	return IllumError(ASTRO_SEARCH_FAILURE);
	9037	}
	9038
	9039	static double MoonDistance(astro_time_t t)
	9040	{
	9041	double lon, lat, dist;
	9042	CalcMoon(t.tt / 36525.0, &lon, &lat, &dist);
	9043	return dist;
	9044	}
	9045
	9046	static astro_func_result_t moon_distance_slope(void *context, astro_time_t time)
	9047	{
	9048	static const double dt = 0.001;
	9049	astro_time_t t1 = Astronomy_AddDays(time, -dt/2.0);
	9050	astro_time_t t2 = Astronomy_AddDays(time, +dt/2.0);
	9051	double dist1, dist2;
	9052	int direction = ((int )context);
	9053	astro_func_result_t result;
	9054
	9055	dist1 = MoonDistance(t1);
	9056	dist2 = MoonDistance(t2);
	9057	result.value = direction * (dist2 - dist1) / dt;
	9058	result.status = ASTRO_SUCCESS;
	9059	return result;
	9060	}
	9061
	9062	/**
	9063	* @brief
	9064	* Finds the date and time of the Moon's closest distance (perigee)
	9065	* or farthest distance (apogee) with respect to the Earth.
	9066	*
	9067	* Given a date and time to start the search in `startTime`, this function finds the
	9068	* next date and time that the center of the Moon reaches the closest or farthest point
	9069	* in its orbit with respect to the center of the Earth, whichever comes first
	9070	* after `startTime`.
	9071	*
	9072	* The closest point is called perigee and the farthest point is called apogee.
	9073	* The word apsis refers to either event.
	9074	*
	9075	* To iterate through consecutive alternating perigee and apogee events, call `Astronomy_SearchLunarApsis`
	9076	* once, then use the return value to call #Astronomy_NextLunarApsis. After that,
	9077	* keep feeding the previous return value from `Astronomy_NextLunarApsis` into another
	9078	* call of `Astronomy_NextLunarApsis` as many times as desired.
	9079	*
	9080	* @param startTime
	9081	* The date and time at which to start searching for the next perigee or apogee.
	9082	*
	9083	* @return
	9084	* If successful, the `status` field in the returned structure holds `ASTRO_SUCCESS`,
	9085	* `time` holds the date and time of the next lunar apsis, `kind` holds either
	9086	* `APSIS_PERICENTER` for perigee or `APSIS_APOCENTER` for apogee, and the distance
	9087	* values `dist_au` (astronomical units) and `dist_km` (kilometers) are valid.
	9088	* If the function fails, `status` holds some value other than `ASTRO_SUCCESS` that
	9089	* indicates what went wrong, and the other structure fields are invalid.
	9090	*/
	9091	astro_apsis_t Astronomy_SearchLunarApsis(astro_time_t startTime)
	9092	{
	9093	astro_time_t t1, t2;
	9094	astro_search_result_t search;
	9095	astro_func_result_t m1, m2;
	9096	int positive_direction = +1;
	9097	int negative_direction = -1;
	9098	const double increment = 5.0; /* number of days to skip in each iteration */
	9099	astro_apsis_t result;
	9100	int iter;
	9101
	9102	/*
	9103	Check the rate of change of the distance dr/dt at the start time.
	9104	If it is positive, the Moon is currently getting farther away,
	9105	so start looking for apogee.
	9106	Conversely, if dr/dt < 0, start looking for perigee.
	9107	Either way, the polarity of the slope will change, so the product will be negative.
	9108	Handle the crazy corner case of exactly touching zero by checking for m1*m2 <= 0.
	9109	*/
	9110
	9111	t1 = startTime;
	9112	m1 = moon_distance_slope(&positive_direction, t1);
	9113	if (m1.status != ASTRO_SUCCESS)
	9114	return ApsisError(m1.status);
	9115
	9116	for (iter=0; iter * increment < 2.0 * MEAN_SYNODIC_MONTH; ++iter)
	9117	{
	9118	t2 = Astronomy_AddDays(t1, increment);
	9119	m2 = moon_distance_slope(&positive_direction, t2);
	9120	if (m2.status != ASTRO_SUCCESS)
	9121	return ApsisError(m2.status);
	9122
	9123	if (m1.value * m2.value <= 0.0)
	9124	{
	9125	/* There is a change of slope polarity within the time range [t1, t2]. */
	9126	/* Therefore this time range contains an apsis. */
	9127	/* Figure out whether it is perigee or apogee. */
	9128
	9129	if (m1.value < 0.0 \|\| m2.value > 0.0)
	9130	{
	9131	/* We found a minimum-distance event: perigee. */
	9132	/* Search the time range for the time when the slope goes from negative to positive. */
	9133	search = Astronomy_Search(moon_distance_slope, &positive_direction, t1, t2, 1.0);
	9134	result.kind = APSIS_PERICENTER;
	9135	}
	9136	else if (m1.value > 0.0 \|\| m2.value < 0.0)
	9137	{
	9138	/* We found a maximum-distance event: apogee. */
	9139	/* Search the time range for the time when the slope goes from positive to negative. */
	9140	search = Astronomy_Search(moon_distance_slope, &negative_direction, t1, t2, 1.0);
	9141	result.kind = APSIS_APOCENTER;
	9142	}
	9143	else
	9144	{
	9145	/* This should never happen. It should not be possible for both slopes to be zero. */
	9146	return ApsisError(ASTRO_INTERNAL_ERROR);
	9147	}
	9148
	9149	if (search.status != ASTRO_SUCCESS)
	9150	return ApsisError(search.status);
	9151
	9152	result.status = ASTRO_SUCCESS;
	9153	result.time = search.time;
	9154	result.dist_au = MoonDistance(search.time);
	9155	result.dist_km = result.dist_au * KM_PER_AU;
	9156	return result;
	9157	}
	9158
	9159	/* We have not yet found a slope polarity change. Keep searching. */
	9160	t1 = t2;
	9161	m1 = m2;
	9162	}
	9163
	9164	/* It should not be possible to fail to find an apsis within 2 synodic months. */
	9165	return ApsisError(ASTRO_INTERNAL_ERROR);
	9166	}
	9167
	9168	/**
	9169	* @brief
	9170	* Finds the next lunar perigee or apogee event in a series.
	9171	*
	9172	* This function requires an #astro_apsis_t value obtained from a call
	9173	* to #Astronomy_SearchLunarApsis or `Astronomy_NextLunarApsis`. Given
	9174	* an apogee event, this function finds the next perigee event, and vice versa.
	9175	*
	9176	* See #Astronomy_SearchLunarApsis for more details.
	9177	*
	9178	* @param apsis
	9179	* An apsis event obtained from a call to #Astronomy_SearchLunarApsis or `Astronomy_NextLunarApsis`.
	9180	* See #Astronomy_SearchLunarApsis for more details.
	9181	*
	9182	* @return
	9183	* Same as the return value for #Astronomy_SearchLunarApsis.
	9184	*/
	9185	astro_apsis_t Astronomy_NextLunarApsis(astro_apsis_t apsis)
	9186	{
	9187	static const double skip = 11.0; /* number of days to skip to start looking for next apsis event */
	9188	astro_apsis_t next;
	9189	astro_time_t time;
	9190
	9191	if (apsis.status != ASTRO_SUCCESS)
	9192	return ApsisError(ASTRO_INVALID_PARAMETER);
	9193
	9194	if (apsis.kind != APSIS_APOCENTER && apsis.kind != APSIS_PERICENTER)
	9195	return ApsisError(ASTRO_INVALID_PARAMETER);
	9196
	9197	time = Astronomy_AddDays(apsis.time, skip);
	9198	next = Astronomy_SearchLunarApsis(time);
	9199	if (next.status == ASTRO_SUCCESS)
	9200	{
	9201	/* Verify that we found the opposite apsis from the previous one. */
	9202	if (next.kind + apsis.kind != 1)
	9203	return ApsisError(ASTRO_INTERNAL_ERROR);
	9204	}
	9205	return next;
	9206	}
	9207
	9208
	9209	/** @cond DOXYGEN_SKIP */
	9210	typedef struct
	9211	{
	9212	int direction;
	9213	astro_body_t body;
	9214	}
	9215	planet_distance_context_t;
	9216	/** @endcond */
	9217
	9218
	9219	static astro_func_result_t planet_distance_slope(void *context, astro_time_t time)
	9220	{
	9221	static const double dt = 0.001;
	9222	const planet_distance_context_t pc = (const planet_distance_context_t ) context;
	9223	astro_time_t t1 = Astronomy_AddDays(time, -dt/2.0);
	9224	astro_time_t t2 = Astronomy_AddDays(time, +dt/2.0);
	9225	astro_func_result_t dist1, dist2, result;
	9226
	9227	dist1 = Astronomy_HelioDistance(pc->body, t1);
	9228	if (dist1.status != ASTRO_SUCCESS)
	9229	return dist1;
	9230
	9231	dist2 = Astronomy_HelioDistance(pc->body, t2);
	9232	if (dist2.status != ASTRO_SUCCESS)
	9233	return dist2;
	9234
	9235	result.value = pc->direction * (dist2.value - dist1.value) / dt;
	9236	result.status = ASTRO_SUCCESS;
	9237	return result;
	9238	}
	9239
	9240	static astro_apsis_t PlanetExtreme(
	9241	astro_body_t body,
	9242	astro_apsis_kind_t kind,
	9243	astro_time_t start_time,
	9244	double dayspan)
	9245	{
	9246	astro_apsis_t apsis;
	9247	const double direction = (kind == APSIS_APOCENTER) ? +1.0 : -1.0;
	9248	const int npoints = 10;
	9249	int i, best_i;
	9250	double interval;
	9251	double dist, best_dist;
	9252	astro_time_t time;
	9253	astro_func_result_t result;
	9254
	9255	for(;;)
	9256	{
	9257	interval = dayspan / (npoints - 1);
	9258
	9259	if (interval < 1.0 / 1440.0) /* iterate until uncertainty is less than one minute */
	9260	{
	9261	apsis.status = ASTRO_SUCCESS;
	9262	apsis.kind = kind;
	9263	apsis.time = Astronomy_AddDays(start_time, interval / 2.0);
	9264	result = Astronomy_HelioDistance(body, apsis.time);
	9265	if (result.status != ASTRO_SUCCESS)
	9266	return ApsisError(result.status);
	9267	apsis.dist_au = result.value;
	9268	apsis.dist_km = apsis.dist_au * KM_PER_AU;
	9269	return apsis;
	9270	}
	9271
	9272	best_i = -1;
	9273	best_dist = 0.0;
	9274	for (i=0; i < npoints; ++i)
	9275	{
	9276	time = Astronomy_AddDays(start_time, i * interval);
	9277	result = Astronomy_HelioDistance(body, time);
	9278	if (result.status != ASTRO_SUCCESS)
	9279	return ApsisError(result.status);
	9280	dist = direction * result.value;
	9281	if (i==0 \|\| dist > best_dist)
	9282	{
	9283	best_i = i;
	9284	best_dist = dist;
	9285	}
	9286	}
	9287
	9288	/* Narrow in on the extreme point. */
	9289	start_time = Astronomy_AddDays(start_time, (best_i - 1) * interval);
	9290	dayspan = 2.0 * interval;
	9291	}
	9292	}
	9293
	9294
	9295	static astro_apsis_t BruteSearchPlanetApsis(astro_body_t body, astro_time_t startTime)
	9296	{
	9297	const int npoints = 100;
	9298	int i;
	9299	astro_time_t t1, t2, time, t_min, t_max;
	9300	double dist, max_dist, min_dist;
	9301	astro_apsis_t perihelion, aphelion;
	9302	double interval;
	9303	double period;
	9304	astro_func_result_t result;
	9305
	9306	/*
	9307	Neptune is a special case for two reasons:
	9308	1. Its orbit is nearly circular (low orbital eccentricity).
	9309	2. It is so distant from the Sun that the orbital period is very long.
	9310	Put together, this causes wobbling of the Sun around the Solar System Barycenter (SSB)
	9311	to be so significant that there are 3 local minima in the distance-vs-time curve
	9312	near each apsis. Therefore, unlike for other planets, we can't use an optimized
	9313	algorithm for finding dr/dt = 0.
	9314	Instead, we use a dumb, brute-force algorithm of sampling and finding min/max
	9315	heliocentric distance.
	9316
	9317	There is a similar problem in the TOP2013 model for Pluto:
	9318	Its position vector has high-frequency oscillations that confuse the
	9319	slope-based determination of apsides.
	9320	*/
	9321
	9322	/*
	9323	Rewind approximately 30 degrees in the orbit,
	9324	then search forward for 270 degrees.
	9325	This is a very cautious way to prevent missing an apsis.
	9326	Typically we will find two apsides, and we pick whichever
	9327	apsis is ealier, but after startTime.
	9328	Sample points around this orbital arc and find when the distance
	9329	is greatest and smallest.
	9330	*/
	9331	period = Astronomy_PlanetOrbitalPeriod(body);
	9332	t1 = Astronomy_AddDays(startTime, period * ( -30.0 / 360.0));
	9333	t2 = Astronomy_AddDays(startTime, period * (+270.0 / 360.0));
	9334	t_min = t_max = t1;
	9335	min_dist = max_dist = -1.0; /* prevent warning about uninitialized variables */
	9336	interval = (t2.ut - t1.ut) / (npoints - 1.0);
	9337
	9338	for (i=0; i < npoints; ++i)
	9339	{
	9340	double ut = t1.ut + (i * interval);
	9341	time = Astronomy_TimeFromDays(ut);
	9342	result = Astronomy_HelioDistance(body, time);
	9343	if (result.status != ASTRO_SUCCESS)
	9344	return ApsisError(result.status);
	9345	dist = result.value;
	9346	if (i == 0)
	9347	{
	9348	max_dist = min_dist = dist;
	9349	}
	9350	else
	9351	{
	9352	if (dist > max_dist)
	9353	{
	9354	max_dist = dist;
	9355	t_max = time;
	9356	}
	9357	if (dist < min_dist)
	9358	{
	9359	min_dist = dist;
	9360	t_min = time;
	9361	}
	9362	}
	9363	}
	9364
	9365	t1 = Astronomy_AddDays(t_min, -2 * interval);
	9366	perihelion = PlanetExtreme(body, APSIS_PERICENTER, t1, 4 * interval);
	9367
	9368	t1 = Astronomy_AddDays(t_max, -2 * interval);
	9369	aphelion = PlanetExtreme(body, APSIS_APOCENTER, t1, 4 * interval);
	9370
	9371	if (perihelion.status == ASTRO_SUCCESS && perihelion.time.tt >= startTime.tt)
	9372	{
	9373	if (aphelion.status == ASTRO_SUCCESS && aphelion.time.tt >= startTime.tt)
	9374	{
	9375	/* Perihelion and aphelion are both valid. Pick the one that comes first. */
	9376	if (aphelion.time.tt < perihelion.time.tt)
	9377	return aphelion;
	9378	}
	9379	return perihelion;
	9380	}
	9381
	9382	if (aphelion.status == ASTRO_SUCCESS && aphelion.time.tt >= startTime.tt)
	9383	return aphelion;
	9384
	9385	return ApsisError(ASTRO_FAIL_APSIS);
	9386	}
	9387
	9388
	9389	/**
	9390	* @brief
	9391	* Finds the date and time of a planet's perihelion (closest approach to the Sun)
	9392	* or aphelion (farthest distance from the Sun) after a given time.
	9393	*
	9394	* Given a date and time to start the search in `startTime`, this function finds the
	9395	* next date and time that the center of the specified planet reaches the closest or farthest point
	9396	* in its orbit with respect to the center of the Sun, whichever comes first
	9397	* after `startTime`.
	9398	*
	9399	* The closest point is called perihelion and the farthest point is called aphelion.
	9400	* The word apsis refers to either event.
	9401	*
	9402	* To iterate through consecutive alternating perihelion and aphelion events,
	9403	* call `Astronomy_SearchPlanetApsis` once, then use the return value to call
	9404	* #Astronomy_NextPlanetApsis. After that, keep feeding the previous return value
	9405	* from `Astronomy_NextPlanetApsis` into another call of `Astronomy_NextPlanetApsis`
	9406	* as many times as desired.
	9407	*
	9408	* @param body
	9409	* The planet for which to find the next perihelion/aphelion event.
	9410	* Not allowed to be `BODY_SUN` or `BODY_MOON`.
	9411	*
	9412	* @param startTime
	9413	* The date and time at which to start searching for the next perihelion or aphelion.
	9414	*
	9415	* @return
	9416	* If successful, the `status` field in the returned structure holds `ASTRO_SUCCESS`,
	9417	* `time` holds the date and time of the next planetary apsis, `kind` holds either
	9418	* `APSIS_PERICENTER` for perihelion or `APSIS_APOCENTER` for aphelion, and the distance
	9419	* values `dist_au` (astronomical units) and `dist_km` (kilometers) are valid.
	9420	* If the function fails, `status` holds some value other than `ASTRO_SUCCESS` that
	9421	* indicates what went wrong, and the other structure fields are invalid.
	9422	*/
	9423	astro_apsis_t Astronomy_SearchPlanetApsis(astro_body_t body, astro_time_t startTime)
	9424	{
	9425	astro_time_t t1, t2;
	9426	astro_search_result_t search;
	9427	astro_func_result_t m1, m2;
	9428	planet_distance_context_t context;
	9429	astro_apsis_t result;
	9430	int iter;
	9431	double orbit_period_days;
	9432	double increment; /* number of days to skip in each iteration */
	9433	astro_func_result_t dist;
	9434
	9435	if (body == BODY_NEPTUNE \|\| body == BODY_PLUTO)
	9436	return BruteSearchPlanetApsis(body, startTime);
	9437
	9438	orbit_period_days = Astronomy_PlanetOrbitalPeriod(body);
	9439	if (orbit_period_days == 0.0)
	9440	return ApsisError(ASTRO_INVALID_BODY); /* The body must be a planet. */
	9441
	9442	increment = orbit_period_days / 6.0;
	9443
	9444	context.body = body;
	9445
	9446	t1 = startTime;
	9447	context.direction = +1;
	9448	m1 = planet_distance_slope(&context, t1);
	9449	if (m1.status != ASTRO_SUCCESS)
	9450	return ApsisError(m1.status);
	9451
	9452	for (iter=0; iter * increment < 2.0 * orbit_period_days; ++iter)
	9453	{
	9454	t2 = Astronomy_AddDays(t1, increment);
	9455	context.direction = +1;
	9456	m2 = planet_distance_slope(&context, t2);
	9457	if (m2.status != ASTRO_SUCCESS)
	9458	return ApsisError(m2.status);
	9459
	9460	if (m1.value * m2.value <= 0.0)
	9461	{
	9462	/* There is a change of slope polarity within the time range [t1, t2]. */
	9463	/* Therefore this time range contains an apsis. */
	9464	/* Figure out whether it is perihelion or aphelion. */
	9465
	9466	if (m1.value < 0.0 \|\| m2.value > 0.0)
	9467	{
	9468	/* We found a minimum-distance event: perihelion. */
	9469	/* Search the time range for the time when the slope goes from negative to positive. */
	9470	context.direction = +1;
	9471	result.kind = APSIS_PERICENTER;
	9472	}
	9473	else if (m1.value > 0.0 \|\| m2.value < 0.0)
	9474	{
	9475	/* We found a maximum-distance event: aphelion. */
	9476	/* Search the time range for the time when the slope goes from positive to negative. */
	9477	context.direction = -1;
	9478	result.kind = APSIS_APOCENTER;
	9479	}
	9480	else
	9481	{
	9482	/* This should never happen. It should not be possible for both slopes to be zero. */
	9483	return ApsisError(ASTRO_INTERNAL_ERROR);
	9484	}
	9485
	9486	search = Astronomy_Search(planet_distance_slope, &context, t1, t2, 1.0);
	9487	if (search.status != ASTRO_SUCCESS)
	9488	return ApsisError(search.status);
	9489
	9490	dist = Astronomy_HelioDistance(body, search.time);
	9491	if (dist.status != ASTRO_SUCCESS)
	9492	return ApsisError(dist.status);
	9493
	9494	result.status = ASTRO_SUCCESS;
	9495	result.time = search.time;
	9496	result.dist_au = dist.value;
	9497	result.dist_km = dist.value * KM_PER_AU;
	9498	return result;
	9499	}
	9500
	9501	/* We have not yet found a slope polarity change. Keep searching. */
	9502	t1 = t2;
	9503	m1 = m2;
	9504	}
	9505
	9506	/* It should not be possible to fail to find an apsis within 2 orbits. */
	9507	return ApsisError(ASTRO_INTERNAL_ERROR);
	9508	}
	9509
	9510	/**
	9511	* @brief
	9512	* Finds the next planetary perihelion or aphelion event in a series.
	9513	*
	9514	* This function requires an #astro_apsis_t value obtained from a call
	9515	* to #Astronomy_SearchPlanetApsis or `Astronomy_NextPlanetApsis`.
	9516	* Given an aphelion event, this function finds the next perihelion event, and vice versa.
	9517	*
	9518	* See #Astronomy_SearchPlanetApsis for more details.
	9519	*
	9520	* @param body
	9521	* The planet for which to find the next perihelion/aphelion event.
	9522	* Not allowed to be `BODY_SUN` or `BODY_MOON`.
	9523	* Must match the body passed into the call that produced the `apsis` parameter.
	9524	*
	9525	* @param apsis
	9526	* An apsis event obtained from a call to #Astronomy_SearchPlanetApsis or `Astronomy_NextPlanetApsis`.
	9527	*
	9528	* @return
	9529	* Same as the return value for #Astronomy_SearchPlanetApsis.
	9530	*/
	9531	astro_apsis_t Astronomy_NextPlanetApsis(astro_body_t body, astro_apsis_t apsis)
	9532	{
	9533	double skip; /* number of days to skip to start looking for next apsis event */
	9534	astro_apsis_t next;
	9535	astro_time_t time;
	9536
	9537	if (apsis.status != ASTRO_SUCCESS)
	9538	return ApsisError(ASTRO_INVALID_PARAMETER);
	9539
	9540	if (apsis.kind != APSIS_APOCENTER && apsis.kind != APSIS_PERICENTER)
	9541	return ApsisError(ASTRO_INVALID_PARAMETER);
	9542
	9543	skip = 0.25 * Astronomy_PlanetOrbitalPeriod(body); /* skip 1/4 of an orbit before starting search again */
	9544	if (skip <= 0.0)
	9545	return ApsisError(ASTRO_INVALID_BODY); /* body must be a planet */
	9546
	9547	time = Astronomy_AddDays(apsis.time, skip);
	9548	next = Astronomy_SearchPlanetApsis(body, time);
	9549	if (next.status == ASTRO_SUCCESS)
	9550	{
	9551	/* Verify that we found the opposite apsis from the previous one. */
	9552	if (next.kind + apsis.kind != 1)
	9553	return ApsisError(ASTRO_INTERNAL_ERROR);
	9554	}
	9555	return next;
	9556	}
	9557
	9558
	9559	/**
	9560	* @brief Calculates the inverse of a rotation matrix.
	9561	*
	9562	* Given a rotation matrix that performs some coordinate transform,
	9563	* this function returns the matrix that reverses that transform.
	9564	*
	9565	* @param rotation
	9566	* The rotation matrix to be inverted.
	9567	*
	9568	* @return
	9569	* A rotation matrix that performs the opposite transformation.
	9570	*/
	9571	astro_rotation_t Astronomy_InverseRotation(astro_rotation_t rotation)
	9572	{
	9573	astro_rotation_t inverse;
	9574
	9575	if (rotation.status != ASTRO_SUCCESS)
	9576	return RotationErr(ASTRO_INVALID_PARAMETER);
	9577
	9578	inverse.status = ASTRO_SUCCESS;
	9579	inverse.rot[0][0] = rotation.rot[0][0];
	9580	inverse.rot[0][1] = rotation.rot[1][0];
	9581	inverse.rot[0][2] = rotation.rot[2][0];
	9582	inverse.rot[1][0] = rotation.rot[0][1];
	9583	inverse.rot[1][1] = rotation.rot[1][1];
	9584	inverse.rot[1][2] = rotation.rot[2][1];
	9585	inverse.rot[2][0] = rotation.rot[0][2];
	9586	inverse.rot[2][1] = rotation.rot[1][2];
	9587	inverse.rot[2][2] = rotation.rot[2][2];
	9588
	9589	return inverse;
	9590	}
	9591
	9592	/**
	9593	* @brief Creates a rotation based on applying one rotation followed by another.
	9594	*
	9595	* Given two rotation matrices, returns a combined rotation matrix that is
	9596	* equivalent to rotating based on the first matrix, followed by the second.
	9597	*
	9598	* @param a
	9599	* The first rotation to apply.
	9600	*
	9601	* @param b
	9602	* The second rotation to apply.
	9603	*
	9604	* @return
	9605	* The combined rotation matrix.
	9606	*/
	9607	astro_rotation_t Astronomy_CombineRotation(astro_rotation_t a, astro_rotation_t b)
	9608	{
	9609	astro_rotation_t c;
	9610
	9611	if (a.status != ASTRO_SUCCESS \|\| b.status != ASTRO_SUCCESS)
	9612	return RotationErr(ASTRO_INVALID_PARAMETER);
	9613
	9614	/*
	9615	Use matrix multiplication: c = b*a.
	9616	We put 'b' on the left and 'a' on the right because,
	9617	just like when you use a matrix M to rotate a vector V,
	9618	you put the M on the left in the product M*V.
	9619	We can think of this as 'b' rotating all the 3 column vectors in 'a'.
	9620	*/
	9621	c.rot[0][0] = b.rot[0][0]a.rot[0][0] + b.rot[1][0]a.rot[0][1] + b.rot[2][0]*a.rot[0][2];
	9622	c.rot[1][0] = b.rot[0][0]a.rot[1][0] + b.rot[1][0]a.rot[1][1] + b.rot[2][0]*a.rot[1][2];
	9623	c.rot[2][0] = b.rot[0][0]a.rot[2][0] + b.rot[1][0]a.rot[2][1] + b.rot[2][0]*a.rot[2][2];
	9624	c.rot[0][1] = b.rot[0][1]a.rot[0][0] + b.rot[1][1]a.rot[0][1] + b.rot[2][1]*a.rot[0][2];
	9625	c.rot[1][1] = b.rot[0][1]a.rot[1][0] + b.rot[1][1]a.rot[1][1] + b.rot[2][1]*a.rot[1][2];
	9626	c.rot[2][1] = b.rot[0][1]a.rot[2][0] + b.rot[1][1]a.rot[2][1] + b.rot[2][1]*a.rot[2][2];
	9627	c.rot[0][2] = b.rot[0][2]a.rot[0][0] + b.rot[1][2]a.rot[0][1] + b.rot[2][2]*a.rot[0][2];
	9628	c.rot[1][2] = b.rot[0][2]a.rot[1][0] + b.rot[1][2]a.rot[1][1] + b.rot[2][2]*a.rot[1][2];
	9629	c.rot[2][2] = b.rot[0][2]a.rot[2][0] + b.rot[1][2]a.rot[2][1] + b.rot[2][2]*a.rot[2][2];
	9630
	9631	c.status = ASTRO_SUCCESS;
	9632	return c;
	9633	}
	9634
	9635	/**
	9636	* @brief Creates an identity rotation matrix.
	9637	*
	9638	* Returns a rotation matrix that has no effect on orientation.
	9639	* This matrix can be the starting point for other operations,
	9640	* such as using a series of calls to #Astronomy_Pivot to
	9641	* create a custom rotation matrix.
	9642	*
	9643	* @return
	9644	* The identity matrix.
	9645	*/
	9646	astro_rotation_t Astronomy_IdentityMatrix(void)
	9647	{
	9648	astro_rotation_t r;
	9649
	9650	r.rot[0][0] = 1.0; r.rot[1][0] = 0.0; r.rot[2][0] = 0.0;
	9651	r.rot[0][1] = 0.0; r.rot[1][1] = 1.0; r.rot[2][1] = 0.0;
	9652	r.rot[0][2] = 0.0; r.rot[1][2] = 0.0; r.rot[2][2] = 1.0;
	9653
	9654	r.status = ASTRO_SUCCESS;
	9655
	9656	return r;
	9657	}
	9658
	9659	/**
	9660	* @brief Re-orients a rotation matrix by pivoting it by an angle around one of its axes.
	9661	*
	9662	* Given a rotation matrix, a selected coordinate axis, and an angle in degrees,
	9663	* this function pivots the rotation matrix by that angle around that coordinate axis.
	9664	*
	9665	* For example, if you have rotation matrix that converts ecliptic coordinates (ECL)
	9666	* to horizontal coordinates (HOR), but you really want to convert ECL to the orientation
	9667	* of a telescope camera pointed at a given body, you can use `Astronomy_Pivot` twice:
	9668	* (1) pivot around the zenith axis by the body's azimuth, then (2) pivot around the
	9669	* western axis by the body's altitude angle. The resulting rotation matrix will then
	9670	* reorient ECL coordinates to the orientation of your telescope camera.
	9671	*
	9672	* @param rotation
	9673	* The input rotation matrix.
	9674	*
	9675	* @param axis
	9676	* An integer that selects which coordinate axis to rotate around:
	9677	* 0 = x, 1 = y, 2 = z. Any other value will fail with the error code
	9678	* `ASTRO_INVALID_PARAMETER` in the `status` field of the return value.
	9679	*
	9680	* @param angle
	9681	* An angle in degrees indicating the amount of rotation around the specified axis.
	9682	* Positive angles indicate rotation counterclockwise as seen from the positive
	9683	* direction along that axis, looking towards the origin point of the orientation system.
	9684	* If `angle` is NAN or infinite, the function will fail with the error code
	9685	* `ASTRO_INVALID_PARAMETER`. Any finite number of degrees is allowed, but best
	9686	* precision will result from keeping `angle` in the range [-360, +360].
	9687	*
	9688	* @return
	9689	* If successful, the return value will have `ASTRO_SUCCESS` in the `status`
	9690	* field, along with a pivoted rotation matrix. Otherwise, `status` holds
	9691	* an appropriate error code and the rotation matrix is invalid.
	9692	*/
	9693	astro_rotation_t Astronomy_Pivot(astro_rotation_t rotation, int axis, double angle)
	9694	{
	9695	astro_rotation_t p;
	9696	double radians, c, s;
	9697	int i, j, k;
	9698
	9699	/* Check for an invalid input matrix. */
	9700	if (rotation.status != ASTRO_SUCCESS)
	9701	return RotationErr(ASTRO_INVALID_PARAMETER);
	9702
	9703	/* Check for an invalid coordinate axis. */
	9704	if (axis < 0 \|\| axis > 2)
	9705	return RotationErr(ASTRO_INVALID_PARAMETER);
	9706
	9707	/* Check for an invalid angle value. */
	9708	if (!isfinite(angle))
	9709	return RotationErr(ASTRO_INVALID_PARAMETER);
	9710
	9711	radians = angle * DEG2RAD;
	9712	c = cos(radians);
	9713	s = sin(radians);
	9714
	9715	/*
	9716	We need to maintain the "right-hand" rule, no matter which
	9717	axis was selected. That means we pick (i, j, k) axis order
	9718	such that the following vector cross product is satisfied:
	9719	i x j = k
	9720	*/
	9721	i = (axis + 1) % 3;
	9722	j = (axis + 2) % 3;
	9723	k = axis;
	9724
	9725	p.rot[i][i] = crotation.rot[i][i] - srotation.rot[i][j];
	9726	p.rot[i][j] = srotation.rot[i][i] + crotation.rot[i][j];
	9727	p.rot[i][k] = rotation.rot[i][k];
	9728
	9729	p.rot[j][i] = crotation.rot[j][i] - srotation.rot[j][j];
	9730	p.rot[j][j] = srotation.rot[j][i] + crotation.rot[j][j];
	9731	p.rot[j][k] = rotation.rot[j][k];
	9732
	9733	p.rot[k][i] = crotation.rot[k][i] - srotation.rot[k][j];
	9734	p.rot[k][j] = srotation.rot[k][i] + crotation.rot[k][j];
	9735	p.rot[k][k] = rotation.rot[k][k];
	9736
	9737	p.status = ASTRO_SUCCESS;
	9738	return p;
	9739	}
	9740
	9741	/**
	9742	* @brief Converts spherical coordinates to Cartesian coordinates.
	9743	*
	9744	* Given spherical coordinates and a time at which they are valid,
	9745	* returns a vector of Cartesian coordinates. The returned value
	9746	* includes the time, as required by the type #astro_vector_t.
	9747	*
	9748	* @param sphere
	9749	* Spherical coordinates to be converted.
	9750	*
	9751	* @param time
	9752	* The time that should be included in the return value.
	9753	*
	9754	* @return
	9755	* The vector form of the supplied spherical coordinates.
	9756	*/
	9757	astro_vector_t Astronomy_VectorFromSphere(astro_spherical_t sphere, astro_time_t time)
	9758	{
	9759	astro_vector_t vector;
	9760	double radlat, radlon, rcoslat;
	9761
	9762	if (sphere.status != ASTRO_SUCCESS)
	9763	return VecError(ASTRO_INVALID_PARAMETER, time);
	9764
	9765	radlat = sphere.lat * DEG2RAD;
	9766	radlon = sphere.lon * DEG2RAD;
	9767	rcoslat = sphere.dist * cos(radlat);
	9768
	9769	vector.status = ASTRO_SUCCESS;
	9770	vector.t = time;
	9771	vector.x = rcoslat * cos(radlon);
	9772	vector.y = rcoslat * sin(radlon);
	9773	vector.z = sphere.dist * sin(radlat);
	9774
	9775	return vector;
	9776	}
	9777
	9778
	9779	/**
	9780	* @brief Converts Cartesian coordinates to spherical coordinates.
	9781	*
	9782	* Given a Cartesian vector, returns latitude, longitude, and distance.
	9783	*
	9784	* @param vector
	9785	* Cartesian vector to be converted to spherical coordinates.
	9786	*
	9787	* @return
	9788	* Spherical coordinates that are equivalent to the given vector.
	9789	*/
	9790	astro_spherical_t Astronomy_SphereFromVector(astro_vector_t vector)
	9791	{
	9792	double xyproj;
	9793	astro_spherical_t sphere;
	9794
	9795	if (vector.status != ASTRO_SUCCESS)
	9796	return SphereError(vector.status);
	9797
	9798	xyproj = vector.xvector.x + vector.yvector.y;
	9799	sphere.dist = sqrt(xyproj + vector.z*vector.z);
	9800	if (xyproj == 0.0)
	9801	{
	9802	if (vector.z == 0.0)
	9803	{
	9804	/* Indeterminate coordinates; pos vector has zero length. */
	9805	return SphereError(ASTRO_INVALID_PARAMETER);
	9806	}
	9807
	9808	sphere.lon = 0.0;
	9809	sphere.lat = (vector.z < 0.0) ? -90.0 : +90.0;
	9810	}
	9811	else
	9812	{
	9813	sphere.lon = RAD2DEG * atan2(vector.y, vector.x);
	9814	if (sphere.lon < 0.0)
	9815	sphere.lon += 360.0;
	9816
	9817	sphere.lat = RAD2DEG * atan2(vector.z, sqrt(xyproj));
	9818	}
	9819
	9820	sphere.status = ASTRO_SUCCESS;
	9821	return sphere;
	9822	}
	9823
	9824
	9825	/**
	9826	* @brief
	9827	* Given an equatorial vector, calculates equatorial angular coordinates.
	9828	*
	9829	* @param vector
	9830	* A vector in an equatorial coordinate system.
	9831	*
	9832	* @return
	9833	* Angular coordinates expressed in the same equatorial system as `vector`.
	9834	*/
	9835	astro_equatorial_t Astronomy_EquatorFromVector(astro_vector_t vector)
	9836	{
	9837	astro_equatorial_t equ;
	9838	astro_spherical_t sphere;
	9839
	9840	sphere = Astronomy_SphereFromVector(vector);
	9841	if (sphere.status != ASTRO_SUCCESS)
	9842	return EquError(sphere.status);
	9843
	9844	equ.status = ASTRO_SUCCESS;
	9845	equ.dec = sphere.lat;
	9846	equ.ra = sphere.lon / 15.0; /* convert degrees to sidereal hours */
	9847	equ.dist = sphere.dist;
	9848	equ.vec = vector;
	9849
	9850	return equ;
	9851	}
	9852
	9853
	9854	static double ToggleAzimuthDirection(double az)
	9855	{
	9856	az = 360.0 - az;
	9857	if (az >= 360.0)
	9858	az -= 360.0;
	9859	else if (az < 0.0)
	9860	az += 360.0;
	9861	return az;
	9862	}
	9863
	9864	/**
	9865	* @brief Converts Cartesian coordinates to horizontal coordinates.
	9866	*
	9867	* Given a horizontal Cartesian vector, returns horizontal azimuth and altitude.
	9868	*
	9869	* IMPORTANT: This function differs from #Astronomy_SphereFromVector in two ways:
	9870	* - `Astronomy_SphereFromVector` returns a `lon` value that represents azimuth defined counterclockwise
	9871	* from north (e.g., west = +90), but this function represents a clockwise rotation
	9872	* (e.g., east = +90). The difference is because `Astronomy_SphereFromVector` is intended
	9873	* to preserve the vector "right-hand rule", while this function defines azimuth in a more
	9874	* traditional way as used in navigation and cartography.
	9875	* - This function optionally corrects for atmospheric refraction, while `Astronomy_SphereFromVector`
	9876	* does not.
	9877	*
	9878	* The returned structure contains the azimuth in `lon`.
	9879	* It is measured in degrees clockwise from north: east = +90 degrees, west = +270 degrees.
	9880	*
	9881	* The altitude is stored in `lat`.
	9882	*
	9883	* The distance to the observed object is stored in `dist`,
	9884	* and is expressed in astronomical units (AU).
	9885	*
	9886	* @param vector
	9887	* Cartesian vector to be converted to horizontal coordinates.
	9888	*
	9889	* @param refraction
	9890	* `REFRACTION_NORMAL`: correct altitude for atmospheric refraction (recommended).
	9891	* `REFRACTION_NONE`: no atmospheric refraction correction is performed.
	9892	* `REFRACTION_JPLHOR`: for JPL Horizons compatibility testing only; not recommended for normal use.
	9893	*
	9894	* @return
	9895	* If successful, `status` holds `ASTRO_SUCCESS` and the other fields are valid as described
	9896	* in the function remarks.
	9897	* Otherwise `status` holds an error code and the other fields are undefined.
	9898	*/
	9899	astro_spherical_t Astronomy_HorizonFromVector(astro_vector_t vector, astro_refraction_t refraction)
	9900	{
	9901	astro_spherical_t sphere;
	9902
	9903	sphere = Astronomy_SphereFromVector(vector);
	9904	if (sphere.status == ASTRO_SUCCESS)
	9905	{
	9906	/* Convert azimuth from counterclockwise-from-north to clockwise-from-north. */
	9907	sphere.lon = ToggleAzimuthDirection(sphere.lon);
	9908	sphere.lat += Astronomy_Refraction(refraction, sphere.lat);
	9909	}
	9910
	9911	return sphere;
	9912	}
	9913
	9914
	9915	/**
	9916	* @brief
	9917	* Given apparent angular horizontal coordinates in `sphere`, calculate horizontal vector.
	9918	*
	9919	* @param sphere
	9920	* A structure that contains apparent horizontal coordinates:
	9921	* `lat` holds the refracted altitude angle,
	9922	* `lon` holds the azimuth in degrees clockwise from north,
	9923	* and `dist` holds the distance from the observer to the object in AU.
	9924	*
	9925	* @param time
	9926	* The date and time of the observation. This is needed because the returned
	9927	* #astro_vector_t structure requires a valid time value when passed to certain other functions.
	9928	*
	9929	* @param refraction
	9930	* The refraction option used to model atmospheric lensing. See #Astronomy_Refraction.
	9931	* This specifies how refraction is to be removed from the altitude stored in `sphere.lat`.
	9932	*
	9933	* @return
	9934	* A vector in the horizontal system: `x` = north, `y` = west, and `z` = zenith (up).
	9935	*/
	9936	astro_vector_t Astronomy_VectorFromHorizon(astro_spherical_t sphere, astro_time_t time, astro_refraction_t refraction)
	9937	{
	9938	if (sphere.status != ASTRO_SUCCESS)
	9939	return VecError(ASTRO_INVALID_PARAMETER, time);
	9940
	9941	/* Convert azimuth from clockwise-from-north to counterclockwise-from-north. */
	9942	sphere.lon = ToggleAzimuthDirection(sphere.lon);
	9943
	9944	/* Reverse any applied refraction. */
	9945	sphere.lat += Astronomy_InverseRefraction(refraction, sphere.lat);
	9946
	9947	return Astronomy_VectorFromSphere(sphere, time);
	9948	}
	9949
	9950
	9951	/**
	9952	* @brief
	9953	* Calculates the amount of "lift" to an altitude angle caused by atmospheric refraction.
	9954	*
	9955	* Given an altitude angle and a refraction option, calculates
	9956	* the amount of "lift" caused by atmospheric refraction.
	9957	* This is the number of degrees higher in the sky an object appears
	9958	* due to the lensing of the Earth's atmosphere.
	9959	* This function works best near sea level.
	9960	* To correct for higher elevations, call #Astronomy_Atmosphere for that
	9961	* elevation and multiply the refraction angle by the resulting relative density.
	9962	*
	9963	* @param refraction
	9964	* The option selecting which refraction correction to use.
	9965	* If `REFRACTION_NORMAL`, uses a well-behaved refraction model that works well for
	9966	* all valid values (-90 to +90) of `altitude`.
	9967	* If `REFRACTION_JPLHOR`, this function returns a compatible value with the JPL Horizons tool.
	9968	* If any other value (including `REFRACTION_NONE`), this function returns 0.
	9969	*
	9970	* @param altitude
	9971	* An altitude angle in a horizontal coordinate system. Must be a value between -90 and +90.
	9972	*
	9973	* @return
	9974	* The angular adjustment in degrees to be added to the altitude angle to correct for atmospheric lensing.
	9975	*/
	9976	double Astronomy_Refraction(astro_refraction_t refraction, double altitude)
	9977	{
	9978	double refr, hd;
	9979
	9980	if (altitude < -90.0 \|\| altitude > +90.0)
	9981	return 0.0; /* no attempt to correct an invalid altitude */
	9982
	9983	if (refraction == REFRACTION_NORMAL \|\| refraction == REFRACTION_JPLHOR)
	9984	{
	9985	/*
	9986	http://extras.springer.com/1999/978-1-4471-0555-8/chap4/horizons/horizons.pdf
	9987	JPL Horizons says it uses refraction algorithm from
	9988	Meeus "Astronomical Algorithms", 1991, p. 101-102.
	9989	I found the following Go implementation:
	9990	https://github.com/soniakeys/meeus/blob/master/v3/refraction/refract.go
	9991	This is a translation from the function "Saemundsson" there.
	9992	I found experimentally that JPL Horizons clamps the angle to 1 degree below the horizon.
	9993	This is important because the 'refr' formula below goes crazy near hd = -5.11.
	9994	*/
	9995
	9996	hd = altitude;
	9997	if (hd < -1.0)
	9998	hd = -1.0;
	9999
	10000	refr = (1.02 / tan((hd+10.3/(hd+5.11))*DEG2RAD)) / 60.0;
	10001
	10002	if (refraction == REFRACTION_NORMAL && altitude < -1.0)
	10003	{
	10004	/*
	10005	In "normal" mode we gradually reduce refraction toward the nadir
	10006	so that we never get an altitude angle less than -90 degrees.
	10007	When horizon angle is -1 degrees, the factor is exactly 1.
	10008	As altitude approaches -90 (the nadir), the fraction approaches 0 linearly.
	10009	*/
	10010	refr *= (altitude + 90.0) / 89.0;
	10011	}
	10012	}
	10013	else
	10014	{
	10015	/* No refraction, or the refraction option is invalid. */
	10016	refr = 0.0;
	10017	}
	10018
	10019	return refr;
	10020	}
	10021
	10022
	10023	/**
	10024	* @brief
	10025	* Calculates the inverse of an atmospheric refraction angle.
	10026	*
	10027	* Given an observed altitude angle that includes atmospheric refraction,
	10028	* calculates the negative angular correction to obtain the unrefracted
	10029	* altitude. This is useful for cases where observed horizontal
	10030	* coordinates are to be converted to another orientation system,
	10031	* but refraction first must be removed from the observed position.
	10032	*
	10033	* @param refraction
	10034	* The option selecting which refraction correction to use.
	10035	* See #Astronomy_Refraction.
	10036	*
	10037	* @param bent_altitude
	10038	* The apparent altitude that includes atmospheric refraction.
	10039	*
	10040	* @return
	10041	* The angular adjustment in degrees to be added to the
	10042	* altitude angle to correct for atmospheric lensing.
	10043	* This will be less than or equal to zero.
	10044	*/
	10045	double Astronomy_InverseRefraction(astro_refraction_t refraction, double bent_altitude)
	10046	{
	10047	double altitude, diff;
	10048
	10049	if (bent_altitude < -90.0 \|\| bent_altitude > +90.0)
	10050	return 0.0; /* no attempt to correct an invalid altitude */
	10051
	10052	/* Find the pre-adjusted altitude whose refraction correction leads to 'altitude'. */
	10053	altitude = bent_altitude - Astronomy_Refraction(refraction, bent_altitude);
	10054	for(;;)
	10055	{
	10056	/* See how close we got. */
	10057	diff = (altitude + Astronomy_Refraction(refraction, altitude)) - bent_altitude;
	10058	if (fabs(diff) < 1.0e-14)
	10059	return altitude - bent_altitude;
	10060
	10061	altitude -= diff;
	10062	}
	10063	}
	10064
	10065	/**
	10066	* @brief Applies a rotation to a vector, yielding a rotated vector.
	10067	*
	10068	* This function transforms a vector in one orientation to a vector
	10069	* in another orientation.
	10070	*
	10071	* @param rotation
	10072	* A rotation matrix that specifies how the orientation of the vector is to be changed.
	10073	*
	10074	* @param vector
	10075	* The vector whose orientation is to be changed.
	10076	*
	10077	* @return
	10078	* A vector in the orientation specified by `rotation`.
	10079	*/
	10080	astro_vector_t Astronomy_RotateVector(astro_rotation_t rotation, astro_vector_t vector)
	10081	{
	10082	astro_vector_t target;
	10083
	10084	if (rotation.status != ASTRO_SUCCESS \|\| vector.status != ASTRO_SUCCESS)
	10085	return VecError(ASTRO_INVALID_PARAMETER, vector.t);
	10086
	10087	target.status = ASTRO_SUCCESS;
	10088	target.t = vector.t;
	10089	target.x = rotation.rot[0][0]vector.x + rotation.rot[1][0]vector.y + rotation.rot[2][0]*vector.z;
	10090	target.y = rotation.rot[0][1]vector.x + rotation.rot[1][1]vector.y + rotation.rot[2][1]*vector.z;
	10091	target.z = rotation.rot[0][2]vector.x + rotation.rot[1][2]vector.y + rotation.rot[2][2]*vector.z;
	10092
	10093	return target;
	10094	}
	10095
	10096
	10097	/**
	10098	* @brief Applies a rotation to a state vector, yielding a rotated vector.
	10099	*
	10100	* This function transforms a state vector in one orientation to a vector
	10101	* in another orientation.
	10102	*
	10103	* @param rotation
	10104	* A rotation matrix that specifies how the orientation of the state vector is to be changed.
	10105	*
	10106	* @param state
	10107	* The state vector whose orientation is to be changed.
	10108	* Both the position and velocity components are transformed.
	10109	*
	10110	* @return
	10111	* A state vector in the orientation specified by `rotation`.
	10112	*/
	10113	astro_state_vector_t Astronomy_RotateState(astro_rotation_t rotation, astro_state_vector_t state)
	10114	{
	10115	astro_state_vector_t target;
	10116
	10117	if (rotation.status != ASTRO_SUCCESS \|\| state.status != ASTRO_SUCCESS)
	10118	return StateVecError(ASTRO_INVALID_PARAMETER, state.t);
	10119
	10120	target.status = ASTRO_SUCCESS;
	10121	target.t = state.t;
	10122
	10123	target.x = rotation.rot[0][0]state.x + rotation.rot[1][0]state.y + rotation.rot[2][0]*state.z;
	10124	target.y = rotation.rot[0][1]state.x + rotation.rot[1][1]state.y + rotation.rot[2][1]*state.z;
	10125	target.z = rotation.rot[0][2]state.x + rotation.rot[1][2]state.y + rotation.rot[2][2]*state.z;
	10126
	10127	target.vx = rotation.rot[0][0]state.vx + rotation.rot[1][0]state.vy + rotation.rot[2][0]*state.vz;
	10128	target.vy = rotation.rot[0][1]state.vx + rotation.rot[1][1]state.vy + rotation.rot[2][1]*state.vz;
	10129	target.vz = rotation.rot[0][2]state.vx + rotation.rot[1][2]state.vy + rotation.rot[2][2]*state.vz;
	10130
	10131	return target;
	10132	}
	10133
	10134
	10135	/**
	10136	* @brief
	10137	* Calculates a rotation matrix from J2000 mean equator (EQJ) to J2000 mean ecliptic (ECL).
	10138	*
	10139	* This is one of the family of functions that returns a rotation matrix
	10140	* for converting from one orientation to another.
	10141	* Source: EQJ = equatorial system, using equator at J2000 epoch.
	10142	* Target: ECL = ecliptic system, using equator at J2000 epoch.
	10143	*
	10144	* @return
	10145	* A rotation matrix that converts EQJ to ECL.
	10146	*/
	10147	astro_rotation_t Astronomy_Rotation_EQJ_ECL(void)
	10148	{
	10149	static const double c = COS_OBLIQ_2000;
	10150	static const double s = SIN_OBLIQ_2000;
	10151	astro_rotation_t r;
	10152
	10153	r.status = ASTRO_SUCCESS;
	10154	r.rot[0][0] = 1.0; r.rot[1][0] = 0.0; r.rot[2][0] = 0.0;
	10155	r.rot[0][1] = 0.0; r.rot[1][1] = +c; r.rot[2][1] = +s;
	10156	r.rot[0][2] = 0.0; r.rot[1][2] = -s; r.rot[2][2] = +c;
	10157	return r;
	10158	}
	10159
	10160	/**
	10161	* @brief
	10162	* Calculates a rotation matrix from J2000 mean ecliptic (ECL) to J2000 mean equator (EQJ).
	10163	*
	10164	* This is one of the family of functions that returns a rotation matrix
	10165	* for converting from one orientation to another.
	10166	* Source: ECL = ecliptic system, using equator at J2000 epoch.
	10167	* Target: EQJ = equatorial system, using equator at J2000 epoch.
	10168	*
	10169	* @return
	10170	* A rotation matrix that converts ECL to EQJ.
	10171	*/
	10172	astro_rotation_t Astronomy_Rotation_ECL_EQJ(void)
	10173	{
	10174	static const double c = COS_OBLIQ_2000;
	10175	static const double s = SIN_OBLIQ_2000;
	10176	astro_rotation_t r;
	10177
	10178	r.status = ASTRO_SUCCESS;
	10179	r.rot[0][0] = 1.0; r.rot[1][0] = 0.0; r.rot[2][0] = 0.0;
	10180	r.rot[0][1] = 0.0; r.rot[1][1] = +c; r.rot[2][1] = -s;
	10181	r.rot[0][2] = 0.0; r.rot[1][2] = +s; r.rot[2][2] = +c;
	10182	return r;
	10183	}
	10184
	10185	/**
	10186	* @brief
	10187	* Calculates a rotation matrix from J2000 mean equator (EQJ) to equatorial of-date (EQD).
	10188	*
	10189	* This is one of the family of functions that returns a rotation matrix
	10190	* for converting from one orientation to another.
	10191	* Source: EQJ = equatorial system, using equator at J2000 epoch.
	10192	* Target: EQD = equatorial system, using equator of the specified date/time.
	10193	*
	10194	* @param time
	10195	* The date and time at which the Earth's equator defines the target orientation.
	10196	*
	10197	* @return
	10198	* A rotation matrix that converts EQJ to EQD at `time`.
	10199	*/
	10200	astro_rotation_t Astronomy_Rotation_EQJ_EQD(astro_time_t *time)
	10201	{
	10202	astro_rotation_t prec, nut;
	10203
	10204	if (time == NULL)
	10205	return RotationErr(ASTRO_INVALID_PARAMETER);
	10206
	10207	prec = precession_rot(*time, FROM_2000);
	10208	nut = nutation_rot(time, FROM_2000);
	10209	return Astronomy_CombineRotation(prec, nut);
	10210	}
	10211
	10212
	10213	/**
	10214	* @brief
	10215	* Calculates a rotation matrix from J2000 mean equator (EQJ) to true ecliptic of date (ECT).
	10216	*
	10217	* This is one of the family of functions that returns a rotation matrix
	10218	* for converting from one orientation to another.
	10219	* Source: EQJ = equatorial system, using mean equator at J2000 epoch.
	10220	* Target: ECT = ecliptic system, using true equinox of the specified date/time.
	10221	*
	10222	* @param time
	10223	* The date and time at which the Earth's equator defines the target orientation.
	10224	*
	10225	* @return
	10226	* A rotation matrix that converts EQJ to ECT at `time`.
	10227	*/
	10228	astro_rotation_t Astronomy_Rotation_EQJ_ECT(astro_time_t *time)
	10229	{
	10230	astro_rotation_t rot, step;
	10231
	10232	if (time == NULL)
	10233	return RotationErr(ASTRO_INVALID_PARAMETER);
	10234
	10235	rot = Astronomy_Rotation_EQJ_EQD(time);
	10236	step = Astronomy_Rotation_EQD_ECT(time);
	10237	return Astronomy_CombineRotation(rot, step);
	10238	}
	10239
	10240
	10241	/**
	10242	* @brief
	10243	* Calculates a rotation matrix from true ecliptic of date (ECT) to J2000 mean equator (EQJ).
	10244	*
	10245	* This is one of the family of functions that returns a rotation matrix
	10246	* for converting from one orientation to another.
	10247	* Source: ECT = ecliptic system, using true equinox of the specified date/time.
	10248	* Target: EQJ = equatorial system, using mean equator at J2000 epoch.
	10249	*
	10250	* @param time
	10251	* The date and time at which the Earth's equator defines the target orientation.
	10252	*
	10253	* @return
	10254	* A rotation matrix that converts ECT to EQJ at `time`.
	10255	*/
	10256	astro_rotation_t Astronomy_Rotation_ECT_EQJ(astro_time_t *time)
	10257	{
	10258	astro_rotation_t rot, step;
	10259
	10260	if (time == NULL)
	10261	return RotationErr(ASTRO_INVALID_PARAMETER);
	10262
	10263	rot = Astronomy_Rotation_ECT_EQD(time);
	10264	step = Astronomy_Rotation_EQD_EQJ(time);
	10265	return Astronomy_CombineRotation(rot, step);
	10266	}
	10267
	10268
	10269	/**
	10270	* @brief
	10271	* Calculates a rotation matrix from equatorial of-date (EQD) to J2000 mean equator (EQJ).
	10272	*
	10273	* This is one of the family of functions that returns a rotation matrix
	10274	* for converting from one orientation to another.
	10275	* Source: EQD = equatorial system, using equator of the specified date/time.
	10276	* Target: EQJ = equatorial system, using equator at J2000 epoch.
	10277	*
	10278	* @param time
	10279	* The date and time at which the Earth's equator defines the source orientation.
	10280	*
	10281	* @return
	10282	* A rotation matrix that converts EQD at `time` to EQJ.
	10283	*/
	10284	astro_rotation_t Astronomy_Rotation_EQD_EQJ(astro_time_t *time)
	10285	{
	10286	astro_rotation_t prec, nut;
	10287
	10288	if (time == NULL)
	10289	return RotationErr(ASTRO_INVALID_PARAMETER);
	10290
	10291	nut = nutation_rot(time, INTO_2000);
	10292	prec = precession_rot(*time, INTO_2000);
	10293	return Astronomy_CombineRotation(nut, prec);
	10294	}
	10295
	10296
	10297	/**
	10298	* @brief
	10299	* Calculates a rotation matrix from equatorial of-date (EQD) to horizontal (HOR).
	10300	*
	10301	* This is one of the family of functions that returns a rotation matrix
	10302	* for converting from one orientation to another.
	10303	* Source: EQD = equatorial system, using equator of the specified date/time.
	10304	* Target: HOR = horizontal system.
	10305	*
	10306	* @param time
	10307	* The date and time at which the Earth's equator applies.
	10308	*
	10309	* @param observer
	10310	* A location near the Earth's mean sea level that defines the observer's horizon.
	10311	*
	10312	* @return
	10313	* A rotation matrix that converts EQD to HOR at `time` and for `observer`.
	10314	* The components of the horizontal vector are:
	10315	* x = north, y = west, z = zenith (straight up from the observer).
	10316	* These components are chosen so that the "right-hand rule" works for the vector
	10317	* and so that north represents the direction where azimuth = 0.
	10318	*/
	10319	astro_rotation_t Astronomy_Rotation_EQD_HOR(astro_time_t *time, astro_observer_t observer)
	10320	{
	10321	astro_rotation_t rot;
	10322	double uze[3], une[3], uwe[3];
	10323	double uz[3], un[3], uw[3];
	10324	double spin_angle;
	10325
	10326	if (time == NULL)
	10327	return RotationErr(ASTRO_INVALID_PARAMETER);
	10328
	10329	double sinlat = sin(observer.latitude * DEG2RAD);
	10330	double coslat = cos(observer.latitude * DEG2RAD);
	10331	double sinlon = sin(observer.longitude * DEG2RAD);
	10332	double coslon = cos(observer.longitude * DEG2RAD);
	10333
	10334	uze[0] = coslat * coslon;
	10335	uze[1] = coslat * sinlon;
	10336	uze[2] = sinlat;
	10337
	10338	une[0] = -sinlat * coslon;
	10339	une[1] = -sinlat * sinlon;
	10340	une[2] = coslat;
	10341
	10342	uwe[0] = sinlon;
	10343	uwe[1] = -coslon;
	10344	uwe[2] = 0.0;
	10345
	10346	spin_angle = -15.0 * Astronomy_SiderealTime(time);
	10347	spin(spin_angle, uze, uz);
	10348	spin(spin_angle, une, un);
	10349	spin(spin_angle, uwe, uw);
	10350
	10351	rot.rot[0][0] = un[0]; rot.rot[1][0] = un[1]; rot.rot[2][0] = un[2];
	10352	rot.rot[0][1] = uw[0]; rot.rot[1][1] = uw[1]; rot.rot[2][1] = uw[2];
	10353	rot.rot[0][2] = uz[0]; rot.rot[1][2] = uz[1]; rot.rot[2][2] = uz[2];
	10354
	10355	rot.status = ASTRO_SUCCESS;
	10356	return rot;
	10357	}
	10358
	10359
	10360	/**
	10361	* @brief
	10362	* Calculates a rotation matrix from horizontal (HOR) to equatorial of-date (EQD).
	10363	*
	10364	* This is one of the family of functions that returns a rotation matrix
	10365	* for converting from one orientation to another.
	10366	* Source: HOR = horizontal system (x=North, y=West, z=Zenith).
	10367	* Target: EQD = equatorial system, using equator of the specified date/time.
	10368	*
	10369	* @param time
	10370	* The date and time at which the Earth's equator applies.
	10371	*
	10372	* @param observer
	10373	* A location near the Earth's mean sea level that defines the observer's horizon.
	10374	*
	10375	* @return
	10376	* A rotation matrix that converts HOR to EQD at `time` and for `observer`.
	10377	*/
	10378	astro_rotation_t Astronomy_Rotation_HOR_EQD(astro_time_t *time, astro_observer_t observer)
	10379	{
	10380	astro_rotation_t rot = Astronomy_Rotation_EQD_HOR(time, observer);
	10381	return Astronomy_InverseRotation(rot);
	10382	}
	10383
	10384
	10385	/**
	10386	* @brief
	10387	* Calculates a rotation matrix from horizontal (HOR) to J2000 equatorial (EQJ).
	10388	*
	10389	* This is one of the family of functions that returns a rotation matrix
	10390	* for converting from one orientation to another.
	10391	* Source: HOR = horizontal system (x=North, y=West, z=Zenith).
	10392	* Target: EQJ = equatorial system, using equator at the J2000 epoch.
	10393	*
	10394	* @param time
	10395	* The date and time of the observation.
	10396	*
	10397	* @param observer
	10398	* A location near the Earth's mean sea level that defines the observer's horizon.
	10399	*
	10400	* @return
	10401	* A rotation matrix that converts HOR to EQJ at `time` and for `observer`.
	10402	*/
	10403	astro_rotation_t Astronomy_Rotation_HOR_EQJ(astro_time_t *time, astro_observer_t observer)
	10404	{
	10405	astro_rotation_t hor_eqd, eqd_eqj;
	10406
	10407	if (time == NULL)
	10408	return RotationErr(ASTRO_INVALID_PARAMETER);
	10409
	10410	hor_eqd = Astronomy_Rotation_HOR_EQD(time, observer);
	10411	eqd_eqj = Astronomy_Rotation_EQD_EQJ(time);
	10412	return Astronomy_CombineRotation(hor_eqd, eqd_eqj);
	10413	}
	10414
	10415
	10416	/**
	10417	* @brief
	10418	* Calculates a rotation matrix from J2000 mean equator (EQJ) to horizontal (HOR).
	10419	*
	10420	* This is one of the family of functions that returns a rotation matrix
	10421	* for converting from one orientation to another.
	10422	* Source: EQJ = equatorial system, using the equator at the J2000 epoch.
	10423	* Target: HOR = horizontal system.
	10424	*
	10425	* @param time
	10426	* The date and time of the desired horizontal orientation.
	10427	*
	10428	* @param observer
	10429	* A location near the Earth's mean sea level that defines the observer's horizon.
	10430	*
	10431	* @return
	10432	* A rotation matrix that converts EQJ to HOR at `time` and for `observer`.
	10433	* The components of the horizontal vector are:
	10434	* x = north, y = west, z = zenith (straight up from the observer).
	10435	* These components are chosen so that the "right-hand rule" works for the vector
	10436	* and so that north represents the direction where azimuth = 0.
	10437	*/
	10438	astro_rotation_t Astronomy_Rotation_EQJ_HOR(astro_time_t *time, astro_observer_t observer)
	10439	{
	10440	astro_rotation_t rot = Astronomy_Rotation_HOR_EQJ(time, observer);
	10441	return Astronomy_InverseRotation(rot);
	10442	}
	10443
	10444
	10445	/**
	10446	* @brief
	10447	* Calculates a rotation matrix from equatorial of-date (EQD) to J2000 mean ecliptic (ECL).
	10448	*
	10449	* This is one of the family of functions that returns a rotation matrix
	10450	* for converting from one orientation to another.
	10451	* Source: EQD = equatorial system, using equator of date.
	10452	* Target: ECL = ecliptic system, using equator at J2000 epoch.
	10453	*
	10454	* @param time
	10455	* The date and time of the source equator.
	10456	*
	10457	* @return
	10458	* A rotation matrix that converts EQD to ECL.
	10459	*/
	10460	astro_rotation_t Astronomy_Rotation_EQD_ECL(astro_time_t *time)
	10461	{
	10462	astro_rotation_t eqd_eqj;
	10463	astro_rotation_t eqj_ecl;
	10464
	10465	if (time == NULL)
	10466	return RotationErr(ASTRO_INVALID_PARAMETER);
	10467
	10468	eqd_eqj = Astronomy_Rotation_EQD_EQJ(time);
	10469	eqj_ecl = Astronomy_Rotation_EQJ_ECL();
	10470	return Astronomy_CombineRotation(eqd_eqj, eqj_ecl);
	10471	}
	10472
	10473
	10474	/**
	10475	* @brief
	10476	* Calculates a rotation matrix from J2000 mean ecliptic (ECL) to equatorial of-date (EQD).
	10477	*
	10478	* This is one of the family of functions that returns a rotation matrix
	10479	* for converting from one orientation to another.
	10480	* Source: ECL = ecliptic system, using equator at J2000 epoch.
	10481	* Target: EQD = equatorial system, using equator of date.
	10482	*
	10483	* @param time
	10484	* The date and time of the desired equator.
	10485	*
	10486	* @return
	10487	* A rotation matrix that converts ECL to EQD.
	10488	*/
	10489	astro_rotation_t Astronomy_Rotation_ECL_EQD(astro_time_t *time)
	10490	{
	10491	astro_rotation_t rot = Astronomy_Rotation_EQD_ECL(time);
	10492	return Astronomy_InverseRotation(rot);
	10493	}
	10494
	10495	/**
	10496	* @brief
	10497	* Calculates a rotation matrix from J2000 mean ecliptic (ECL) to horizontal (HOR).
	10498	*
	10499	* This is one of the family of functions that returns a rotation matrix
	10500	* for converting from one orientation to another.
	10501	* Source: ECL = ecliptic system, using equator at J2000 epoch.
	10502	* Target: HOR = horizontal system.
	10503	*
	10504	* @param time
	10505	* The date and time of the desired horizontal orientation.
	10506	*
	10507	* @param observer
	10508	* A location near the Earth's mean sea level that defines the observer's horizon.
	10509	*
	10510	* @return
	10511	* A rotation matrix that converts ECL to HOR at `time` and for `observer`.
	10512	* The components of the horizontal vector are:
	10513	* x = north, y = west, z = zenith (straight up from the observer).
	10514	* These components are chosen so that the "right-hand rule" works for the vector
	10515	* and so that north represents the direction where azimuth = 0.
	10516	*/
	10517	astro_rotation_t Astronomy_Rotation_ECL_HOR(astro_time_t *time, astro_observer_t observer)
	10518	{
	10519	astro_rotation_t ecl_eqd;
	10520	astro_rotation_t eqd_hor;
	10521
	10522	if (time == NULL)
	10523	return RotationErr(ASTRO_INVALID_PARAMETER);
	10524
	10525	ecl_eqd = Astronomy_Rotation_ECL_EQD(time);
	10526	eqd_hor = Astronomy_Rotation_EQD_HOR(time, observer);
	10527	return Astronomy_CombineRotation(ecl_eqd, eqd_hor);
	10528	}
	10529
	10530	/**
	10531	* @brief
	10532	* Calculates a rotation matrix from horizontal (HOR) to J2000 mean ecliptic (ECL).
	10533	*
	10534	* This is one of the family of functions that returns a rotation matrix
	10535	* for converting from one orientation to another.
	10536	* Source: HOR = horizontal system.
	10537	* Target: ECL = ecliptic system, using equator at J2000 epoch.
	10538	*
	10539	* @param time
	10540	* The date and time of the horizontal observation.
	10541	*
	10542	* @param observer
	10543	* The location of the horizontal observer.
	10544	*
	10545	* @return
	10546	* A rotation matrix that converts HOR to ECL.
	10547	*/
	10548	astro_rotation_t Astronomy_Rotation_HOR_ECL(astro_time_t *time, astro_observer_t observer)
	10549	{
	10550	astro_rotation_t rot = Astronomy_Rotation_ECL_HOR(time, observer);
	10551	return Astronomy_InverseRotation(rot);
	10552	}
	10553
	10554	/**
	10555	* @brief
	10556	* Returns a rotation matrix from J2000 mean ecliptic (EQJ) to galactic (GAL).
	10557	*
	10558	* This is one of the family of functions that returns a rotation matrix
	10559	* for converting from one orientation to another.
	10560	* Source: EQJ = equatorial system, using the equator at the J2000 epoch.
	10561	* Target: GAL = galactic system (IAU 1958 definition).
	10562	*
	10563	* @return
	10564	* A rotation matrix that converts EQJ to GAL.
	10565	*/
	10566	astro_rotation_t Astronomy_Rotation_EQJ_GAL(void)
	10567	{
	10568	astro_rotation_t rot;
	10569
	10570	/*
	10571	This rotation matrix was calculated by the following script
	10572	in this same source code repository:
	10573	demo/python/galeqj_matrix.py
	10574	*/
	10575
	10576	rot.rot[0][0] = -0.0548624779711344;
	10577	rot.rot[0][1] = +0.4941095946388765;
	10578	rot.rot[0][2] = -0.8676668813529025;
	10579
	10580	rot.rot[1][0] = -0.8734572784246782;
	10581	rot.rot[1][1] = -0.4447938112296831;
	10582	rot.rot[1][2] = -0.1980677870294097;
	10583
	10584	rot.rot[2][0] = -0.4838000529948520;
	10585	rot.rot[2][1] = +0.7470034631630423;
	10586	rot.rot[2][2] = +0.4559861124470794;
	10587
	10588	rot.status = ASTRO_SUCCESS;
	10589
	10590	return rot;
	10591	}
	10592
	10593	/**
	10594	* @brief
	10595	* Returns a rotation matrix from ecliptic galactic (GAL) to J2000 (EQJ).
	10596	*
	10597	* This is one of the family of functions that returns a rotation matrix
	10598	* for converting from one orientation to another.
	10599	* Source: GAL = galactic system (IAU 1958 definition).
	10600	* Target: EQJ = equatorial system, using the equator at the J2000 epoch.
	10601	*
	10602	* @return
	10603	* A rotation matrix that converts GAL to EQJ.
	10604	*/
	10605	astro_rotation_t Astronomy_Rotation_GAL_EQJ(void)
	10606	{
	10607	astro_rotation_t rot;
	10608
	10609	/*
	10610	This rotation matrix was calculated by the following script
	10611	in this same source code repository:
	10612	demo/python/galeqj_matrix.py
	10613	*/
	10614
	10615	rot.rot[0][0] = -0.0548624779711344;
	10616	rot.rot[0][1] = -0.8734572784246782;
	10617	rot.rot[0][2] = -0.4838000529948520;
	10618
	10619	rot.rot[1][0] = +0.4941095946388765;
	10620	rot.rot[1][1] = -0.4447938112296831;
	10621	rot.rot[1][2] = +0.7470034631630423;
	10622
	10623	rot.rot[2][0] = -0.8676668813529025;
	10624	rot.rot[2][1] = -0.1980677870294097;
	10625	rot.rot[2][2] = +0.4559861124470794;
	10626
	10627	rot.status = ASTRO_SUCCESS;
	10628
	10629	return rot;
	10630	}
	10631
	10632
	10633	/**
	10634	* @brief
	10635	* Returns a rotation matrix from true ecliptic of date (ECT) to equator of date (EQD).
	10636	*
	10637	* This is one of the family of functions that returns a rotation matrix
	10638	* for converting from one orientation to another.
	10639	* Source: ECT = true ecliptic of date.
	10640	* Target: EQD = equator of date.
	10641	*
	10642	* @param time
	10643	* The date and time of the ecliptic/equator conversion.
	10644	*
	10645	* @return
	10646	* A rotation matrix that converts ECT to EQD.
	10647	*/
	10648	astro_rotation_t Astronomy_Rotation_ECT_EQD(astro_time_t *time)
	10649	{
	10650	astro_rotation_t m;
	10651	earth_tilt_t et;
	10652	double tobl, cos_tobl, sin_tobl;
	10653
	10654	if (time == NULL)
	10655	return RotationErr(ASTRO_INVALID_PARAMETER);
	10656
	10657	/* Find true ecliptic obliquity for this time. */
	10658	et = e_tilt(time);
	10659	tobl = et.tobl * DEG2RAD;
	10660	cos_tobl = cos(tobl);
	10661	sin_tobl = sin(tobl);
	10662
	10663	/* EQD.x = ECT.x */
	10664	m.rot[0][0] = 1.0;
	10665	m.rot[1][0] = 0.0;
	10666	m.rot[2][0] = 0.0;
	10667
	10668	/* EQD.y = +cosECT.y - sinECT.z */
	10669	m.rot[0][1] = 0.0;
	10670	m.rot[1][1] = +cos_tobl;
	10671	m.rot[2][1] = -sin_tobl;
	10672
	10673	/* EQD.z = +sinECT.y + cosECT.z */
	10674	m.rot[0][2] = 0.0;
	10675	m.rot[1][2] = +sin_tobl;
	10676	m.rot[2][2] = +cos_tobl;
	10677
	10678	m.status = ASTRO_SUCCESS;
	10679	return m;
	10680	}
	10681
	10682
	10683	/**
	10684	* @brief
	10685	* Returns a rotation matrix from equator of date (EQD) to true ecliptic of date (ECT).
	10686	*
	10687	* This is one of the family of functions that returns a rotation matrix
	10688	* for converting from one orientation to another.
	10689	* Source: EQD = equator of date.
	10690	* Target: ECT = true ecliptic of date.
	10691	*
	10692	* @param time
	10693	* The date and time of the equator/ecliptic conversion.
	10694	*
	10695	* @return
	10696	* A rotation matrix that converts EQD to ECT.
	10697	*/
	10698	astro_rotation_t Astronomy_Rotation_EQD_ECT(astro_time_t *time)
	10699	{
	10700	astro_rotation_t m;
	10701	earth_tilt_t et;
	10702	double tobl, cos_tobl, sin_tobl;
	10703
	10704	if (time == NULL)
	10705	return RotationErr(ASTRO_INVALID_PARAMETER);
	10706
	10707	/* Find true ecliptic obliquity for this time. */
	10708	et = e_tilt(time);
	10709	tobl = et.tobl * DEG2RAD;
	10710	cos_tobl = cos(tobl);
	10711	sin_tobl = sin(tobl);
	10712
	10713	/* ECT.x = EQD.x */
	10714	m.rot[0][0] = 1.0;
	10715	m.rot[1][0] = 0.0;
	10716	m.rot[2][0] = 0.0;
	10717
	10718	/* ECT.y = +cosEQJ.y + sinEQJ.z */
	10719	m.rot[0][1] = 0.0;
	10720	m.rot[1][1] = +cos_tobl;
	10721	m.rot[2][1] = +sin_tobl;
	10722
	10723	/* ECT.z = -sinEQJ.y + cosEQJ.z */
	10724	m.rot[0][2] = 0.0;
	10725	m.rot[1][2] = -sin_tobl;
	10726	m.rot[2][2] = +cos_tobl;
	10727
	10728	m.status = ASTRO_SUCCESS;
	10729	return m;
	10730	}
	10731
	10732
	10733	/** @cond DOXYGEN_SKIP */
	10734	typedef struct
	10735	{
	10736	const char *symbol;
	10737	const char *name;
	10738	}
	10739	constel_info_t;
	10740
	10741
	10742	typedef struct
	10743	{
	10744	int index;
	10745	double ra_lo;
	10746	double ra_hi;
	10747	double dec_lo;
	10748	}
	10749	constel_boundary_t;
	10750	/** @endcond */
	10751
	10752	#define NUM_CONSTELLATIONS 88
	10753
	10754	static const constel_info_t ConstelInfo[] = {
	10755	/* 0 */ { "And", "Andromeda" }
	10756	, /* 1 */ { "Ant", "Antila" }
	10757	, /* 2 */ { "Aps", "Apus" }
	10758	, /* 3 */ { "Aql", "Aquila" }
	10759	, /* 4 */ { "Aqr", "Aquarius" }
	10760	, /* 5 */ { "Ara", "Ara" }
	10761	, /* 6 */ { "Ari", "Aries" }
	10762	, /* 7 */ { "Aur", "Auriga" }
	10763	, /* 8 */ { "Boo", "Bootes" }
	10764	, /* 9 */ { "Cae", "Caelum" }
	10765	, /* 10 */ { "Cam", "Camelopardis" }
	10766	, /* 11 */ { "Cap", "Capricornus" }
	10767	, /* 12 */ { "Car", "Carina" }
	10768	, /* 13 */ { "Cas", "Cassiopeia" }
	10769	, /* 14 */ { "Cen", "Centaurus" }
	10770	, /* 15 */ { "Cep", "Cepheus" }
	10771	, /* 16 */ { "Cet", "Cetus" }
	10772	, /* 17 */ { "Cha", "Chamaeleon" }
	10773	, /* 18 */ { "Cir", "Circinus" }
	10774	, /* 19 */ { "CMa", "Canis Major" }
	10775	, /* 20 */ { "CMi", "Canis Minor" }
	10776	, /* 21 */ { "Cnc", "Cancer" }
	10777	, /* 22 */ { "Col", "Columba" }
	10778	, /* 23 */ { "Com", "Coma Berenices" }
	10779	, /* 24 */ { "CrA", "Corona Australis" }
	10780	, /* 25 */ { "CrB", "Corona Borealis" }
	10781	, /* 26 */ { "Crt", "Crater" }
	10782	, /* 27 */ { "Cru", "Crux" }
	10783	, /* 28 */ { "Crv", "Corvus" }
	10784	, /* 29 */ { "CVn", "Canes Venatici" }
	10785	, /* 30 */ { "Cyg", "Cygnus" }
	10786	, /* 31 */ { "Del", "Delphinus" }
	10787	, /* 32 */ { "Dor", "Dorado" }
	10788	, /* 33 */ { "Dra", "Draco" }
	10789	, /* 34 */ { "Equ", "Equuleus" }
	10790	, /* 35 */ { "Eri", "Eridanus" }
	10791	, /* 36 */ { "For", "Fornax" }
	10792	, /* 37 */ { "Gem", "Gemini" }
	10793	, /* 38 */ { "Gru", "Grus" }
	10794	, /* 39 */ { "Her", "Hercules" }
	10795	, /* 40 */ { "Hor", "Horologium" }
	10796	, /* 41 */ { "Hya", "Hydra" }
	10797	, /* 42 */ { "Hyi", "Hydrus" }
	10798	, /* 43 */ { "Ind", "Indus" }
	10799	, /* 44 */ { "Lac", "Lacerta" }
	10800	, /* 45 */ { "Leo", "Leo" }
	10801	, /* 46 */ { "Lep", "Lepus" }
	10802	, /* 47 */ { "Lib", "Libra" }
	10803	, /* 48 */ { "LMi", "Leo Minor" }
	10804	, /* 49 */ { "Lup", "Lupus" }
	10805	, /* 50 */ { "Lyn", "Lynx" }
	10806	, /* 51 */ { "Lyr", "Lyra" }
	10807	, /* 52 */ { "Men", "Mensa" }
	10808	, /* 53 */ { "Mic", "Microscopium" }
	10809	, /* 54 */ { "Mon", "Monoceros" }
	10810	, /* 55 */ { "Mus", "Musca" }
	10811	, /* 56 */ { "Nor", "Norma" }
	10812	, /* 57 */ { "Oct", "Octans" }
	10813	, /* 58 */ { "Oph", "Ophiuchus" }
	10814	, /* 59 */ { "Ori", "Orion" }
	10815	, /* 60 */ { "Pav", "Pavo" }
	10816	, /* 61 */ { "Peg", "Pegasus" }
	10817	, /* 62 */ { "Per", "Perseus" }
	10818	, /* 63 */ { "Phe", "Phoenix" }
	10819	, /* 64 */ { "Pic", "Pictor" }
	10820	, /* 65 */ { "PsA", "Pisces Austrinus" }
	10821	, /* 66 */ { "Psc", "Pisces" }
	10822	, /* 67 */ { "Pup", "Puppis" }
	10823	, /* 68 */ { "Pyx", "Pyxis" }
	10824	, /* 69 */ { "Ret", "Reticulum" }
	10825	, /* 70 */ { "Scl", "Sculptor" }
	10826	, /* 71 */ { "Sco", "Scorpius" }
	10827	, /* 72 */ { "Sct", "Scutum" }
	10828	, /* 73 */ { "Ser", "Serpens" }
	10829	, /* 74 */ { "Sex", "Sextans" }
	10830	, /* 75 */ { "Sge", "Sagitta" }
	10831	, /* 76 */ { "Sgr", "Sagittarius" }
	10832	, /* 77 */ { "Tau", "Taurus" }
	10833	, /* 78 */ { "Tel", "Telescopium" }
	10834	, /* 79 */ { "TrA", "Triangulum Australe" }
	10835	, /* 80 */ { "Tri", "Triangulum" }
	10836	, /* 81 */ { "Tuc", "Tucana" }
	10837	, /* 82 */ { "UMa", "Ursa Major" }
	10838	, /* 83 */ { "UMi", "Ursa Minor" }
	10839	, /* 84 */ { "Vel", "Vela" }
	10840	, /* 85 */ { "Vir", "Virgo" }
	10841	, /* 86 */ { "Vol", "Volans" }
	10842	, /* 87 */ { "Vul", "Vulpecula" }
	10843	};
	10844
	10845	static const constel_boundary_t ConstelBounds[] = {
	10846	{ 83, 0, 8640, 2112 } /* UMi */
	10847	, { 83, 2880, 5220, 2076 } /* UMi */
	10848	, { 83, 7560, 8280, 2068 } /* UMi */
	10849	, { 83, 6480, 7560, 2064 } /* UMi */
	10850	, { 15, 0, 2880, 2040 } /* Cep */
	10851	, { 10, 3300, 3840, 1968 } /* Cam */
	10852	, { 15, 0, 1800, 1920 } /* Cep */
	10853	, { 10, 3840, 5220, 1920 } /* Cam */
	10854	, { 83, 6300, 6480, 1920 } /* UMi */
	10855	, { 33, 7260, 7560, 1920 } /* Dra */
	10856	, { 15, 0, 1263, 1848 } /* Cep */
	10857	, { 10, 4140, 4890, 1848 } /* Cam */
	10858	, { 83, 5952, 6300, 1800 } /* UMi */
	10859	, { 15, 7260, 7440, 1800 } /* Cep */
	10860	, { 10, 2868, 3300, 1764 } /* Cam */
	10861	, { 33, 3300, 4080, 1764 } /* Dra */
	10862	, { 83, 4680, 5952, 1680 } /* UMi */
	10863	, { 13, 1116, 1230, 1632 } /* Cas */
	10864	, { 33, 7350, 7440, 1608 } /* Dra */
	10865	, { 33, 4080, 4320, 1596 } /* Dra */
	10866	, { 15, 0, 120, 1584 } /* Cep */
	10867	, { 83, 5040, 5640, 1584 } /* UMi */
	10868	, { 15, 8490, 8640, 1584 } /* Cep */
	10869	, { 33, 4320, 4860, 1536 } /* Dra */
	10870	, { 33, 4860, 5190, 1512 } /* Dra */
	10871	, { 15, 8340, 8490, 1512 } /* Cep */
	10872	, { 10, 2196, 2520, 1488 } /* Cam */
	10873	, { 33, 7200, 7350, 1476 } /* Dra */
	10874	, { 15, 7393.2, 7416, 1462 } /* Cep */
	10875	, { 10, 2520, 2868, 1440 } /* Cam */
	10876	, { 82, 2868, 3030, 1440 } /* UMa */
	10877	, { 33, 7116, 7200, 1428 } /* Dra */
	10878	, { 15, 7200, 7393.2, 1428 } /* Cep */
	10879	, { 15, 8232, 8340, 1418 } /* Cep */
	10880	, { 13, 0, 876, 1404 } /* Cas */
	10881	, { 33, 6990, 7116, 1392 } /* Dra */
	10882	, { 13, 612, 687, 1380 } /* Cas */
	10883	, { 13, 876, 1116, 1368 } /* Cas */
	10884	, { 10, 1116, 1140, 1368 } /* Cam */
	10885	, { 15, 8034, 8232, 1350 } /* Cep */
	10886	, { 10, 1800, 2196, 1344 } /* Cam */
	10887	, { 82, 5052, 5190, 1332 } /* UMa */
	10888	, { 33, 5190, 6990, 1332 } /* Dra */
	10889	, { 10, 1140, 1200, 1320 } /* Cam */
	10890	, { 15, 7968, 8034, 1320 } /* Cep */
	10891	, { 15, 7416, 7908, 1316 } /* Cep */
	10892	, { 13, 0, 612, 1296 } /* Cas */
	10893	, { 50, 2196, 2340, 1296 } /* Lyn */
	10894	, { 82, 4350, 4860, 1272 } /* UMa */
	10895	, { 33, 5490, 5670, 1272 } /* Dra */
	10896	, { 15, 7908, 7968, 1266 } /* Cep */
	10897	, { 10, 1200, 1800, 1260 } /* Cam */
	10898	, { 13, 8232, 8400, 1260 } /* Cas */
	10899	, { 33, 5670, 6120, 1236 } /* Dra */
	10900	, { 62, 735, 906, 1212 } /* Per */
	10901	, { 33, 6120, 6564, 1212 } /* Dra */
	10902	, { 13, 0, 492, 1200 } /* Cas */
	10903	, { 62, 492, 600, 1200 } /* Per */
	10904	, { 50, 2340, 2448, 1200 } /* Lyn */
	10905	, { 13, 8400, 8640, 1200 } /* Cas */
	10906	, { 82, 4860, 5052, 1164 } /* UMa */
	10907	, { 13, 0, 402, 1152 } /* Cas */
	10908	, { 13, 8490, 8640, 1152 } /* Cas */
	10909	, { 39, 6543, 6564, 1140 } /* Her */
	10910	, { 33, 6564, 6870, 1140 } /* Dra */
	10911	, { 30, 6870, 6900, 1140 } /* Cyg */
	10912	, { 62, 600, 735, 1128 } /* Per */
	10913	, { 82, 3030, 3300, 1128 } /* UMa */
	10914	, { 13, 60, 312, 1104 } /* Cas */
	10915	, { 82, 4320, 4350, 1080 } /* UMa */
	10916	, { 50, 2448, 2652, 1068 } /* Lyn */
	10917	, { 30, 7887, 7908, 1056 } /* Cyg */
	10918	, { 30, 7875, 7887, 1050 } /* Cyg */
	10919	, { 30, 6900, 6984, 1044 } /* Cyg */
	10920	, { 82, 3300, 3660, 1008 } /* UMa */
	10921	, { 82, 3660, 3882, 960 } /* UMa */
	10922	, { 8, 5556, 5670, 960 } /* Boo */
	10923	, { 39, 5670, 5880, 960 } /* Her */
	10924	, { 50, 3330, 3450, 954 } /* Lyn */
	10925	, { 0, 0, 906, 882 } /* And */
	10926	, { 62, 906, 924, 882 } /* Per */
	10927	, { 51, 6969, 6984, 876 } /* Lyr */
	10928	, { 62, 1620, 1689, 864 } /* Per */
	10929	, { 30, 7824, 7875, 864 } /* Cyg */
	10930	, { 44, 7875, 7920, 864 } /* Lac */
	10931	, { 7, 2352, 2652, 852 } /* Aur */
	10932	, { 50, 2652, 2790, 852 } /* Lyn */
	10933	, { 0, 0, 720, 840 } /* And */
	10934	, { 44, 7920, 8214, 840 } /* Lac */
	10935	, { 44, 8214, 8232, 828 } /* Lac */
	10936	, { 0, 8232, 8460, 828 } /* And */
	10937	, { 62, 924, 978, 816 } /* Per */
	10938	, { 82, 3882, 3960, 816 } /* UMa */
	10939	, { 29, 4320, 4440, 816 } /* CVn */
	10940	, { 50, 2790, 3330, 804 } /* Lyn */
	10941	, { 48, 3330, 3558, 804 } /* LMi */
	10942	, { 0, 258, 507, 792 } /* And */
	10943	, { 8, 5466, 5556, 792 } /* Boo */
	10944	, { 0, 8460, 8550, 770 } /* And */
	10945	, { 29, 4440, 4770, 768 } /* CVn */
	10946	, { 0, 8550, 8640, 752 } /* And */
	10947	, { 29, 5025, 5052, 738 } /* CVn */
	10948	, { 80, 870, 978, 736 } /* Tri */
	10949	, { 62, 978, 1620, 736 } /* Per */
	10950	, { 7, 1620, 1710, 720 } /* Aur */
	10951	, { 51, 6543, 6969, 720 } /* Lyr */
	10952	, { 82, 3960, 4320, 696 } /* UMa */
	10953	, { 30, 7080, 7530, 696 } /* Cyg */
	10954	, { 7, 1710, 2118, 684 } /* Aur */
	10955	, { 48, 3558, 3780, 684 } /* LMi */
	10956	, { 29, 4770, 5025, 684 } /* CVn */
	10957	, { 0, 0, 24, 672 } /* And */
	10958	, { 80, 507, 600, 672 } /* Tri */
	10959	, { 7, 2118, 2352, 672 } /* Aur */
	10960	, { 37, 2838, 2880, 672 } /* Gem */
	10961	, { 30, 7530, 7824, 672 } /* Cyg */
	10962	, { 30, 6933, 7080, 660 } /* Cyg */
	10963	, { 80, 690, 870, 654 } /* Tri */
	10964	, { 25, 5820, 5880, 648 } /* CrB */
	10965	, { 8, 5430, 5466, 624 } /* Boo */
	10966	, { 25, 5466, 5820, 624 } /* CrB */
	10967	, { 51, 6612, 6792, 624 } /* Lyr */
	10968	, { 48, 3870, 3960, 612 } /* LMi */
	10969	, { 51, 6792, 6933, 612 } /* Lyr */
	10970	, { 80, 600, 690, 600 } /* Tri */
	10971	, { 66, 258, 306, 570 } /* Psc */
	10972	, { 48, 3780, 3870, 564 } /* LMi */
	10973	, { 87, 7650, 7710, 564 } /* Vul */
	10974	, { 77, 2052, 2118, 548 } /* Tau */
	10975	, { 0, 24, 51, 528 } /* And */
	10976	, { 73, 5730, 5772, 528 } /* Ser */
	10977	, { 37, 2118, 2238, 516 } /* Gem */
	10978	, { 87, 7140, 7290, 510 } /* Vul */
	10979	, { 87, 6792, 6930, 506 } /* Vul */
	10980	, { 0, 51, 306, 504 } /* And */
	10981	, { 87, 7290, 7404, 492 } /* Vul */
	10982	, { 37, 2811, 2838, 480 } /* Gem */
	10983	, { 87, 7404, 7650, 468 } /* Vul */
	10984	, { 87, 6930, 7140, 460 } /* Vul */
	10985	, { 6, 1182, 1212, 456 } /* Ari */
	10986	, { 75, 6792, 6840, 444 } /* Sge */
	10987	, { 59, 2052, 2076, 432 } /* Ori */
	10988	, { 37, 2238, 2271, 420 } /* Gem */
	10989	, { 75, 6840, 7140, 388 } /* Sge */
	10990	, { 77, 1788, 1920, 384 } /* Tau */
	10991	, { 39, 5730, 5790, 384 } /* Her */
	10992	, { 75, 7140, 7290, 378 } /* Sge */
	10993	, { 77, 1662, 1788, 372 } /* Tau */
	10994	, { 77, 1920, 2016, 372 } /* Tau */
	10995	, { 23, 4620, 4860, 360 } /* Com */
	10996	, { 39, 6210, 6570, 344 } /* Her */
	10997	, { 23, 4272, 4620, 336 } /* Com */
	10998	, { 37, 2700, 2811, 324 } /* Gem */
	10999	, { 39, 6030, 6210, 308 } /* Her */
	11000	, { 61, 0, 51, 300 } /* Peg */
	11001	, { 77, 2016, 2076, 300 } /* Tau */
	11002	, { 37, 2520, 2700, 300 } /* Gem */
	11003	, { 61, 7602, 7680, 300 } /* Peg */
	11004	, { 37, 2271, 2496, 288 } /* Gem */
	11005	, { 39, 6570, 6792, 288 } /* Her */
	11006	, { 31, 7515, 7578, 284 } /* Del */
	11007	, { 61, 7578, 7602, 284 } /* Peg */
	11008	, { 45, 4146, 4272, 264 } /* Leo */
	11009	, { 59, 2247, 2271, 240 } /* Ori */
	11010	, { 37, 2496, 2520, 240 } /* Gem */
	11011	, { 21, 2811, 2853, 240 } /* Cnc */
	11012	, { 61, 8580, 8640, 240 } /* Peg */
	11013	, { 6, 600, 1182, 238 } /* Ari */
	11014	, { 31, 7251, 7308, 204 } /* Del */
	11015	, { 8, 4860, 5430, 192 } /* Boo */
	11016	, { 61, 8190, 8580, 180 } /* Peg */
	11017	, { 21, 2853, 3330, 168 } /* Cnc */
	11018	, { 45, 3330, 3870, 168 } /* Leo */
	11019	, { 58, 6570, 6718.4, 150 } /* Oph */
	11020	, { 3, 6718.4, 6792, 150 } /* Aql */
	11021	, { 31, 7500, 7515, 144 } /* Del */
	11022	, { 20, 2520, 2526, 132 } /* CMi */
	11023	, { 73, 6570, 6633, 108 } /* Ser */
	11024	, { 39, 5790, 6030, 96 } /* Her */
	11025	, { 58, 6570, 6633, 72 } /* Oph */
	11026	, { 61, 7728, 7800, 66 } /* Peg */
	11027	, { 66, 0, 720, 48 } /* Psc */
	11028	, { 73, 6690, 6792, 48 } /* Ser */
	11029	, { 31, 7308, 7500, 48 } /* Del */
	11030	, { 34, 7500, 7680, 48 } /* Equ */
	11031	, { 61, 7680, 7728, 48 } /* Peg */
	11032	, { 61, 7920, 8190, 48 } /* Peg */
	11033	, { 61, 7800, 7920, 42 } /* Peg */
	11034	, { 20, 2526, 2592, 36 } /* CMi */
	11035	, { 77, 1290, 1662, 0 } /* Tau */
	11036	, { 59, 1662, 1680, 0 } /* Ori */
	11037	, { 20, 2592, 2910, 0 } /* CMi */
	11038	, { 85, 5280, 5430, 0 } /* Vir */
	11039	, { 58, 6420, 6570, 0 } /* Oph */
	11040	, { 16, 954, 1182, -42 } /* Cet */
	11041	, { 77, 1182, 1290, -42 } /* Tau */
	11042	, { 73, 5430, 5856, -78 } /* Ser */
	11043	, { 59, 1680, 1830, -96 } /* Ori */
	11044	, { 59, 2100, 2247, -96 } /* Ori */
	11045	, { 73, 6420, 6468, -96 } /* Ser */
	11046	, { 73, 6570, 6690, -96 } /* Ser */
	11047	, { 3, 6690, 6792, -96 } /* Aql */
	11048	, { 66, 8190, 8580, -96 } /* Psc */
	11049	, { 45, 3870, 4146, -144 } /* Leo */
	11050	, { 85, 4146, 4260, -144 } /* Vir */
	11051	, { 66, 0, 120, -168 } /* Psc */
	11052	, { 66, 8580, 8640, -168 } /* Psc */
	11053	, { 85, 5130, 5280, -192 } /* Vir */
	11054	, { 58, 5730, 5856, -192 } /* Oph */
	11055	, { 3, 7200, 7392, -216 } /* Aql */
	11056	, { 4, 7680, 7872, -216 } /* Aqr */
	11057	, { 58, 6180, 6468, -240 } /* Oph */
	11058	, { 54, 2100, 2910, -264 } /* Mon */
	11059	, { 35, 1770, 1830, -264 } /* Eri */
	11060	, { 59, 1830, 2100, -264 } /* Ori */
	11061	, { 41, 2910, 3012, -264 } /* Hya */
	11062	, { 74, 3450, 3870, -264 } /* Sex */
	11063	, { 85, 4260, 4620, -264 } /* Vir */
	11064	, { 58, 6330, 6360, -280 } /* Oph */
	11065	, { 3, 6792, 7200, -288.8 } /* Aql */
	11066	, { 35, 1740, 1770, -348 } /* Eri */
	11067	, { 4, 7392, 7680, -360 } /* Aqr */
	11068	, { 73, 6180, 6570, -384 } /* Ser */
	11069	, { 72, 6570, 6792, -384 } /* Sct */
	11070	, { 41, 3012, 3090, -408 } /* Hya */
	11071	, { 58, 5856, 5895, -438 } /* Oph */
	11072	, { 41, 3090, 3270, -456 } /* Hya */
	11073	, { 26, 3870, 3900, -456 } /* Crt */
	11074	, { 71, 5856, 5895, -462 } /* Sco */
	11075	, { 47, 5640, 5730, -480 } /* Lib */
	11076	, { 28, 4530, 4620, -528 } /* Crv */
	11077	, { 85, 4620, 5130, -528 } /* Vir */
	11078	, { 41, 3270, 3510, -576 } /* Hya */
	11079	, { 16, 600, 954, -585.2 } /* Cet */
	11080	, { 35, 954, 1350, -585.2 } /* Eri */
	11081	, { 26, 3900, 4260, -588 } /* Crt */
	11082	, { 28, 4260, 4530, -588 } /* Crv */
	11083	, { 47, 5130, 5370, -588 } /* Lib */
	11084	, { 58, 5856, 6030, -590 } /* Oph */
	11085	, { 16, 0, 600, -612 } /* Cet */
	11086	, { 11, 7680, 7872, -612 } /* Cap */
	11087	, { 4, 7872, 8580, -612 } /* Aqr */
	11088	, { 16, 8580, 8640, -612 } /* Cet */
	11089	, { 41, 3510, 3690, -636 } /* Hya */
	11090	, { 35, 1692, 1740, -654 } /* Eri */
	11091	, { 46, 1740, 2202, -654 } /* Lep */
	11092	, { 11, 7200, 7680, -672 } /* Cap */
	11093	, { 41, 3690, 3810, -700 } /* Hya */
	11094	, { 41, 4530, 5370, -708 } /* Hya */
	11095	, { 47, 5370, 5640, -708 } /* Lib */
	11096	, { 71, 5640, 5760, -708 } /* Sco */
	11097	, { 35, 1650, 1692, -720 } /* Eri */
	11098	, { 58, 6030, 6336, -720 } /* Oph */
	11099	, { 76, 6336, 6420, -720 } /* Sgr */
	11100	, { 41, 3810, 3900, -748 } /* Hya */
	11101	, { 19, 2202, 2652, -792 } /* CMa */
	11102	, { 41, 4410, 4530, -792 } /* Hya */
	11103	, { 41, 3900, 4410, -840 } /* Hya */
	11104	, { 36, 1260, 1350, -864 } /* For */
	11105	, { 68, 3012, 3372, -882 } /* Pyx */
	11106	, { 35, 1536, 1650, -888 } /* Eri */
	11107	, { 76, 6420, 6900, -888 } /* Sgr */
	11108	, { 65, 7680, 8280, -888 } /* PsA */
	11109	, { 70, 8280, 8400, -888 } /* Scl */
	11110	, { 36, 1080, 1260, -950 } /* For */
	11111	, { 1, 3372, 3960, -954 } /* Ant */
	11112	, { 70, 0, 600, -960 } /* Scl */
	11113	, { 36, 600, 1080, -960 } /* For */
	11114	, { 35, 1392, 1536, -960 } /* Eri */
	11115	, { 70, 8400, 8640, -960 } /* Scl */
	11116	, { 14, 5100, 5370, -1008 } /* Cen */
	11117	, { 49, 5640, 5760, -1008 } /* Lup */
	11118	, { 71, 5760, 5911.5, -1008 } /* Sco */
	11119	, { 9, 1740, 1800, -1032 } /* Cae */
	11120	, { 22, 1800, 2370, -1032 } /* Col */
	11121	, { 67, 2880, 3012, -1032 } /* Pup */
	11122	, { 35, 1230, 1392, -1056 } /* Eri */
	11123	, { 71, 5911.5, 6420, -1092 } /* Sco */
	11124	, { 24, 6420, 6900, -1092 } /* CrA */
	11125	, { 76, 6900, 7320, -1092 } /* Sgr */
	11126	, { 53, 7320, 7680, -1092 } /* Mic */
	11127	, { 35, 1080, 1230, -1104 } /* Eri */
	11128	, { 9, 1620, 1740, -1116 } /* Cae */
	11129	, { 49, 5520, 5640, -1152 } /* Lup */
	11130	, { 63, 0, 840, -1156 } /* Phe */
	11131	, { 35, 960, 1080, -1176 } /* Eri */
	11132	, { 40, 1470, 1536, -1176 } /* Hor */
	11133	, { 9, 1536, 1620, -1176 } /* Cae */
	11134	, { 38, 7680, 7920, -1200 } /* Gru */
	11135	, { 67, 2160, 2880, -1218 } /* Pup */
	11136	, { 84, 2880, 2940, -1218 } /* Vel */
	11137	, { 35, 870, 960, -1224 } /* Eri */
	11138	, { 40, 1380, 1470, -1224 } /* Hor */
	11139	, { 63, 0, 660, -1236 } /* Phe */
	11140	, { 12, 2160, 2220, -1260 } /* Car */
	11141	, { 84, 2940, 3042, -1272 } /* Vel */
	11142	, { 40, 1260, 1380, -1276 } /* Hor */
	11143	, { 32, 1380, 1440, -1276 } /* Dor */
	11144	, { 63, 0, 570, -1284 } /* Phe */
	11145	, { 35, 780, 870, -1296 } /* Eri */
	11146	, { 64, 1620, 1800, -1296 } /* Pic */
	11147	, { 49, 5418, 5520, -1296 } /* Lup */
	11148	, { 84, 3042, 3180, -1308 } /* Vel */
	11149	, { 12, 2220, 2340, -1320 } /* Car */
	11150	, { 14, 4260, 4620, -1320 } /* Cen */
	11151	, { 49, 5100, 5418, -1320 } /* Lup */
	11152	, { 56, 5418, 5520, -1320 } /* Nor */
	11153	, { 32, 1440, 1560, -1356 } /* Dor */
	11154	, { 84, 3180, 3960, -1356 } /* Vel */
	11155	, { 14, 3960, 4050, -1356 } /* Cen */
	11156	, { 5, 6300, 6480, -1368 } /* Ara */
	11157	, { 78, 6480, 7320, -1368 } /* Tel */
	11158	, { 38, 7920, 8400, -1368 } /* Gru */
	11159	, { 40, 1152, 1260, -1380 } /* Hor */
	11160	, { 64, 1800, 1980, -1380 } /* Pic */
	11161	, { 12, 2340, 2460, -1392 } /* Car */
	11162	, { 63, 0, 480, -1404 } /* Phe */
	11163	, { 35, 480, 780, -1404 } /* Eri */
	11164	, { 63, 8400, 8640, -1404 } /* Phe */
	11165	, { 32, 1560, 1650, -1416 } /* Dor */
	11166	, { 56, 5520, 5911.5, -1440 } /* Nor */
	11167	, { 43, 7320, 7680, -1440 } /* Ind */
	11168	, { 64, 1980, 2160, -1464 } /* Pic */
	11169	, { 18, 5460, 5520, -1464 } /* Cir */
	11170	, { 5, 5911.5, 5970, -1464 } /* Ara */
	11171	, { 18, 5370, 5460, -1526 } /* Cir */
	11172	, { 5, 5970, 6030, -1526 } /* Ara */
	11173	, { 64, 2160, 2460, -1536 } /* Pic */
	11174	, { 12, 2460, 3252, -1536 } /* Car */
	11175	, { 14, 4050, 4260, -1536 } /* Cen */
	11176	, { 27, 4260, 4620, -1536 } /* Cru */
	11177	, { 14, 4620, 5232, -1536 } /* Cen */
	11178	, { 18, 4860, 4920, -1560 } /* Cir */
	11179	, { 5, 6030, 6060, -1560 } /* Ara */
	11180	, { 40, 780, 1152, -1620 } /* Hor */
	11181	, { 69, 1152, 1650, -1620 } /* Ret */
	11182	, { 18, 5310, 5370, -1620 } /* Cir */
	11183	, { 5, 6060, 6300, -1620 } /* Ara */
	11184	, { 60, 6300, 6480, -1620 } /* Pav */
	11185	, { 81, 7920, 8400, -1620 } /* Tuc */
	11186	, { 32, 1650, 2370, -1680 } /* Dor */
	11187	, { 18, 4920, 5310, -1680 } /* Cir */
	11188	, { 79, 5310, 6120, -1680 } /* TrA */
	11189	, { 81, 0, 480, -1800 } /* Tuc */
	11190	, { 42, 1260, 1650, -1800 } /* Hyi */
	11191	, { 86, 2370, 3252, -1800 } /* Vol */
	11192	, { 12, 3252, 4050, -1800 } /* Car */
	11193	, { 55, 4050, 4920, -1800 } /* Mus */
	11194	, { 60, 6480, 7680, -1800 } /* Pav */
	11195	, { 43, 7680, 8400, -1800 } /* Ind */
	11196	, { 81, 8400, 8640, -1800 } /* Tuc */
	11197	, { 81, 270, 480, -1824 } /* Tuc */
	11198	, { 42, 0, 1260, -1980 } /* Hyi */
	11199	, { 17, 2760, 4920, -1980 } /* Cha */
	11200	, { 2, 4920, 6480, -1980 } /* Aps */
	11201	, { 52, 1260, 2760, -2040 } /* Men */
	11202	, { 57, 0, 8640, -2160 } /* Oct */
	11203	};
	11204
	11205	#define NUM_CONSTEL_BOUNDARIES 357
	11206
	11207
	11208
	11209	/**
	11210	* @brief
	11211	* Determines the constellation that contains the given point in the sky.
	11212	*
	11213	* Given J2000 equatorial (EQJ) coordinates of a point in the sky, determines the
	11214	* constellation that contains that point.
	11215	*
	11216	* @param ra
	11217	* The right ascension (RA) of a point in the sky, using the J2000 equatorial system.
	11218	*
	11219	* @param dec
	11220	* The declination (DEC) of a point in the sky, using the J2000 equatorial system.
	11221	*
	11222	* @return
	11223	* If successful, `status` holds `ASTRO_SUCCESS`,
	11224	* `symbol` holds a pointer to a 3-character string like "Ori", and
	11225	* `name` holds a pointer to the full constellation name like "Orion".
	11226	*/
	11227	astro_constellation_t Astronomy_Constellation(double ra, double dec)
	11228	{
	11229	static astro_time_t epoch2000;
	11230	static astro_rotation_t rot = { ASTRO_NOT_INITIALIZED };
	11231	astro_constellation_t constel;
	11232	astro_spherical_t s2000;
	11233	astro_equatorial_t b1875;
	11234	astro_vector_t vec2000, vec1875;
	11235	double x_ra, x_dec;
	11236	int i, c;
	11237
	11238	if (dec < -90.0 \|\| dec > +90.0)
	11239	return ConstelErr(ASTRO_INVALID_PARAMETER);
	11240
	11241	/* Allow right ascension to "wrap around". Clamp to [0, 24) sidereal hours. */
	11242	ra = fmod(ra, 24.0);
	11243	if (ra < 0.0)
	11244	ra += 24.0;
	11245
	11246	/* Lazy-initialize the rotation matrix for converting J2000 to B1875. */
	11247	if (rot.status != ASTRO_SUCCESS)
	11248	{
	11249	/*
	11250	Need to calculate the B1875 epoch. Based on this:
	11251	https://en.wikipedia.org/wiki/Epoch_(astronomy)#Besselian_years
	11252	B = 1900 + (JD - 2415020.31352) / 365.242198781
	11253	I'm interested in using TT instead of JD, giving:
	11254	B = 1900 + ((TT+2451545) - 2415020.31352) / 365.242198781
	11255	B = 1900 + (TT + 36524.68648) / 365.242198781
	11256	TT = 365.242198781*(B - 1900) - 36524.68648 = -45655.741449525
	11257	But Astronomy_TimeFromDays() wants UT, not TT.
	11258	Near that date, I get a historical correction of ut-tt = 3.2 seconds.
	11259	That gives UT = -45655.74141261017 for the B1875 epoch,
	11260	or 1874-12-31T18:12:21.950Z.
	11261	*/
	11262	astro_time_t time = Astronomy_TimeFromDays(-45655.74141261017);
	11263	rot = Astronomy_Rotation_EQJ_EQD(&time);
	11264	if (rot.status != ASTRO_SUCCESS)
	11265	return ConstelErr(rot.status);
	11266
	11267	epoch2000 = Astronomy_TimeFromDays(0.0);
	11268	}
	11269
	11270	/* Convert coordinates from J2000 to year 1875. */
	11271	s2000.status = ASTRO_SUCCESS;
	11272	s2000.lon = ra * 15.0;
	11273	s2000.lat = dec;
	11274	s2000.dist = 1.0;
	11275	vec2000 = Astronomy_VectorFromSphere(s2000, epoch2000);
	11276	if (vec2000.status != ASTRO_SUCCESS)
	11277	return ConstelErr(vec2000.status);
	11278
	11279	vec1875 = Astronomy_RotateVector(rot, vec2000);
	11280	if (vec1875.status != ASTRO_SUCCESS)
	11281	return ConstelErr(vec1875.status);
	11282
	11283	b1875 = Astronomy_EquatorFromVector(vec1875);
	11284	if (b1875.status != ASTRO_SUCCESS)
	11285	return ConstelErr(b1875.status);
	11286
	11287	/* Convert DEC from degrees, and RA from hours, to compact angle units used in the ContelBounds table. */
	11288	x_ra = (24.0 * 15.0) * b1875.ra;
	11289	x_dec = 24.0 * b1875.dec;
	11290
	11291	/* Search for the constellation using the B1875 coordinates. */
	11292	c = -1; /* constellation not (yet) found */
	11293	for (i=0; i < NUM_CONSTEL_BOUNDARIES; ++i)
	11294	{
	11295	const constel_boundary_t *b = &ConstelBounds[i];
	11296	if ((b->dec_lo <= x_dec) && (b->ra_hi > x_ra) && (b->ra_lo <= x_ra))
	11297	{
	11298	c = b->index;
	11299	break;
	11300	}
	11301	}
	11302
	11303	if (c < 0 \|\| c >= NUM_CONSTELLATIONS)
	11304	return ConstelErr(ASTRO_INTERNAL_ERROR); /* should have been able to find the constellation */
	11305
	11306	constel.status = ASTRO_SUCCESS;
	11307	constel.symbol = ConstelInfo[c].symbol;
	11308	constel.name = ConstelInfo[c].name;
	11309	constel.ra_1875 = b1875.ra;
	11310	constel.dec_1875 = b1875.dec;
	11311	return constel;
	11312	}
	11313
	11314
	11315	static astro_lunar_eclipse_t LunarEclipseError(astro_status_t status)
	11316	{
	11317	astro_lunar_eclipse_t eclipse;
	11318	eclipse.status = status;
	11319	eclipse.kind = ECLIPSE_NONE;
	11320	eclipse.peak = TimeError();
	11321	eclipse.obscuration = eclipse.sd_penum = eclipse.sd_partial = eclipse.sd_total = NAN;
	11322	return eclipse;
	11323	}
	11324
	11325
	11326	/** @cond DOXYGEN_SKIP */
	11327	typedef struct
	11328	{
	11329	astro_status_t status;
	11330	astro_time_t time;
	11331	double u; /* dot product of (heliocentric earth) and (geocentric moon): defines the shadow plane where the Moon is */
	11332	double r; /* km distance between center of Moon/Earth (shaded body) and the line passing through the centers of the Sun and Earth/Moon (casting body). */
	11333	double k; /* umbra radius in km, at the shadow plane */
	11334	double p; /* penumbra radius in km, at the shadow plane */
	11335	astro_vector_t target; /* coordinates of target body relative to shadow-casting body at 'time' */
	11336	astro_vector_t dir; /* heliocentric coordinates of shadow-casting body at 'time' */
	11337	}
	11338	shadow_t; /* Represents alignment of the Moon/Earth with the Earth's/Moon's shadow, for finding eclipses. */
	11339
	11340	typedef struct
	11341	{
	11342	double radius_limit;
	11343	double direction;
	11344	}
	11345	shadow_context_t;
	11346	/** @endcond */
	11347
	11348
	11349	static double Obscuration( /* returns area of intersection of the two discs, divided by area of first disc. */
	11350	double a, /* radius of first disc */
	11351	double b, /* radius of second disc */
	11352	double c) /* distance between the centers of the discs */
	11353	{
	11354	double x; /* Horizontal location of intersection point on both circumferences */
	11355	double y; /* Positive vertical location of intersection point on both circumferences */
	11356	double radicand, lens1, lens2, obs;
	11357
	11358	if (a <= 0.0 \|\| b <= 0.0)
	11359	return 0.0; /* invalid radius */
	11360
	11361	if (c < 0.0)
	11362	return 0.0; /* invalid distance between centers */
	11363
	11364	if (c >= a + b)
	11365	return 0.0; /* the discs are too far apart to have any overlapping area */
	11366
	11367	if (c == 0.0)
	11368	{
	11369	/* The discs have a common center. Therefore, one disc is inside the other. */
	11370	return (a <= b) ? 1.0 : (bb)/(aa);
	11371	}
	11372
	11373	x = (aa - bb + cc) / (2 c);
	11374
	11375	radicand = aa - xx;
	11376	if (radicand <= 0.0)
	11377	{
	11378	/* The circumferences do not intersect, or are tangent. */
	11379	/* We already ruled out the case of non-overlapping discs. */
	11380	/* Therefore, one disc is inside the other. */
	11381	return (a <= b) ? 1.0 : (bb)/(aa);
	11382	}
	11383
	11384	/* The discs overlap fractionally in a pair of lens-shaped areas. */
	11385
	11386	y = sqrt(radicand);
	11387
	11388	/* Return the overlapping fractional area. */
	11389	/* There are two lens-shaped areas, one to the left of x, the other to the right of x. */
	11390	/* Each part is calculated by subtracting a triangular area from a sector's area. */
	11391	lens1 = aaacos(x/a) - x*y;
	11392	lens2 = bbacos((c-x)/b) - (c-x)*y;
	11393
	11394	/* Find the fractional area with respect to the first disc. */
	11395	obs = (lens1 + lens2) / (PIaa);
	11396	return obs;
	11397	}
	11398
	11399
	11400	static shadow_t ShadowError(astro_status_t status)
	11401	{
	11402	shadow_t shadow;
	11403	memset(&shadow, 0, sizeof(shadow));
	11404	shadow.status = status;
	11405	return shadow;
	11406	}
	11407
	11408
	11409	static shadow_t CalcShadow(
	11410	double body_radius_km,
	11411	astro_time_t time,
	11412	astro_vector_t target,
	11413	astro_vector_t dir)
	11414	{
	11415	double dx, dy, dz;
	11416	shadow_t shadow;
	11417
	11418	shadow.target = target;
	11419	shadow.dir = dir;
	11420
	11421	shadow.u = (dir.xtarget.x + dir.ytarget.y + dir.ztarget.z) / (dir.xdir.x + dir.ydir.y + dir.zdir.z);
	11422
	11423	dx = (shadow.u * dir.x) - target.x;
	11424	dy = (shadow.u * dir.y) - target.y;
	11425	dz = (shadow.u * dir.z) - target.z;
	11426	shadow.r = KM_PER_AU * sqrt(dxdx + dydy + dz*dz);
	11427
	11428	shadow.k = +SUN_RADIUS_KM - (1.0 + shadow.u)*(SUN_RADIUS_KM - body_radius_km);
	11429	shadow.p = -SUN_RADIUS_KM + (1.0 + shadow.u)*(SUN_RADIUS_KM + body_radius_km);
	11430	shadow.status = ASTRO_SUCCESS;
	11431	shadow.time = time;
	11432
	11433	return shadow;
	11434	}
	11435
	11436
	11437	static shadow_t PlanetShadow(astro_body_t body, double planet_radius_km, astro_time_t time)
	11438	{
	11439	astro_vector_t e, p, g;
	11440
	11441	/* Calculate light-travel-corrected vector from Earth to planet. */
	11442	g = Astronomy_GeoVector(body, time, ABERRATION);
	11443	if (g.status != ASTRO_SUCCESS)
	11444	return ShadowError(g.status);
	11445
	11446	/* Calculate light-travel-corrected vector from Earth to Sun. */
	11447	e = Astronomy_GeoVector(BODY_SUN, time, ABERRATION);
	11448	if (e.status != ASTRO_SUCCESS)
	11449	return ShadowError(e.status);
	11450
	11451	/* Deduce light-travel-corrected vector from Sun to planet. */
	11452	p.status = ASTRO_SUCCESS;
	11453	p.t = time;
	11454	p.x = g.x - e.x;
	11455	p.y = g.y - e.y;
	11456	p.z = g.z - e.z;
	11457
	11458	/* Calcluate Earth's position from the planet's point of view. */
	11459	e.x = -g.x;
	11460	e.y = -g.y;
	11461	e.z = -g.z;
	11462
	11463	return CalcShadow(planet_radius_km, time, e, p);
	11464	}
	11465
	11466
	11467	static shadow_t EarthShadow(astro_time_t time)
	11468	{
	11469	/* This function helps find when the Earth's shadow falls upon the Moon. */
	11470	astro_vector_t e, m;
	11471
	11472	/* Find geocentric Sun with aberration correction. */
	11473	e = Astronomy_GeoVector(BODY_SUN, time, ABERRATION);
	11474	if (e.status != ASTRO_SUCCESS)
	11475	return ShadowError(e.status);
	11476
	11477	/* Convert geocentric Sun to heliocentric Earth. */
	11478	/* Thus `e` points in the direction of sunlight heading toward the Earth's center. */
	11479	e.x = -e.x;
	11480	e.y = -e.y;
	11481	e.z = -e.z;
	11482
	11483	/* Find geocentric Moon. */
	11484	m = Astronomy_GeoMoon(time); /* This function never fails; no need to check return value */
	11485
	11486	return CalcShadow(EARTH_ECLIPSE_RADIUS_KM, time, m, e);
	11487	}
	11488
	11489
	11490	static shadow_t MoonShadow(astro_time_t time)
	11491	{
	11492	/* This function helps find when the Moon's shadow falls upon the Earth. */
	11493
	11494	astro_vector_t s, e, m;
	11495
	11496	/* Calculate geocentric Sun with aberration correction. */
	11497	s = Astronomy_GeoVector(BODY_SUN, time, ABERRATION);
	11498	if (s.status != ASTRO_SUCCESS)
	11499	return ShadowError(s.status);
	11500
	11501	m = Astronomy_GeoMoon(time); /* geocentric Moon */
	11502
	11503	/* Calculate lunacentric Earth. */
	11504	e.status = m.status;
	11505	e.x = -m.x;
	11506	e.y = -m.y;
	11507	e.z = -m.z;
	11508	e.t = m.t;
	11509
	11510	/* Convert geocentric moon to heliocentric Moon. */
	11511	m.x -= s.x;
	11512	m.y -= s.y;
	11513	m.z -= s.z;
	11514
	11515	return CalcShadow(MOON_MEAN_RADIUS_KM, time, e, m);
	11516	}
	11517
	11518
	11519	/** @cond DOXYGEN_SKIP */
	11520	typedef shadow_t (* shadow_func_t) (astro_time_t time);
	11521	/** @endcond */
	11522
	11523
	11524	static astro_func_result_t shadow_distance_slope(void *context, astro_time_t time)
	11525	{
	11526	const double dt = 1.0 / 86400.0;
	11527	astro_time_t t1, t2;
	11528	astro_func_result_t result;
	11529	shadow_t shadow1, shadow2;
	11530	shadow_func_t shadowfunc = (shadow_func_t) context;
	11531
	11532	t1 = Astronomy_AddDays(time, -dt);
	11533	t2 = Astronomy_AddDays(time, +dt);
	11534
	11535	shadow1 = shadowfunc(t1);
	11536	if (shadow1.status != ASTRO_SUCCESS)
	11537	return FuncError(shadow1.status);
	11538
	11539	shadow2 = shadowfunc(t2);
	11540	if (shadow2.status != ASTRO_SUCCESS)
	11541	return FuncError(shadow2.status);
	11542
	11543	result.value = (shadow2.r - shadow1.r) / dt;
	11544	result.status = ASTRO_SUCCESS;
	11545	return result;
	11546	}
	11547
	11548
	11549	static shadow_t PeakEarthShadow(astro_time_t search_center_time)
	11550	{
	11551	/* Search for when the Earth's shadow axis is closest to the center of the Moon. */
	11552
	11553	astro_time_t t1, t2;
	11554	astro_search_result_t result;
	11555	const double window = 0.03; /* days before/after full moon to search for minimum shadow distance */
	11556
	11557	t1 = Astronomy_AddDays(search_center_time, -window);
	11558	t2 = Astronomy_AddDays(search_center_time, +window);
	11559
	11560	result = Astronomy_Search(shadow_distance_slope, (void *)EarthShadow, t1, t2, 1.0);
	11561	if (result.status != ASTRO_SUCCESS)
	11562	return ShadowError(result.status);
	11563
	11564	return EarthShadow(result.time);
	11565	}
	11566
	11567
	11568	static shadow_t PeakMoonShadow(astro_time_t search_center_time)
	11569	{
	11570	/* Search for when the Moon's shadow axis is closest to the center of the Earth. */
	11571
	11572	astro_time_t t1, t2;
	11573	astro_search_result_t result;
	11574	const double window = 0.03; /* days before/after new moon to search for minimum shadow distance */
	11575
	11576	t1 = Astronomy_AddDays(search_center_time, -window);
	11577	t2 = Astronomy_AddDays(search_center_time, +window);
	11578
	11579	result = Astronomy_Search(shadow_distance_slope, (void *)MoonShadow, t1, t2, 1.0);
	11580	if (result.status != ASTRO_SUCCESS)
	11581	return ShadowError(result.status);
	11582
	11583	return MoonShadow(result.time);
	11584	}
	11585
	11586
	11587	/** @cond DOXYGEN_SKIP */
	11588	typedef struct
	11589	{
	11590	astro_body_t body;
	11591	double planet_radius_km;
	11592	double direction; /* used for transit start/finish search only */
	11593	}
	11594	planet_shadow_context_t;
	11595	/** @endcond */
	11596
	11597
	11598	static astro_func_result_t planet_shadow_distance_slope(void *context, astro_time_t time)
	11599	{
	11600	const double dt = 1.0 / 86400.0;
	11601	astro_time_t t1, t2;
	11602	astro_func_result_t result;
	11603	shadow_t shadow1, shadow2;
	11604	const planet_shadow_context_t p = (const planet_shadow_context_t ) context;
	11605
	11606	t1 = Astronomy_AddDays(time, -dt);
	11607	t2 = Astronomy_AddDays(time, +dt);
	11608
	11609	shadow1 = PlanetShadow(p->body, p->planet_radius_km, t1);
	11610	if (shadow1.status != ASTRO_SUCCESS)
	11611	return FuncError(shadow1.status);
	11612
	11613	shadow2 = PlanetShadow(p->body, p->planet_radius_km, t2);
	11614	if (shadow2.status != ASTRO_SUCCESS)
	11615	return FuncError(shadow2.status);
	11616
	11617	result.value = (shadow2.r - shadow1.r) / dt;
	11618	result.status = ASTRO_SUCCESS;
	11619	return result;
	11620	}
	11621
	11622
	11623	static shadow_t PeakPlanetShadow(astro_body_t body, double planet_radius_km, astro_time_t search_center_time)
	11624	{
	11625	/* Search for when the body's shadow is closest to the center of the Earth. */
	11626
	11627	astro_time_t t1, t2;
	11628	astro_search_result_t result;
	11629	planet_shadow_context_t context;
	11630	const double window = 1.0; /* days before/after inferior conjunction to search for minimum shadow distance */
	11631
	11632	t1 = Astronomy_AddDays(search_center_time, -window);
	11633	t2 = Astronomy_AddDays(search_center_time, +window);
	11634
	11635	context.body = body;
	11636	context.planet_radius_km = planet_radius_km;
	11637	context.direction = 0.0; /* not used in this search */
	11638
	11639	result = Astronomy_Search(planet_shadow_distance_slope, &context, t1, t2, 1.0);
	11640	if (result.status != ASTRO_SUCCESS)
	11641	return ShadowError(result.status);
	11642
	11643	return PlanetShadow(body, planet_radius_km, result.time);
	11644	}
	11645
	11646
	11647	static astro_func_result_t shadow_distance(void *context, astro_time_t time)
	11648	{
	11649	astro_func_result_t result;
	11650	const shadow_context_t p = (const shadow_context_t ) context;
	11651	shadow_t shadow = EarthShadow(time);
	11652	if (shadow.status != ASTRO_SUCCESS)
	11653	return FuncError(shadow.status);
	11654
	11655	result.value = p->direction * (shadow.r - p->radius_limit);
	11656	result.status = ASTRO_SUCCESS;
	11657	return result;
	11658	}
	11659
	11660
	11661	static double ShadowSemiDurationMinutes(astro_time_t center_time, double radius_limit, double window_minutes)
	11662	{
	11663	/* Search backwards and forwards from the center time until shadow axis distance crosses radius limit. */
	11664	double window = window_minutes / (24.0 * 60.0);
	11665	shadow_context_t context;
	11666	astro_search_result_t s1, s2;
	11667	astro_time_t before, after;
	11668
	11669	before = Astronomy_AddDays(center_time, -window);
	11670	after = Astronomy_AddDays(center_time, +window);
	11671
	11672	context.radius_limit = radius_limit;
	11673	context.direction = -1.0;
	11674	s1 = Astronomy_Search(shadow_distance, &context, before, center_time, 1.0);
	11675
	11676	context.direction = +1.0;
	11677	s2 = Astronomy_Search(shadow_distance, &context, center_time, after, 1.0);
	11678
	11679	if (s1.status != ASTRO_SUCCESS \|\| s2.status != ASTRO_SUCCESS)
	11680	return -1.0; /* something went wrong! */
	11681
	11682	return (s2.time.ut - s1.time.ut) * ((24.0 * 60.0) / 2.0); /* convert days to minutes and average the semi-durations. */
	11683	}
	11684
	11685
	11686	/**
	11687	* @brief Searches for a lunar eclipse.
	11688	*
	11689	* This function finds the first lunar eclipse that occurs after `startTime`.
	11690	* A lunar eclipse may be penumbral, partial, or total.
	11691	* See #astro_lunar_eclipse_t for more information.
	11692	* To find a series of lunar eclipses, call this function once,
	11693	* then keep calling #Astronomy_NextLunarEclipse as many times as desired,
	11694	* passing in the `peak` value returned from the previous call.
	11695	*
	11696	* @param startTime
	11697	* The date and time for starting the search for a lunar eclipse.
	11698	*
	11699	* @return
	11700	* If successful, the `status` field in the returned structure will contain `ASTRO_SUCCESS`
	11701	* and the remaining structure fields will be valid.
	11702	* Any other value indicates an error.
	11703	*/
	11704	astro_lunar_eclipse_t Astronomy_SearchLunarEclipse(astro_time_t startTime)
	11705	{
	11706	const double PruneLatitude = 1.8; /* full Moon's ecliptic latitude above which eclipse is impossible */
	11707	astro_time_t fmtime;
	11708	astro_lunar_eclipse_t eclipse;
	11709	astro_search_result_t fullmoon;
	11710	shadow_t shadow;
	11711	int fmcount;
	11712	double eclip_lat, eclip_lon, distance;
	11713
	11714	/* Iterate through consecutive full moons until we find any kind of lunar eclipse. */
	11715	fmtime = startTime;
	11716	for (fmcount=0; fmcount < 12; ++fmcount)
	11717	{
	11718	/* Search for the next full moon. Any eclipse will be near it. */
	11719	fullmoon = Astronomy_SearchMoonPhase(180.0, fmtime, 40.0);
	11720	if (fullmoon.status != ASTRO_SUCCESS)
	11721	return LunarEclipseError(fullmoon.status);
	11722
	11723	/* Pruning: if the full Moon's ecliptic latitude is too large, a lunar eclipse is not possible. */
	11724	CalcMoon(fullmoon.time.tt / 36525.0, &eclip_lon, &eclip_lat, &distance);
	11725	if (RAD2DEG * fabs(eclip_lat) < PruneLatitude)
	11726	{
	11727	/* Search near the full moon for the time when the center of the Moon */
	11728	/* is closest to the line passing through the centers of the Sun and Earth. */
	11729	shadow = PeakEarthShadow(fullmoon.time);
	11730	if (shadow.status != ASTRO_SUCCESS)
	11731	return LunarEclipseError(shadow.status);
	11732
	11733	if (shadow.r < shadow.p + MOON_MEAN_RADIUS_KM)
	11734	{
	11735	/* This is at least a penumbral eclipse. We will return a result. */
	11736	eclipse.status = ASTRO_SUCCESS;
	11737	eclipse.kind = ECLIPSE_PENUMBRAL;
	11738	eclipse.obscuration = 0.0;
	11739	eclipse.peak = shadow.time;
	11740	eclipse.sd_total = 0.0;
	11741	eclipse.sd_partial = 0.0;
	11742	eclipse.sd_penum = ShadowSemiDurationMinutes(shadow.time, shadow.p + MOON_MEAN_RADIUS_KM, 200.0);
	11743	if (eclipse.sd_penum <= 0.0)
	11744	return LunarEclipseError(ASTRO_SEARCH_FAILURE);
	11745
	11746	if (shadow.r < shadow.k + MOON_MEAN_RADIUS_KM)
	11747	{
	11748	/* This is at least a partial eclipse. */
	11749	eclipse.kind = ECLIPSE_PARTIAL;
	11750	eclipse.sd_partial = ShadowSemiDurationMinutes(shadow.time, shadow.k + MOON_MEAN_RADIUS_KM, eclipse.sd_penum);
	11751	if (eclipse.sd_partial <= 0.0)
	11752	return LunarEclipseError(ASTRO_SEARCH_FAILURE);
	11753
	11754	if (shadow.r + MOON_MEAN_RADIUS_KM < shadow.k)
	11755	{
	11756	/* This is a total eclipse. */
	11757	eclipse.kind = ECLIPSE_TOTAL;
	11758	eclipse.obscuration = 1.0;
	11759	eclipse.sd_total = ShadowSemiDurationMinutes(shadow.time, shadow.k - MOON_MEAN_RADIUS_KM, eclipse.sd_partial);
	11760	if (eclipse.sd_total <= 0.0)
	11761	return LunarEclipseError(ASTRO_SEARCH_FAILURE);
	11762	}
	11763	else
	11764	{
	11765	/* For lunar eclipses, we calculate the fraction of the Moon's disc covered by the Earth's umbra. */
	11766	eclipse.obscuration = Obscuration(MOON_MEAN_RADIUS_KM, shadow.k, shadow.r);
	11767	}
	11768	}
	11769	return eclipse;
	11770	}
	11771	}
	11772
	11773	/* We didn't find an eclipse on this full moon, so search for the next one. */
	11774	fmtime = Astronomy_AddDays(fullmoon.time, 10.0);
	11775	}
	11776
	11777	/* Safety valve to prevent infinite loop. */
	11778	/* This should never happen, because at least 2 lunar eclipses happen per year. */
	11779	return LunarEclipseError(ASTRO_INTERNAL_ERROR);
	11780	}
	11781
	11782	/**
	11783	* @brief Searches for the next lunar eclipse in a series.
	11784	*
	11785	* After using #Astronomy_SearchLunarEclipse to find the first lunar eclipse
	11786	* in a series, you can call this function to find the next consecutive lunar eclipse.
	11787	* Pass in the `peak` value from the #astro_lunar_eclipse_t returned by the
	11788	* previous call to `Astronomy_SearchLunarEclipse` or `Astronomy_NextLunarEclipse`
	11789	* to find the next lunar eclipse.
	11790	*
	11791	* @param prevEclipseTime
	11792	* A date and time near a full moon. Lunar eclipse search will start at the next full moon.
	11793	*
	11794	* @return
	11795	* If successful, the `status` field in the returned structure will contain `ASTRO_SUCCESS`
	11796	* and the remaining structure fields will be valid.
	11797	* Any other value indicates an error.
	11798	*/
	11799	astro_lunar_eclipse_t Astronomy_NextLunarEclipse(astro_time_t prevEclipseTime)
	11800	{
	11801	astro_time_t startTime = Astronomy_AddDays(prevEclipseTime, 10.0);
	11802	return Astronomy_SearchLunarEclipse(startTime);
	11803	}
	11804
	11805
	11806	static astro_global_solar_eclipse_t GlobalSolarEclipseError(astro_status_t status)
	11807	{
	11808	astro_global_solar_eclipse_t eclipse;
	11809
	11810	eclipse.status = status;
	11811	eclipse.kind = ECLIPSE_NONE;
	11812	eclipse.peak = TimeError();
	11813	eclipse.obscuration = eclipse.distance = eclipse.latitude = eclipse.longitude = NAN;
	11814
	11815	return eclipse;
	11816	}
	11817
	11818	/* The umbra radius tells us what kind of eclipse the observer sees. */
	11819	/* If the umbra radius is positive, this is a total eclipse. Otherwise, it's annular. */
	11820	/* HACK: I added a tiny bias (14 meters) to match Espenak test data. */
	11821	#define EclipseKindFromUmbra(k) (((k) > 0.014) ? ECLIPSE_TOTAL : ECLIPSE_ANNULAR)
	11822
	11823	static double SolarEclipseObscuration(
	11824	astro_vector_t hm, /* heliocentric Moon */
	11825	astro_vector_t lo) /* lunacentric observer */
	11826	{
	11827	astro_vector_t ho; /* heliocentric observer */
	11828	astro_angle_result_t sun_moon_separation;
	11829	double obscuration, sun_au, sun_radius, moon_radius;
	11830
	11831	/* Find heliocentric observer. */
	11832	ho.status = ASTRO_SUCCESS;
	11833	ho.t = lo.t;
	11834	ho.x = hm.x + lo.x;
	11835	ho.y = hm.y + lo.y;
	11836	ho.z = hm.z + lo.z;
	11837
	11838	/* Find the distance from the Sun's center to the observer. */
	11839	sun_au = Astronomy_VectorLength(ho);
	11840
	11841	/* Calculate the apparent angular radius of the Sun for the observer. */
	11842	sun_radius = asin(SUN_RADIUS_AU / sun_au);
	11843
	11844	/* Calculate the apparent angular radius of the Moon for the observer. */
	11845	moon_radius = asin(MOON_POLAR_RADIUS_AU / Astronomy_VectorLength(lo));
	11846
	11847	/* Calculate the apparent angular separation between the Sun's center and the Moon's center. */
	11848	sun_moon_separation = Astronomy_AngleBetween(lo, ho);
	11849
	11850	if (sun_moon_separation.status != ASTRO_SUCCESS)
	11851	return -1.0; /* internal error! should never happen. */
	11852
	11853	obscuration = Obscuration(sun_radius, moon_radius, sun_moon_separation.angle * DEG2RAD);
	11854
	11855	/* HACK: In marginal cases, we need to clamp obscuration to less than 1.0. */
	11856	if (obscuration > 0.9999)
	11857	obscuration = 0.9999;
	11858
	11859	return obscuration;
	11860	}
	11861
	11862	static astro_global_solar_eclipse_t GeoidIntersect(shadow_t shadow)
	11863	{
	11864	astro_global_solar_eclipse_t eclipse;
	11865	astro_rotation_t rot, inv;
	11866	astro_vector_t v, e, o;
	11867	shadow_t surface;
	11868	double A, B, C, radic, u, R;
	11869	double px, py, pz, proj;
	11870	double gast;
	11871
	11872	eclipse.status = ASTRO_SUCCESS;
	11873	eclipse.kind = ECLIPSE_PARTIAL;
	11874	eclipse.peak = shadow.time;
	11875	eclipse.distance = shadow.r;
	11876	eclipse.latitude = eclipse.longitude = NAN;
	11877
	11878	/*
	11879	We want to calculate the intersection of the shadow axis with the Earth's geoid.
	11880	First we must convert EQJ (equator of J2000) coordinates to EQD (equator of date)
	11881	coordinates that are perfectly aligned with the Earth's equator at this
	11882	moment in time.
	11883	*/
	11884	rot = Astronomy_Rotation_EQJ_EQD(&shadow.time);
	11885	if (rot.status != ASTRO_SUCCESS)
	11886	return GlobalSolarEclipseError(rot.status);
	11887
	11888	v = Astronomy_RotateVector(rot, shadow.dir); /* shadow-axis vector in equator-of-date coordinates */
	11889	if (v.status != ASTRO_SUCCESS)
	11890	return GlobalSolarEclipseError(v.status);
	11891
	11892	e = Astronomy_RotateVector(rot, shadow.target); /* lunacentric Earth in equator-of-date coordinates */
	11893	if (e.status != ASTRO_SUCCESS)
	11894	return GlobalSolarEclipseError(e.status);
	11895
	11896	/*
	11897	Convert all distances from AU to km.
	11898	But dilate the z-coordinates so that the Earth becomes a perfect sphere.
	11899	Then find the intersection of the vector with the sphere.
	11900	See p 184 in Montenbruck & Pfleger's "Astronomy on the Personal Computer", second edition.
	11901	*/
	11902	v.x *= KM_PER_AU;
	11903	v.y *= KM_PER_AU;
	11904	v.z *= KM_PER_AU / EARTH_FLATTENING;
	11905
	11906	e.x *= KM_PER_AU;
	11907	e.y *= KM_PER_AU;
	11908	e.z *= KM_PER_AU / EARTH_FLATTENING;
	11909
	11910	/*
	11911	Solve the quadratic equation that finds whether and where
	11912	the shadow axis intersects with the Earth in the dilated coordinate system.
	11913	*/
	11914	R = EARTH_EQUATORIAL_RADIUS_KM;
	11915	A = v.xv.x + v.yv.y + v.z*v.z;
	11916	B = -2.0 * (v.xe.x + v.ye.y + v.z*e.z);
	11917	C = (e.xe.x + e.ye.y + e.ze.z) - RR;
	11918	radic = BB - 4A*C;
	11919
	11920	if (radic > 0.0)
	11921	{
	11922	/* Calculate the closer of the two intersection points. */
	11923	/* This will be on the day side of the Earth. */
	11924	u = (-B - sqrt(radic)) / (2 * A);
	11925
	11926	/* Convert lunacentric dilated coordinates to geocentric coordinates. */
	11927	px = u*v.x - e.x;
	11928	py = u*v.y - e.y;
	11929	pz = (uv.z - e.z) EARTH_FLATTENING;
	11930
	11931	/* Convert cartesian coordinates into geodetic latitude/longitude. */
	11932	proj = hypot(px, py) * (EARTH_FLATTENING * EARTH_FLATTENING);
	11933	if (proj == 0.0)
	11934	eclipse.latitude = (pz > 0.0) ? +90.0 : -90.0;
	11935	else
	11936	eclipse.latitude = RAD2DEG * atan(pz / proj);
	11937
	11938	/* Adjust longitude for Earth's rotation at the given UT. */
	11939	gast = Astronomy_SiderealTime(&eclipse.peak);
	11940	eclipse.longitude = fmod((RAD2DEGatan2(py, px)) - (15gast), 360.0);
	11941	if (eclipse.longitude <= -180.0)
	11942	eclipse.longitude += 360.0;
	11943	else if (eclipse.longitude > +180.0)
	11944	eclipse.longitude -= 360.0;
	11945
	11946	/* We want to determine whether the observer sees a total eclipse or an annular eclipse. */
	11947	/* We need to perform a series of vector calculations... */
	11948	/* Calculate the inverse rotation matrix, so we can convert EQD to EQJ. */
	11949	inv = Astronomy_InverseRotation(rot);
	11950	if (inv.status != ASTRO_SUCCESS)
	11951	return GlobalSolarEclipseError(inv.status);
	11952
	11953	/* Put the EQD geocentric coordinates of the observer into the vector 'o'. */
	11954	/* Also convert back from kilometers to astronomical units. */
	11955	o.status = ASTRO_SUCCESS;
	11956	o.t = shadow.time;
	11957	o.x = px / KM_PER_AU;
	11958	o.y = py / KM_PER_AU;
	11959	o.z = pz / KM_PER_AU;
	11960
	11961	/* Rotate the observer's geocentric EQD back to the EQJ system. */
	11962	o = Astronomy_RotateVector(inv, o);
	11963
	11964	/* Convert geocentric vector to lunacentric vector. */
	11965	o.x += shadow.target.x;
	11966	o.y += shadow.target.y;
	11967	o.z += shadow.target.z;
	11968
	11969	/* Recalculate the shadow using a vector from the Moon's center toward the observer. */
	11970	surface = CalcShadow(MOON_POLAR_RADIUS_KM, shadow.time, o, shadow.dir);
	11971
	11972	/* If we did everything right, the shadow distance should be very close to zero. */
	11973	/* That's because we already determined the observer 'o' is on the shadow axis! */
	11974	if (surface.r > 1.0e-9 \|\| surface.r < 0.0)
	11975	return GlobalSolarEclipseError(ASTRO_INTERNAL_ERROR);
	11976
	11977	eclipse.kind = EclipseKindFromUmbra(surface.k);
	11978	if (eclipse.kind == ECLIPSE_TOTAL)
	11979	eclipse.obscuration = 1.0;
	11980	else
	11981	eclipse.obscuration = SolarEclipseObscuration(shadow.dir, o);
	11982	}
	11983	else
	11984	{
	11985	/* This is a partial solar eclipse. It does not make practical sense to calculate obscuration. */
	11986	/* Anyone who wants obscuration should use Astronomy_SearchLocalSolarEclipse for a specific location on the Earth. */
	11987	eclipse.obscuration = NAN;
	11988	}
	11989
	11990	return eclipse;
	11991	}
	11992
	11993
	11994	/**
	11995	* @brief Searches for a solar eclipse visible anywhere on the Earth's surface.
	11996	*
	11997	* This function finds the first solar eclipse that occurs after `startTime`.
	11998	* A solar eclipse may be partial, annular, or total.
	11999	* See #astro_global_solar_eclipse_t for more information.
	12000	* To find a series of solar eclipses, call this function once,
	12001	* then keep calling #Astronomy_NextGlobalSolarEclipse as many times as desired,
	12002	* passing in the `peak` value returned from the previous call.
	12003	*
	12004	* @param startTime
	12005	* The date and time for starting the search for a solar eclipse.
	12006	*
	12007	* @return
	12008	* If successful, the `status` field in the returned structure will contain `ASTRO_SUCCESS`
	12009	* and the remaining structure fields are as described in #astro_global_solar_eclipse_t.
	12010	* Any other value indicates an error.
	12011	*/
	12012	astro_global_solar_eclipse_t Astronomy_SearchGlobalSolarEclipse(astro_time_t startTime)
	12013	{
	12014	const double PruneLatitude = 1.8; /* Moon's ecliptic latitude beyond which eclipse is impossible */
	12015	astro_time_t nmtime;
	12016	astro_search_result_t newmoon;
	12017	shadow_t shadow;
	12018	int nmcount;
	12019	double eclip_lat, eclip_lon, distance;
	12020
	12021	/* Iterate through consecutive new moons until we find a solar eclipse visible somewhere on Earth. */
	12022	nmtime = startTime;
	12023	for (nmcount=0; nmcount < 12; ++nmcount)
	12024	{
	12025	/* Search for the next new moon. Any eclipse will be near it. */
	12026	newmoon = Astronomy_SearchMoonPhase(0.0, nmtime, 40.0);
	12027	if (newmoon.status != ASTRO_SUCCESS)
	12028	return GlobalSolarEclipseError(newmoon.status);
	12029
	12030	/* Pruning: if the new moon's ecliptic latitude is too large, a solar eclipse is not possible. */
	12031	CalcMoon(newmoon.time.tt / 36525.0, &eclip_lon, &eclip_lat, &distance);
	12032	if (RAD2DEG * fabs(eclip_lat) < PruneLatitude)
	12033	{
	12034	/* Search near the new moon for the time when the center of the Earth */
	12035	/* is closest to the line passing through the centers of the Sun and Moon. */
	12036	shadow = PeakMoonShadow(newmoon.time);
	12037	if (shadow.status != ASTRO_SUCCESS)
	12038	return GlobalSolarEclipseError(shadow.status);
	12039
	12040	if (shadow.r < shadow.p + EARTH_MEAN_RADIUS_KM)
	12041	{
	12042	/* This is at least a partial solar eclipse visible somewhere on Earth. */
	12043	/* Try to find an intersection between the shadow axis and the Earth's oblate geoid. */
	12044	return GeoidIntersect(shadow);
	12045	}
	12046	}
	12047
	12048	/* We didn't find an eclipse on this new moon, so search for the next one. */
	12049	nmtime = Astronomy_AddDays(newmoon.time, 10.0);
	12050	}
	12051
	12052	/* Safety valve to prevent infinite loop. */
	12053	/* This should never happen, because at least 2 solar eclipses happen per year. */
	12054	return GlobalSolarEclipseError(ASTRO_INTERNAL_ERROR);
	12055	}
	12056
	12057
	12058	/**
	12059	* @brief Searches for the next global solar eclipse in a series.
	12060	*
	12061	* After using #Astronomy_SearchGlobalSolarEclipse to find the first solar eclipse
	12062	* in a series, you can call this function to find the next consecutive solar eclipse.
	12063	* Pass in the `peak` value from the #astro_global_solar_eclipse_t returned by the
	12064	* previous call to `Astronomy_SearchGlobalSolarEclipse` or `Astronomy_NextGlobalSolarEclipse`
	12065	* to find the next solar eclipse.
	12066	*
	12067	* @param prevEclipseTime
	12068	* A date and time near a new moon. Solar eclipse search will start at the next new moon.
	12069	*
	12070	* @return
	12071	* If successful, the `status` field in the returned structure will contain `ASTRO_SUCCESS`
	12072	* and the remaining structure fields are as described in #astro_global_solar_eclipse_t.
	12073	* Any other value indicates an error.
	12074	*/
	12075	astro_global_solar_eclipse_t Astronomy_NextGlobalSolarEclipse(astro_time_t prevEclipseTime)
	12076	{
	12077	astro_time_t startTime = Astronomy_AddDays(prevEclipseTime, 10.0);
	12078	return Astronomy_SearchGlobalSolarEclipse(startTime);
	12079	}
	12080
	12081
	12082	static astro_eclipse_event_t EclipseEventError(void)
	12083	{
	12084	astro_eclipse_event_t evt;
	12085	evt.time = TimeError();
	12086	evt.altitude = NAN;
	12087	return evt;
	12088	}
	12089
	12090
	12091	static astro_local_solar_eclipse_t LocalSolarEclipseError(astro_status_t status)
	12092	{
	12093	astro_local_solar_eclipse_t eclipse;
	12094
	12095	eclipse.status = status;
	12096	eclipse.kind = ECLIPSE_NONE;
	12097	eclipse.obscuration = NAN;
	12098
	12099	eclipse.partial_begin = EclipseEventError();
	12100	eclipse.total_begin = EclipseEventError();
	12101	eclipse.peak = EclipseEventError();
	12102	eclipse.total_end = EclipseEventError();
	12103	eclipse.partial_end = EclipseEventError();
	12104
	12105	return eclipse;
	12106	}
	12107
	12108
	12109	static shadow_t LocalMoonShadow(astro_time_t time, astro_observer_t observer)
	12110	{
	12111	astro_vector_t s, o, m;
	12112	double pos[3];
	12113
	12114	/* Calculate observer's geocentric position. */
	12115	/* For efficiency, do this first, to populate the earth rotation parameters in 'time'. */
	12116	/* That way they can be recycled instead of recalculated. */
	12117	geo_pos(&time, observer, pos);
	12118
	12119	/* Calculate geocentric Sun with aberration correction. */
	12120	s = Astronomy_GeoVector(BODY_SUN, time, ABERRATION);
	12121	if (s.status != ASTRO_SUCCESS)
	12122	return ShadowError(s.status);
	12123
	12124	m = Astronomy_GeoMoon(time); /* geocentric Moon */
	12125
	12126	/* Calculate lunacentric location of an observer on the Earth's surface. */
	12127	o.status = m.status;
	12128	o.x = pos[0] - m.x;
	12129	o.y = pos[1] - m.y;
	12130	o.z = pos[2] - m.z;
	12131	o.t = m.t;
	12132
	12133	/* Convert geocentric moon to heliocentric Moon. */
	12134	m.x -= s.x;
	12135	m.y -= s.y;
	12136	m.z -= s.z;
	12137
	12138	return CalcShadow(MOON_MEAN_RADIUS_KM, time, o, m);
	12139	}
	12140
	12141
	12142	static astro_func_result_t local_shadow_distance_slope(void *context, astro_time_t time)
	12143	{
	12144	const double dt = 1.0 / 86400.0;
	12145	astro_time_t t1, t2;
	12146	astro_func_result_t result;
	12147	shadow_t shadow1, shadow2;
	12148	const astro_observer_t observer = (const astro_observer_t ) context;
	12149
	12150	t1 = Astronomy_AddDays(time, -dt);
	12151	t2 = Astronomy_AddDays(time, +dt);
	12152
	12153	shadow1 = LocalMoonShadow(t1, *observer);
	12154	if (shadow1.status != ASTRO_SUCCESS)
	12155	return FuncError(shadow1.status);
	12156
	12157	shadow2 = LocalMoonShadow(t2, *observer);
	12158	if (shadow2.status != ASTRO_SUCCESS)
	12159	return FuncError(shadow2.status);
	12160
	12161	result.value = (shadow2.r - shadow1.r) / dt;
	12162	result.status = ASTRO_SUCCESS;
	12163	return result;
	12164	}
	12165
	12166
	12167	static shadow_t PeakLocalMoonShadow(astro_time_t search_center_time, astro_observer_t observer)
	12168	{
	12169	astro_time_t t1, t2;
	12170	astro_search_result_t result;
	12171	const double window = 0.2;
	12172
	12173	/*
	12174	Search for the time near search_center_time that the Moon's shadow comes
	12175	closest to the given observer.
	12176	*/
	12177
	12178	t1 = Astronomy_AddDays(search_center_time, -window);
	12179	t2 = Astronomy_AddDays(search_center_time, +window);
	12180
	12181	result = Astronomy_Search(local_shadow_distance_slope, &observer, t1, t2, 1.0);
	12182	if (result.status != ASTRO_SUCCESS)
	12183	return ShadowError(result.status);
	12184
	12185	return LocalMoonShadow(result.time, observer);
	12186	}
	12187
	12188
	12189	static double local_partial_distance(const shadow_t *shadow)
	12190	{
	12191	return shadow->p - shadow->r;
	12192	}
	12193
	12194	static double local_total_distance(const shadow_t *shadow)
	12195	{
	12196	/* Must take the absolute value of the umbra radius 'k' */
	12197	/* because it can be negative for an annular eclipse. */
	12198	return fabs(shadow->k) - shadow->r;
	12199	}
	12200
	12201	/** @cond DOXYGEN_SKIP */
	12202	typedef double (* local_distance_func) (const shadow_t *shadow);
	12203
	12204	typedef struct
	12205	{
	12206	local_distance_func func;
	12207	double direction;
	12208	astro_observer_t observer;
	12209	}
	12210	eclipse_transition_t;
	12211	/* @endcond */
	12212
	12213
	12214	static astro_func_result_t local_eclipse_func(void *context, astro_time_t time)
	12215	{
	12216	const eclipse_transition_t trans = (const eclipse_transition_t ) context;
	12217	shadow_t shadow;
	12218	astro_func_result_t result;
	12219
	12220	shadow = LocalMoonShadow(time, trans->observer);
	12221	if (shadow.status != ASTRO_SUCCESS)
	12222	return FuncError(shadow.status);
	12223
	12224	result.value = trans->direction * trans->func(&shadow);
	12225	result.status = ASTRO_SUCCESS;
	12226	return result;
	12227	}
	12228
	12229
	12230	astro_func_result_t SunAltitude(
	12231	astro_time_t time,
	12232	astro_observer_t observer)
	12233	{
	12234	astro_equatorial_t equ;
	12235	astro_horizon_t hor;
	12236	astro_func_result_t result;
	12237
	12238	equ = Astronomy_Equator(BODY_SUN, &time, observer, EQUATOR_OF_DATE, ABERRATION);
	12239	if (equ.status != ASTRO_SUCCESS)
	12240	return FuncError(equ.status);
	12241
	12242	hor = Astronomy_Horizon(&time, observer, equ.ra, equ.dec, REFRACTION_NORMAL);
	12243	result.value = hor.altitude;
	12244	result.status = ASTRO_SUCCESS;
	12245	return result;
	12246	}
	12247
	12248
	12249	static astro_status_t CalcEvent(
	12250	astro_observer_t observer,
	12251	astro_time_t time,
	12252	astro_eclipse_event_t *evt)
	12253	{
	12254	astro_func_result_t result;
	12255
	12256	result = SunAltitude(time, observer);
	12257	if (result.status != ASTRO_SUCCESS)
	12258	{
	12259	evt->time = TimeError();
	12260	evt->altitude = NAN;
	12261	return result.status;
	12262	}
	12263
	12264	evt->time = time;
	12265	evt->altitude = result.value;
	12266	return ASTRO_SUCCESS;
	12267	}
	12268
	12269
	12270	static astro_status_t LocalEclipseTransition(
	12271	astro_observer_t observer,
	12272	double direction,
	12273	local_distance_func func,
	12274	astro_time_t t1,
	12275	astro_time_t t2,
	12276	astro_eclipse_event_t *evt)
	12277	{
	12278	eclipse_transition_t trans;
	12279	astro_search_result_t search;
	12280
	12281	trans.func = func;
	12282	trans.direction = direction;
	12283	trans.observer = observer;
	12284
	12285	search = Astronomy_Search(local_eclipse_func, &trans, t1, t2, 1.0);
	12286	if (search.status != ASTRO_SUCCESS)
	12287	{
	12288	evt->time = TimeError();
	12289	evt->altitude = NAN;
	12290	return search.status;
	12291	}
	12292
	12293	return CalcEvent(observer, search.time, evt);
	12294	}
	12295
	12296
	12297	static astro_local_solar_eclipse_t LocalEclipse(
	12298	shadow_t shadow,
	12299	astro_observer_t observer)
	12300	{
	12301	const double PARTIAL_WINDOW = 0.2;
	12302	const double TOTAL_WINDOW = 0.01;
	12303	astro_local_solar_eclipse_t eclipse;
	12304	astro_time_t t1, t2;
	12305	astro_status_t status;
	12306
	12307	status = CalcEvent(observer, shadow.time, &eclipse.peak);
	12308	if (status != ASTRO_SUCCESS)
	12309	return LocalSolarEclipseError(status);
	12310
	12311	t1 = Astronomy_AddDays(shadow.time, -PARTIAL_WINDOW);
	12312	t2 = Astronomy_AddDays(shadow.time, +PARTIAL_WINDOW);
	12313
	12314	status = LocalEclipseTransition(observer, +1.0, local_partial_distance, t1, shadow.time, &eclipse.partial_begin);
	12315	if (status != ASTRO_SUCCESS)
	12316	return LocalSolarEclipseError(status);
	12317
	12318	status = LocalEclipseTransition(observer, -1.0, local_partial_distance, shadow.time, t2, &eclipse.partial_end);
	12319	if (status != ASTRO_SUCCESS)
	12320	return LocalSolarEclipseError(status);
	12321
	12322	if (shadow.r < fabs(shadow.k)) /* take absolute value of 'k' to handle annular eclipses too. */
	12323	{
	12324	t1 = Astronomy_AddDays(shadow.time, -TOTAL_WINDOW);
	12325	t2 = Astronomy_AddDays(shadow.time, +TOTAL_WINDOW);
	12326
	12327	status = LocalEclipseTransition(observer, +1.0, local_total_distance, t1, shadow.time, &eclipse.total_begin);
	12328	if (status != ASTRO_SUCCESS)
	12329	return LocalSolarEclipseError(status);
	12330
	12331	status = LocalEclipseTransition(observer, -1.0, local_total_distance, shadow.time, t2, &eclipse.total_end);
	12332	if (status != ASTRO_SUCCESS)
	12333	return LocalSolarEclipseError(status);
	12334
	12335	eclipse.kind = EclipseKindFromUmbra(shadow.k);
	12336	if (eclipse.kind == ECLIPSE_TOTAL)
	12337	eclipse.obscuration = 1.0;
	12338	else
	12339	eclipse.obscuration = SolarEclipseObscuration(shadow.dir, shadow.target);
	12340	}
	12341	else
	12342	{
	12343	eclipse.total_begin = eclipse.total_end = EclipseEventError();
	12344	eclipse.kind = ECLIPSE_PARTIAL;
	12345	eclipse.obscuration = SolarEclipseObscuration(shadow.dir, shadow.target);
	12346	}
	12347
	12348	eclipse.status = ASTRO_SUCCESS;
	12349	return eclipse;
	12350	}
	12351
	12352
	12353	/**
	12354	* @brief Searches for a solar eclipse visible at a specific location on the Earth's surface.
	12355	*
	12356	* This function finds the first solar eclipse that occurs after `startTime`.
	12357	* A solar eclipse may be partial, annular, or total.
	12358	* See #astro_local_solar_eclipse_t for more information.
	12359	* To find a series of solar eclipses, call this function once,
	12360	* then keep calling #Astronomy_NextLocalSolarEclipse as many times as desired,
	12361	* passing in the `peak` value returned from the previous call.
	12362	*
	12363	* IMPORTANT: An eclipse reported by this function might be partly or
	12364	* completely invisible to the observer due to the time of day.
	12365	*
	12366	* @param startTime
	12367	* The date and time for starting the search for a solar eclipse.
	12368	*
	12369	* @param observer
	12370	* The geographic location of the observer.
	12371	*
	12372	* @return
	12373	* If successful, the `status` field in the returned structure will contain `ASTRO_SUCCESS`
	12374	* and the remaining structure fields are as described in #astro_local_solar_eclipse_t.
	12375	* Any other value indicates an error.
	12376	*/
	12377	astro_local_solar_eclipse_t Astronomy_SearchLocalSolarEclipse(
	12378	astro_time_t startTime,
	12379	astro_observer_t observer)
	12380	{
	12381	const double PruneLatitude = 1.8; /* Moon's ecliptic latitude beyond which eclipse is impossible */
	12382	astro_time_t nmtime;
	12383	astro_search_result_t newmoon;
	12384	shadow_t shadow;
	12385	double eclip_lat, eclip_lon, distance;
	12386	astro_local_solar_eclipse_t eclipse;
	12387
	12388	/* Iterate through consecutive new moons until we find a solar eclipse visible somewhere on Earth. */
	12389	nmtime = startTime;
	12390	for(;;)
	12391	{
	12392	/* Search for the next new moon. Any eclipse will be near it. */
	12393	newmoon = Astronomy_SearchMoonPhase(0.0, nmtime, 40.0);
	12394	if (newmoon.status != ASTRO_SUCCESS)
	12395	return LocalSolarEclipseError(newmoon.status);
	12396
	12397	/* Pruning: if the new moon's ecliptic latitude is too large, a solar eclipse is not possible. */
	12398	CalcMoon(newmoon.time.tt / 36525.0, &eclip_lon, &eclip_lat, &distance);
	12399	if (RAD2DEG * fabs(eclip_lat) < PruneLatitude)
	12400	{
	12401	/* Search near the new moon for the time when the observer */
	12402	/* is closest to the line passing through the centers of the Sun and Moon. */
	12403	shadow = PeakLocalMoonShadow(newmoon.time, observer);
	12404	if (shadow.status != ASTRO_SUCCESS)
	12405	return LocalSolarEclipseError(shadow.status);
	12406
	12407	if (shadow.r < shadow.p)
	12408	{
	12409	/* This is at least a partial solar eclipse for the observer. */
	12410	eclipse = LocalEclipse(shadow, observer);
	12411
	12412	/* If any error occurs, something is really wrong and we should bail out. */
	12413	if (eclipse.status != ASTRO_SUCCESS)
	12414	return eclipse;
	12415
	12416	/* Ignore any eclipse that happens completely at night. */
	12417	/* More precisely, the center of the Sun must be above the horizon */
	12418	/* at the beginning or the end of the eclipse, or we skip the event. */
	12419	if (eclipse.partial_begin.altitude > 0.0 \|\| eclipse.partial_end.altitude > 0.0)
	12420	return eclipse;
	12421	}
	12422	}
	12423
	12424	/* We didn't find an eclipse on this new moon, so search for the next one. */
	12425	nmtime = Astronomy_AddDays(newmoon.time, 10.0);
	12426	}
	12427	}
	12428
	12429
	12430	/**
	12431	* @brief Searches for the next local solar eclipse in a series.
	12432	*
	12433	* After using #Astronomy_SearchLocalSolarEclipse to find the first solar eclipse
	12434	* in a series, you can call this function to find the next consecutive solar eclipse.
	12435	* Pass in the `peak` value from the #astro_local_solar_eclipse_t returned by the
	12436	* previous call to `Astronomy_SearchLocalSolarEclipse` or `Astronomy_NextLocalSolarEclipse`
	12437	* to find the next solar eclipse.
	12438	*
	12439	* @param prevEclipseTime
	12440	* A date and time near a new moon. Solar eclipse search will start at the next new moon.
	12441	*
	12442	* @param observer
	12443	* The geographic location of the observer.
	12444	*
	12445	* @return
	12446	* If successful, the `status` field in the returned structure will contain `ASTRO_SUCCESS`
	12447	* and the remaining structure fields are as described in #astro_local_solar_eclipse_t.
	12448	* Any other value indicates an error.
	12449	*/
	12450	astro_local_solar_eclipse_t Astronomy_NextLocalSolarEclipse(
	12451	astro_time_t prevEclipseTime,
	12452	astro_observer_t observer)
	12453	{
	12454	astro_time_t startTime = Astronomy_AddDays(prevEclipseTime, 10.0);
	12455	return Astronomy_SearchLocalSolarEclipse(startTime, observer);
	12456	}
	12457
	12458
	12459	static astro_func_result_t planet_transit_bound(void *context, astro_time_t time)
	12460	{
	12461	shadow_t shadow;
	12462	astro_func_result_t result;
	12463	const planet_shadow_context_t p = (const planet_shadow_context_t ) context;
	12464
	12465	shadow = PlanetShadow(p->body, p->planet_radius_km, time);
	12466	if (shadow.status != ASTRO_SUCCESS)
	12467	return FuncError(shadow.status);
	12468
	12469	result.status = ASTRO_SUCCESS;
	12470	result.value = p->direction * (shadow.r - shadow.p);
	12471	return result;
	12472	}
	12473
	12474
	12475	static astro_search_result_t PlanetTransitBoundary(
	12476	astro_body_t body,
	12477	double planet_radius_km,
	12478	astro_time_t t1,
	12479	astro_time_t t2,
	12480	double direction)
	12481	{
	12482	/* Search for the time the planet's penumbra begins/ends making contact with the center of the Earth. */
	12483	planet_shadow_context_t context;
	12484
	12485	context.body = body;
	12486	context.planet_radius_km = planet_radius_km;
	12487	context.direction = direction;
	12488
	12489	return Astronomy_Search(planet_transit_bound, &context, t1, t2, 1.0);
	12490	}
	12491
	12492
	12493	/**
	12494	* @brief Searches for the first transit of Mercury or Venus after a given date.
	12495	*
	12496	* Finds the first transit of Mercury or Venus after a specified date.
	12497	* A transit is when an inferior planet passes between the Sun and the Earth
	12498	* so that the silhouette of the planet is visible against the Sun in the background.
	12499	* To continue the search, pass the `finish` time in the returned structure to
	12500	* #Astronomy_NextTransit.
	12501	*
	12502	* @param body
	12503	* The planet whose transit is to be found. Must be `BODY_MERCURY` or `BODY_VENUS`.
	12504	*
	12505	* @param startTime
	12506	* The date and time for starting the search for a transit.
	12507	*
	12508	* @return
	12509	* If successful, the `status` field in the returned structure hold `ASTRO_SUCCESS`
	12510	* and the other fields are as documented in #astro_transit_t.
	12511	* Otherwise, `status` holds an error code and the other structure members are undefined.
	12512	*/
	12513	astro_transit_t Astronomy_SearchTransit(astro_body_t body, astro_time_t startTime)
	12514	{
	12515	astro_time_t search_time;
	12516	astro_transit_t transit;
	12517	astro_search_result_t conj, search;
	12518	astro_angle_result_t conj_separation, min_separation;
	12519	shadow_t shadow;
	12520	double planet_radius_km;
	12521	astro_time_t tx;
	12522	const double threshold_angle = 0.4; /* maximum angular separation to attempt transit calculation */
	12523	const double dt_days = 1.0;
	12524
	12525	/* Validate the planet and find its mean radius. */
	12526	switch (body)
	12527	{
	12528	case BODY_MERCURY: planet_radius_km = 2439.7; break;
	12529	case BODY_VENUS: planet_radius_km = 6051.8; break;
	12530	default:
	12531	return TransitErr(ASTRO_INVALID_BODY);
	12532	}
	12533
	12534	search_time = startTime;
	12535	for(;;)
	12536	{
	12537	/*
	12538	Search for the next inferior conjunction of the given planet.
	12539	This is the next time the Earth and the other planet have the same
	12540	ecliptic longitude as seen from the Sun.
	12541	*/
	12542	conj = Astronomy_SearchRelativeLongitude(body, 0.0, search_time);
	12543	if (conj.status != ASTRO_SUCCESS)
	12544	return TransitErr(conj.status);
	12545
	12546	/* Calculate the angular separation between the body and the Sun at this time. */
	12547	conj_separation = Astronomy_AngleFromSun(body, conj.time);
	12548	if (conj_separation.status != ASTRO_SUCCESS)
	12549	return TransitErr(conj_separation.status);
	12550
	12551	if (conj_separation.angle < threshold_angle)
	12552	{
	12553	/*
	12554	The planet's angular separation from the Sun is small enough
	12555	to consider it a transit candidate.
	12556	Search for the moment when the line passing through the Sun
	12557	and planet are closest to the Earth's center.
	12558	*/
	12559	shadow = PeakPlanetShadow(body, planet_radius_km, conj.time);
	12560	if (shadow.status != ASTRO_SUCCESS)
	12561	return TransitErr(shadow.status);
	12562
	12563	if (shadow.r < shadow.p) /* does the planet's penumbra touch the Earth's center? */
	12564	{
	12565	/* Find the beginning and end of the penumbral contact. */
	12566	tx = Astronomy_AddDays(shadow.time, -dt_days);
	12567	search = PlanetTransitBoundary(body, planet_radius_km, tx, shadow.time, -1.0);
	12568	if (search.status != ASTRO_SUCCESS)
	12569	return TransitErr(search.status);
	12570	transit.start = search.time;
	12571
	12572	tx = Astronomy_AddDays(shadow.time, +dt_days);
	12573	search = PlanetTransitBoundary(body, planet_radius_km, shadow.time, tx, +1.0);
	12574	if (search.status != ASTRO_SUCCESS)
	12575	return TransitErr(search.status);
	12576	transit.finish = search.time;
	12577	transit.status = ASTRO_SUCCESS;
	12578	transit.peak = shadow.time;
	12579
	12580	min_separation = Astronomy_AngleFromSun(body, shadow.time);
	12581	if (min_separation.status != ASTRO_SUCCESS)
	12582	return TransitErr(min_separation.status);
	12583
	12584	transit.separation = 60.0 * min_separation.angle; /* convert degrees to arcminutes */
	12585	return transit;
	12586	}
	12587	}
	12588
	12589	/* This inferior conjunction was not a transit. Try the next inferior conjunction. */
	12590	search_time = Astronomy_AddDays(conj.time, 10.0);
	12591	}
	12592	}
	12593
	12594
	12595	/**
	12596	* @brief Searches for another transit of Mercury or Venus.
	12597	*
	12598	* After calling #Astronomy_SearchTransit to find a transit of Mercury or Venus,
	12599	* this function finds the next transit after that.
	12600	* Keep calling this function as many times as you want to keep finding more transits.
	12601	*
	12602	* @param body
	12603	* The planet whose transit is to be found. Must be `BODY_MERCURY` or `BODY_VENUS`.
	12604	*
	12605	* @param prevTransitTime
	12606	* A date and time near the previous transit.
	12607	*
	12608	* @return
	12609	* If successful, the `status` field in the returned structure holds `ASTRO_SUCCESS`
	12610	* and the other fields are as documented in #astro_transit_t.
	12611	* Otherwise, `status` holds an error code and the other structure members are undefined.
	12612	*/
	12613	astro_transit_t Astronomy_NextTransit(astro_body_t body, astro_time_t prevTransitTime)
	12614	{
	12615	astro_time_t startTime;
	12616
	12617	startTime = Astronomy_AddDays(prevTransitTime, 100.0);
	12618	return Astronomy_SearchTransit(body, startTime);
	12619	}
	12620
	12621
	12622	static astro_node_event_t NodeError(astro_status_t status)
	12623	{
	12624	astro_node_event_t node;
	12625
	12626	node.status = status;
	12627	node.time = TimeError();
	12628	node.kind = INVALID_NODE;
	12629
	12630	return node;
	12631	}
	12632
	12633	static astro_func_result_t MoonNodeSearchFunc(void *context, astro_time_t time)
	12634	{
	12635	astro_func_result_t result;
	12636	astro_spherical_t eclip;
	12637	astro_node_kind_t kind = ((astro_node_kind_t )context);
	12638
	12639	eclip = Astronomy_EclipticGeoMoon(time);
	12640
	12641	result.value = eclip.lat * (double)kind;
	12642	result.status = ASTRO_SUCCESS;
	12643	return result;
	12644	}
	12645
	12646	static const double MOON_NODE_STEP_DAYS = +10.0; /* a safe number of days to step without missing a Moon node */
	12647
	12648	/**
	12649	* @brief Searches for a time when the Moon's center crosses through the ecliptic plane.
	12650	*
	12651	* Searches for the first ascending or descending node of the Moon after `startTime`.
	12652	* An ascending node is when the Moon's center passes through the ecliptic plane
	12653	* (the plane of the Earth's orbit around the Sun) from south to north.
	12654	* A descending node is when the Moon's center passes through the ecliptic plane
	12655	* from north to south. Nodes indicate possible times of solar or lunar eclipses,
	12656	* if the Moon also happens to be in the correct phase (new or full, respectively).
	12657	*
	12658	* Call `Astronomy_SearchMoonNode` to find the first of a series of nodes.
	12659	* Then call #Astronomy_NextMoonNode to find as many more consecutive nodes as desired.
	12660	*
	12661	* @param startTime
	12662	* The date and time for starting the search for an ascending or descending node of the Moon.
	12663	*
	12664	* @return
	12665	* If successful, the `status` field in the returned structure holds `ASTRO_SUCCESS`
	12666	* and the other fields are as documented in #astro_node_event_t.
	12667	* Otherwise, `status` holds an error code and the other structure members are undefined.
	12668	*/
	12669	astro_node_event_t Astronomy_SearchMoonNode(astro_time_t startTime)
	12670	{
	12671	astro_node_event_t node;
	12672	astro_time_t time1, time2;
	12673	astro_spherical_t eclip1, eclip2;
	12674	astro_node_kind_t kind;
	12675	astro_search_result_t result;
	12676
	12677	/* Start at the given moment in time and sample the Moon's ecliptic latitude. */
	12678	/* Step 10 days at a time, searching for an interval where that latitude crosses zero. */
	12679	time1 = startTime;
	12680	eclip1 = Astronomy_EclipticGeoMoon(time1); /* never returns a failure code */
	12681
	12682	for(;;)
	12683	{
	12684	time2 = Astronomy_AddDays(time1, MOON_NODE_STEP_DAYS);
	12685	eclip2 = Astronomy_EclipticGeoMoon(time2); /* never returns a failure code */
	12686	if (eclip1.lat * eclip2.lat <= 0.0)
	12687	{
	12688	/* There is a node somewhere inside this closed time interval. */
	12689	/* Figure out whether it is an ascending node or a descending node. */
	12690	kind = (eclip2.lat > eclip1.lat) ? ASCENDING_NODE : DESCENDING_NODE;
	12691	result = Astronomy_Search(MoonNodeSearchFunc, &kind, time1, time2, 1.0);
	12692	if (result.status != ASTRO_SUCCESS)
	12693	return NodeError(result.status);
	12694
	12695	node.status = ASTRO_SUCCESS;
	12696	node.time = result.time;
	12697	node.kind = kind;
	12698	return node;
	12699	}
	12700	time1 = time2;
	12701	eclip1 = eclip2;
	12702	}
	12703	}
	12704
	12705
	12706	/**
	12707	* @brief Searches for the next time when the Moon's center crosses through the ecliptic plane.
	12708	*
	12709	* Call #Astronomy_SearchMoonNode to find the first of a series of nodes.
	12710	* Then call `Astronomy_NextMoonNode` to find as many more consecutive nodes as desired.
	12711	*
	12712	* @param prevNode
	12713	* The previous node found from calling #Astronomy_SearchMoonNode or `Astronomy_NextMoonNode`.
	12714	*
	12715	* @return
	12716	* If successful, the `status` field in the returned structure holds `ASTRO_SUCCESS`
	12717	* and the other fields are as documented in #astro_node_event_t.
	12718	* Otherwise, `status` holds an error code and the other structure members are undefined.
	12719	*/
	12720	astro_node_event_t Astronomy_NextMoonNode(astro_node_event_t prevNode)
	12721	{
	12722	astro_time_t time;
	12723	astro_node_event_t node;
	12724
	12725	if (prevNode.status != ASTRO_SUCCESS)
	12726	return NodeError(ASTRO_INVALID_PARAMETER);
	12727
	12728	if (prevNode.kind != ASCENDING_NODE && prevNode.kind != DESCENDING_NODE)
	12729	return NodeError(ASTRO_INVALID_PARAMETER);
	12730
	12731	time = Astronomy_AddDays(prevNode.time, MOON_NODE_STEP_DAYS);
	12732	node = Astronomy_SearchMoonNode(time);
	12733	if (node.status == ASTRO_SUCCESS)
	12734	{
	12735	/* Verify nodes are alternating as expected. */
	12736	if (prevNode.kind == ASCENDING_NODE)
	12737	{
	12738	if (node.kind != DESCENDING_NODE)
	12739	return NodeError(ASTRO_INTERNAL_ERROR);
	12740	}
	12741	else
	12742	{
	12743	if (node.kind != ASCENDING_NODE)
	12744	return NodeError(ASTRO_INTERNAL_ERROR);
	12745	}
	12746	}
	12747	return node;
	12748	}
	12749
	12750
	12751	/**
	12752	* @brief Frees up all dynamic memory allocated by Astronomy Engine.
	12753	*
	12754	* Astronomy Engine uses dynamic memory allocation in only one place:
	12755	* it makes calculation of Pluto's orbit more efficient by caching 11 KB
	12756	* segments and recycling them. To force purging this cache and
	12757	* freeing all the dynamic memory, you can call this function at any time.
	12758	* It is always safe to call, although it will slow down the very next
	12759	* calculation of Pluto's position for a nearby time value.
	12760	* Calling this function before your program exits is optional, but
	12761	* it will be helpful for leak-checkers like valgrind.
	12762	*/
	12763	void Astronomy_Reset(void)
	12764	{
	12765	int i;
	12766	for (i=0; i < PLUTO_NUM_STATES-1; ++i)
	12767	{
	12768	free(pluto_cache[i]);
	12769	pluto_cache[i] = NULL;
	12770	}
	12771	}
	12772
	12773
	12774	static astro_axis_t EarthRotationAxis(astro_time_t *time)
	12775	{
	12776	astro_axis_t axis;
	12777	double pos1[3];
	12778	double pos2[3];
	12779	astro_equatorial_t equ;
	12780
	12781	if (time == NULL)
	12782	return AxisErr(ASTRO_INVALID_PARAMETER, TimeError());
	12783
	12784	/*
	12785	Unlike the other planets, we have a model of precession and nutation
	12786	for the Earth's axis that provides a north pole vector.
	12787	So calculate the vector first, then derive the (RA,DEC) angles from the vector.
	12788	*/
	12789
	12790	/* Start with a north pole vector in equator-of-date coordinates: (0,0,1). */
	12791	pos1[0] = 0.0;
	12792	pos1[1] = 0.0;
	12793	pos1[2] = 1.0;
	12794
	12795	/* Convert the vector into J2000 coordinates. */
	12796	nutation(pos1, time, INTO_2000, pos2);
	12797	precession(pos2, *time, INTO_2000, pos1);
	12798	axis.north.x = pos1[0];
	12799	axis.north.y = pos1[1];
	12800	axis.north.z = pos1[2];
	12801	axis.north.t = *time;
	12802	axis.north.status = ASTRO_SUCCESS;
	12803
	12804	/* Derive angular values: right ascension and declination. */
	12805	equ = Astronomy_EquatorFromVector(axis.north);
	12806	if (equ.status != ASTRO_SUCCESS)
	12807	return AxisErr(equ.status, *time);
	12808	axis.ra = equ.ra;
	12809	axis.dec = equ.dec;
	12810
	12811	/* Use a modified version of the era() function that does not trim to 0..360 degrees. */
	12812	/* This expression is also corrected to give the correct angle at the J2000 epoch. */
	12813	axis.spin = 190.41375788700253 + (360.9856122880876 * time->ut);
	12814
	12815	axis.status = ASTRO_SUCCESS;
	12816
	12817	return axis;
	12818	}
	12819
	12820
	12821	/**
	12822	* @brief Calculates information about a body's rotation axis at a given time.
	12823	*
	12824	* Calculates the orientation of a body's rotation axis, along with
	12825	* the rotation angle of its prime meridian, at a given moment in time.
	12826	*
	12827	* This function uses formulas standardized by the IAU Working Group
	12828	* on Cartographics and Rotational Elements 2015 report, as described
	12829	* in the following document:
	12830	*
	12831	* https://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE2015reprint.pdf
	12832	*
	12833	* See #astro_axis_t for more detailed information.
	12834	*
	12835	* @param body
	12836	* The body whose rotation axis is to be found. The supported bodies are:
	12837	* `BODY_SUN`, `BODY_MOON`, `BODY_MERCURY`, `BODY_VENUS`, `BODY_EARTH`, `BODY_MARS`,
	12838	* `BODY_JUPITER`, `BODY_SATURN`, `BODY_URANUS`, `BODY_NEPTUNE`, `BODY_PLUTO`.
	12839	*
	12840	* @param time
	12841	* The time for which the body's rotation axis is to be found.
	12842	*
	12843	* @return astro_axis_t
	12844	*/
	12845	astro_axis_t Astronomy_RotationAxis(astro_body_t body, astro_time_t *time)
	12846	{
	12847	astro_axis_t axis;
	12848	double ra, dec, w;
	12849	double radlat, radlon, rcoslat;
	12850	double Ja, Jb, Jc, Jd, Je, N;
	12851	double E1, E2, E3, E4, E5, E6, E7, E8, E9, E10, E11, E12, E13;
	12852	double d, T;
	12853
	12854	if (time == NULL)
	12855	return AxisErr(ASTRO_INVALID_PARAMETER, TimeError());
	12856
	12857	d = time->tt;
	12858	T = d / 36525.0;
	12859
	12860	switch (body)
	12861	{
	12862	case BODY_SUN:
	12863	ra = 286.13;
	12864	dec = 63.87;
	12865	w = 84.176 + (14.1844 * d);
	12866	break;
	12867
	12868	case BODY_MERCURY:
	12869	ra = 281.0103 - (0.0328 * T);
	12870	dec = 61.4155 - (0.0049 * T);
	12871	w = (
	12872	329.5988
	12873	+ (6.1385108 * d)
	12874	+ (0.01067257 * sin(DEG2RAD(174.7910857 + 4.092335d)))
	12875	- (0.00112309 * sin(DEG2RAD(349.5821714 + 8.184670d)))
	12876	- (0.00011040 * sin(DEG2RAD(164.3732571 + 12.277005d)))
	12877	- (0.00002539 * sin(DEG2RAD(339.1643429 + 16.369340d)))
	12878	- (0.00000571 * sin(DEG2RAD(153.9554286 + 20.461675d)))
	12879	);
	12880	break;
	12881
	12882	case BODY_VENUS:
	12883	ra = 272.76;
	12884	dec = 67.16;
	12885	w = 160.20 - (1.4813688 * d);
	12886	break;
	12887
	12888	case BODY_EARTH:
	12889	return EarthRotationAxis(time);
	12890
	12891	case BODY_MOON:
	12892	/*
	12893	https://astropedia.astrogeology.usgs.gov/alfresco/d/d/workspace/SpacesStore/28fd9e81-1964-44d6-a58b-fbbf61e64e15/WGCCRE2009reprint.pdf
	12894	Page 8, Table 2.
	12895	*/
	12896	E1 = DEG2RAD * (125.045 - 0.0529921*d);
	12897	E2 = DEG2RAD * (250.089 - 0.1059842*d);
	12898	E3 = DEG2RAD * (260.008 + 13.0120009*d);
	12899	E4 = DEG2RAD * (176.625 + 13.3407154*d);
	12900	E5 = DEG2RAD * (357.529 + 0.9856003*d);
	12901	E6 = DEG2RAD * (311.589 + 26.4057084*d);
	12902	E7 = DEG2RAD * (134.963 + 13.0649930*d);
	12903	E8 = DEG2RAD * (276.617 + 0.3287146*d);
	12904	E9 = DEG2RAD * (34.226 + 1.7484877*d);
	12905	E10 = DEG2RAD * (15.134 - 0.1589763*d);
	12906	E11 = DEG2RAD * (119.743 + 0.0036096*d);
	12907	E12 = DEG2RAD * (239.961 + 0.1643573*d);
	12908	E13 = DEG2RAD * (25.053 + 12.9590088*d);
	12909
	12910	ra = (
	12911	269.9949 + 0.0031*T
	12912	- 3.8787*sin(E1)
	12913	- 0.1204*sin(E2)
	12914	+ 0.0700*sin(E3)
	12915	- 0.0172*sin(E4)
	12916	+ 0.0072*sin(E6)
	12917	- 0.0052*sin(E10)
	12918	+ 0.0043*sin(E13)
	12919	);
	12920
	12921	dec = (
	12922	66.5392 + 0.0130*T
	12923	+ 1.5419*cos(E1)
	12924	+ 0.0239*cos(E2)
	12925	- 0.0278*cos(E3)
	12926	+ 0.0068*cos(E4)
	12927	- 0.0029*cos(E6)
	12928	+ 0.0009*cos(E7)
	12929	+ 0.0008*cos(E10)
	12930	- 0.0009*cos(E13)
	12931	);
	12932
	12933	w = (
	12934	38.3213 + (13.17635815 - 1.4e-12d)d
	12935	+ 3.5610*sin(E1)
	12936	+ 0.1208*sin(E2)
	12937	- 0.0642*sin(E3)
	12938	+ 0.0158*sin(E4)
	12939	+ 0.0252*sin(E5)
	12940	- 0.0066*sin(E6)
	12941	- 0.0047*sin(E7)
	12942	- 0.0046*sin(E8)
	12943	+ 0.0028*sin(E9)
	12944	+ 0.0052*sin(E10)
	12945	+ 0.0040*sin(E11)
	12946	+ 0.0019*sin(E12)
	12947	- 0.0044*sin(E13)
	12948	);
	12949	break;
	12950
	12951	case BODY_MARS:
	12952	ra = (
	12953	317.269202 - 0.10927547*T
	12954	+ 0.000068 * sin(DEG2RAD(198.991226 + 19139.4819985T))
	12955	+ 0.000238 * sin(DEG2RAD(226.292679 + 38280.8511281T))
	12956	+ 0.000052 * sin(DEG2RAD(249.663391 + 57420.7251593T))
	12957	+ 0.000009 * sin(DEG2RAD(266.183510 + 76560.6367950T))
	12958	+ 0.419057 * sin(DEG2RAD(79.398797 + 0.5042615T))
	12959	);
	12960
	12961	dec = (
	12962	54.432516 - 0.05827105*T
	12963	+ 0.000051cos(DEG2RAD(122.433576 + 19139.9407476*T))
	12964	+ 0.000141cos(DEG2RAD(43.058401 + 38280.8753272*T))
	12965	+ 0.000031cos(DEG2RAD(57.663379 + 57420.7517205*T))
	12966	+ 0.000005cos(DEG2RAD(79.476401 + 76560.6495004*T))
	12967	+ 1.591274cos(DEG2RAD(166.325722 + 0.5042615*T))
	12968	);
	12969
	12970	w = (
	12971	176.049863 + 350.891982443297*d
	12972	+ 0.000145sin(DEG2RAD(129.071773 + 19140.0328244*T))
	12973	+ 0.000157sin(DEG2RAD(36.352167 + 38281.0473591*T))
	12974	+ 0.000040sin(DEG2RAD(56.668646 + 57420.9295360*T))
	12975	+ 0.000001sin(DEG2RAD(67.364003 + 76560.2552215*T))
	12976	+ 0.000001sin(DEG2RAD(104.792680 + 95700.4387578*T))
	12977	+ 0.584542sin(DEG2RAD(95.391654 + 0.5042615*T))
	12978	);
	12979	break;
	12980
	12981	case BODY_JUPITER:
	12982	Ja = DEG2RAD(99.360714 + 4850.4046T);
	12983	Jb = DEG2RAD(175.895369 + 1191.9605T);
	12984	Jc = DEG2RAD(300.323162 + 262.5475T);
	12985	Jd = DEG2RAD(114.012305 + 6070.2476T);
	12986	Je = DEG2RAD(49.511251 + 64.3000T);
	12987
	12988	ra = (
	12989	268.056595 - 0.006499*T
	12990	+ 0.000117*sin(Ja)
	12991	+ 0.000938*sin(Jb)
	12992	+ 0.001432*sin(Jc)
	12993	+ 0.000030*sin(Jd)
	12994	+ 0.002150*sin(Je)
	12995	);
	12996
	12997	dec = (
	12998	64.495303 + 0.002413*T
	12999	+ 0.000050*cos(Ja)
	13000	+ 0.000404*cos(Jb)
	13001	+ 0.000617*cos(Jc)
	13002	- 0.000013*cos(Jd)
	13003	+ 0.000926*cos(Je)
	13004	);
	13005
	13006	w = 284.95 + 870.536*d;
	13007	break;
	13008
	13009	case BODY_SATURN:
	13010	ra = 40.589 - 0.036*T;
	13011	dec = 83.537 - 0.004*T;
	13012	w = 38.90 + 810.7939024*d;
	13013	break;
	13014
	13015	case BODY_URANUS:
	13016	ra = 257.311;
	13017	dec = -15.175;
	13018	w = 203.81 - 501.1600928*d;
	13019	break;
	13020
	13021	case BODY_NEPTUNE:
	13022	N = DEG2RAD(357.85 + 52.316T);
	13023	ra = 299.36 + 0.70*sin(N);
	13024	dec = 43.46 - 0.51*cos(N);
	13025	w = 249.978 + 541.1397757d - 0.48sin(N);
	13026	break;
	13027
	13028	case BODY_PLUTO:
	13029	ra = 132.993;
	13030	dec = -6.163;
	13031	w = 302.695 + 56.3625225*d;
	13032	break;
	13033
	13034	default:
	13035	return AxisErr(ASTRO_INVALID_BODY, *time);
	13036	}
	13037
	13038	axis.ra = ra / 15.0; /* convert degrees to sidereal hours */
	13039	axis.dec = dec;
	13040	axis.spin = w;
	13041
	13042	/* calculate the north pole vector using the given angles. */
	13043	radlat = dec * DEG2RAD;
	13044	radlon = ra * DEG2RAD;
	13045	rcoslat = cos(radlat);
	13046	axis.north.x = rcoslat * cos(radlon);
	13047	axis.north.y = rcoslat * sin(radlon);
	13048	axis.north.z = sin(radlat);
	13049	axis.north.t = *time;
	13050	axis.north.status = ASTRO_SUCCESS;
	13051
	13052	axis.status = ASTRO_SUCCESS;
	13053	return axis;
	13054	}
	13055
	13056	#ifdef __cplusplus
	13057	}
	13058	#endif

Packages/MoonriseKit/Sources/CAstronomy/include/astronomy.h added +1431

@@ -0,0 +1,1431 @@
	1	/*
	2	Astronomy Engine for C/C++.
	3	https://github.com/cosinekitty/astronomy
	4
	5	MIT License
	6
	7	Copyright (c) 2019-2023 Don Cross <cosinekitty@gmail.com>
	8
	9	Permission is hereby granted, free of charge, to any person obtaining a copy
	10	of this software and associated documentation files (the "Software"), to deal
	11	in the Software without restriction, including without limitation the rights
	12	to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
	13	copies of the Software, and to permit persons to whom the Software is
	14	furnished to do so, subject to the following conditions:
	15
	16	The above copyright notice and this permission notice shall be included in all
	17	copies or substantial portions of the Software.
	18
	19	THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
	20	IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
	21	FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
	22	AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
	23	LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
	24	OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
	25	SOFTWARE.
	26	*/
	27
	28	#ifndef __ASTRONOMY_H
	29	#define __ASTRONOMY_H
	30
	31	#include <stddef.h> /* for size_t */
	32
	33	#ifdef __cplusplus
	34	extern "C" {
	35	#endif
	36
	37	/---------- numeric constants ----------/
	38
	39	/**
	40	* \def C_AUDAY
	41	* @brief The speed of light in AU/day.
	42	*/
	43	#define C_AUDAY 173.1446326846693
	44
	45	/**
	46	* \def KM_PER_AU
	47	* @brief The number of kilometers in one astronomical unit (AU).
	48	*/
	49	#define KM_PER_AU 1.4959787069098932e+8
	50
	51	/**
	52	* \def AU_PER_LY
	53	* @brief The number of astronomical units per light-year.
	54	*/
	55	#define AU_PER_LY 63241.07708807546
	56
	57	/**
	58	* \def DEG2RAD
	59	* @brief The factor to convert degrees to radians = pi/180.
	60	*/
	61	#define DEG2RAD 0.017453292519943296
	62
	63	/**
	64	* \def HOUR2RAD
	65	* @brief The factor to convert sidereal hours to radians = pi/12.
	66	*/
	67	#define HOUR2RAD 0.2617993877991494365
	68
	69	/**
	70	* \def RAD2DEG
	71	* @brief The factor to convert radians to degrees = 180/pi.
	72	*/
	73	#define RAD2DEG 57.295779513082321
	74
	75	/**
	76	* \def RAD2HOUR
	77	* @brief The factor to convert radians to sidereal hours = 12/pi.
	78	*/
	79	#define RAD2HOUR 3.819718634205488
	80
	81	/**
	82	* \def SUN_RADIUS_KM
	83	* @brief The mean radius of the Sun's photosphere, expressed in kilometers. The Sun is nearly spherical.
	84	*/
	85	#define SUN_RADIUS_KM 695700.0
	86
	87	/**
	88	* \def MERCURY_EQUATORIAL_RADIUS_KM
	89	* @brief The equatorial radius of Mercury, expressed in kilometers.
	90	*/
	91	#define MERCURY_EQUATORIAL_RADIUS_KM 2440.5
	92
	93	/**
	94	* \def MERCURY_POLAR_RADIUS_KM
	95	* @brief The polar radius of Mercury, expressed in kilometers.
	96	*/
	97	#define MERCURY_POLAR_RADIUS_KM 2438.3
	98
	99	/**
	100	* \def VENUS_RADIUS_KM
	101	* @brief The mean radius of Venus, expressed in kilometers. Venus is nearly spherical.
	102	*/
	103	#define VENUS_RADIUS_KM 6051.8
	104
	105	/**
	106	* \def EARTH_EQUATORIAL_RADIUS_KM
	107	* @brief The equatorial radius of the Earth, expressed in kilometers.
	108	*/
	109	#define EARTH_EQUATORIAL_RADIUS_KM 6378.1366
	110
	111	/**
	112	* \def EARTH_FLATTENING
	113	* @brief The Earth's polar radius divided by its equatorial radius.
	114	*/
	115	#define EARTH_FLATTENING 0.996647180302104
	116
	117	/**
	118	* \def EARTH_POLAR_RADIUS_KM
	119	* @brief The polar radius of the Earth, expressed in kilometers.
	120	*/
	121	#define EARTH_POLAR_RADIUS_KM (EARTH_EQUATORIAL_RADIUS_KM * EARTH_FLATTENING)
	122
	123	/**
	124	* \def MOON_EQUATORIAL_RADIUS_KM
	125	* @brief The equatorial radius of the Moon, expressed in kilometers.
	126	*/
	127	#define MOON_EQUATORIAL_RADIUS_KM 1738.1
	128
	129	/**
	130	* \def MOON_POLAR_RADIUS_KM
	131	* @brief The polar radius of the Moon, expressed in kilometers.
	132	*/
	133	#define MOON_POLAR_RADIUS_KM 1736.0
	134
	135	/**
	136	* \def MARS_EQUATORIAL_RADIUS_KM
	137	* @brief The equatorial radius of Mars, expressed in kilometers.
	138	*/
	139	#define MARS_EQUATORIAL_RADIUS_KM 3396.2
	140
	141	/**
	142	* \def MARS_POLAR_RADIUS_KM
	143	* @brief The polar radius of Mars, expressed in kilometers.
	144	*/
	145	#define MARS_POLAR_RADIUS_KM 3376.2
	146
	147	/*
	148	Jupiter radius data are nominal values obtained from:
	149	https://www.iau.org/static/resolutions/IAU2015_English.pdf
	150	https://nssdc.gsfc.nasa.gov/planetary/factsheet/jupiterfact.html
	151	*/
	152
	153	/**
	154	* \def JUPITER_EQUATORIAL_RADIUS_KM
	155	* @brief The equatorial radius of Jupiter, expressed in kilometers.
	156	*/
	157	#define JUPITER_EQUATORIAL_RADIUS_KM 71492.0
	158
	159	/**
	160	* \def JUPITER_POLAR_RADIUS_KM
	161	* @brief The polar radius of Jupiter, expressed in kilometers.
	162	*/
	163	#define JUPITER_POLAR_RADIUS_KM 66854.0
	164
	165	/**
	166	* \def JUPITER_MEAN_RADIUS_KM
	167	* @brief The volumetric mean radius of Jupiter, expressed in kilometers.
	168	*/
	169	#define JUPITER_MEAN_RADIUS_KM 69911.0
	170
	171	/*
	172	The radii of Jupiter's four major moons are obtained from:
	173	https://ssd.jpl.nasa.gov/?sat_phys_par
	174	*/
	175
	176	/**
	177	* \def IO_RADIUS_KM
	178	* @brief The mean radius of Jupiter's moon Io, expressed in kilometers.
	179	*/
	180	#define IO_RADIUS_KM 1821.6
	181
	182	/**
	183	* \def EUROPA_RADIUS_KM
	184	* @brief The mean radius of Jupiter's moon Europa, expressed in kilometers.
	185	*/
	186	#define EUROPA_RADIUS_KM 1560.8
	187
	188	/**
	189	* \def GANYMEDE_RADIUS_KM
	190	* @brief The mean radius of Jupiter's moon Ganymede, expressed in kilometers.
	191	*/
	192	#define GANYMEDE_RADIUS_KM 2631.2
	193
	194	/**
	195	* \def CALLISTO_RADIUS_KM
	196	* @brief The mean radius of Jupiter's moon Callisto, expressed in kilometers.
	197	*/
	198	#define CALLISTO_RADIUS_KM 2410.3
	199
	200	/**
	201	* \def SATURN_EQUATORIAL_RADIUS_KM
	202	* @brief The equatorial radius of Saturn, expressed in kilometers.
	203	*/
	204	#define SATURN_EQUATORIAL_RADIUS_KM 60268.0
	205
	206	/**
	207	* \def SATURN_POLAR_RADIUS_KM
	208	* @brief The polar radius of Saturn, expressed in kilometers.
	209	*/
	210	#define SATURN_POLAR_RADIUS_KM 54364.0
	211
	212	/**
	213	* \def URANUS_EQUATORIAL_RADIUS_KM
	214	* @brief The equatorial radius of Uranus, expressed in kilometers.
	215	*/
	216	#define URANUS_EQUATORIAL_RADIUS_KM 25559.0
	217
	218	/**
	219	* \def URANUS_POLAR_RADIUS_KM
	220	* @brief The polar radius of Uranus, expressed in kilometers.
	221	*/
	222	#define URANUS_POLAR_RADIUS_KM 24973.0
	223
	224	/**
	225	* \def NEPTUNE_EQUATORIAL_RADIUS_KM
	226	* @brief The equatorial radius of Neptune, expressed in kilometers.
	227	*/
	228	#define NEPTUNE_EQUATORIAL_RADIUS_KM 24764.0
	229
	230	/**
	231	* \def NEPTUNE_POLAR_RADIUS_KM
	232	* @brief The polar radius of Neptune, expressed in kilometers.
	233	*/
	234	#define NEPTUNE_POLAR_RADIUS_KM 24341.0
	235
	236	/**
	237	* \def PLUTO_RADIUS_KM
	238	* @brief The mean radius of Pluto, expressed in kilometers. Pluto is nearly spherical.
	239	*/
	240	#define PLUTO_RADIUS_KM 1188.3
	241
	242
	243	/---------- types ----------/
	244
	245	/**
	246	* @brief Indicates success/failure of an Astronomy Engine function call.
	247	*/
	248	typedef enum
	249	{
	250	ASTRO_SUCCESS, /*< The operation was successful. /
	251	ASTRO_NOT_INITIALIZED, /*< A placeholder that can be used for data that is not yet initialized. /
	252	ASTRO_INVALID_BODY, /*< The celestial body was not valid. Different sets of bodies are supported depending on the function. /
	253	ASTRO_NO_CONVERGE, /*< A numeric solver failed to converge. This should not happen unless there is a bug in Astronomy Engine. /
	254	ASTRO_BAD_TIME, /*< The provided date/time is outside the range allowed by this function. /
	255	ASTRO_BAD_VECTOR, /*< Vector magnitude is too small to be normalized into a unit vector. /
	256	ASTRO_SEARCH_FAILURE, /*< Search was not able to find an ascending root crossing of the function in the specified time interval. /
	257	ASTRO_EARTH_NOT_ALLOWED, /*< The Earth cannot be treated as a celestial body seen from an observer on the Earth itself. /
	258	ASTRO_NO_MOON_QUARTER, /*< No lunar quarter occurs inside the specified time range. /
	259	ASTRO_WRONG_MOON_QUARTER, /*< Internal error: Astronomy_NextMoonQuarter found the wrong moon quarter. /
	260	ASTRO_INTERNAL_ERROR, /*< A self-check failed inside the code somewhere, indicating a bug needs to be fixed. /
	261	ASTRO_INVALID_PARAMETER, /*< A parameter value passed to a function was not valid. /
	262	ASTRO_FAIL_APSIS, /*< Special-case logic for finding Neptune/Pluto apsis failed. /
	263	ASTRO_BUFFER_TOO_SMALL, /*< A provided buffer's size is too small to receive the requested data. /
	264	ASTRO_OUT_OF_MEMORY, /*< An attempt to allocate memory failed. /
	265	ASTRO_INCONSISTENT_TIMES /*< The provided initial state vectors did not have matching times. /
	266	}
	267	astro_status_t;
	268
	269	/**
	270	* @brief A date and time used for astronomical calculations.
	271	*
	272	* This type is of fundamental importance to Astronomy Engine.
	273	* It is used to represent dates and times for all astronomical calculations.
	274	* It is also included in the values returned by many Astronomy Engine functions.
	275	*
	276	* To create a valid astro_time_t value from scratch, call #Astronomy_MakeTime
	277	* (for a given calendar date and time) or #Astronomy_CurrentTime (for the system's
	278	* current date and time).
	279	*
	280	* To adjust an existing astro_time_t by a certain real number of days,
	281	* call #Astronomy_AddDays.
	282	*
	283	* The astro_time_t type contains `ut` to represent Universal Time (UT1/UTC) and
	284	* `tt` to represent Terrestrial Time (TT, also known as ephemeris time).
	285	* The difference `tt-ut` is known as ΔT, using a best-fit piecewise model devised by
	286	* [Espenak and Meeus](https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html).
	287	*
	288	* Both `tt` and `ut` are necessary for performing different astronomical calculations.
	289	* Indeed, certain calculations (such as rise/set times) require both time scales.
	290	* See the documentation for the `ut` and `tt` fields for more detailed information.
	291	*
	292	* In cases where `astro_time_t` is included in a structure returned by
	293	* a function that can fail, the `astro_status_t` field `status` will contain a value
	294	* other than `ASTRO_SUCCESS`; in that case the `ut` and `tt` will hold `NAN` (not a number).
	295	* In general, when there is an error code stored in a struct field `status`, the
	296	* caller should ignore all other values in that structure, including the `ut` and `tt`
	297	* inside `astro_time_t`.
	298	*/
	299	typedef struct
	300	{
	301	/**
	302	* @brief UT1/UTC number of days since noon on January 1, 2000.
	303	*
	304	* The floating point number of days of Universal Time since noon UTC January 1, 2000.
	305	* Astronomy Engine approximates UTC and UT1 as being the same thing, although they are
	306	* not exactly equivalent; UTC and UT1 can disagree by up to ±0.9 seconds.
	307	* This approximation is sufficient for the accuracy requirements of Astronomy Engine.
	308	*
	309	* Universal Time Coordinate (UTC) is the international standard for legal and civil
	310	* timekeeping and replaces the older Greenwich Mean Time (GMT) standard.
	311	* UTC is kept in sync with unpredictable observed changes in the Earth's rotation
	312	* by occasionally adding leap seconds as needed.
	313	*
	314	* UT1 is an idealized time scale based on observed rotation of the Earth, which
	315	* gradually slows down in an unpredictable way over time, due to tidal drag by the Moon and Sun,
	316	* large scale weather events like hurricanes, and internal seismic and convection effects.
	317	* Conceptually, UT1 drifts from atomic time continuously and erratically, whereas UTC
	318	* is adjusted by a scheduled whole number of leap seconds as needed.
	319	*
	320	* The value in `ut` is appropriate for any calculation involving the Earth's rotation,
	321	* such as calculating rise/set times, culumination, and anything involving apparent
	322	* sidereal time.
	323	*
	324	* Before the era of atomic timekeeping, days based on the Earth's rotation
	325	* were often known as mean solar days.
	326	*/
	327	double ut;
	328
	329	/**
	330	* @brief Terrestrial Time days since noon on January 1, 2000.
	331	*
	332	* Terrestrial Time is an atomic time scale defined as a number of days since noon on January 1, 2000.
	333	* In this system, days are not based on Earth rotations, but instead by
	334	* the number of elapsed [SI seconds](https://physics.nist.gov/cuu/Units/second.html)
	335	* divided by 86400. Unlike `ut`, `tt` increases uniformly without adjustments
	336	* for changes in the Earth's rotation.
	337	*
	338	* The value in `tt` is used for calculations of movements not involving the Earth's rotation,
	339	* such as the orbits of planets around the Sun, or the Moon around the Earth.
	340	*
	341	* Historically, Terrestrial Time has also been known by the term Ephemeris Time (ET).
	342	*/
	343	double tt;
	344
	345	/**
	346	* @brief For internal use only. Used to optimize Earth tilt calculations.
	347	*/
	348	double psi;
	349
	350	/**
	351	* @brief For internal use only. Used to optimize Earth tilt calculations.
	352	*/
	353	double eps;
	354
	355	/**
	356	* @brief For internal use only. Lazy-caches sidereal time (Earth rotation).
	357	*/
	358	double st;
	359	}
	360	astro_time_t;
	361
	362	/**
	363	* @brief A calendar date and time expressed in UTC.
	364	*/
	365	typedef struct
	366	{
	367	int year; /*< The year value, e.g. 2019. /
	368	int month; /*< The month value: 1=January, 2=February, ..., 12=December. /
	369	int day; /*< The day of the month in the range 1..31. /
	370	int hour; /*< The hour of the day in the range 0..23. /
	371	int minute; /*< The minute of the hour in the range 0..59. /
	372	double second; /*< The floating point number of seconds in the range [0,60). /
	373	}
	374	astro_utc_t;
	375
	376	/**
	377	* @brief A 3D Cartesian vector whose components are expressed in Astronomical Units (AU).
	378	*/
	379	typedef struct
	380	{
	381	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	382	double x; /*< The Cartesian x-coordinate of the vector in AU. /
	383	double y; /*< The Cartesian y-coordinate of the vector in AU. /
	384	double z; /*< The Cartesian z-coordinate of the vector in AU. /
	385	astro_time_t t; /*< The date and time at which this vector is valid. /
	386	}
	387	astro_vector_t;
	388
	389	/**
	390	* @brief A state vector that contains a position (AU) and velocity (AU/day).
	391	*/
	392	typedef struct
	393	{
	394	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	395	double x; /*< The Cartesian position x-coordinate of the vector in AU. /
	396	double y; /*< The Cartesian position y-coordinate of the vector in AU. /
	397	double z; /*< The Cartesian position z-coordinate of the vector in AU. /
	398	double vx; /*< The Cartesian velocity x-coordinate of the vector in AU/day. /
	399	double vy; /*< The Cartesian velocity y-coordinate of the vector in AU/day. /
	400	double vz; /*< The Cartesian velocity z-coordinate of the vector in AU/day. /
	401	astro_time_t t; /*< The date and time at which this state vector is valid. /
	402	}
	403	astro_state_vector_t;
	404
	405	/**
	406	* @brief Spherical coordinates: latitude, longitude, distance.
	407	*/
	408	typedef struct
	409	{
	410	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	411	double lat; /*< The latitude angle: -90..+90 degrees. /
	412	double lon; /*< The longitude angle: 0..360 degrees. /
	413	double dist; /*< Distance in AU. /
	414	}
	415	astro_spherical_t;
	416
	417	/**
	418	* @brief An angular value expressed in degrees.
	419	*/
	420	typedef struct
	421	{
	422	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	423	double angle; /*< An angle expressed in degrees. /
	424	}
	425	astro_angle_result_t;
	426
	427	/**
	428	* @brief A celestial body.
	429	*/
	430	typedef enum
	431	{
	432	BODY_INVALID = -1, /*< An invalid or undefined celestial body. /
	433	BODY_MERCURY, /*< Mercury /
	434	BODY_VENUS, /*< Venus /
	435	BODY_EARTH, /*< Earth /
	436	BODY_MARS, /*< Mars /
	437	BODY_JUPITER, /*< Jupiter /
	438	BODY_SATURN, /*< Saturn /
	439	BODY_URANUS, /*< Uranus /
	440	BODY_NEPTUNE, /*< Neptune /
	441	BODY_PLUTO, /*< Pluto /
	442	BODY_SUN, /*< Sun /
	443	BODY_MOON, /*< Moon /
	444	BODY_EMB, /*< Earth/Moon Barycenter /
	445	BODY_SSB, /*< Solar System Barycenter /
	446	BODY_STAR1 = 101, /*< user-defined star #1 /
	447	BODY_STAR2, /*< user-defined star #2 /
	448	BODY_STAR3, /*< user-defined star #3 /
	449	BODY_STAR4, /*< user-defined star #4 /
	450	BODY_STAR5, /*< user-defined star #5 /
	451	BODY_STAR6, /*< user-defined star #6 /
	452	BODY_STAR7, /*< user-defined star #7 /
	453	BODY_STAR8, /*< user-defined star #8 /
	454	}
	455	astro_body_t;
	456
	457	/**
	458	* @brief The location of an observer on (or near) the surface of the Earth.
	459	*
	460	* This structure is passed to functions that calculate phenomena as observed
	461	* from a particular place on the Earth.
	462	*
	463	* You can create this structure directly, or you can call the convenience function
	464	* #Astronomy_MakeObserver to create one for you.
	465	*/
	466	typedef struct
	467	{
	468	double latitude; /*< Geographic latitude in degrees north (positive) or south (negative) of the equator. /
	469	double longitude; /*< Geographic longitude in degrees east (positive) or west (negative) of the prime meridian at Greenwich, England. /
	470	double height; /*< The height above (positive) or below (negative) sea level, expressed in meters. /
	471	}
	472	astro_observer_t;
	473
	474	/**
	475	* @brief Equatorial angular and cartesian coordinates.
	476	*
	477	* Coordinates of a celestial body as seen from the Earth (geocentric or topocentric, depending on context),
	478	* oriented with respect to the projection of the Earth's equator onto the sky.
	479	*/
	480	typedef struct
	481	{
	482	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	483	double ra; /*< right ascension in sidereal hours. /
	484	double dec; /*< declination in degrees /
	485	double dist; /*< distance to the celestial body in AU. /
	486	astro_vector_t vec; /*< equatorial coordinates in cartesian vector form: x = March equinox, y = June solstice, z = north. /
	487	}
	488	astro_equatorial_t;
	489
	490	/**
	491	* @brief Ecliptic angular and Cartesian coordinates.
	492	*
	493	* Coordinates of a celestial body as seen from the center of the Sun (heliocentric),
	494	* oriented with respect to the plane of the Earth's orbit around the Sun (the ecliptic).
	495	*/
	496	typedef struct
	497	{
	498	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	499	astro_vector_t vec; /*< Cartesian ecliptic vector: x=equinox, y=90 degrees prograde in ecliptic plane, z=northward perpendicular to ecliptic. /
	500	double elat; /*< Latitude in degrees north (positive) or south (negative) of the ecliptic plane. /
	501	double elon; /*< Longitude in degrees around the ecliptic plane prograde from the equinox. /
	502	}
	503	astro_ecliptic_t;
	504
	505	/**
	506	* @brief Coordinates of a celestial body as seen by a topocentric observer.
	507	*
	508	* Contains horizontal and equatorial coordinates seen by an observer on or near
	509	* the surface of the Earth (a topocentric observer).
	510	* Optionally corrected for atmospheric refraction.
	511	*/
	512	typedef struct
	513	{
	514	double azimuth; /*< Compass direction around the horizon in degrees. 0=North, 90=East, 180=South, 270=West. /
	515	double altitude; /*< Angle in degrees above (positive) or below (negative) the observer's horizon. /
	516	double ra; /*< Right ascension in sidereal hours. /
	517	double dec; /*< Declination in degrees. /
	518	}
	519	astro_horizon_t;
	520
	521	/**
	522	* @brief Contains a rotation matrix that can be used to transform one coordinate system to another.
	523	*/
	524	typedef struct
	525	{
	526	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	527	double rot[3][3]; /*< A normalized 3x3 rotation matrix. /
	528	}
	529	astro_rotation_t;
	530
	531	/**
	532	* @brief Selects whether to correct for atmospheric refraction, and if so, how.
	533	*/
	534	typedef enum
	535	{
	536	REFRACTION_NONE, /*< No atmospheric refraction correction (airless). /
	537	REFRACTION_NORMAL, /*< Recommended correction for standard atmospheric refraction. /
	538	REFRACTION_JPLHOR /*< Used only for compatibility testing with JPL Horizons online tool. /
	539	}
	540	astro_refraction_t;
	541
	542	/**
	543	* @brief Information about idealized atmospheric variables at a given elevation.
	544	*/
	545	typedef struct
	546	{
	547	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	548	double pressure; /*< Atmospheric pressure in pascals /
	549	double temperature; /*< Atmospheric temperature in kelvins /
	550	double density; /*< Atmospheric density relative to sea level /
	551	}
	552	astro_atmosphere_t;
	553
	554	/**
	555	* @brief The result of a search for an astronomical event.
	556	*/
	557	typedef struct
	558	{
	559	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	560	astro_time_t time; /*< The time at which a searched-for event occurs. /
	561	}
	562	astro_search_result_t;
	563
	564	/**
	565	* @brief
	566	* The dates and times of changes of season for a given calendar year.
	567	* Call #Astronomy_Seasons to calculate this data structure for a given year.
	568	*/
	569	typedef struct
	570	{
	571	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	572	astro_time_t mar_equinox; /*< The date and time of the March equinox for the specified year. /
	573	astro_time_t jun_solstice; /*< The date and time of the June soltice for the specified year. /
	574	astro_time_t sep_equinox; /*< The date and time of the September equinox for the specified year. /
	575	astro_time_t dec_solstice; /*< The date and time of the December solstice for the specified year. /
	576	}
	577	astro_seasons_t;
	578
	579	/**
	580	* @brief A lunar quarter event (new moon, first quarter, full moon, or third quarter) along with its date and time.
	581	*/
	582	typedef struct
	583	{
	584	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	585	int quarter; /*< 0=new moon, 1=first quarter, 2=full moon, 3=third quarter. /
	586	astro_time_t time; /*< The date and time of the lunar quarter. /
	587	}
	588	astro_moon_quarter_t;
	589
	590	/**
	591	* @brief A real value returned by a function whose ascending root is to be found.
	592	*
	593	* When calling #Astronomy_Search, the caller must pass in a callback function
	594	* compatible with the function-pointer type #astro_search_func_t
	595	* whose ascending root is to be found. That callback function must return astro_func_result_t.
	596	* If the function call is successful, it will set `status` to `ASTRO_SUCCESS` and `value`
	597	* to the numeric value appropriate for the given date and time.
	598	* If the call fails for some reason, it should set `status` to an appropriate error value
	599	* other than `ASTRO_SUCCESS`; in the error case, to guard against any possible misuse of `value`,
	600	* it is recommended to set `value` to `NAN`, though this is not strictly necessary.
	601	*/
	602	typedef struct
	603	{
	604	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	605	double value; /*< The value returned by a function whose ascending root is to be found. /
	606	}
	607	astro_func_result_t;
	608
	609	/**
	610	* @brief A pointer to a function that is to be passed as a callback to #Astronomy_Search.
	611	*
	612	* The function #Astronomy_Search numerically solves for the time that a given event occurs.
	613	* An event is defined as the time when an arbitrary function transitions between having
	614	* a negative value and a non-negative value. This transition is called an ascending root.
	615	*
	616	* The type astro_search_func_t represents such a callback function that accepts a
	617	* custom `context` pointer and an astro_time_t representing the time to probe.
	618	* The function returns an astro_func_result_t that contains either a real
	619	* number in `value` or an error code in `status` that aborts the search.
	620	*
	621	* The `context` points to some data whose type varies depending on the callback function.
	622	* It can contain any auxiliary parameters (other than time) needed to evaluate the function.
	623	* For example, a function may pertain to a specific celestial body, in which case `context`
	624	* may point to a value of type astro_body_t. The `context` parameter is supplied by
	625	* the caller of #Astronomy_Search, which passes it along to every call to the callback function.
	626	* If the caller of `Astronomy_Search` knows that the callback function does not need a context,
	627	* it is safe to pass `NULL` as the context pointer.
	628	*/
	629	typedef astro_func_result_t (* astro_search_func_t) (void *context, astro_time_t time);
	630
	631	/**
	632	* @brief A pointer to a function that calculates Delta T.
	633	*
	634	* Delta T is the discrepancy between times measured using an atomic clock
	635	* and times based on observations of the Earth's rotation, which is gradually
	636	* slowing down over time. Delta T = TT - UT, where
	637	* TT = Terrestrial Time, based on atomic time, and
	638	* UT = Universal Time, civil time based on the Earth's rotation.
	639	* Astronomy Engine defaults to using a Delta T function defined by
	640	* Espenak and Meeus in their "Five Millennium Canon of Solar Eclipses".
	641	* See: https://eclipse.gsfc.nasa.gov/SEhelp/deltatpoly2004.html
	642	*/
	643	typedef double (* astro_deltat_func) (double ut);
	644
	645	double Astronomy_DeltaT_EspenakMeeus(double ut);
	646	double Astronomy_DeltaT_JplHorizons(double ut);
	647
	648	void Astronomy_SetDeltaTFunction(astro_deltat_func func);
	649
	650	/**
	651	* @brief Indicates whether a body (especially Mercury or Venus) is best seen in the morning or evening.
	652	*/
	653	typedef enum
	654	{
	655	VISIBLE_MORNING, /*< The body is best visible in the morning, before sunrise. /
	656	VISIBLE_EVENING /*< The body is best visible in the evening, after sunset. /
	657	}
	658	astro_visibility_t;
	659
	660	/**
	661	* @brief
	662	* Contains information about the visibility of a celestial body at a given date and time.
	663	* See #Astronomy_Elongation for more detailed information about the members of this structure.
	664	* See also #Astronomy_SearchMaxElongation for how to search for maximum elongation events.
	665	*/
	666	typedef struct
	667	{
	668	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	669	astro_time_t time; /*< The date and time of the observation. /
	670	astro_visibility_t visibility; /*< Whether the body is best seen in the morning or the evening. /
	671	double elongation; /*< The angle in degrees between the body and the Sun, as seen from the Earth. /
	672	double ecliptic_separation; /*< The difference between the ecliptic longitudes of the body and the Sun, as seen from the Earth. /
	673	}
	674	astro_elongation_t;
	675
	676	/**
	677	* @brief Information about a celestial body crossing a specific hour angle.
	678	*
	679	* Returned by the function #Astronomy_SearchHourAngleEx to report information about
	680	* a celestial body crossing a certain hour angle as seen by a specified topocentric observer.
	681	*/
	682	typedef struct
	683	{
	684	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	685	astro_time_t time; /*< The date and time when the body crosses the specified hour angle. /
	686	astro_horizon_t hor; /*< Apparent coordinates of the body at the time it crosses the specified hour angle. /
	687	}
	688	astro_hour_angle_t;
	689
	690	/**
	691	* @brief Information about the brightness and illuminated shape of a celestial body.
	692	*
	693	* Returned by the functions #Astronomy_Illumination and #Astronomy_SearchPeakMagnitude
	694	* to report the visual magnitude and illuminated fraction of a celestial body at a given date and time.
	695	*/
	696	typedef struct
	697	{
	698	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	699	astro_time_t time; /*< The date and time of the observation. /
	700	double mag; /*< The visual magnitude of the body. Smaller values are brighter. /
	701	double phase_angle; /*< The angle in degrees between the Sun and the Earth, as seen from the body. Indicates the body's phase as seen from the Earth. /
	702	double phase_fraction; /*< A value in the range [0.0, 1.0] indicating what fraction of the body's apparent disc is illuminated, as seen from the Earth. /
	703	double helio_dist; /*< The distance between the Sun and the body at the observation time. /
	704	double ring_tilt; /*< For Saturn, the tilt angle in degrees of its rings as seen from Earth. For all other bodies, 0. /
	705	}
	706	astro_illum_t;
	707
	708	/**
	709	* @brief The type of apsis: pericenter (closest approach) or apocenter (farthest distance).
	710	*/
	711	typedef enum
	712	{
	713	APSIS_PERICENTER, /*< The body is at its closest approach to the object it orbits. /
	714	APSIS_APOCENTER, /*< The body is at its farthest distance from the object it orbits. /
	715	APSIS_INVALID /*< Undefined or invalid apsis. /
	716	}
	717	astro_apsis_kind_t;
	718
	719	/**
	720	* @brief An apsis event: pericenter (closest approach) or apocenter (farthest distance).
	721	*
	722	* For the Moon orbiting the Earth, or a planet orbiting the Sun, an apsis is an
	723	* event where the orbiting body reaches its closest or farthest point from the primary body.
	724	* The closest approach is called pericenter and the farthest point is apocenter.
	725	*
	726	* More specific terminology is common for particular orbiting bodies.
	727	* The Moon's closest approach to the Earth is called perigee and its farthest
	728	* point is called apogee. The closest approach of a planet to the Sun is called
	729	* perihelion and the furthest point is called aphelion.
	730	*
	731	* This data structure is returned by #Astronomy_SearchLunarApsis and #Astronomy_NextLunarApsis
	732	* to iterate through consecutive alternating perigees and apogees.
	733	*/
	734	typedef struct
	735	{
	736	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	737	astro_time_t time; /*< The date and time of the apsis. /
	738	astro_apsis_kind_t kind; /*< Whether this is a pericenter or apocenter event. /
	739	double dist_au; /*< The distance between the centers of the bodies in astronomical units. /
	740	double dist_km; /*< The distance between the centers of the bodies in kilometers. /
	741	}
	742	astro_apsis_t;
	743
	744	/**
	745	* @brief The different kinds of lunar/solar eclipses.
	746	*/
	747	typedef enum
	748	{
	749	ECLIPSE_NONE, /*< No eclipse found. /
	750	ECLIPSE_PENUMBRAL, /*< A penumbral lunar eclipse. (Never used for a solar eclipse.) /
	751	ECLIPSE_PARTIAL, /*< A partial lunar/solar eclipse. /
	752	ECLIPSE_ANNULAR, /*< An annular solar eclipse. (Never used for a lunar eclipse.) /
	753	ECLIPSE_TOTAL /*< A total lunar/solar eclipse. /
	754	}
	755	astro_eclipse_kind_t;
	756
	757	/**
	758	* @brief Information about a lunar eclipse.
	759	*
	760	* Returned by #Astronomy_SearchLunarEclipse or #Astronomy_NextLunarEclipse
	761	* to report information about a lunar eclipse event.
	762	* If a lunar eclipse is found, `status` holds `ASTRO_SUCCESS` and the other fields are set.
	763	* If `status` holds any other value, it is an error code and the other fields are undefined.
	764	*
	765	* When a lunar eclipse is found, it is classified as penumbral, partial, or total.
	766	* Penumbral eclipses are difficult to observe, because the Moon is only slightly dimmed
	767	* by the Earth's penumbra; no part of the Moon touches the Earth's umbra.
	768	* Partial eclipses occur when part, but not all, of the Moon touches the Earth's umbra.
	769	* Total eclipses occur when the entire Moon passes into the Earth's umbra.
	770	*
	771	* The `kind` field thus holds `ECLIPSE_PENUMBRAL`, `ECLIPSE_PARTIAL`, or `ECLIPSE_TOTAL`,
	772	* depending on the kind of lunar eclipse found.
	773	*
	774	* The `obscuration` field holds a value in the range [0, 1] that indicates what fraction
	775	* of the Moon's apparent disc area is covered by the Earth's umbra at the eclipse's peak.
	776	* This indicates how dark the peak eclipse appears. For penumbral eclipses, the obscuration
	777	* is 0, because the Moon does not pass through the Earth's umbra. For partial eclipses,
	778	* the obscuration is somewhere between 0 and 1. For total lunar eclipses, the obscuration is 1.
	779	*
	780	* Field `peak` holds the date and time of the center of the eclipse, when it is at its peak.
	781	*
	782	* Fields `sd_penum`, `sd_partial`, and `sd_total` hold the semi-duration of each phase
	783	* of the eclipse, which is half of the amount of time the eclipse spends in each
	784	* phase (expressed in minutes), or 0 if the eclipse never reaches that phase.
	785	* By converting from minutes to days, and subtracting/adding with `center`, the caller
	786	* may determine the date and time of the beginning/end of each eclipse phase.
	787	*/
	788	typedef struct
	789	{
	790	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	791	astro_eclipse_kind_t kind; /*< The type of lunar eclipse found. /
	792	double obscuration; /*< The peak fraction of the Moon's apparent disc that is covered by the Earth's umbra. /
	793	astro_time_t peak; /*< The time of the eclipse at its peak. /
	794	double sd_penum; /*< The semi-duration of the penumbral phase in minutes. /
	795	double sd_partial; /*< The semi-duration of the partial phase in minutes, or 0.0 if none. /
	796	double sd_total; /*< The semi-duration of the total phase in minutes, or 0.0 if none. /
	797	}
	798	astro_lunar_eclipse_t;
	799
	800
	801	/**
	802	* @brief Reports the time and geographic location of the peak of a solar eclipse.
	803	*
	804	* Returned by #Astronomy_SearchGlobalSolarEclipse or #Astronomy_NextGlobalSolarEclipse
	805	* to report information about a solar eclipse event.
	806	* If a solar eclipse is found, `status` holds `ASTRO_SUCCESS` and `kind`, `peak`, and `distance`
	807	* have valid values. The `latitude` and `longitude` are set only for total and annular eclipses
	808	* (see more below).
	809	* If `status` holds any value other than `ASTRO_SUCCESS`, it is an error code;
	810	* in that case, `kind` holds `ECLIPSE_NONE` and all the other fields are undefined.
	811	*
	812	* The eclipse is classified as partial, annular, or total, depending on the
	813	* maximum amount of the Sun's disc obscured, as seen at the peak location
	814	* on the surface of the Earth.
	815	*
	816	* The `kind` field thus holds `ECLIPSE_PARTIAL`, `ECLIPSE_ANNULAR`, or `ECLIPSE_TOTAL`.
	817	* A total eclipse is when the peak observer sees the Sun completely blocked by the Moon.
	818	* An annular eclipse is like a total eclipse, but the Moon is too far from the Earth's surface
	819	* to completely block the Sun; instead, the Sun takes on a ring-shaped appearance.
	820	* A partial eclipse is when the Moon blocks part of the Sun's disc, but nobody on the Earth
	821	* observes either a total or annular eclipse.
	822	*
	823	* If `kind` is `ECLIPSE_TOTAL` or `ECLIPSE_ANNULAR`, the `latitude` and `longitude`
	824	* fields give the geographic coordinates of the center of the Moon's shadow projected
	825	* onto the daytime side of the Earth at the instant of the eclipse's peak.
	826	* If `kind` has any other value, `latitude` and `longitude` are undefined and should
	827	* not be used.
	828	*
	829	* For total or annular eclipses, the `obscuration` field holds the fraction (0, 1]
	830	* of the Sun's apparent disc area that is blocked from view by the Moon's silhouette,
	831	* as seen by an observer located at the geographic coordinates `latitude`, `longitude`
	832	* at the darkest time `peak`. The value will always be 1 for total eclipses, and less than
	833	* 1 for annular eclipses.
	834	* For partial eclipses, `obscuration` is undefined and should not be used.
	835	* This is because there is little practical use for an obscuration value of
	836	* a partial eclipse without supplying a particular observation location.
	837	* Developers who wish to find an obscuration value for partial solar eclipses should therefore use
	838	* #Astronomy_SearchLocalSolarEclipse and provide the geographic coordinates of an observer.
	839	*/
	840	typedef struct
	841	{
	842	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	843	astro_eclipse_kind_t kind; /*< The type of solar eclipse found. /
	844	double obscuration; /*< The peak fraction of the Sun's apparent disc area obscured by the Moon (total and annular eclipses only). /
	845	astro_time_t peak; /*< The date and time when the solar eclipse is darkest. This is the instant when the axis of the Moon's shadow cone passes closest to the Earth's center. /
	846	double distance; /*< The distance between the Sun/Moon shadow axis and the center of the Earth, in kilometers. /
	847	double latitude; /*< The geographic latitude at the center of the peak eclipse shadow. /
	848	double longitude; /*< The geographic longitude at the center of the peak eclipse shadow. /
	849	}
	850	astro_global_solar_eclipse_t;
	851
	852
	853	/**
	854	* @brief Holds a time and the observed altitude of the Sun at that time.
	855	*
	856	* When reporting a solar eclipse observed at a specific location on the Earth
	857	* (a "local" solar eclipse), a series of events occur. In addition
	858	* to the time of each event, it is important to know the altitude of the Sun,
	859	* because each event may be invisible to the observer if the Sun is below
	860	* the horizon.
	861	*
	862	* If `altitude` is negative, the event is theoretical only; it would be
	863	* visible if the Earth were transparent, but the observer cannot actually see it.
	864	* If `altitude` is positive but less than a few degrees, visibility will be impaired by
	865	* atmospheric interference (sunrise or sunset conditions).
	866	*/
	867	typedef struct
	868	{
	869	astro_time_t time; /*< The date and time of the event. /
	870	double altitude; /*< The angular altitude of the center of the Sun above/below the horizon, at `time`, corrected for atmospheric refraction and expressed in degrees. /
	871	}
	872	astro_eclipse_event_t;
	873
	874
	875	/**
	876	* @brief Information about a solar eclipse as seen by an observer at a given time and geographic location.
	877	*
	878	* Returned by #Astronomy_SearchLocalSolarEclipse or #Astronomy_NextLocalSolarEclipse
	879	* to report information about a solar eclipse as seen at a given geographic location.
	880	* If a solar eclipse is found, `status` holds `ASTRO_SUCCESS` and the other fields are set.
	881	* If `status` holds any other value, it is an error code and the other fields are undefined.
	882	*
	883	* When a solar eclipse is found, it is classified as partial, annular, or total.
	884	* The `kind` field thus holds `ECLIPSE_PARTIAL`, `ECLIPSE_ANNULAR`, or `ECLIPSE_TOTAL`.
	885	* A partial solar eclipse is when the Moon does not line up directly enough with the Sun
	886	* to completely block the Sun's light from reaching the observer.
	887	* An annular eclipse occurs when the Moon's disc is completely visible against the Sun
	888	* but the Moon is too far away to completely block the Sun's light; this leaves the
	889	* Sun with a ring-like appearance.
	890	* A total eclipse occurs when the Moon is close enough to the Earth and aligned with the
	891	* Sun just right to completely block all sunlight from reaching the observer.
	892	*
	893	* The `obscuration` field reports what fraction of the Sun's disc appears blocked
	894	* by the Moon when viewed by the observer at the peak eclipse time.
	895	* This is a value that ranges from 0 (no blockage) to 1 (total eclipse).
	896	* The obscuration value will be between 0 and 1 for partial eclipses and annular eclipses.
	897	* The value will be exactly 1 for total eclipses. Obscuration gives an indication
	898	* of how dark the eclipse appears.
	899	*
	900	* There are 5 "event" fields, each of which contains a time and a solar altitude.
	901	* Field `peak` holds the date and time of the center of the eclipse, when it is at its peak.
	902	* The fields `partial_begin` and `partial_end` are always set, and indicate when
	903	* the eclipse begins/ends. If the eclipse reaches totality or becomes annular,
	904	* `total_begin` and `total_end` indicate when the total/annular phase begins/ends.
	905	* When an event field is valid, the caller must also check its `altitude` field to
	906	* see whether the Sun is above the horizon at that time. See #astro_eclipse_kind_t
	907	* for more information.
	908	*/
	909	typedef struct
	910	{
	911	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	912	astro_eclipse_kind_t kind; /*< The type of solar eclipse found: `ECLIPSE_PARTIAL`, `ECLIPSE_ANNULAR`, or `ECLIPSE_TOTAL`. /
	913	double obscuration; /*< The fraction of the Sun's apparent disc area obscured by the Moon at the eclipse peak. /
	914	astro_eclipse_event_t partial_begin; /*< The time and Sun altitude at the beginning of the eclipse. /
	915	astro_eclipse_event_t total_begin; /*< If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase begins; otherwise invalid. /
	916	astro_eclipse_event_t peak; /*< The time and Sun altitude when the eclipse reaches its peak. /
	917	astro_eclipse_event_t total_end; /*< If this is an annular or a total eclipse, the time and Sun altitude when annular/total phase ends; otherwise invalid. /
	918	astro_eclipse_event_t partial_end; /*< The time and Sun altitude at the end of the eclipse. /
	919	}
	920	astro_local_solar_eclipse_t;
	921
	922
	923	/**
	924	* @brief Information about a transit of Mercury or Venus, as seen from the Earth.
	925	*
	926	* Returned by #Astronomy_SearchTransit or #Astronomy_NextTransit to report
	927	* information about a transit of Mercury or Venus.
	928	* A transit is when Mercury or Venus passes between the Sun and Earth so that
	929	* the other planet is seen in silhouette against the Sun.
	930	*
	931	* The `start` field reports the moment in time when the planet first becomes
	932	* visible against the Sun in its background.
	933	* The `peak` field reports when the planet is most aligned with the Sun,
	934	* as seen from the Earth.
	935	* The `finish` field reports the last moment when the planet is visible
	936	* against the Sun in its background.
	937	*
	938	* The calculations are performed from the point of view of a geocentric observer.
	939	*/
	940	typedef struct
	941	{
	942	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	943	astro_time_t start; /*< Date and time at the beginning of the transit. /
	944	astro_time_t peak; /*< Date and time of the peak of the transit. /
	945	astro_time_t finish; /*< Date and time at the end of the transit. /
	946	double separation; /*< Angular separation in arcminutes between the centers of the Sun and the planet at time `peak`. /
	947	}
	948	astro_transit_t;
	949
	950
	951	/**
	952	* @brief Aberration calculation options.
	953	*
	954	* [Aberration](https://en.wikipedia.org/wiki/Aberration_of_light) is an effect
	955	* causing the apparent direction of an observed body to be shifted due to transverse
	956	* movement of the Earth with respect to the rays of light coming from that body.
	957	* This angular correction can be anywhere from 0 to about 20 arcseconds,
	958	* depending on the position of the observed body relative to the instantaneous
	959	* velocity vector of the Earth.
	960	*
	961	* Some Astronomy Engine functions allow optional correction for aberration by
	962	* passing in a value of this enumerated type.
	963	*
	964	* Aberration correction is useful to improve accuracy of coordinates of
	965	* apparent locations of bodies seen from the Earth.
	966	* However, because aberration affects not only the observed body (such as a planet)
	967	* but the surrounding stars, aberration may be unhelpful (for example)
	968	* for determining exactly when a planet crosses from one constellation to another.
	969	*/
	970	typedef enum
	971	{
	972	ABERRATION, /*< Request correction for aberration. /
	973	NO_ABERRATION /*< Do not correct for aberration. /
	974	}
	975	astro_aberration_t;
	976
	977	/**
	978	* @brief Selects the date for which the Earth's equator is to be used for representing equatorial coordinates.
	979	*
	980	* The Earth's equator is not always in the same plane due to precession and nutation.
	981	*
	982	* Sometimes it is useful to have a fixed plane of reference for equatorial coordinates
	983	* across different calendar dates. In these cases, a fixed epoch, or reference time,
	984	* is helpful. Astronomy Engine provides the J2000 epoch for such cases. This refers
	985	* to the plane of the Earth's orbit as it was on noon UTC on 1 January 2000.
	986	*
	987	* For some other purposes, it is more helpful to represent coordinates using the Earth's
	988	* equator exactly as it is on that date. For example, when calculating rise/set times
	989	* or horizontal coordinates, it is most accurate to use the orientation of the Earth's
	990	* equator at that same date and time. For these uses, Astronomy Engine allows of-date
	991	* calculations.
	992	*/
	993	typedef enum
	994	{
	995	EQUATOR_J2000, /*< Represent equatorial coordinates in the J2000 epoch. /
	996	EQUATOR_OF_DATE /*< Represent equatorial coordinates using the Earth's equator at the given date and time. /
	997	}
	998	astro_equator_date_t;
	999
	1000	/**
	1001	* @brief Selects whether to search for a rise time or a set time.
	1002	*
	1003	* The #Astronomy_SearchRiseSetEx function finds the rise or set time of a body
	1004	* depending on the value of its `direction` parameter.
	1005	*/
	1006	typedef enum
	1007	{
	1008	DIRECTION_RISE = +1, /*< Search for the time a body begins to rise above the horizon. /
	1009	DIRECTION_SET = -1, /*< Search for the time a body finishes sinking below the horizon. /
	1010	}
	1011	astro_direction_t;
	1012
	1013
	1014	/**
	1015	* @brief Reports the constellation that a given celestial point lies within.
	1016	*
	1017	* The #Astronomy_Constellation function returns this struct
	1018	* to report which constellation corresponds with a given point in the sky.
	1019	* Constellations are defined with respect to the B1875 equatorial system
	1020	* per IAU standard. Although `Astronomy.Constellation` requires J2000 equatorial
	1021	* coordinates, the struct contains converted B1875 coordinates for reference.
	1022	*/
	1023	typedef struct
	1024	{
	1025	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	1026	const char symbol; /< 3-character mnemonic symbol for the constellation, e.g. "Ori". /
	1027	const char name; /< Full name of constellation, e.g. "Orion". /
	1028	double ra_1875; /*< Right ascension expressed in B1875 coordinates. /
	1029	double dec_1875; /*< Declination expressed in B1875 coordinates. /
	1030	}
	1031	astro_constellation_t;
	1032
	1033
	1034	/**
	1035	* @brief Selects the output format of the function #Astronomy_FormatTime.
	1036	*/
	1037	typedef enum
	1038	{
	1039	TIME_FORMAT_DAY, /*< Truncate to UTC calendar date only, e.g. `2020-12-31`. Buffer size must be at least 11 characters. /
	1040	TIME_FORMAT_MINUTE, /*< Round to nearest UTC minute, e.g. `2020-12-31T15:47Z`. Buffer size must be at least 18 characters. /
	1041	TIME_FORMAT_SECOND, /*< Round to nearest UTC second, e.g. `2020-12-31T15:47:32Z`. Buffer size must be at least 21 characters. /
	1042	TIME_FORMAT_MILLI /*< Round to nearest UTC millisecond, e.g. `2020-12-31T15:47:32.397Z`. Buffer size must be at least 25 characters. /
	1043	}
	1044	astro_time_format_t;
	1045
	1046	/**
	1047	* @brief Lunar libration angles, returned by #Astronomy_Libration.
	1048	*/
	1049	typedef struct
	1050	{
	1051	double elat; /*< Sub-Earth libration ecliptic latitude angle, in degrees. /
	1052	double elon; /*< Sub-Earth libration ecliptic longitude angle, in degrees. /
	1053	double mlat; /*< Moon's geocentric ecliptic latitude, in degrees. /
	1054	double mlon; /*< Moon's geocentric ecliptic longitude, in degrees. /
	1055	double dist_km; /*< Distance between the centers of the Earth and Moon in kilometers. /
	1056	double diam_deg; /*< The apparent angular diameter of the Moon, in degrees, as seen from the center of the Earth. /
	1057	}
	1058	astro_libration_t;
	1059
	1060	/**
	1061	* @brief Information about a body's rotation axis at a given time.
	1062	*
	1063	* This structure is returned by #Astronomy_RotationAxis to report
	1064	* the orientation of a body's rotation axis at a given moment in time.
	1065	* The axis is specified by the direction in space that the body's north pole
	1066	* points, using angular equatorial coordinates in the J2000 system (EQJ).
	1067	*
	1068	* Thus `ra` is the right ascension, and `dec` is the declination, of the
	1069	* body's north pole vector at the given moment in time. The north pole
	1070	* of a body is defined as the pole that lies on the north side of the
	1071	* [Solar System's invariable plane](https://en.wikipedia.org/wiki/Invariable_plane),
	1072	* regardless of the body's direction of rotation.
	1073	*
	1074	* The `spin` field indicates the angular position of a prime meridian
	1075	* arbitrarily recommended for the body by the International Astronomical
	1076	* Union (IAU).
	1077	*
	1078	* The fields `ra`, `dec`, and `spin` correspond to the variables
	1079	* α0, δ0, and W, respectively, from
	1080	* [Report of the IAU Working Group on Cartographic Coordinates and Rotational Elements: 2015](https://astropedia.astrogeology.usgs.gov/download/Docs/WGCCRE/WGCCRE2015reprint.pdf).
	1081	*
	1082	* The field `north` is a unit vector pointing in the direction of the body's north pole.
	1083	* It is expressed in the equatorial J2000 system (EQJ).
	1084	*/
	1085	typedef struct
	1086	{
	1087	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	1088	double ra; /*< The J2000 right ascension of the body's north pole direction, in sidereal hours. /
	1089	double dec; /*< The J2000 declination of the body's north pole direction, in degrees. /
	1090	double spin; /*< Rotation angle of the body's prime meridian, in degrees. /
	1091	astro_vector_t north; /*< A J2000 dimensionless unit vector pointing in the direction of the body's north pole. /
	1092	}
	1093	astro_axis_t;
	1094
	1095
	1096	/**
	1097	* \def TIME_TEXT_BYTES
	1098	* @brief The smallest number of characters that is always large enough for #Astronomy_FormatTime.
	1099	*/
	1100	#define TIME_TEXT_BYTES 28
	1101
	1102	/**
	1103	* @brief Holds the positions and velocities of Jupiter's major 4 moons.
	1104	*
	1105	* The #Astronomy_JupiterMoons function returns this struct
	1106	* to report position and velocity vectors for Jupiter's largest 4 moons
	1107	* Io, Europa, Ganymede, and Callisto. Each position vector is relative
	1108	* to the center of Jupiter. Both position and velocity are oriented in
	1109	* the EQJ system (that is, using Earth's equator at the J2000 epoch.)
	1110	* The positions are expressed in astronomical units (AU),
	1111	* and the velocities in AU/day.
	1112	*/
	1113	typedef struct
	1114	{
	1115	astro_state_vector_t io; /*< Jovicentric position and velocity of Io. /
	1116	astro_state_vector_t europa; /*< Jovicentric position and velocity of Europa. /
	1117	astro_state_vector_t ganymede; /*< Jovicentric position and velocity of Ganymede. /
	1118	astro_state_vector_t callisto; /*< Jovicentric position and velocity of Callisto. /
	1119	}
	1120	astro_jupiter_moons_t;
	1121
	1122
	1123	/**
	1124	* @brief Indicates whether a crossing through the ecliptic plane is ascending or descending.
	1125	*/
	1126	typedef enum
	1127	{
	1128	INVALID_NODE = 0, /*< Placeholder value for a missing or invalid node. /
	1129	ASCENDING_NODE = +1, /*< The body passes through the ecliptic plane from south to north. /
	1130	DESCENDING_NODE = -1 /*< The body passes through the ecliptic plane from north to south. /
	1131	}
	1132	astro_node_kind_t;
	1133
	1134	/**
	1135	* @brief Information about an ascending or descending node of a body.
	1136	*
	1137	* This structure is returned by #Astronomy_SearchMoonNode and #Astronomy_NextMoonNode
	1138	* to report information about the center of the Moon passing through the ecliptic plane.
	1139	*/
	1140	typedef struct
	1141	{
	1142	astro_status_t status; /*< `ASTRO_SUCCESS` if this struct is valid; otherwise an error code. /
	1143	astro_time_t time; /*< The time when the body passes through the ecliptic plane. /
	1144	astro_node_kind_t kind; /*< Either `ASCENDING_NODE` or `DESCENDING_NODE`, depending on the direction of the ecliptic plane crossing. /
	1145	}
	1146	astro_node_event_t;
	1147
	1148
	1149	/**
	1150	* @brief A data type used for managing simulation of the gravitational forces on a small body.
	1151	*
	1152	* This is an opaque data type used to hold the internal state of
	1153	* a numeric integrator used to calculate the trajectory of a small
	1154	* body moving through the Solar System.
	1155	*/
	1156	typedef struct astro_grav_sim_s astro_grav_sim_t;
	1157
	1158
	1159	/---------- functions ----------/
	1160
	1161	void Astronomy_Reset(void);
	1162	double Astronomy_VectorLength(astro_vector_t vector);
	1163	astro_angle_result_t Astronomy_AngleBetween(astro_vector_t a, astro_vector_t b);
	1164	const char *Astronomy_BodyName(astro_body_t body);
	1165	astro_body_t Astronomy_BodyCode(const char *name);
	1166	astro_observer_t Astronomy_MakeObserver(double latitude, double longitude, double height);
	1167	#if !defined(ASTRONOMY_ENGINE_NO_CURRENT_TIME)
	1168	astro_time_t Astronomy_CurrentTime(void);
	1169	#endif
	1170	astro_time_t Astronomy_MakeTime(int year, int month, int day, int hour, int minute, double second);
	1171	astro_time_t Astronomy_TimeFromUtc(astro_utc_t utc);
	1172	astro_utc_t Astronomy_UtcFromTime(astro_time_t time);
	1173	astro_status_t Astronomy_FormatTime(astro_time_t time, astro_time_format_t format, char *text, size_t size);
	1174	astro_time_t Astronomy_TimeFromDays(double ut);
	1175	astro_time_t Astronomy_TerrestrialTime(double tt);
	1176	astro_time_t Astronomy_AddDays(astro_time_t time, double days);
	1177	double Astronomy_SiderealTime(astro_time_t *time);
	1178	astro_func_result_t Astronomy_HelioDistance(astro_body_t body, astro_time_t time);
	1179	astro_vector_t Astronomy_HelioVector(astro_body_t body, astro_time_t time);
	1180	astro_vector_t Astronomy_GeoVector(astro_body_t body, astro_time_t time, astro_aberration_t aberration);
	1181	astro_vector_t Astronomy_GeoMoon(astro_time_t time);
	1182	astro_spherical_t Astronomy_EclipticGeoMoon(astro_time_t time);
	1183	astro_state_vector_t Astronomy_GeoMoonState(astro_time_t time);
	1184	astro_state_vector_t Astronomy_GeoEmbState(astro_time_t time);
	1185	astro_libration_t Astronomy_Libration(astro_time_t time);
	1186	astro_state_vector_t Astronomy_BaryState(astro_body_t body, astro_time_t time);
	1187	astro_state_vector_t Astronomy_HelioState(astro_body_t body, astro_time_t time);
	1188
	1189	double Astronomy_MassProduct(astro_body_t body);
	1190	double Astronomy_PlanetOrbitalPeriod(astro_body_t body);
	1191
	1192	astro_state_vector_t Astronomy_LagrangePoint(
	1193	int point,
	1194	astro_time_t time,
	1195	astro_body_t major_body,
	1196	astro_body_t minor_body
	1197	);
	1198
	1199	astro_state_vector_t Astronomy_LagrangePointFast(
	1200	int point,
	1201	astro_state_vector_t major_state,
	1202	double major_mass,
	1203	astro_state_vector_t minor_state,
	1204	double minor_mass
	1205	);
	1206
	1207	astro_jupiter_moons_t Astronomy_JupiterMoons(astro_time_t time);
	1208
	1209	astro_equatorial_t Astronomy_Equator(
	1210	astro_body_t body,
	1211	astro_time_t *time,
	1212	astro_observer_t observer,
	1213	astro_equator_date_t equdate,
	1214	astro_aberration_t aberration
	1215	);
	1216
	1217	astro_vector_t Astronomy_ObserverVector(
	1218	astro_time_t *time,
	1219	astro_observer_t observer,
	1220	astro_equator_date_t equdate
	1221	);
	1222
	1223	astro_state_vector_t Astronomy_ObserverState(
	1224	astro_time_t *time,
	1225	astro_observer_t observer,
	1226	astro_equator_date_t equdate
	1227	);
	1228
	1229	astro_observer_t Astronomy_VectorObserver(astro_vector_t *vector, astro_equator_date_t equdate);
	1230
	1231	double Astronomy_ObserverGravity(double latitude, double height);
	1232
	1233	astro_ecliptic_t Astronomy_SunPosition(astro_time_t time);
	1234	astro_ecliptic_t Astronomy_Ecliptic(astro_vector_t eqj);
	1235	astro_angle_result_t Astronomy_EclipticLongitude(astro_body_t body, astro_time_t time);
	1236
	1237	astro_horizon_t Astronomy_Horizon(
	1238	astro_time_t *time,
	1239	astro_observer_t observer,
	1240	double ra,
	1241	double dec,
	1242	astro_refraction_t refraction);
	1243
	1244	astro_angle_result_t Astronomy_AngleFromSun(astro_body_t body, astro_time_t time);
	1245	astro_elongation_t Astronomy_Elongation(astro_body_t body, astro_time_t time);
	1246	astro_elongation_t Astronomy_SearchMaxElongation(astro_body_t body, astro_time_t startTime);
	1247	astro_angle_result_t Astronomy_PairLongitude(astro_body_t body1, astro_body_t body2, astro_time_t time);
	1248
	1249	/** @cond DOXYGEN_SKIP */
	1250	/* Provided for backward compatibility. Newer code can use Astronomy_PairLongitude. */
	1251	#define Astronomy_LongitudeFromSun(body,time) (Astronomy_PairLongitude((body), BODY_SUN, (time)))
	1252	/** @endcond */
	1253
	1254	astro_search_result_t Astronomy_SearchRelativeLongitude(astro_body_t body, double targetRelLon, astro_time_t startTime);
	1255	astro_angle_result_t Astronomy_MoonPhase(astro_time_t time);
	1256	astro_search_result_t Astronomy_SearchMoonPhase(double targetLon, astro_time_t startTime, double limitDays);
	1257	astro_moon_quarter_t Astronomy_SearchMoonQuarter(astro_time_t startTime);
	1258	astro_moon_quarter_t Astronomy_NextMoonQuarter(astro_moon_quarter_t mq);
	1259	astro_lunar_eclipse_t Astronomy_SearchLunarEclipse(astro_time_t startTime);
	1260	astro_lunar_eclipse_t Astronomy_NextLunarEclipse(astro_time_t prevEclipseTime);
	1261	astro_global_solar_eclipse_t Astronomy_SearchGlobalSolarEclipse(astro_time_t startTime);
	1262	astro_global_solar_eclipse_t Astronomy_NextGlobalSolarEclipse(astro_time_t prevEclipseTime);
	1263	astro_local_solar_eclipse_t Astronomy_SearchLocalSolarEclipse(astro_time_t startTime, astro_observer_t observer);
	1264	astro_local_solar_eclipse_t Astronomy_NextLocalSolarEclipse(astro_time_t prevEclipseTime, astro_observer_t observer);
	1265	astro_transit_t Astronomy_SearchTransit(astro_body_t body, astro_time_t startTime);
	1266	astro_transit_t Astronomy_NextTransit(astro_body_t body, astro_time_t prevTransitTime);
	1267	astro_node_event_t Astronomy_SearchMoonNode(astro_time_t startTime);
	1268	astro_node_event_t Astronomy_NextMoonNode(astro_node_event_t prevNode);
	1269
	1270	astro_search_result_t Astronomy_Search(
	1271	astro_search_func_t func,
	1272	void *context,
	1273	astro_time_t t1,
	1274	astro_time_t t2,
	1275	double dt_tolerance_seconds);
	1276
	1277	astro_search_result_t Astronomy_SearchSunLongitude(
	1278	double targetLon,
	1279	astro_time_t startTime,
	1280	double limitDays);
	1281
	1282	astro_hour_angle_t Astronomy_SearchHourAngleEx(
	1283	astro_body_t body,
	1284	astro_observer_t observer,
	1285	double hourAngle,
	1286	astro_time_t startTime,
	1287	int direction);
	1288
	1289	astro_func_result_t Astronomy_HourAngle(
	1290	astro_body_t body,
	1291	astro_time_t *time,
	1292	astro_observer_t observer);
	1293
	1294	/** @cond DOXYGEN_SKIP */
	1295
	1296	/* The following are provided for backward compatibility. */
	1297	#define Astronomy_SearchHourAngle(body,observer,hourAngle,startTime) \
	1298	Astronomy_SearchHourAngleEx((body), (observer), (hourAngle), (startTime), +1)
	1299
	1300	#define Astronomy_SearchRiseSet(body,observer,direction,startTime,limitDays) \
	1301	Astronomy_SearchRiseSetEx((body), (observer), (direction), (startTime), (limitDays), 0.0)
	1302
	1303	/** @endcond */
	1304
	1305	astro_search_result_t Astronomy_SearchRiseSetEx(
	1306	astro_body_t body,
	1307	astro_observer_t observer,
	1308	astro_direction_t direction,
	1309	astro_time_t startTime,
	1310	double limitDays,
	1311	double metersAboveGround);
	1312
	1313	astro_search_result_t Astronomy_SearchAltitude(
	1314	astro_body_t body,
	1315	astro_observer_t observer,
	1316	astro_direction_t direction,
	1317	astro_time_t startTime,
	1318	double limitDays,
	1319	double altitude);
	1320
	1321	astro_atmosphere_t Astronomy_Atmosphere(double elevationMeters);
	1322
	1323	astro_axis_t Astronomy_RotationAxis(astro_body_t body, astro_time_t *time);
	1324
	1325	astro_seasons_t Astronomy_Seasons(int year);
	1326	astro_illum_t Astronomy_Illumination(astro_body_t body, astro_time_t time);
	1327	astro_illum_t Astronomy_SearchPeakMagnitude(astro_body_t body, astro_time_t startTime);
	1328	astro_apsis_t Astronomy_SearchLunarApsis(astro_time_t startTime);
	1329	astro_apsis_t Astronomy_NextLunarApsis(astro_apsis_t apsis);
	1330	astro_apsis_t Astronomy_SearchPlanetApsis(astro_body_t body, astro_time_t startTime);
	1331	astro_apsis_t Astronomy_NextPlanetApsis(astro_body_t body, astro_apsis_t apsis);
	1332
	1333	astro_rotation_t Astronomy_IdentityMatrix(void);
	1334	astro_rotation_t Astronomy_InverseRotation(astro_rotation_t rotation);
	1335	astro_rotation_t Astronomy_CombineRotation(astro_rotation_t a, astro_rotation_t b);
	1336	astro_rotation_t Astronomy_Pivot(astro_rotation_t rotation, int axis, double angle);
	1337	astro_vector_t Astronomy_VectorFromSphere(astro_spherical_t sphere, astro_time_t time);
	1338	astro_spherical_t Astronomy_SphereFromVector(astro_vector_t vector);
	1339	astro_equatorial_t Astronomy_EquatorFromVector(astro_vector_t vector);
	1340	astro_vector_t Astronomy_VectorFromHorizon(astro_spherical_t sphere, astro_time_t time, astro_refraction_t refraction);
	1341	astro_spherical_t Astronomy_HorizonFromVector(astro_vector_t vector, astro_refraction_t refraction);
	1342	astro_vector_t Astronomy_RotateVector(astro_rotation_t rotation, astro_vector_t vector);
	1343	astro_state_vector_t Astronomy_RotateState(astro_rotation_t rotation, astro_state_vector_t state);
	1344
	1345	astro_rotation_t Astronomy_Rotation_EQD_EQJ(astro_time_t *time);
	1346	astro_rotation_t Astronomy_Rotation_EQD_ECL(astro_time_t *time);
	1347	astro_rotation_t Astronomy_Rotation_EQD_ECT(astro_time_t *time);
	1348	astro_rotation_t Astronomy_Rotation_EQD_HOR(astro_time_t *time, astro_observer_t observer);
	1349	astro_rotation_t Astronomy_Rotation_EQJ_EQD(astro_time_t *time);
	1350	astro_rotation_t Astronomy_Rotation_EQJ_ECT(astro_time_t *time);
	1351	astro_rotation_t Astronomy_Rotation_EQJ_ECL(void);
	1352	astro_rotation_t Astronomy_Rotation_EQJ_HOR(astro_time_t *time, astro_observer_t observer);
	1353	astro_rotation_t Astronomy_Rotation_ECL_EQD(astro_time_t *time);
	1354	astro_rotation_t Astronomy_Rotation_ECL_EQJ(void);
	1355	astro_rotation_t Astronomy_Rotation_ECL_HOR(astro_time_t *time, astro_observer_t observer);
	1356	astro_rotation_t Astronomy_Rotation_ECT_EQJ(astro_time_t *time);
	1357	astro_rotation_t Astronomy_Rotation_ECT_EQD(astro_time_t *time);
	1358	astro_rotation_t Astronomy_Rotation_HOR_EQD(astro_time_t *time, astro_observer_t observer);
	1359	astro_rotation_t Astronomy_Rotation_HOR_EQJ(astro_time_t *time, astro_observer_t observer);
	1360	astro_rotation_t Astronomy_Rotation_HOR_ECL(astro_time_t *time, astro_observer_t observer);
	1361	astro_rotation_t Astronomy_Rotation_EQJ_GAL(void);
	1362	astro_rotation_t Astronomy_Rotation_GAL_EQJ(void);
	1363
	1364	double Astronomy_Refraction(astro_refraction_t refraction, double altitude);
	1365	double Astronomy_InverseRefraction(astro_refraction_t refraction, double bent_altitude);
	1366
	1367	astro_constellation_t Astronomy_Constellation(double ra, double dec);
	1368
	1369	astro_status_t Astronomy_GravSimInit(
	1370	astro_grav_sim_t **simOut,
	1371	astro_body_t originBody,
	1372	astro_time_t time,
	1373	int numBodies,
	1374	const astro_state_vector_t *bodyStateArray
	1375	);
	1376
	1377	astro_status_t Astronomy_GravSimUpdate(
	1378	astro_grav_sim_t *sim,
	1379	astro_time_t time,
	1380	int numBodies,
	1381	astro_state_vector_t *bodyStateArray
	1382	);
	1383
	1384	astro_state_vector_t Astronomy_GravSimBodyState(
	1385	astro_grav_sim_t *sim,
	1386	astro_body_t body
	1387	);
	1388
	1389	astro_time_t Astronomy_GravSimTime(const astro_grav_sim_t *sim);
	1390	int Astronomy_GravSimNumBodies(const astro_grav_sim_t *sim);
	1391	astro_body_t Astronomy_GravSimOrigin(const astro_grav_sim_t *sim);
	1392	void Astronomy_GravSimSwap(astro_grav_sim_t *sim);
	1393	void Astronomy_GravSimFree(astro_grav_sim_t *sim);
	1394
	1395	/**
	1396	* @brief A function for which to solve a light-travel time problem.
	1397	*
	1398	* The function #Astronomy_CorrectLightTravel solves a generalized
	1399	* problem of deducing how far in the past light must have left
	1400	* a target object to be seen by an observer at a specified time.
	1401	* This function pointer type expresses an arbitrary position vector
	1402	* as function of time. Such a function must be passed to
	1403	* `Astronomy_CorrectLightTravel`.
	1404	*/
	1405	typedef astro_vector_t (* astro_position_func_t) (void *context, astro_time_t time);
	1406
	1407	astro_vector_t Astronomy_CorrectLightTravel(
	1408	void *context,
	1409	astro_position_func_t func,
	1410	astro_time_t time
	1411	);
	1412
	1413	astro_vector_t Astronomy_BackdatePosition(
	1414	astro_time_t time,
	1415	astro_body_t observerBody,
	1416	astro_body_t targetBody,
	1417	astro_aberration_t aberration
	1418	);
	1419
	1420	astro_status_t Astronomy_DefineStar(
	1421	astro_body_t body,
	1422	double ra,
	1423	double dec,
	1424	double distanceLightYears
	1425	);
	1426
	1427	#ifdef __cplusplus
	1428	}
	1429	#endif
	1430
	1431	#endif /* ifndef __ASTRONOMY_H */

Packages/MoonriseKit/Sources/SkyEngine/SkyEngine.swift added +131

@@ -0,0 +1,131 @@
	1	import CAstronomy
	2	import Foundation
	3
	4	/// A place on Earth. Latitude and longitude in degrees (east positive), height in metres.
	5	public struct Observer: Sendable, Equatable {
	6	public var latitude: Double
	7	public var longitude: Double
	8	public var height: Double
	9
	10	public init(latitude: Double, longitude: Double, height: Double = 0) {
	11	self.latitude = latitude
	12	self.longitude = longitude
	13	self.height = height
	14	}
	15
	16	var astro: astro_observer_t { Astronomy_MakeObserver(latitude, longitude, height) }
	17	}
	18
	19	public enum Body: String, CaseIterable, Sendable {
	20	case sun, moon, mercury, venus, mars, jupiter, saturn, uranus, neptune, pluto
	21
	22	public static let planets: [Body] = [.mercury, .venus, .mars, .jupiter, .saturn, .uranus, .neptune]
	23
	24	var astro: astro_body_t {
	25	switch self {
	26	case .sun: BODY_SUN
	27	case .moon: BODY_MOON
	28	case .mercury: BODY_MERCURY
	29	case .venus: BODY_VENUS
	30	case .mars: BODY_MARS
	31	case .jupiter: BODY_JUPITER
	32	case .saturn: BODY_SATURN
	33	case .uranus: BODY_URANUS
	34	case .neptune: BODY_NEPTUNE
	35	case .pluto: BODY_PLUTO
	36	}
	37	}
	38	}
	39
	40	/// Apparent right ascension (hours) and declination (degrees) of date, distance in AU.
	41	public struct Equatorial: Sendable, Equatable {
	42	public var rightAscension: Double
	43	public var declination: Double
	44	public var distance: Double
	45	}
	46
	47	/// Altitude above the horizon and azimuth from north through east, both in degrees.
	48	public struct Horizontal: Sendable, Equatable {
	49	public var altitude: Double
	50	public var azimuth: Double
	51
	52	public init(altitude: Double, azimuth: Double) {
	53	self.altitude = altitude
	54	self.azimuth = azimuth
	55	}
	56	}
	57
	58	public struct Illumination: Sendable, Equatable {
	59	public var magnitude: Double
	60	/// Fraction of the disc that is lit, 0...1.
	61	public var phaseFraction: Double
	62	}
	63
	64	public enum SkyEngineError: Error, Equatable {
	65	case astronomy(status: Int)
	66	}
	67
	68	/// Positions and phases from Astronomy Engine. Its C code keeps internal caches,
	69	/// so call it from one thread at a time.
	70	public enum SkyEngine {
	71	static func time(_ date: Date) -> astro_time_t {
	72	// Days since J2000 (2000-01-01 12:00 UTC).
	73	Astronomy_TimeFromDays((date.timeIntervalSince1970 - 946_728_000) / 86_400)
	74	}
	75
	76	static func check(_ status: astro_status_t) throws {
	77	guard status == ASTRO_SUCCESS else { throw SkyEngineError.astronomy(status: Int(status.rawValue)) }
	78	}
	79
	80	public static func equatorial(_ body: Body, at date: Date, from observer: Observer) throws -> Equatorial {
	81	var t = time(date)
	82	let eq = Astronomy_Equator(body.astro, &t, observer.astro, EQUATOR_OF_DATE, ABERRATION)
	83	try check(eq.status)
	84	return Equatorial(rightAscension: eq.ra, declination: eq.dec, distance: eq.dist)
	85	}
	86
	87	public static func horizontal(_ body: Body, at date: Date, from observer: Observer, refraction: Bool = false) throws -> Horizontal {
	88	let eq = try equatorial(body, at: date, from: observer)
	89	return horizontal(rightAscension: eq.rightAscension, declination: eq.declination, at: date, from: observer, refraction: refraction)
	90	}
	91
	92	/// For fixed objects such as stars: RA in hours, declination in degrees, both of date.
	93	public static func horizontal(rightAscension: Double, declination: Double, at date: Date, from observer: Observer, refraction: Bool = false) -> Horizontal {
	94	var t = time(date)
	95	let hor = Astronomy_Horizon(&t, observer.astro, rightAscension, declination, refraction ? REFRACTION_NORMAL : REFRACTION_NONE)
	96	return Horizontal(altitude: hor.altitude, azimuth: hor.azimuth)
	97	}
	98
	99	/// Horizontal positions for many fixed objects at once, from J2000 RA and declination in degrees.
	100	/// Applies precession and nutation; no aberration or refraction.
	101	public static func horizontal(j2000 coordinates: [(ra: Double, dec: Double)], at date: Date, from observer: Observer) -> [Horizontal] {
	102	var t = time(date)
	103	let rotation = Astronomy_Rotation_EQJ_HOR(&t, observer.astro)
	104	return coordinates.map { c in
	105	let ra = c.ra * .pi / 180, dec = c.dec * .pi / 180
	106	let v = astro_vector_t(status: ASTRO_SUCCESS, x: cos(dec) * cos(ra), y: cos(dec) * sin(ra), z: sin(dec), t: t)
	107	let s = Astronomy_HorizonFromVector(Astronomy_RotateVector(rotation, v), REFRACTION_NONE)
	108	return Horizontal(altitude: s.lat, azimuth: s.lon)
	109	}
	110	}
	111
	112	/// Heliocentric position in AU, J2000 equatorial axes.
	113	public static func heliocentric(_ body: Body, at date: Date) throws -> SIMD3<Double> {
	114	let v = Astronomy_HelioVector(body.astro, time(date))
	115	try check(v.status)
	116	return SIMD3(v.x, v.y, v.z)
	117	}
	118
	119	public static func illumination(_ body: Body, at date: Date) throws -> Illumination {
	120	let i = Astronomy_Illumination(body.astro, time(date))
	121	try check(i.status)
	122	return Illumination(magnitude: i.mag, phaseFraction: i.phase_fraction)
	123	}
	124
	125	/// Moon's ecliptic longitude east of the sun in degrees: 0 new, 90 first quarter, 180 full, 270 last quarter.
	126	public static func moonPhase(at date: Date) throws -> Double {
	127	let a = Astronomy_MoonPhase(time(date))
	128	try check(a.status)
	129	return a.angle
	130	}
	131	}

Packages/MoonriseKit/Sources/SkyRenderer/Resources/bsc5.json added +1

	@@ -0,0 +1 @@
		1	[[1,1.29125,45.22917,6.7,0.07],[2,1.26583,-0.50306,6.29,1.1],[3,1.33375,-5.7075,4.61,1.04],[4,1.425,13.39611,5.51,0.9],[5,1.56667,58.43667,5.96,0.67],[6,1.57917,-49.075,5.7,0.52],[7,1.61042,64.19611,5.59,-0.03],[8,1.65333,29.02139,6.13,0.75],[9,1.70875,-23.1075,6.18,0.38],[10,1.82583,-17.38639,6.19,0.14],[11,1.93375,-2.54889,6.43,-0.14],[12,1.945,-22.50889,5.94,0.14],[13,2.01458,-33.52944,5.68,1.12],[14,2.05042,-2.44778,6.07,1.38],[15,2.09708,29.09056,2.06,-0.11],[16,2.0725,-8.82389,5.99,1.04],[17,2.17083,36.62667,6.19,0.48],[18,2.13917,-17.5775,6.06,1.67],[19,2.2175,25.46278,6.23,0.97],[20,2.33417,79.71472,6.01,0.19],[21,2.29458,59.14972,2.27,0.34],[22,2.26,18.21194,5.53,1.04],[23,2.26,-54.00194,6.33,0.74],[24,2.3375,-27.98778,5.42,0.42],[25,2.35292,-45.7475,3.88,1.03],[26,2.50958,11.14556,5.51,-0.07],[27,2.58042,46.07222,5.03,0.4],[28,2.62375,57.16556,6.74,-0.08],[29,2.57833,-5.24861,5.84,0.98],[30,2.50875,-82.22389,5.28,1.05],[31,2.67833,-12.58,5.85,1.01],[32,2.66083,-73.22444,6.64,0.37],[33,2.81625,-15.46806,4.89,0.49],[34,2.89333,-27.79972,5.41,1.34],[35,2.93333,-35.13306,5.25,0.44],[36,2.99625,48.1525,6.16,1.45],[37,3.04167,-17.93833,5.25,1.48],[38,3.21,37.69333,6.73,-0.13],[39,3.30917,15.18361,2.83,-0.23],[40,3.35,26.98722,6.3,0.65],[41,3.37833,41.03528,5.72,0.31],[42,3.42542,-26.02194,5.94,1.55],[43,3.43417,-26.28472,6.31,1.48],[44,3.50958,33.20611,6.25,-0.01],[45,3.65083,20.20667,4.8,1.57],[46,3.615,-7.78056,5.12,1.62],[47,3.33083,-84.99417,5.77,1.72],[48,3.66,-18.93278,4.44,1.66],[49,3.73375,22.28417,6.24,-0.01],[50,3.745,8.82083,5.79,0.31],[51,3.72708,-9.56972,5.75,-0.08],[52,3.77917,31.53583,6.45,0.6],[53,3.79417,27.28306,6.35,-0.02],[54,3.7425,-34.90444,6.17,1.34],[55,4.05833,76.95083,6.35,-0.07],[56,4.09,43.59472,6.15,0.05],[57,4.03708,-31.44639,5.67,1.35],[58,3.98,-75.91139,6.49,1.0],[59,4.14208,8.24,6.11,0.92],[60,4.23792,61.53333,5.74,0.88],[61,4.17708,-20.21056,6.47,-0.09],[62,4.28792,47.9475,5.89,-0.09],[63,4.27292,38.68167,4.61,0.06],[64,4.20417,-78.78056,6.77,0.46],[65,4.42917,51.43306,6.14,-0.13],[66,4.38583,-19.05111,6.45,0.37],[67,4.44875,1.68889,6.17,0.94],[68,4.58208,36.78528,4.52,0.05],[69,4.57167,11.20583,6.05,1.03],[70,4.67542,43.79111,6.11,-0.08],[71,4.65958,31.51722,5.87,-0.01],[72,4.67417,-8.05278,6.46,0.68],[73,4.6775,-43.23528,6.33,1.21],[74,4.85708,-8.82389,3.56,1.22],[75,4.92333,40.72972,6.33,1.18],[76,5.02167,48.86528,6.52,0.6],[77,5.01792,-64.87472,4.23,0.58],[78,5.10167,30.93583,5.9,-0.1],[79,5.18958,32.91139,5.79,1.59],[80,5.14958,8.19028,5.37,1.34],[81,5.22708,10.97694,6.56,0.6],[82,5.28042,37.96861,5.18,0.42],[83,5.1625,-69.625,5.51,-0.05],[84,5.38,-28.98167,5.18,1.0],[85,5.44292,-20.05778,5.12,1.82],[86,5.60625,13.4825,6.23,1.22],[87,5.36917,-77.42694,5.97,1.4],[88,5.71583,-12.20944,6.39,0.66],[89,5.8025,-31.03611,6.55,0.0],[90,6.00833,38.57722,7.39,1.97],[91,6.065,52.02,5.57,-0.12],[93,6.19792,61.83111,5.4,0.0],[94,6.12375,-2.21917,6.07,1.22],[96,6.27667,53.04694,5.74,-0.06],[97,6.35083,1.93972,5.77,0.86],[98,6.43792,-77.25417,2.8,0.62],[99,6.57083,-42.30611,2.39,1.09],[100,6.55083,-43.68,3.94,0.17],[101,6.65583,-0.04972,6.19,0.9],[102,6.81125,-25.54722,5.98,1.03],[103,7.01208,17.89306,5.06,1.65],[104,7.05708,44.39444,5.17,0.03],[105,6.98208,-33.00722,4.81,1.64],[106,7.05292,16.445,6.06,1.58],[107,7.08375,10.18972,6.04,0.43],[108,7.08792,-20.335,6.43,0.59],[109,7.11,-39.915,5.43,1.56],[110,7.23583,36.9,6.26,0.92],[111,7.17958,-50.53278,6.26,1.09],[112,7.72917,77.01944,6.21,0.84],[113,7.58292,59.97722,5.94,0.01],[114,7.53042,29.75167,5.23,0.24],[115,7.46625,-14.86417,6.14,0.37],[116,7.45375,-32.11667,6.57,1.34],[117,7.51,-3.95722,5.72,1.56],[118,7.59458,-23.78778,5.19,0.12],[119,7.61583,-40.93944,6.19,0.33],[120,7.60875,-48.215,5.69,0.35],[121,7.85542,66.51944,6.18,-0.1],[122,7.85667,33.58167,5.87,1.14],[123,7.94333,54.52222,4.73,-0.1],[124,7.92167,52.83944,5.6,1.15],[125,7.85417,-48.80361,4.77,0.02],[126,7.88625,-62.95806,4.37,-0.07],[127,7.89,-62.96583,4.54,0.15],[128,8.11167,43.49472,6.7,-0.01],[129,8.33042,70.98167,6.42,-0.01],[130,8.25,62.93167,4.16,0.14],[131,8.14792,20.29444,5.38,1.08],[132,8.09917,6.95556,5.67,0.0],[133,8.14375,27.58056,6.67,0.6],[134,8.20458,28.28028,6.3,1.0],[135,8.29333,54.895,5.93,1.04],[136,8.1825,-63.03111,5.09,0.04],[137,8.60375,66.75028,6.48,-0.08],[138,8.42125,-29.55833,5.55,1.27],[139,8.34708,-71.26611,6.13,0.23],[140,8.61583,-52.37306,5.57,0.47],[141,8.73042,13.37111,6.4,0.6],[142,8.81208,-3.59278,5.2,0.56],[143,8.88667,-0.50556,5.93,0.44],[144,9.03458,54.16861,5.08,-0.11],[145,8.97792,13.20667,6.41,0.52],[146,9.11375,60.32611,5.79,0.29],[147,8.92125,-48.00083,5.51,0.44],[148,8.88917,-54.82194,6.06,1.01],[149,9.08333,27.25472,6.5,-0.09],[150,9.0125,-14.97361,6.45,1.06],[151,9.02875,-22.8425,6.06,0.29],[152,9.19417,44.48861,5.13,1.6],[153,9.24292,53.89694,3.66,-0.2],[154,9.22042,33.71944,4.36,-0.14],[155,9.19708,15.23167,5.89,-0.15],[156,9.28,24.01417,6.47,0.6],[157,9.33792,35.39944,5.48,0.88],[158,9.94708,82.49389,6.4,0.55],[159,9.33625,-24.76722,5.57,0.72],[160,9.15583,-65.12472,6.42,1.26],[161,9.37708,3.13528,6.39,1.33],[162,9.32542,-54.39417,6.41,1.0],[163,9.63875,29.31167,4.37,0.87],[164,9.79125,49.35444,5.43,1.64],[165,9.83208,30.86083,3.27,1.28],[166,9.84083,21.25056,5.87,0.85],[167,9.98167,21.43833,5.36,1.16],[168,10.12708,56.53722,2.23,1.17],[169,9.67,-73.13722,6.85,0.11],[170,9.99125,-33.96167,6.69,0.51],[171,9.96667,-44.79667,6.01,1.14],[172,10.11917,-16.51694,6.49,0.92],[173,10.13708,-23.80444,6.14,0.7],[174,10.17667,-4.35194,5.91,1.1],[175,10.28,39.45861,5.33,0.89],[176,10.11,-59.45444,5.89,0.55],[177,10.51417,66.1475,5.83,1.04],[178,10.4,24.62917,6.04,0.26],[179,10.51625,50.5125,4.8,-0.11],[180,10.33167,-46.085,4.59,0.97],[181,10.62958,58.75333,6.17,-0.01],[183,10.44333,-56.50167,5.7,0.2],[184,10.86708,47.02472,4.94,0.18],[185,10.67875,-38.46333,6.06,-0.03],[186,10.67417,-60.2625,5.98,1.32],[187,10.61833,-65.46806,5.39,0.5],[188,10.8975,-17.98667,2.04,1.02],[189,11.11,47.86417,5.67,-0.12],[190,10.95917,-12.01167,6.02,1.1],[191,10.83833,-57.46306,4.36,0.0],[192,11.4125,74.98806,5.66,0.05],[193,11.18125,48.28444,4.54,-0.07],[194,11.0475,-10.60944,4.76,1.01],[195,11.05042,-38.42167,5.9,1.16],[196,11.32167,55.22167,5.42,0.04],[197,11.185,-22.00611,5.24,0.33],[198,11.23792,-42.67667,5.94,0.28],[199,11.13458,-62.49778,6.07,0.44],[200,11.6625,69.325,6.33,0.6],[201,11.35042,-4.62917,6.15,1.62],[202,11.25,-53.715,6.15,0.53],[203,11.36958,-12.88083,6.15,0.61],[204,11.56292,55.30528,6.52,0.6],[205,11.54542,44.86139,6.05,-0.07],[206,11.42375,-16.42417,6.47,0.31],[207,11.67667,59.57444,6.39,1.09],[208,11.94208,74.8475,5.41,-0.08],[209,11.44,-47.55167,5.8,0.64],[210,11.54917,-22.52194,5.5,0.98],[211,11.6375,15.47556,5.38,1.65],[212,12.03792,72.675,5.87,1.01],[213,11.75625,11.97389,5.5,0.97],[214,11.80667,19.57889,6.13,0.27],[215,11.83458,24.26722,4.06,1.12],[216,11.84833,6.74083,5.99,0.94],[217,11.97833,20.92528,6.54,0.5],[218,11.93042,-18.06139,5.7,1.3],[219,12.275,57.81583,3.44,0.57],[220,12.00458,-21.7225,5.57,-0.06],[221,12.0725,7.3,5.93,1.1],[222,12.09583,5.28056,5.75,0.88],[223,12.20875,50.96833,4.89,-0.11],[224,12.17083,7.585,4.43,1.5],[225,12.24458,16.94056,5.07,0.51],[226,12.45333,41.07889,4.53,-0.15],[227,12.35667,-13.56139,5.59,1.3],[228,12.30792,-24.13639,5.9,0.95],[229,12.23625,-46.69778,6.27,0.9],[230,12.47,27.71083,7.0,0.36],[231,12.47167,27.71028,7.1,0.6],[232,12.38917,-23.36167,6.28,0.13],[233,12.68167,64.2475,5.39,0.49],[234,12.57625,45.00222,6.15,0.01],[235,12.53167,-10.64444,5.19,0.5],[236,12.1475,-74.92333,5.07,1.37],[237,12.81833,61.80583,6.07,1.88],[238,12.73917,51.50806,6.39,0.28],[239,12.51542,-43.39472,6.48,0.29],[240,13.72125,83.70722,5.62,0.09],[241,12.89042,51.57111,6.21,0.6],[242,12.67167,-50.98694,5.22,0.36],[243,12.82625,3.385,6.37,1.07],[244,13.26708,61.12417,4.82,0.53],[245,12.96708,-43.70917,6.9,0.35],[246,13.2225,38.54861,6.69,0.02],[247,13.16917,-24.00583,5.46,1.24],[248,13.25208,-1.14417,4.77,1.57],[249,13.3675,37.41806,6.06,1.14],[250,13.44833,52.68917,6.27,0.19],[251,13.30167,-24.77694,6.46,0.44],[252,13.10125,-69.50444,6.22,0.56],[253,13.75042,58.97278,4.83,1.21],[254,13.64667,19.18833,5.74,-0.01],[255,13.57333,-8.74083,6.16,0.92],[256,13.77167,48.67861,6.27,1.68],[257,13.40792,-62.87139,5.7,1.56],[258,13.74167,23.62833,5.47,1.0],[259,13.81125,24.55694,6.2,1.62],[260,14.05375,57.99667,6.21,1.37],[261,14.23167,68.77611,6.37,0.38],[262,13.99375,27.20944,6.09,0.14],[263,13.92667,-7.34722,5.85,1.52],[264,14.17708,60.71667,2.47,-0.15],[265,14.16583,59.18111,4.63,0.96],[266,14.19625,60.36278,5.55,-0.07],[267,14.00625,-11.26667,5.31,1.52],[268,13.98125,-27.77556,6.1,1.67],[269,14.18833,38.49944,3.87,0.13],[270,13.75125,-69.52694,5.45,1.09],[271,14.30167,23.4175,4.42,0.94],[272,14.41542,45.83972,6.12,1.02],[273,14.62958,66.35222,5.97,-0.02],[274,14.45917,28.99222,5.42,1.08],[275,14.55917,33.95083,5.98,1.0],[276,14.47708,13.69583,6.32,0.89],[277,14.57875,21.40444,6.37,0.09],[278,15.12917,70.98306,6.39,0.13],[279,14.68292,-11.38,5.61,0.97],[280,14.65167,-29.3575,4.31,-0.16],[281,14.59333,-60.69639,6.23,0.1],[282,15.01417,44.71111,6.84,0.6],[283,15.015,44.71333,6.04,-0.01],[284,14.95708,6.48306,6.11,1.67],[285,17.18625,86.25694,4.25,1.21],[286,23.46,89.01556,6.46,0.11],[287,15.57667,51.035,6.47,0.6],[288,15.32625,-38.91667,5.59,1.18],[289,15.75625,47.37611,6.45,0.25],[290,15.72625,41.345,5.98,0.16],[291,15.70458,31.80444,5.5,-0.05],[292,15.90417,61.075,5.92,0.49],[293,15.61,-31.55194,5.5,0.08],[294,15.73583,7.89,4.28,0.96],[295,15.5075,-57.0025,6.11,0.94],[296,15.76083,-4.83667,5.43,1.11],[297,16.08167,61.58028,5.84,0.54],[298,16.01,52.50222,5.99,1.47],[299,15.705,-46.3975,5.36,0.9],[300,15.82333,-29.52583,6.29,0.93],[301,15.95417,1.36667,6.04,0.27],[302,16.195,51.01,6.54,-0.08],[303,16.115,29.65861,6.19,0.43],[304,15.67875,-65.45611,6.21,1.64],[305,16.15167,39.99111,6.72,0.31],[306,19.05625,87.14528,6.25,1.12],[307,16.21917,5.65639,6.0,1.51],[308,16.2725,14.94611,5.68,0.41],[309,16.595,62.76167,6.54,0.19],[310,16.42042,21.47333,5.34,-0.03],[311,16.42375,21.46528,5.56,-0.07],[312,17.30125,80.01167,6.29,0.6],[313,16.455,4.90833,6.35,0.38],[314,16.46417,4.90944,7.25,0.49],[315,16.40333,-9.97917,6.12,1.01],[316,16.75083,56.935,6.43,1.18],[317,16.52125,-9.83944,5.58,0.01],[318,16.78958,53.49833,6.38,0.6],[319,16.64,12.95611,6.12,0.96],[320,16.53208,-23.9925,6.14,1.09],[321,17.06833,54.92028,5.17,0.69],[322,16.52083,-46.71861,3.31,0.89],[323,16.61042,-35.66083,6.61,0.14],[324,17.00375,43.94194,5.03,0.11],[325,16.80458,-23.99639,6.37,0.23],[326,17.13875,58.26361,5.79,-0.01],[327,17.00542,32.01222,6.25,0.4],[328,16.98833,20.73917,5.55,0.13],[329,16.9425,-9.78556,5.82,0.43],[330,17.0925,5.64972,5.52,0.34],[331,16.94958,-41.48694,5.21,0.16],[332,16.82792,-61.77528,5.37,0.88],[333,18.06958,79.67389,5.64,0.01],[334,17.1475,-10.18222,3.45,1.16],[335,17.37583,47.24194,4.25,-0.07],[336,17.66375,68.77861,5.29,-0.02],[337,17.43292,35.62056,2.06,1.58],[338,17.09625,-55.24583,3.92,-0.08],[339,17.455,19.65861,5.55,0.69],[340,17.57833,42.08139,5.65,0.6],[341,17.58083,25.45778,5.8,1.47],[342,17.85667,64.20278,5.55,-0.07],[343,17.77583,55.14972,4.33,0.17],[344,17.54792,15.67417,6.06,1.49],[345,17.9225,65.01889,5.57,-0.09],[346,17.55,-8.90611,6.4,1.04],[347,17.64,2.44556,5.95,1.51],[348,17.79292,37.72417,5.81,-0.1],[349,17.77833,31.42472,5.16,0.23],[350,17.53083,-57.69444,6.41,0.89],[351,17.86333,21.03472,4.66,1.03],[352,17.915,30.08972,4.51,1.09],[353,17.93125,-2.25111,5.94,1.4],[354,18.29125,61.70583,6.41,0.01],[355,18.14167,45.33778,6.11,1.64],[356,18.24792,30.06417,6.19,1.0],[357,19.12792,79.91,6.26,0.42],[358,18.0975,-30.80222,6.52,0.48],[359,18.18917,-37.85639,5.92,0.28],[360,18.43708,24.58361,4.65,1.04],[361,18.43292,7.57528,5.24,0.32],[362,18.43875,7.57833,6.3,0.49],[363,18.52083,28.52972,6.43,1.7],[364,18.53167,16.13361,5.98,-0.08],[365,19.05042,71.74389,7.83,0.78],[366,18.6,-7.92306,5.13,0.46],[367,18.67667,6.99528,6.03,1.08],[368,18.705,-0.97389,5.7,0.42],[369,19.10208,48.08222,6.61,-0.05],[370,18.79625,-45.53139,4.96,0.58],[371,19.07833,33.11472,6.02,1.15],[372,19.27125,44.90194,6.34,0.6],[373,19.15125,-2.50028,5.41,0.9],[374,19.35042,31.74472,6.73,0.6],[375,20.08125,77.57056,6.31,0.92],[376,19.5425,47.41972,6.25,1.35],[377,18.94208,-68.87611,4.86,0.47],[378,19.45,3.61444,5.16,0.07],[379,19.69583,37.38611,6.46,0.23],[380,19.265,-66.39806,6.24,0.05],[381,20.49625,76.23889,6.38,0.28],[382,20.02042,58.23167,4.98,0.68],[383,19.86667,27.26417,4.76,0.03],[384,20.27167,64.65833,6.34,0.09],[385,19.95125,-0.50889,5.87,0.64],[386,20.945,78.72583,6.07,0.39],[387,20.14375,-3.24694,6.23,1.02],[388,20.11583,-11.23889,6.15,1.11],[389,20.28083,28.73806,5.23,1.39],[390,20.585,45.52889,4.88,1.08],[391,20.84,58.14306,6.45,0.6],[392,20.65417,1.72639,6.2,1.52],[393,20.645,-0.44972,6.49,1.08],[394,20.62708,-19.08139,6.35,0.48],[395,20.91917,37.715,5.58,0.26],[396,20.90625,34.24583,6.29,0.83],[397,20.85375,20.46889,5.97,1.71],[398,21.44375,70.98,6.49,0.6],[399,21.48333,68.13,4.74,1.05],[400,20.87917,-30.94556,5.84,1.61],[401,21.01042,-8.0075,6.21,0.23],[402,21.00583,-8.18333,3.6,1.06],[403,21.45417,60.23528,2.68,0.13],[404,21.08583,-6.91472,5.91,0.41],[405,21.16583,-15.66028,6.14,0.91],[406,21.20292,-2.84861,6.15,0.96],[407,21.39875,23.51167,6.18,0.43],[408,21.17,-41.4925,5.42,1.04],[409,21.5775,43.45778,5.96,0.49],[410,21.53625,34.57972,6.31,0.47],[411,21.17458,-44.52833,6.26,1.14],[412,21.405,-14.59889,4.9,1.23],[413,21.56375,19.17222,5.38,0.39],[414,21.67375,19.24028,5.5,1.11],[415,21.77583,34.3775,6.27,0.46],[416,21.61375,-0.39861,6.41,1.24],[417,21.91417,45.40667,4.83,0.42],[418,21.86083,41.10056,6.46,0.27],[419,21.72292,3.53528,6.58,-0.04],[420,21.27208,-64.36944,5.93,1.56],[421,21.715,-13.05667,5.66,0.35],[422,21.94583,40.33556,6.6,-0.04],[423,21.74208,-32.54306,5.79,3.86],[424,37.95292,89.26417,2.02,0.6],[425,21.94417,-10.90167,6.13,1.32],[426,22.09542,7.96139,6.2,1.12],[427,22.8075,70.26472,5.81,0.47],[428,22.71792,66.09806,6.14,0.08],[429,22.09125,-43.31833,3.41,1.57],[430,22.52583,47.00722,5.27,1.0],[431,22.18042,-33.76361,6.58,0.3],[432,22.47042,18.35556,6.02,0.14],[433,22.40042,-21.62944,5.12,0.02],[434,22.54625,6.14389,4.84,1.37],[435,22.37667,-46.75639,6.31,1.66],[436,22.59542,-26.20778,5.93,1.34],[437,22.87083,15.34583,3.62,0.97],[438,23.03167,34.8,6.39,-0.12],[439,23.3575,58.3275,5.7,1.52],[440,22.81292,-49.07278,3.95,0.99],[441,22.93042,-30.28333,5.82,1.08],[442,23.48292,59.23194,4.71,1.0],[443,22.91292,-45.57556,6.17,0.06],[444,23.26458,-9.01472,6.59,-0.04],[445,23.23333,-36.86528,5.51,1.02],[446,23.56917,37.23722,5.88,-0.07],[447,23.15125,-49.72778,6.28,0.46],[448,23.42875,-7.02528,5.76,0.64],[449,24.34375,74.30083,6.58,0.03],[450,23.70458,18.46056,5.89,1.52],[451,23.6575,-15.67611,5.63,0.07],[452,23.96875,41.07639,6.38,1.11],[453,23.71125,-31.89222,6.12,1.11],[454,24.11333,48.72278,5.92,1.21],[455,23.94333,14.66139,6.22,-0.04],[456,24.62875,73.04,5.28,0.96],[457,23.97833,17.43361,5.8,0.6],[458,24.19917,41.40556,4.09,0.54],[459,23.99583,-15.40028,5.42,1.21],[460,23.81333,-58.13944,6.01,0.38],[461,24.53167,57.9775,5.56,1.38],[462,24.035,-29.9075,5.69,0.33],[463,24.27458,12.14167,5.57,0.35],[464,24.49833,48.62833,3.57,1.28],[465,24.63208,45.4,6.36,0.04],[466,24.40708,-9.40389,6.24,0.53],[467,23.41333,-78.50472,6.11,0.97],[468,24.18667,-58.27083,6.18,1.61],[469,24.8375,44.38611,4.98,0.89],[470,25.05458,53.86833,6.39,1.61],[471,24.61417,-36.52833,5.94,1.05],[472,24.42875,-57.23667,0.46,-0.16],[473,24.71583,-21.27528,5.58,0.34],[474,24.70833,-25.02194,6.7,-0.08],[475,24.92,16.40583,5.97,1.12],[476,25.16583,43.29778,5.61,0.21],[477,25.145,40.57694,4.94,-0.09],[478,25.58542,68.04306,5.59,-0.07],[479,24.70083,-53.43889,6.84,0.44],[480,25.73292,70.6225,5.18,-0.04],[481,25.5125,61.03833,6.71,-0.03],[482,25.57417,58.62778,6.37,-0.02],[483,25.44667,42.61361,4.95,0.62],[484,25.32667,25.74583,6.17,0.44],[485,25.41333,30.04722,5.99,1.01],[486,24.9475,-56.19806,5.87,0.9],[487,24.94917,-56.19472,5.76,0.87],[488,25.74333,61.42167,6.34,0.01],[489,25.35792,5.4875,4.44,1.36],[490,25.51458,35.24556,5.64,-0.07],[491,25.83208,60.55111,5.78,-0.02],[492,25.43625,-11.32472,5.75,0.44],[493,25.62417,20.26861,5.24,0.84],[494,25.36375,-38.13306,6.17,0.42],[495,25.81875,45.32222,6.34,1.01],[496,25.915,50.68861,4.07,-0.04],[497,25.53583,-32.32694,5.25,1.05],[498,25.5125,-36.8325,5.72,-0.01],[499,26.07458,57.53639,6.21,0.1],[500,25.68125,-3.69028,4.99,1.38],[501,25.42125,-50.03889,6.64,0.12],[502,26.19208,57.08917,6.25,0.04],[503,25.95833,32.19167,6.34,0.6],[504,26.11042,46.13972,6.35,0.6],[505,25.45,-60.78944,5.71,1.27],[506,25.62208,-53.74056,5.52,0.53],[507,25.97833,-4.76556,6.19,1.54],[508,26.2325,20.08306,6.27,0.75],[509,26.01708,-15.9375,3.5,0.72],[510,26.34833,9.15778,4.26,0.96],[511,26.93667,63.85222,5.63,0.81],[512,24.48167,-82.975,5.87,0.61],[513,26.49708,-5.73333,5.34,1.52],[514,26.41167,-25.0525,5.31,0.39],[515,26.64708,17.41306,6.55,0.25],[516,25.33875,-79.14833,6.33,0.94],[517,26.50417,-27.34917,6.39,0.36],[518,26.95,46.22972,6.32,0.43],[519,26.52417,-50.81639,5.49,1.6],[520,26.52625,-53.52194,5.04,0.04],[521,27.16208,37.95278,5.94,0.97],[522,27.04542,16.95556,5.84,-0.03],[523,27.17333,32.69028,5.79,0.55],[524,26.82,-41.76,6.18,1.54],[525,24.36667,-84.76972,5.69,0.94],[526,27.31542,47.89694,5.82,0.29],[527,27.10833,3.68556,5.91,0.97],[528,26.94917,-37.15972,6.32,1.02],[529,27.73792,51.93333,5.9,0.43],[530,27.53542,22.27528,5.86,0.74],[531,27.39625,-10.68639,4.67,0.33],[532,27.33125,-31.07278,6.34,1.22],[533,27.99708,55.1475,5.52,-0.18],[534,27.71667,11.04333,5.94,0.3],[535,27.45333,-38.40389,6.37,0.52],[536,28.03917,50.79278,5.79,-0.07],[537,27.58417,-47.81639,6.14,1.01],[538,28.21167,51.47472,6.26,0.6],[539,27.865,-10.335,3.73,1.14],[540,28.45208,55.59806,6.45,0.18],[541,27.72708,-50.20611,5.94,0.14],[542,28.59875,63.67,3.38,-0.15],[543,28.32208,40.72972,5.4,1.32],[544,28.27042,29.57889,3.41,0.49],[545,28.3825,19.29583,4.83,0.6],[546,28.3825,19.29361,4.75,-0.04],[547,28.21708,-16.92917,5.8,0.27],[548,29.0,68.68528,4.99,-0.1],[549,28.38875,3.1875,4.62,0.94],[550,26.94375,-80.17667,6.06,0.34],[551,28.72417,40.70194,6.24,1.25],[552,28.73958,37.12833,6.26,1.17],[553,28.66,20.80806,2.64,0.13],[554,28.34667,-38.59472,6.1,1.12],[555,28.41167,-46.3025,4.41,1.59],[556,28.97667,37.27778,5.89,1.63],[557,29.03875,37.25167,5.67,1.06],[558,28.59167,-42.49694,5.11,-0.06],[559,28.9625,23.57722,5.74,1.19],[560,28.97417,1.84972,6.01,0.56],[561,29.63875,61.69806,6.02,-0.04],[562,29.485,41.69444,6.78,-0.06],[563,29.33792,17.8175,5.1,0.92],[564,29.4325,27.80444,5.82,1.6],[565,29.1675,-22.52694,4.85,1.42],[566,28.98958,-51.60889,3.7,0.85],[567,29.90833,64.62139,5.26,0.01],[568,29.64,49.20417,5.69,1.01],[569,29.48208,23.59611,4.79,0.28],[570,28.73375,-67.64722,4.69,0.95],[571,28.94333,-60.86139,6.06,0.37],[572,30.73833,77.91639,6.04,1.14],[573,29.25042,-51.76611,6.1,0.48],[574,29.29167,-47.385,4.83,0.88],[575,30.48917,70.90694,4.54,0.16],[576,29.61125,-33.06667,6.35,1.02],[577,29.89875,21.05833,5.87,1.03],[578,29.85792,12.29472,6.09,0.19],[579,30.79375,73.85056,6.23,0.6],[580,30.85875,72.42139,3.98,-0.01],[581,31.28083,77.28139,5.38,0.31],[582,30.03833,3.09722,5.88,0.62],[583,29.94208,-20.82444,5.41,1.65],[584,29.47333,-65.42472,6.37,0.9],[585,30.00125,-21.07778,4.0,1.57],[586,30.71958,64.90139,6.0,0.03],[587,30.11208,-8.52361,5.51,1.52],[588,29.91167,-42.03056,5.57,1.06],[589,30.75125,64.39,5.58,0.38],[590,30.57542,54.4875,5.04,-0.08],[591,29.6925,-61.56972,2.86,0.28],[592,31.38,76.115,5.22,0.95],[593,28.96042,-78.34833,6.16,0.44],[594,30.31125,-30.00167,5.35,0.88],[595,30.51167,2.76361,5.23,0.6],[596,30.51167,2.76361,4.33,0.03],[597,32.35542,81.29583,6.05,0.11],[598,31.16708,65.10333,6.52,0.0],[599,30.74167,33.28389,5.5,0.03],[600,29.92125,-66.06639,6.1,1.17],[601,30.64667,13.47667,5.94,1.59],[602,30.42667,-44.71361,5.14,1.49],[603,30.975,42.32972,2.26,1.37],[654,34.21542,57.05528,6.48,0.28],[604,30.97792,42.33083,4.84,0.03],[605,30.91375,25.93556,5.63,0.54],[606,30.61708,-29.665,6.42,0.14],[607,30.79875,0.12833,5.43,0.15],[608,30.74417,-15.30583,5.86,0.98],[609,30.9275,18.25333,6.21,1.42],[610,30.95083,-0.34028,5.93,0.88],[611,30.91875,-4.10361,5.62,1.59],[612,31.1225,-29.29694,4.69,-0.17],[613,31.64125,22.64833,5.03,0.11],[614,31.55125,8.2475,6.31,1.65],[615,31.705,25.70472,6.15,-0.03],[616,31.62208,0.035,6.28,0.9],[617,31.79333,23.4625,2.0,1.15],[618,32.16875,58.42361,5.67,0.61],[619,32.14,44.45944,6.42,0.6],[620,32.12208,37.85917,4.82,0.12],[621,32.5325,53.84306,6.31,0.95],[622,32.38583,34.98722,3.0,0.14],[623,32.35542,25.93972,4.98,0.33],[624,32.34625,17.22444,6.43,0.6],[625,32.19042,-17.77944,6.1,1.61],[626,33.33833,74.02778,6.29,0.91],[627,32.87083,57.64583,6.36,0.33],[628,32.72,39.03944,5.63,-0.02],[629,32.72375,39.04306,6.1,-0.07],[630,32.395,-24.34583,6.48,0.29],[631,32.65667,19.50028,5.7,1.65],[632,32.28875,-43.51667,5.85,1.19],[633,32.8,25.93694,6.02,1.36],[634,32.85417,31.52639,6.23,0.11],[635,32.83792,8.56972,5.63,0.56],[636,32.52042,-43.81556,6.32,0.9],[637,32.60667,-50.82444,6.12,0.82],[638,32.8425,-10.05222,6.01,0.39],[639,32.89917,-1.82528,5.93,0.97],[640,33.62125,66.52444,6.07,0.63],[641,33.42292,58.56111,6.44,0.6],[642,33.09292,30.30306,4.94,0.78],[643,33.30542,44.23167,4.83,1.48],[644,33.15625,24.16778,5.96,1.37],[645,33.40125,51.06583,5.31,0.93],[646,33.20042,21.21083,5.27,0.43],[647,33.51083,47.48417,6.06,0.4],[648,33.26375,15.27972,5.71,1.55],[649,33.25,8.84667,4.37,0.89],[650,33.19792,-2.39361,5.54,0.57],[651,33.25375,-21.00028,5.86,1.01],[652,33.22708,-30.72389,5.28,-0.02],[653,33.99125,47.81139,6.33,0.6],[655,33.98417,33.35889,5.28,-0.01],[656,33.94167,25.78306,5.79,0.44],[657,33.92833,25.04306,5.58,0.49],[658,33.86792,-9.46556,6.55,-0.02],[659,33.63333,-41.16667,5.91,0.97],[660,34.26333,34.22417,4.87,0.61],[661,34.49958,57.89972,5.75,1.17],[662,34.51875,57.51667,5.98,1.05],[663,34.38917,44.30694,6.7,0.6],[664,34.32875,33.84722,4.01,0.02],[665,34.29333,23.76778,6.55,1.02],[666,34.24583,-6.42222,5.51,0.96],[667,33.56125,-67.84167,5.55,1.55],[668,35.05375,64.33722,6.6,-0.03],[669,34.53125,19.90111,5.62,0.01],[670,34.82,47.38,5.3,-0.01],[671,34.79542,46.4725,6.21,0.6],[672,34.50583,1.75778,5.58,0.6],[673,34.84458,48.95528,6.37,0.6],[674,34.1275,-51.51222,3.56,-0.12],[675,34.7375,28.6425,5.03,0.04],[676,34.74167,23.16778,6.46,0.34],[677,34.90542,39.835,6.63,-0.09],[678,33.86875,-67.74639,5.69,1.3],[679,35.1725,47.31083,6.11,-0.08],[680,35.01833,30.18833,6.47,0.6],[681,34.83625,-2.9775,3.04,1.42],[682,35.2425,50.15139,5.59,-0.13],[683,34.74375,-25.94556,6.34,0.73],[684,34.92,-4.34556,6.5,0.08],[685,35.58917,55.84556,5.17,0.37],[686,34.85292,-41.84833,6.37,1.16],[687,35.70958,41.39639,5.82,0.27],[688,34.97625,-55.94472,5.81,1.55],[689,35.48583,0.39583,5.28,1.65],[690,35.96583,55.36444,6.28,0.86],[691,35.55167,-0.885,5.42,0.31],[692,35.50583,-10.77778,5.46,0.35],[693,35.52083,-17.66222,5.87,1.23],[694,36.10375,50.00667,5.19,0.98],[695,35.63583,-23.81639,5.2,0.6],[696,36.31667,56.61,6.25,0.31],[697,35.74083,-18.35444,6.22,0.94],[698,35.54917,-43.2,6.31,1.0],[699,36.40583,50.27861,4.71,1.53],[700,35.77708,-37.57639,6.53,1.61],[701,35.7275,-51.09222,5.92,0.22],[702,36.20417,10.61056,5.47,-0.1],[703,36.08375,-25.8475,6.44,1.32],[704,36.24333,-2.78,6.33,0.0],[705,35.43708,-68.65944,4.09,0.03],[706,36.14083,-40.84056,6.18,0.66],[707,37.26667,67.4025,4.52,0.12],[708,36.4875,-12.29056,4.89,-0.03],[709,36.96583,50.56972,6.12,0.41],[710,36.50125,-15.34111,5.83,0.15],[711,36.77917,27.01333,6.18,1.43],[712,36.86542,31.80139,5.54,1.12],[713,36.64667,-20.04278,5.88,1.26],[714,36.22458,-60.31194,5.35,0.39],[715,35.71792,-73.64583,5.01,1.09],[716,37.35417,55.53639,6.51,0.09],[717,37.04167,29.66944,5.29,0.6],[718,37.03958,8.46,4.28,-0.06],[719,37.0,1.96083,6.45,0.97],[720,37.20208,29.93194,5.89,0.58],[721,36.74625,-47.70389,4.25,-0.14],[722,36.35958,-66.49472,6.41,1.54],[723,37.30667,23.46889,6.19,0.15],[724,37.00708,-33.81111,5.14,0.1],[725,37.39708,9.56583,6.07,1.02],[726,37.56917,33.83389,6.25,1.07],[727,37.1475,-31.1025,6.11,1.11],[728,37.635,25.235,5.92,0.41],[729,37.66,19.85528,6.15,0.25],[730,37.48083,-22.68278,6.77,0.19],[731,37.72667,17.70389,6.23,0.9],[732,37.68833,0.25528,6.0,0.17],[733,37.5575,-25.18639,6.51,0.29],[734,37.01833,-64.29972,6.37,-0.04],[735,37.63667,-22.54556,6.1,1.61],[736,38.02583,36.14722,5.15,1.47],[737,37.87542,2.26722,5.25,1.27],[738,38.21875,34.5425,5.83,1.07],[739,38.03917,-1.035,5.35,1.02],[740,38.02167,-15.24472,4.75,0.45],[741,38.22542,15.03472,6.04,0.54],[742,38.06167,-36.4275,6.3,1.02],[743,39.50833,72.81833,5.16,0.88],[744,38.27917,-34.65,5.9,1.06],[745,38.4175,-20.00194,6.21,1.1],[746,38.86625,39.66444,6.36,-0.1],[747,39.40042,65.74556,5.78,1.56],[748,38.91167,37.31222,5.71,1.39],[749,38.46125,-28.2325,4.9,-0.05],[750,38.945,34.6875,5.35,1.66],[751,38.76708,7.47139,6.18,1.06],[752,38.67792,-7.85944,5.75,1.4],[753,39.02042,6.88694,5.82,0.98],[754,38.96875,5.59333,4.86,0.87],[755,38.4775,-51.09361,6.24,0.52],[756,39.23833,38.73278,5.9,0.48],[757,39.17875,31.6075,6.1,1.05],[758,39.26042,34.26389,5.3,1.55],[759,39.0,-7.83167,5.53,1.59],[760,39.33667,39.89583,6.54,-0.12],[761,39.27667,32.89194,6.25,0.48],[762,38.39,-62.58694,6.77,-0.06],[763,39.15792,12.4475,5.68,0.49],[764,39.24042,24.64833,7.09,0.5],[765,39.25208,24.6475,6.5,0.41],[766,39.14625,7.72972,5.81,1.04],[767,39.03875,-30.04472,5.75,1.02],[768,39.57417,37.72667,6.18,0.47],[769,39.61583,38.08944,6.3,-0.03],[770,39.50333,7.69528,6.39,0.44],[771,39.42417,-3.39611,5.65,1.02],[772,39.24417,-34.57833,5.79,0.66],[773,39.70417,21.96139,5.43,0.16],[774,41.94833,81.44833,5.78,1.3],[775,39.65375,3.44306,6.21,1.0],[776,37.91875,-79.10944,5.28,0.98],[777,39.57792,-30.19417,5.83,0.48],[778,39.35167,-52.54306,5.31,0.27],[779,39.87083,0.32861,4.07,-0.22],[780,39.60333,-37.99056,6.49,0.52],[781,39.89083,-11.87222,4.84,0.45],[782,40.17125,27.06083,5.3,0.09],[783,40.06542,6.11194,6.25,0.4],[784,40.05125,-9.45306,5.78,0.52],[785,40.76167,55.10583,5.77,-0.13],[786,40.01042,-30.63389,6.52,1.04],[787,40.74875,53.52611,5.84,1.12],[788,40.56208,40.19389,4.91,0.59],[789,39.95,-42.89167,4.75,0.06],[790,40.30792,-0.69583,5.71,0.52],[791,41.20708,67.82472,5.95,0.1],[792,40.75792,48.26556,6.48,0.6],[793,40.59167,20.01167,5.69,-0.02],[794,40.16667,-39.85556,4.11,1.02],[795,40.45125,-3.21333,6.05,1.17],[796,40.39167,-14.54944,5.98,0.43],[797,40.62042,10.74167,6.3,0.06],[798,39.88208,-64.28194,6.55,-0.08],[799,41.05,49.22833,4.12,0.49],[800,41.02167,44.29694,5.43,0.9],[801,40.86292,27.70722,4.66,-0.13],[802,40.165,-54.55,5.21,0.4],[803,40.96333,25.63806,6.35,0.08],[804,40.825,3.23583,3.47,0.09],[805,40.5275,-38.38389,6.01,0.92],[806,39.8975,-68.26694,4.11,-0.06],[807,40.53542,-46.52444,6.1,0.88],[808,41.07958,17.76389,6.46,1.07],[809,41.13708,15.31167,5.77,-0.01],[810,40.63958,-50.80028,5.41,0.56],[811,41.03083,-13.85861,4.25,-0.14],[812,41.24,12.44583,5.18,0.24],[813,41.23542,10.11417,4.27,0.31],[814,40.83458,-40.5275,6.36,-0.02],[815,42.23125,69.63417,6.18,0.18],[816,41.33708,4.71167,6.03,0.31],[817,41.08542,-32.525,6.22,0.04],[818,41.27583,-18.5725,4.47,0.48],[819,41.74292,35.98361,6.25,0.93],[820,41.76458,35.555,6.3,0.6],[821,41.04458,-52.57056,6.15,0.09],[822,41.31875,-46.28722,6.85,1.36],[823,40.86083,-66.71444,6.26,0.53],[824,41.97708,29.24722,4.51,1.11],[825,42.37833,57.08417,6.25,0.89],[826,41.68833,-21.63972,6.49,0.38],[827,41.79667,-22.48556,6.47,0.39],[828,42.13375,18.28361,5.82,1.2],[829,42.99458,68.88861,5.8,0.64],[830,42.19125,25.18806,5.86,-0.07],[831,42.36292,37.32611,6.45,0.43],[832,41.98333,-12.46056,6.9,1.56],[833,41.36458,-63.70444,5.74,0.93],[834,42.67417,55.89556,3.76,1.68],[835,41.89042,-35.55083,6.51,0.96],[836,42.32292,17.46417,5.22,-0.06],[837,41.38583,-67.61667,4.84,0.06],[838,42.49583,27.26056,3.63,-0.1],[839,42.93958,58.31472,6.45,0.1],[840,42.64625,38.31861,4.23,0.34],[841,42.2725,-32.40583,4.46,0.99],[842,42.92375,46.84194,5.88,0.89],[843,42.87833,35.05972,4.53,1.56],[844,42.4625,-24.56028,6.14,1.07],[845,42.47583,-27.94167,5.39,0.02],[846,43.21667,52.99778,6.36,0.07],[847,42.87333,15.08194,5.49,-0.09],[848,42.56167,-35.84361,5.92,0.9],[849,43.33833,48.56944,6.26,1.18],[850,42.75958,-21.00417,4.75,0.91],[851,42.66833,-35.67611,5.47,1.25],[852,42.25625,-62.80667,5.26,0.1],[853,42.69958,-39.93167,6.36,0.05],[854,43.56458,52.7625,3.95,0.74],[855,43.4275,38.3375,5.33,0.41],[856,43.29875,16.48333,6.31,0.6],[857,43.13375,-12.76944,6.04,0.87],[858,42.98042,-30.81444,6.4,0.48],[859,43.21042,-9.44111,6.32,0.19],[860,43.98708,61.52111,5.59,0.45],[861,44.10333,64.3325,6.24,2.03],[862,43.39708,-22.37639,5.95,1.04],[863,43.39333,-38.43694,5.92,0.44],[864,44.21083,51.26083,6.22,1.57],[865,44.13917,47.16389,6.02,1.34],[866,43.08,-62.90972,6.03,1.25],[867,43.95208,18.33167,5.91,1.47],[868,43.47042,-49.89028,4.0,2.11],[869,44.10875,18.02306,5.63,0.43],[870,44.0575,8.38167,5.97,0.48],[871,43.52708,-50.87139,6.21,1.58],[872,42.61875,-75.06694,4.75,1.33],[873,44.32208,31.93417,5.11,-0.01],[874,44.10708,-8.89806,3.89,1.11],[875,44.15583,-3.71222,5.17,0.08],[876,44.50958,38.615,6.04,1.41],[877,44.26917,4.50111,6.11,1.69],[878,44.52167,20.66861,5.8,0.41],[879,44.69042,39.66278,4.7,0.06],[880,43.58708,-64.43556,6.56,1.39],[881,46.5325,79.41861,5.49,1.57],[882,44.76542,35.18306,4.93,1.23],[883,44.34875,-23.86194,5.45,0.23],[884,44.30458,-29.85528,6.29,0.47],[885,44.95792,47.22083,5.47,0.89],[886,44.91625,41.03306,5.89,1.44],[887,44.80292,21.34028,4.63,0.04],[888,44.80292,21.34028,4.63,0.04],[889,44.52375,-23.60611,5.84,1.33],[890,45.2175,52.35167,5.28,-0.05],[891,45.2225,52.35222,6.74,0.0],[892,44.675,-2.7825,5.23,0.0],[893,44.38625,-38.19111,6.41,-0.03],[894,45.04917,38.13167,6.11,-0.06],[895,44.6975,-9.77639,6.14,0.22],[896,44.92875,8.9075,4.7,-0.12],[897,44.56542,-40.30472,3.24,0.14],[898,44.56792,-40.30444,4.35,0.08],[899,44.92167,-2.465,5.56,-0.08],[900,44.7775,-28.90694,6.14,1.04],[901,44.90042,-25.27417,5.71,0.4],[902,45.18375,10.87028,5.95,1.59],[903,44.90958,-32.50722,6.31,0.0],[904,45.2125,-2.87861,6.11,1.77],[905,45.47542,26.46222,5.9,0.14],[906,47.92833,81.47056,5.95,0.15],[907,45.29167,-7.66278,5.75,1.05],[908,45.46792,5.33611,6.25,1.05],[909,44.69917,-64.07139,4.99,0.13],[910,45.59375,4.35278,5.61,-0.1],[911,45.57,4.08972,2.53,1.64],[912,45.48375,-9.96139,5.83,1.11],[913,45.53875,-6.49472,6.19,0.6],[914,45.40708,-28.09167,5.89,0.79],[915,46.19917,53.50639,2.93,0.7],[916,45.87625,28.26972,6.36,0.6],[917,45.67625,-7.68528,5.32,0.94],[918,46.385,56.70583,4.76,1.02],[919,45.59792,-23.62444,4.09,0.16],[920,46.41625,56.06861,6.11,1.02],[921,46.29417,38.84028,3.39,1.65],[922,46.82917,64.05778,5.89,-0.03],[923,46.33667,40.5825,6.05,1.01],[924,46.16958,15.85611,6.49,0.6],[925,46.06833,-7.60083,5.26,0.2],[926,46.15875,1.86361,6.05,1.04],[927,46.36125,25.25528,6.8,-0.02],[928,46.36125,25.25528,7.0,0.6],[929,45.73292,-46.975,5.82,1.3],[930,47.01625,52.21333,6.31,-0.01],[931,46.59875,13.18722,5.62,1.08],[932,47.98458,74.39361,4.87,0.02],[933,46.9475,47.30833,6.41,0.12],[934,45.90333,-59.73778,5.11,0.34],[935,46.63958,-6.08861,5.27,1.6],[936,47.04208,40.95556,2.12,-0.05],[937,47.26667,49.61333,4.05,0.59],[938,46.85708,17.88,6.11,-0.12],[939,45.56417,-71.9025,5.53,-0.14],[940,47.08833,18.795,6.27,1.58],[941,47.37417,44.85722,3.8,0.98],[942,47.16125,8.47083,6.28,1.06],[943,46.96208,-27.83111,6.19,0.16],[944,47.40292,29.07694,5.72,0.12],[945,47.53667,27.82,6.42,0.01],[946,47.6125,26.89639,6.02,1.28],[947,47.8225,39.61167,4.63,1.11],[948,47.66208,11.8725,5.98,-0.06],[949,48.11,47.72583,6.33,1.43],[950,48.04,42.37611,6.15,-0.09],[951,47.9075,19.72667,4.35,1.03],[952,47.84125,13.04778,6.12,1.02],[953,47.6475,-23.73833,6.38,0.93],[954,48.05917,27.25694,5.79,-0.12],[955,47.82833,-3.81167,6.05,1.66],[956,48.35,48.17694,5.9,0.97],[957,47.82,-16.02528,6.26,1.2],[958,48.11,6.66083,5.56,1.08],[959,46.955,-69.26556,6.15,1.02],[960,47.61417,-48.73417,6.12,1.12],[961,50.08208,77.73472,5.45,0.19],[962,48.19333,-1.19611,5.06,0.57],[963,48.01792,-28.98694,3.87,0.52],[964,48.95,57.14083,5.79,0.73],[965,53.08375,84.91111,5.61,0.92],[966,48.73625,42.50389,6.07,1.07],[967,49.38167,65.65861,6.36,0.09],[968,48.1075,-44.41972,5.93,0.44],[969,49.05083,50.93778,5.03,1.15],[970,48.25625,-35.94389,6.27,-0.08],[971,48.83542,30.55667,5.52,0.01],[972,48.72542,21.04444,4.89,-0.01],[973,49.01958,45.34583,6.16,1.67],[974,48.40833,-29.80417,6.16,1.05],[975,48.94583,32.85639,6.31,0.37],[976,49.00792,34.68861,6.25,0.28],[977,48.13833,-57.32167,5.74,2.28],[978,49.14625,32.18361,6.06,0.99],[979,49.2975,40.48333,6.45,0.6],[980,48.75083,-26.10028,6.25,0.04],[981,46.88333,-78.98944,5.57,0.3],[982,49.4475,44.025,5.47,-0.06],[983,49.00375,-5.91861,6.17,-0.02],[984,48.95833,-8.81972,4.8,0.23],[985,49.9975,65.65222,4.84,-0.15],[986,49.44083,39.28333,5.96,0.07],[987,49.6575,50.22222,5.15,-0.06],[988,49.14875,-9.15444,6.14,0.4],[989,49.78167,50.095,5.03,-0.06],[990,49.04708,-30.8275,6.65,-0.07],[991,49.6825,34.22278,4.82,1.49],[992,49.59333,-0.93028,5.38,1.04],[993,49.51167,-28.79694,5.91,0.33],[994,49.59208,-22.51139,4.88,0.9],[995,49.9825,27.07111,5.9,0.86],[996,49.84042,3.37028,4.83,0.68],[997,49.67167,-18.55972,5.71,0.37],[998,49.36083,-47.75167,5.85,1.24],[999,50.085,29.04833,4.47,1.55],[1000,50.10667,25.66278,6.12,1.24],[1001,50.46917,49.07083,5.93,0.43],[1002,50.36042,43.32944,4.95,0.04],[1003,49.87917,-21.75778,3.69,1.62],[1004,49.895,-24.12306,5.61,1.66],[1005,50.30667,21.14694,5.28,-0.07],[1006,49.4425,-62.57528,5.54,0.64],[1007,50.27833,3.67556,5.69,0.97],[1008,49.98208,-43.06972,4.27,0.71],[1009,51.16875,64.58611,5.23,2.08],[1010,49.55375,-62.50639,5.24,0.6],[1011,50.805,49.21333,5.29,-0.07],[1012,50.54958,27.6075,5.52,1.1],[1013,50.18833,-26.60639,6.39,0.54],[1014,49.49583,-66.92694,6.05,0.13],[1015,50.68833,20.74194,5.09,1.24],[1016,50.35,-23.63528,5.52,0.88],[1017,51.08083,49.86111,1.79,0.48],[1018,50.56792,-25.58778,6.35,0.01],[1019,51.12375,33.53583,5.61,-0.03],[1020,51.45167,53.92167,6.51,0.29],[1021,50.38875,-47.77694,6.39,1.0],[1022,51.07708,24.72417,5.5,1.19],[1023,50.91292,4.88194,6.38,0.86],[1024,50.82417,-7.79417,6.2,0.7],[1025,48.99,-77.38833,5.52,0.44],[1026,51.28917,41.25722,6.51,0.6],[1027,51.10875,20.80361,6.08,-0.04],[1028,51.04208,12.62944,6.04,1.23],[1029,51.48917,49.12083,6.09,-0.07],[1030,51.20333,9.02889,3.6,0.89],[1031,50.93583,-32.70722,6.5,1.37],[1032,52.58125,71.86389,6.32,1.8],[1033,52.09833,60.25556,6.49,0.02],[1034,52.01292,49.06278,4.98,-0.09],[1035,52.26708,59.94028,4.21,0.41],[1036,51.76333,18.75639,6.57,0.15],[1037,52.21833,49.84833,5.58,-0.04],[1038,51.7925,9.73278,3.74,-0.09],[1039,51.82792,12.735,6.28,-0.02],[1040,52.47875,58.87861,4.54,0.56],[1041,52.08667,33.8075,5.61,0.02],[1042,51.4825,-35.92083,6.39,0.08],[1043,52.54708,59.36611,6.13,0.08],[1044,52.34208,49.50889,4.67,-0.09],[1045,51.59375,-27.3175,5.93,0.94],[1046,52.50083,55.45194,5.09,0.05],[1047,52.35917,46.93778,6.24,0.13],[1048,52.11083,22.80417,6.03,0.95],[1049,51.54875,-41.63694,6.32,0.06],[1050,52.00417,-11.28667,5.73,1.1],[1051,52.65417,48.10361,5.82,-0.04],[1052,52.64375,47.99528,4.36,1.35],[1053,51.01042,-69.62472,6.15,0.48],[1054,51.88917,-35.68139,5.71,1.29],[1055,53.80167,73.34694,6.57,0.03],[1056,52.8725,49.20972,6.29,0.09],[1058,52.04792,-35.85333,6.5,0.13],[1059,52.95458,49.40083,6.39,0.09],[1060,52.41292,-6.805,5.99,1.02],[1061,52.60208,11.33639,5.14,-0.03],[1062,52.4,-12.67472,5.59,0.17],[1063,53.03583,48.02361,5.47,-0.1],[1064,51.40083,-69.33639,5.96,0.42],[1065,52.83667,27.57194,5.96,0.6],[1066,52.71833,12.93667,4.11,1.12],[1067,52.68917,6.18861,5.94,0.96],[1068,53.38375,58.765,6.4,0.14],[1069,53.10958,46.05694,5.31,0.4],[1070,52.65458,-5.07528,4.73,-0.09],[1071,53.42167,57.86889,6.37,0.51],[1072,53.16292,44.85556,6.41,0.03],[1073,53.4125,54.97472,5.98,0.11],[1074,53.16667,35.46167,5.9,-0.06],[1075,52.47917,-42.63417,5.78,0.22],[1076,52.55667,-41.37,6.12,0.48],[1077,53.75333,60.04111,6.46,0.39],[1078,53.39625,39.89944,5.81,0.11],[1079,53.15,9.37361,5.77,-0.08],[1080,54.85333,75.73972,6.27,0.97],[1081,52.65417,-47.37528,5.99,0.11],[1082,52.97458,-25.61417,6.38,0.12],[1083,52.34458,-62.9375,4.72,0.4],[1084,53.2325,-9.45833,3.73,0.88],[1085,53.53458,17.83278,6.17,0.89],[1086,53.61083,24.46444,5.92,0.13],[1087,54.1225,48.19278,4.23,-0.06],[1088,53.44708,-21.63278,4.27,-0.11],[1089,53.705,6.41778,6.49,0.63],[1090,53.145,-50.37861,5.68,1.1],[1091,53.65583,-9.86861,6.25,0.02],[1092,52.715,-66.48972,5.83,-0.06],[1093,53.48667,-31.08028,6.2,0.48],[1094,54.58208,56.93278,6.3,-0.13],[1095,53.63958,-31.87472,6.4,1.4],[1096,53.215,-61.01694,6.41,1.04],[1097,54.50083,42.58306,6.42,-0.06],[1098,53.99042,-11.19361,5.57,0.91],[1099,54.19708,0.58778,5.71,0.92],[1100,54.0725,-17.46694,5.23,-0.13],[1101,54.21833,0.40167,4.28,0.58],[1102,54.44917,15.43083,6.39,0.17],[1103,54.75042,20.91583,6.5,0.15],[1104,53.60292,-65.76444,6.75,0.17],[1105,55.53875,63.21667,5.1,1.63],[1106,54.27375,-40.27472,4.58,1.04],[1107,62.50625,86.62611,5.86,0.37],[1108,54.62167,-7.39167,5.85,0.98],[1109,52.495,-78.35194,5.7,0.93],[1110,54.85708,16.53667,6.16,1.0],[1111,54.75458,-5.62611,5.96,0.92],[1112,55.67792,59.96944,5.76,1.71],[1113,55.28292,37.58,5.57,-0.07],[1114,54.69875,-27.94306,6.01,-0.02],[1115,54.96292,3.05694,5.57,0.94],[1116,54.90958,-3.39306,6.23,1.04],[1117,54.85583,-10.43722,6.19,1.03],[1118,55.19292,25.32944,6.11,0.06],[1119,54.99792,-1.12056,6.12,1.0],[1120,55.0475,-15.22667,6.33,0.88],[1121,55.15958,-5.21056,5.53,-0.15],[1122,55.73125,47.7875,3.01,-0.13],[1123,55.59375,33.965,4.97,-0.01],[1124,56.50375,67.20167,5.8,0.35],[1125,55.3075,-11.80306,6.49,0.36],[1126,55.57875,19.70028,5.69,-0.01],[1127,56.02667,48.52361,6.06,1.55],[1128,55.34333,-19.58472,6.59,0.09],[1129,56.50958,63.345,4.8,0.8],[1130,56.17042,46.09972,6.11,0.28],[1131,56.07958,32.28833,3.83,0.05],[1132,55.94667,19.665,6.14,1.01],[1133,56.13083,36.46,5.59,0.06],[1134,55.56208,-31.93833,5.0,-0.16],[1135,56.29833,42.57861,3.77,0.42],[1136,55.81208,-9.76333,3.54,0.92],[1137,56.11708,20.92861,6.1,0.01],[1138,57.3075,70.87111,5.44,0.09],[1139,55.89083,-10.48556,5.6,0.22],[1140,56.20083,24.28944,5.46,-0.04],[1141,56.49708,45.68194,5.66,-0.07],[1142,56.21875,24.11333,3.7,-0.11],[1143,55.70875,-37.31361,4.59,1.2],[1144,56.29042,24.83917,5.64,-0.07],[1145,56.30208,24.46722,4.3,-0.11],[1146,56.12708,-1.16306,5.25,-0.1],[1147,56.88417,55.9225,6.1,-0.03],[1148,57.58958,71.33222,4.63,0.03],[1149,56.45667,24.36778,3.87,-0.07],[1150,56.23542,-0.29667,5.55,1.42],[1151,56.47667,24.55472,5.76,-0.04],[1152,56.51208,24.52806,6.43,-0.02],[1153,56.41833,6.05,5.35,-0.12],[1154,54.125,-78.32306,6.29,1.15],[1155,57.38,65.52611,4.47,1.88],[1156,56.58167,23.94833,4.18,-0.06],[1157,56.02583,-40.66028,6.45,1.06],[1158,57.40292,63.29722,5.85,0.18],[1159,56.53958,6.80306,5.91,0.99],[1160,57.07625,50.73667,6.14,0.06],[1161,57.33167,57.11806,6.46,0.06],[1162,56.53542,-12.10167,4.42,1.63],[1163,56.96917,33.6,6.57,0.08],[1164,56.95375,32.195,6.25,0.47],[1165,56.87125,24.105,2.87,-0.09],[1166,57.92417,68.5075,6.32,-0.08],[1167,56.21083,-48.06139,6.49,1.02],[1168,56.14083,-54.27389,6.3,1.04],[1169,56.31583,-47.35972,5.73,0.96],[1170,57.28417,43.96306,6.02,0.29],[1171,56.61417,-29.33806,5.9,0.12],[1172,57.08708,23.42111,5.45,-0.07],[1173,56.71208,-23.24972,4.23,0.42],[1174,57.06792,11.14333,5.07,-0.13],[1175,56.05,-64.80694,3.85,1.13],[1176,57.51875,44.96778,5.66,0.76],[1177,57.38583,33.09139,5.11,0.07],[1178,57.29042,24.05333,3.63,-0.09],[1179,56.83375,-29.90194,6.55,0.49],[1180,57.29667,24.13667,5.09,-0.08],[1181,56.915,-23.87472,5.24,0.07],[1182,57.16208,0.22778,5.91,1.23],[1183,57.43125,23.71167,6.17,-0.05],[1184,56.98333,-30.16778,5.54,0.98],[1185,57.47917,22.24444,6.07,-0.01],[1186,56.95667,-36.10583,6.21,-0.1],[1187,57.14917,-20.90306,5.81,1.64],[1188,57.57875,25.57944,5.26,0.21],[1189,57.1475,-37.62222,5.4,0.01],[1190,57.14958,-37.62056,4.73,-0.03],[1191,57.97375,34.35917,5.77,0.0],[1192,58.43042,57.975,5.8,0.18],[1193,57.9025,22.03167,6.83,0.6],[1194,57.81583,13.04583,6.3,-0.07],[1195,57.36375,-36.20028,4.17,0.95],[1196,59.12583,71.82167,6.34,0.3],[1197,58.01792,31.16833,6.25,0.2],[1198,58.41125,48.65056,5.76,1.05],[1199,58.00083,6.53472,5.67,0.06],[1200,57.65667,-36.42528,6.86,-0.04],[1201,58.29167,17.32694,5.97,0.34],[1202,58.17333,-5.36139,5.48,-0.1],[1203,58.53292,31.88361,2.85,0.12],[1204,59.35625,63.07222,5.03,-0.09],[1205,59.28458,61.10889,5.0,1.45],[1206,58.30417,-18.43444,6.22,0.88],[1207,58.9925,47.87139,5.37,-0.08],[1208,56.80958,-74.23889,3.24,1.62],[1209,58.84583,31.04583,6.1,0.29],[1210,59.15208,50.69528,5.28,0.41],[1211,58.5725,-2.95278,6.14,0.09],[1212,58.57292,-2.95472,4.79,0.94],[1213,58.4275,-24.6125,4.65,-0.13],[1214,58.41208,-34.73222,5.11,-0.13],[1215,59.11958,35.08111,5.49,-0.03],[1216,58.38875,-46.89361,5.93,1.24],[1217,58.81792,-12.09917,6.0,0.32],[1218,59.21708,22.47806,5.63,0.3],[1219,58.59667,-40.35722,5.71,0.6],[1220,59.46333,40.01028,2.89,-0.18],[1221,59.26583,23.17556,6.06,0.02],[1222,59.36,24.46194,6.16,1.37],[1223,59.51292,34.81444,6.53,0.23],[1224,59.25708,6.04,6.09,0.06],[1225,59.15792,-9.75083,6.19,0.28],[1226,59.62125,38.84028,6.3,1.08],[1227,58.64167,-52.69056,6.46,0.16],[1228,59.74125,35.79111,4.04,0.01],[1229,59.91667,38.82056,6.38,0.1],[1230,62.51167,80.69861,5.1,0.56],[1231,59.5075,-13.50861,2.95,1.59],[1232,59.71792,-5.47,5.83,1.0],[1233,59.91958,10.33083,6.37,0.42],[1234,60.31125,36.99,6.41,-0.01],[1235,59.87542,-12.57417,5.6,1.48],[1236,59.01667,-63.46361,6.14,1.1],[1237,60.15375,17.29667,6.32,0.06],[1238,60.20333,18.19389,5.89,0.32],[1239,60.17,12.49028,3.47,-0.12],[1240,59.98125,-24.01639,4.66,-0.13],[1241,61.51292,68.68,5.87,1.54],[1242,61.11333,59.15556,5.06,0.5],[1243,60.44208,9.99778,5.67,0.02],[1244,60.38333,-1.54972,5.28,-0.15],[1245,59.67875,-57.1025,6.05,0.44],[1246,60.16958,-30.49083,5.93,0.04],[1247,59.68625,-61.40028,4.56,1.62],[1248,61.6625,65.52083,6.17,0.14],[1249,60.65292,-0.26889,5.38,0.5],[1250,60.06542,-51.56472,6.51,1.64],[1251,60.78917,5.98917,3.91,0.03],[1252,61.09042,24.10583,5.47,0.86],[1253,60.93583,5.43556,5.33,-0.08],[1254,60.98583,8.19722,5.46,0.37],[1255,61.6525,54.00861,6.31,0.99],[1256,61.17375,22.08194,4.36,1.07],[1257,61.04125,2.82694,5.36,0.5],[1258,60.85292,-20.14417,6.46,-0.18],[1259,60.90333,-20.15833,7.01,1.22],[1260,61.96292,62.33,6.99,0.42],[1261,61.64583,50.35139,4.29,0.02],[1262,61.33417,22.00889,5.9,0.62],[1263,61.03625,-16.58889,6.39,1.26],[1264,60.22417,-62.15944,4.51,1.65],[1265,61.09458,-12.7925,5.61,1.08],[1266,60.32583,-61.07889,4.97,1.42],[1267,61.17083,-20.38167,6.13,1.16],[1268,61.65167,27.6,5.2,-0.13],[1269,61.75208,29.00139,5.23,0.34],[1270,62.365,59.90806,6.28,1.14],[1271,55.63375,-85.26222,6.41,-0.01],[1272,61.48542,-8.85611,6.26,0.06],[1273,62.16542,47.7125,4.04,-0.03],[1274,61.44458,-20.51222,6.34,0.92],[1275,61.40583,-27.65167,5.59,0.31],[1276,62.34333,54.82889,6.18,0.6],[1277,62.06375,37.72778,6.09,0.95],[1278,62.1525,38.03972,5.51,0.46],[1279,61.925,15.16278,6.01,0.4],[1280,61.9975,17.33972,5.89,1.5],[1281,63.43708,72.12639,6.03,1.01],[1282,63.215,68.50167,6.32,1.18],[1283,62.29167,19.60917,5.5,1.07],[1284,62.25667,13.39833,5.95,0.05],[1285,61.85458,-42.91694,6.59,0.93],[1286,62.74583,33.58667,5.72,1.44],[1287,62.70792,26.48083,5.41,0.34],[1288,62.32417,-16.38583,5.37,-0.15],[1289,67.05417,83.80778,5.57,-0.13],[1290,62.59375,-6.92389,5.44,0.94],[1291,62.14125,-45.86472,6.59,0.38],[1292,62.83458,5.52306,5.72,0.36],[1293,62.69875,-8.81972,5.7,1.06],[1294,61.84,-64.2225,6.38,0.64],[1295,63.13083,17.2775,6.09,1.08],[1296,63.7575,57.46028,6.08,0.61],[1297,63.21333,22.41361,6.12,0.19],[1298,62.96625,-6.8375,4.04,0.33],[1299,62.69083,-35.27389,6.44,1.07],[1300,62.90083,-20.35611,5.79,0.18],[1301,63.49833,37.96694,6.45,0.6],[1302,62.71083,-41.99361,4.93,0.33],[1303,63.72458,48.40944,4.14,0.95],[1304,67.50042,83.34056,5.46,0.87],[1305,64.22333,61.85028,5.7,-0.14],[1306,63.72208,40.48361,4.71,1.01],[1307,63.395,10.21222,6.23,0.05],[1308,63.38042,8.89056,6.51,0.16],[1309,63.38792,7.71611,5.29,0.36],[1310,63.45792,12.75333,6.25,1.16],[1311,63.485,9.26361,4.84,0.8],[1312,63.40917,-1.14972,6.44,-0.13],[1313,64.28417,57.86056,5.71,1.09],[1314,64.17958,53.61194,5.19,0.05],[1315,63.65125,10.01111,5.22,-0.1],[1316,63.13167,-44.36833,6.71,1.48],[1317,66.76167,80.82417,5.43,1.17],[1318,63.59875,-10.25639,4.87,1.17],[1319,63.94292,15.40056,6.32,0.4],[1320,63.88375,8.89222,4.29,-0.06],[1321,63.8575,6.19972,6.93,0.7],[1322,63.87167,6.18667,6.31,0.59],[1323,63.39875,-40.35778,6.37,1.46],[1324,64.56083,50.29556,4.61,0.04],[1325,63.81792,-7.65278,4.43,0.82],[1326,63.50042,-42.29444,3.86,1.1],[1327,65.16792,65.14056,5.27,0.81],[1328,64.53417,42.14111,6.22,-0.08],[1329,64.315,20.57861,4.94,0.26],[1330,64.80542,50.04889,5.45,0.22],[1331,64.59667,21.57917,5.65,0.28],[1332,64.33,-6.47194,5.94,1.08],[1333,65.04792,50.92083,5.55,-0.01],[1334,64.60208,9.48667,6.54,0.16],[1335,65.44833,60.73556,5.39,1.49],[1336,63.60625,-62.47389,3.35,0.91],[1337,65.06,41.80806,5.92,0.94],[1338,64.00667,-51.48667,4.25,0.3],[1339,64.85875,21.14222,5.35,-0.08],[1340,63.70292,-62.19194,5.45,1.1],[1341,64.90292,21.77361,5.38,-0.14],[1342,65.46583,56.50667,5.88,0.6],[1343,65.1025,34.56667,4.93,0.94],[1344,65.04167,31.95333,6.16,1.71],[1345,64.56625,-20.71556,6.0,1.67],[1346,64.94833,15.6275,3.65,0.99],[1347,64.47375,-33.79833,3.56,-0.12],[1348,65.08875,27.35083,4.95,1.15],[1349,64.90625,10.12139,6.31,1.43],[1350,65.38833,46.49889,4.85,-0.03],[1351,64.99042,14.03528,5.59,0.28],[1352,65.74125,59.61639,6.19,0.6],[1353,64.65583,-22.97028,6.07,0.3],[1354,65.10458,18.7425,6.12,0.37],[1355,64.12042,-59.30194,4.44,1.08],[1356,65.15125,15.09528,5.26,0.22],[1357,64.08792,-60.94861,6.37,0.07],[1358,65.22,13.86417,6.17,0.46],[1359,64.7625,-33.905,6.37,0.13],[1360,65.17167,6.13083,5.77,0.92],[1361,65.20417,9.22556,6.53,0.15],[1362,65.16125,-6.24556,6.27,0.91],[1363,65.17833,-7.5925,5.85,-0.13],[1364,64.81917,-44.26806,5.34,1.08],[1365,64.66667,-52.86,6.09,0.49],[1366,65.36292,-0.09806,5.86,1.32],[1367,65.1625,-20.63972,5.38,-0.02],[1368,65.51458,14.07722,5.72,0.32],[1369,65.64542,25.62917,5.37,-0.05],[1370,65.595,20.82139,5.91,1.66],[1371,65.89958,42.42806,6.23,0.0],[1372,64.4175,-63.25556,5.87,-0.07],[1373,65.73375,17.5425,3.76,0.98],[1374,65.38042,-25.72833,6.01,0.35],[1375,65.885,20.98222,5.99,0.03],[1376,65.85417,16.77722,5.64,0.3],[1377,66.12167,34.13056,5.73,-0.06],[1378,65.99917,24.30111,6.36,0.17],[1379,66.15583,33.95972,5.76,0.4],[1380,66.02417,17.44389,4.8,0.15],[1381,65.96625,9.46083,5.12,0.07],[1382,66.75375,57.58528,6.32,0.04],[1383,65.92,-3.74556,5.17,0.08],[1384,65.77375,-24.89222,5.83,1.51],[1385,66.23792,19.04167,5.98,0.37],[1386,65.78208,-35.545,6.39,1.24],[1387,66.34208,22.29389,4.22,0.13],[1388,66.35417,22.19972,5.28,0.25],[1389,66.3725,17.92806,4.29,0.05],[1390,66.52625,31.43889,5.28,0.97],[1391,66.40542,15.94083,6.46,0.49],[1392,66.57708,22.81361,4.28,0.26],[1393,66.00917,-34.01694,3.96,1.49],[1394,66.58667,15.61833,4.49,0.25],[1395,65.47208,-63.38639,5.24,0.96],[1396,66.65167,14.71361,4.69,0.98],[1397,66.58792,8.59028,6.06,0.02],[1398,66.235,-34.75778,6.55,0.44],[1399,66.82292,22.99639,5.53,-0.1],[1400,66.75292,2.07944,6.23,1.09],[1401,68.37792,72.52861,5.94,0.3],[1402,66.87,11.2125,5.88,0.05],[1403,67.00333,21.62,5.72,0.27],[1404,66.32958,-44.16083,6.39,0.44],[1405,66.05083,-57.07139,6.29,0.66],[1406,67.21625,30.36139,6.4,0.52],[1407,67.11,16.35972,4.97,1.13],[1408,67.0975,14.74083,5.9,0.32],[1459,69.12167,23.34083,6.02,0.38],[1409,67.15417,19.18028,3.53,1.01],[1410,66.7375,-24.08139,6.11,0.14],[1411,67.14375,15.96222,3.84,0.95],[1412,67.16542,15.87083,3.4,0.18],[1413,67.015,1.85861,6.15,1.02],[1414,67.20917,13.0475,5.03,0.23],[1415,67.13375,1.38083,5.55,-0.1],[1416,66.27208,-61.23833,5.94,1.54],[1417,68.0075,53.91083,5.77,0.18],[1418,66.775,-46.9475,6.1,0.46],[1419,67.65958,32.45806,6.21,-0.04],[1420,67.42875,10.52167,6.79,0.09],[1421,67.1625,-19.45833,5.96,1.22],[1422,67.53583,15.63806,5.58,0.32],[1423,67.27875,-13.04833,5.6,-0.23],[1424,67.85,40.01028,6.26,0.04],[1425,67.51,10.2625,6.48,1.03],[1426,64.49625,-80.21389,5.69,0.84],[1427,67.64042,16.19389,4.78,0.17],[1428,67.66208,15.69194,5.48,0.26],[1429,67.03917,-41.96,6.44,1.64],[1430,67.65542,13.72444,5.4,0.26],[1431,67.54042,-13.59222,6.24,1.0],[1432,67.96583,15.85167,6.02,0.34],[1433,67.33333,-46.51528,6.16,1.06],[1434,68.35375,43.06389,6.09,0.38],[1435,66.94125,-62.52083,5.75,1.01],[1436,68.02,5.41,6.39,0.42],[1437,67.96958,-0.04389,4.91,1.32],[1438,67.85792,-13.645,6.21,0.12],[1439,67.66792,-35.65361,5.96,1.0],[1440,69.10083,64.26167,5.94,-0.03],[1441,68.15583,-3.20917,5.81,-0.14],[1442,68.38708,18.01667,6.25,0.07],[1443,67.70875,-44.95389,5.07,-0.19],[1444,68.46208,14.84444,4.65,0.25],[1445,68.65833,28.96111,5.88,-0.06],[1446,68.45042,9.41306,6.01,1.06],[1447,68.34167,-10.78583,6.06,1.38],[1448,68.53458,5.56861,5.68,0.05],[1449,68.47833,-6.73889,5.72,-0.13],[1450,68.55917,-6.83778,6.09,1.38],[1451,68.54833,-8.23139,5.11,1.7],[1452,68.54875,-8.97028,5.26,1.47],[1453,68.3775,-29.76667,4.51,0.98],[1454,69.1725,41.26472,4.25,1.22],[1455,68.92792,19.88167,6.36,0.6],[1456,65.24125,-81.58,5.79,0.35],[1457,68.98,16.50917,0.85,1.54],[1458,68.91375,10.16083,4.25,0.18],[1460,68.80833,-9.73667,6.37,0.11],[1461,68.75208,-19.92056,6.13,1.17],[1462,69.00667,-3.61194,6.33,-0.1],[1463,69.07958,-3.3525,3.93,-0.21],[1464,68.8875,-30.56222,3.82,0.98],[1465,68.49917,-55.045,3.27,-0.1],[1466,69.99208,53.47306,5.35,0.32],[1467,69.97792,53.07972,5.05,1.07],[1468,71.50125,76.61111,6.49,0.51],[1469,69.30708,0.99833,5.31,-0.12],[1470,69.62333,26.94,6.47,0.6],[1471,69.56583,20.68472,5.92,-0.05],[1472,69.53917,16.03333,5.79,0.31],[1473,69.53958,12.51083,4.27,0.12],[1474,69.40042,-2.47333,5.23,0.28],[1475,68.39167,-62.82361,5.79,1.04],[1476,69.21208,-30.71667,6.3,-0.1],[1477,69.84625,25.21833,6.22,0.16],[1478,69.78833,15.79972,5.07,0.15],[1479,69.81875,15.91806,4.69,0.15],[1480,69.77583,7.87083,5.39,0.26],[1481,69.545,-14.30389,3.87,1.09],[1482,70.35042,48.30083,5.67,-0.02],[1483,69.72333,-12.12306,5.01,0.07],[1484,70.01417,12.19778,5.46,-0.12],[1485,65.71208,-82.89917,6.76,0.2],[1486,70.82542,59.52083,6.5,0.6],[1487,69.83208,-14.35917,5.45,1.06],[1488,69.94667,-1.05278,6.1,0.94],[1489,70.45958,38.28028,5.99,0.57],[1490,70.3325,28.615,5.78,-0.03],[1491,72.20958,75.94111,6.06,0.28],[1492,69.19,-62.0775,5.4,1.58],[1493,70.84,49.97389,5.87,0.02],[1494,70.72625,43.365,5.29,0.0],[1495,70.02833,-24.4825,5.58,0.92],[1496,70.11042,-19.67167,4.32,1.61],[1497,70.56125,22.95694,4.28,-0.13],[1498,69.76792,-51.67278,6.44,1.32],[1499,70.8075,24.08889,6.13,0.54],[1500,71.05375,40.78694,6.08,0.06],[1501,70.95125,32.86528,6.45,0.6],[1502,70.14042,-41.86389,4.45,0.34],[1503,70.51458,-37.14444,5.05,0.37],[1504,70.07625,-58.94361,6.53,0.68],[1505,70.89417,-8.79361,6.82,0.39],[1506,70.89625,-8.79611,6.7,0.92],[1507,71.1075,11.14611,5.4,0.25],[1508,71.02208,-8.50361,5.9,-0.11],[1509,70.78875,-30.76556,5.68,1.41],[1510,72.65167,70.94167,6.37,-0.08],[1511,72.00125,56.75722,5.3,0.25],[1512,71.42708,23.62806,6.35,0.06],[1513,71.03333,-18.66667,5.53,0.02],[1514,71.685,40.31278,5.97,0.93],[1515,72.02917,55.6025,6.26,0.6],[1516,70.69333,-50.48139,5.31,0.98],[1517,71.57,18.735,6.01,1.21],[1518,70.93417,-41.06472,6.25,1.46],[1519,71.50708,11.70556,5.37,0.19],[1520,71.37542,-3.25472,4.02,-0.15],[1521,71.2675,-21.28361,5.72,1.47],[1522,71.60042,-2.95444,6.33,0.04],[1523,75.08625,81.19389,5.07,1.28],[1524,71.45667,-34.005,6.86,0.0],[1525,71.6075,-28.0875,6.19,0.19],[1526,71.48083,-39.35667,6.05,1.07],[1527,73.02167,63.50528,5.44,1.57],[1528,72.32917,32.58833,5.86,0.24],[1529,72.30333,31.43722,5.58,1.12],[1530,71.08792,-59.73278,5.27,0.2],[1531,69.59042,-77.65611,6.05,1.1],[1532,71.90125,-16.93444,5.51,0.63],[1533,72.4775,37.48833,4.88,1.44],[1534,72.18583,3.58833,6.03,1.19],[1535,72.78875,48.74083,5.66,0.99],[1536,72.15125,-5.67389,5.78,0.62],[1537,72.43375,15.90417,6.08,1.6],[1538,72.13542,-16.32944,5.77,0.55],[1539,71.95667,-30.02028,6.37,1.07],[1540,71.24125,-63.22972,6.46,1.08],[1541,70.76625,-70.93111,5.54,-0.12],[1542,73.5125,66.34278,4.29,0.03],[1543,72.46,6.96139,3.19,0.45],[1544,72.65292,8.90028,4.36,0.01],[1545,72.42583,-13.76972,6.26,0.44],[1546,73.29083,52.84083,6.41,0.6],[1547,72.84375,18.83972,5.1,0.21],[1548,72.14083,-43.98,6.72,0.95],[1549,72.54833,-16.21722,5.03,0.98],[1550,73.19917,42.58667,5.71,0.11],[1551,73.15833,36.70306,4.78,1.41],[1552,72.80167,5.605,3.69,-0.17],[1553,72.93083,9.975,6.11,0.08],[1554,73.19625,27.8975,5.97,0.37],[1555,73.76292,55.25917,5.52,0.04],[1556,73.13333,14.25056,4.74,1.84],[1557,72.5675,-41.32083,6.07,0.37],[1558,73.71375,44.06083,6.08,-0.02],[1559,72.8675,-34.90639,5.86,0.08],[1560,73.22375,-5.45278,4.39,0.25],[1561,74.02958,52.86944,5.75,0.11],[1562,73.345,2.50806,5.33,1.64],[1563,72.73,-53.46139,5.61,0.33],[1564,72.73458,-53.45972,6.42,0.6],[1565,73.4825,1.56944,6.61,0.04],[1566,73.74292,19.48528,6.37,0.29],[1567,73.56292,2.44056,3.72,-0.18],[1568,74.32167,53.75222,4.47,-0.02],[1569,73.69542,11.42611,5.19,0.12],[1570,73.72417,10.15083,4.65,0.09],[1571,73.69917,7.77917,5.33,1.22],[1572,75.58375,74.26917,6.06,1.57],[1573,74.08292,36.16889,6.07,0.41],[1574,73.71125,0.4675,5.99,-0.12],[1575,74.065,24.59222,6.37,0.33],[1576,73.95958,15.04,5.81,-0.08],[1577,74.24833,33.16611,2.69,1.53],[1578,73.99333,5.39917,6.5,0.02],[1579,73.77833,-16.74056,5.7,0.96],[1580,74.09292,13.51444,4.07,1.15],[1581,73.8275,-16.41778,5.72,0.88],[1582,74.10083,-5.17139,5.51,-0.13],[1583,73.87583,-25.72778,6.72,0.27],[1584,73.72833,-39.62861,6.1,1.42],[1585,74.34292,17.15361,5.48,1.31],[1586,74.45292,23.94861,5.79,1.11],[1587,76.05417,73.76389,6.66,0.6],[1588,74.94292,53.15556,6.08,1.46],[1589,76.16583,74.06694,5.96,0.6],[1590,74.53917,25.05028,5.81,0.0],[1591,74.32167,-1.06722,6.23,0.42],[1592,74.81417,37.89028,4.94,0.04],[1593,75.39958,61.07806,6.03,0.41],[1594,75.71,66.82278,6.19,0.48],[1595,74.43667,-14.23139,6.15,-0.21],[1596,74.545,-2.2125,6.35,0.1],[1597,73.72083,-58.54722,6.12,0.44],[1598,73.37708,-66.67556,6.41,1.63],[1599,75.07625,39.39472,5.95,0.41],[1600,74.7475,14.54278,6.09,0.04],[1601,74.63708,1.71417,4.47,1.4],[1602,75.09667,39.655,6.58,0.6],[1603,75.85458,60.44222,4.03,0.92],[1604,74.75542,-16.37583,5.66,0.43],[1605,75.49208,43.82333,2.99,0.54],[1606,73.27292,-72.4075,6.28,0.52],[1607,74.90208,-14.80583,7.71,5.74],[1608,74.96,-10.26333,5.38,0.8],[1609,75.13583,3.61528,7.03,0.6],[1610,75.14125,3.61611,6.66,-0.07],[1611,74.9825,-12.5375,4.79,0.26],[1612,75.61958,41.07583,3.75,1.22],[1613,75.16583,-2.06556,6.32,0.28],[1614,75.20417,-5.75333,6.22,1.06],[1615,75.8275,41.44167,6.14,0.16],[1616,82.95,85.93861,6.51,0.32],[1617,75.35958,-7.17389,4.81,-0.19],[1618,75.45958,0.72222,5.92,1.27],[1619,75.5,1.60889,6.24,-0.04],[1620,75.77375,21.59,4.64,0.16],[1621,75.35667,-20.05194,4.91,-0.05],[1622,76.53542,58.9725,5.08,-0.08],[1623,76.55083,59.02111,6.08,1.12],[1624,76.62375,61.17,6.04,1.37],[1625,75.68958,-4.20972,5.85,1.21],[1626,76.06042,30.49472,6.14,1.21],[1627,76.15375,32.32028,6.62,0.27],[1628,75.54083,-26.275,5.02,1.07],[1629,73.79667,-74.93694,5.47,1.52],[1630,76.59167,54.40583,7.24,0.6],[1631,75.39375,-39.71806,6.03,0.88],[1632,76.15792,27.69611,6.6,0.24],[1633,76.09,21.27806,6.19,1.32],[1634,75.68708,-22.795,5.75,1.2],[1635,75.595,-31.77139,5.94,1.17],[1636,77.40292,69.63944,6.41,1.11],[1637,76.66917,51.59778,5.0,0.33],[1638,76.14208,15.40417,4.68,-0.06],[1639,76.50375,35.93639,6.52,0.16],[1640,75.96667,-14.36944,6.41,-0.18],[1641,76.62875,41.23444,3.17,-0.18],[1642,76.38375,19.80639,6.44,0.21],[1643,78.09333,73.94667,5.43,-0.12],[1644,76.70667,43.17472,6.2,0.43],[1645,75.97208,-24.38778,5.61,0.1],[1646,76.22708,-3.03972,6.05,-0.11],[1647,77.43542,64.91944,6.41,0.4],[1648,76.34875,1.1775,6.17,3.45],[1649,75.7025,-49.15139,5.38,0.42],[1650,78.64833,76.47278,6.37,-0.02],[1651,75.975,-41.745,6.31,0.53],[1652,76.10167,-35.48333,4.55,1.2],[1653,76.10875,-35.70528,6.34,0.3],[1654,76.36542,-22.37111,3.19,1.46],[1655,76.3175,-26.1525,5.73,1.17],[1656,76.8625,18.645,5.0,0.65],[1657,76.69042,-4.655,5.12,-0.06],[1658,76.95167,20.41833,5.3,0.09],[1659,77.0275,24.26528,5.5,0.06],[1660,76.98125,21.70472,5.89,0.19],[1661,76.65292,-13.12194,6.05,-0.06],[1662,76.90958,9.47194,6.17,0.62],[1663,76.24167,-49.57778,5.03,1.49],[1664,76.97042,8.49833,5.34,0.33],[1665,76.85417,-12.49056,5.97,0.6],[1666,76.9625,-5.08639,2.79,0.13],[1667,76.2525,-54.4075,6.27,1.54],[1668,77.67875,46.96222,5.68,0.42],[1669,77.57875,37.30194,6.02,0.72],[1670,77.43792,28.03056,6.01,0.27],[1671,77.08417,-8.665,5.78,-0.06],[1672,77.33167,9.82944,5.43,0.24],[1673,77.18167,-4.45611,5.12,0.44],[1674,76.3775,-57.47278,4.72,0.52],[1675,78.26333,61.85,6.17,0.02],[1676,77.425,15.59722,4.82,0.32],[1677,75.67917,-71.31444,5.31,1.0],[1678,78.38042,62.69139,6.5,0.21],[1679,77.28667,-8.75417,4.27,-0.19],[1680,77.06167,-35.71833,6.52,1.08],[1681,77.51333,-0.56528,6.1,1.1],[1682,75.055,-78.30028,6.29,1.51],[1683,79.55542,73.26806,5.74,0.6],[1684,77.92333,16.04556,5.18,1.49],[1685,77.74167,-2.25389,6.25,0.98],[1686,80.63958,79.23111,5.05,0.47],[1687,77.83,-2.49083,5.9,0.46],[1688,78.79708,59.40556,6.15,1.18],[1689,78.35708,38.48444,4.86,0.18],[1690,77.9225,0.51472,6.67,-0.07],[1691,77.93875,1.03694,5.89,0.66],[1692,78.68458,53.21389,6.2,0.07],[1693,77.845,-11.84917,5.68,1.46],[1694,77.68542,-25.90944,6.41,1.25],[1695,76.89167,-63.39972,5.2,1.65],[1696,78.07458,-11.86917,4.45,-0.1],[1697,78.20083,-6.05722,5.91,0.96],[1698,78.32292,2.86111,4.46,1.19],[1699,77.89958,-37.39528,6.57,1.62],[1700,76.53875,-73.03778,6.27,-0.01],[1701,78.38167,1.96806,6.09,0.42],[1702,78.23292,-16.20556,3.31,-0.11],[1703,78.44667,0.56028,6.32,1.46],[1704,78.38875,-8.14778,6.37,-0.13],[1705,78.30792,-12.94139,4.36,-0.1],[1706,78.85167,32.68778,5.02,0.23],[1707,79.32417,53.58611,6.5,1.66],[1708,79.1725,45.99806,0.08,0.8],[1709,78.68375,5.15611,5.5,1.37],[1710,78.49958,-14.60667,6.21,0.37],[1711,78.86542,22.28472,6.27,0.08],[1712,79.07583,34.31194,5.96,0.22],[1713,78.63458,-8.20167,0.12,-0.03],[1714,85.95292,85.66806,6.6,0.6],[1715,78.44375,-35.82556,6.98,1.47],[1716,74.71208,-82.47056,5.85,0.93],[1717,78.82667,-1.40917,6.15,0.39],[1718,79.01708,11.34139,5.56,-0.04],[1719,79.86583,58.11722,6.13,-0.03],[1720,80.09417,62.65361,5.61,1.75],[1721,78.62,-35.97722,5.76,1.01],[1722,79.56625,42.79222,5.48,1.65],[1723,78.85125,-26.94333,5.07,-0.1],[1724,79.17125,1.94722,6.42,-0.02],[1725,79.66833,40.465,6.18,1.37],[1726,79.54458,33.37167,4.54,1.27],[1727,78.47208,-52.03111,6.05,1.39],[1728,79.57875,33.76722,6.14,-0.06],[1729,79.78542,40.09917,4.71,0.63],[1730,78.94583,-34.92667,6.66,0.15],[1731,79.20042,-17.14167,6.56,-0.16],[1732,79.75,33.74833,5.41,-0.19],[1733,80.00958,44.42556,6.62,0.6],[1734,79.84833,33.98556,6.49,0.24],[1735,79.40167,-6.84444,3.6,-0.11],[1736,80.16375,46.96389,6.54,0.6],[1737,79.4175,-13.51972,5.5,0.93],[1738,80.06167,41.08611,5.52,0.11],[1739,79.81917,22.09639,4.94,0.93],[1740,80.00375,33.95806,5.03,0.27],[1741,79.81125,20.13472,6.08,1.01],[1742,78.91208,-52.18194,6.49,1.21],[1743,79.37125,-34.89528,4.83,1.0],[1744,78.43917,-67.18528,4.83,1.28],[1745,82.35708,77.9775,6.56,0.14],[1746,79.79667,2.59583,5.34,0.41],[1747,79.71,-18.13,5.96,0.58],[1748,79.89667,-1.41222,6.34,-0.11],[1749,80.45167,41.80444,5.23,-0.15],[1750,80.24708,27.95722,6.33,0.04],[1751,80.86583,57.54444,5.28,-0.03],[1752,80.30292,29.57,5.76,0.06],[1753,79.82292,-18.52,6.36,-0.16],[1754,79.82625,-18.50972,6.54,-0.11],[1755,80.23583,19.81417,6.18,1.23],[1756,79.89375,-13.17667,4.29,-0.26],[1757,79.99625,-12.31556,5.3,-0.12],[1758,79.84875,-27.36889,5.99,-0.04],[1759,80.11,-5.36667,6.39,-0.03],[1760,80.70958,41.02944,5.54,0.12],[1761,80.33042,4.01194,6.57,-0.09],[1762,80.11208,-21.23944,4.71,-0.05],[1763,80.43167,8.42861,5.8,-0.13],[1764,80.3825,-0.41639,5.68,-0.12],[1765,80.44042,-0.3825,4.73,-0.17],[1766,80.08583,-34.69889,6.34,0.33],[1767,79.84208,-50.60611,5.45,0.51],[1768,80.84542,28.93667,6.46,-0.04],[1769,80.4625,-13.75611,6.56,-0.09],[1770,80.70833,3.54444,5.0,-0.15],[1771,80.4425,-24.77306,5.06,0.67],[1772,80.32042,-34.34528,6.09,-0.19],[1773,81.16333,37.38556,4.99,1.42],[1774,80.90708,16.69944,6.08,0.14],[1775,81.15958,31.22389,6.28,1.24],[1776,81.16042,31.14306,5.94,0.04],[1777,80.87958,5.3225,6.35,0.12],[1778,80.82708,-8.41583,5.9,-0.03],[1779,81.30417,34.85528,6.55,1.11],[1780,81.10583,17.38333,4.99,0.53],[1781,80.92625,-0.15972,5.7,-0.21],[1782,80.96417,-0.86722,6.11,0.5],[1783,80.87583,-13.92722,5.25,-0.21],[1784,80.98667,-7.80806,4.14,0.96],[1785,80.8,-26.70583,6.49,0.5],[1786,81.15083,2.35278,6.32,-0.15],[1787,81.12042,-0.89139,5.08,0.96],[1788,81.11917,-2.39694,3.36,-0.17],[1789,81.18667,1.84639,4.95,-0.2],[1790,81.28292,6.34972,1.64,-0.22],[1791,81.57292,28.6075,1.65,-0.13],[1792,81.11833,-16.97611,5.65,0.0],[1793,80.85,-39.67861,5.71,1.62],[1794,81.72625,35.45722,6.15,1.45],[1795,81.70375,34.39167,5.94,0.14],[1796,81.71375,33.26278,6.15,1.15],[1797,80.9125,-37.33667,6.82,1.04],[1798,81.52375,16.70028,6.25,-0.08],[1799,81.25667,-10.32917,5.61,1.56],[1800,81.38,-0.54417,6.57,-0.05],[1801,80.59208,-56.13444,6.11,-0.1],[1802,82.5425,63.06722,5.42,1.71],[1803,81.44583,0.52083,6.16,-0.18],[1804,81.78458,30.20861,5.74,0.16],[1805,81.91208,34.47583,5.07,1.4],[1806,81.51,-5.51833,6.23,-0.06],[1807,81.66167,6.86917,6.42,-0.02],[1808,81.79208,17.96222,5.42,-0.1],[1809,81.8075,15.25778,6.16,0.08],[1810,81.90875,21.93694,4.88,-0.15],[1811,81.70917,3.09556,4.59,-0.21],[1812,81.49917,-19.69556,5.89,0.4],[1813,81.23167,-44.22583,6.08,1.2],[1814,81.94,15.87417,5.5,0.01],[1815,78.10708,-81.54167,6.51,1.11],[1816,82.00667,17.23889,5.77,1.63],[1817,81.77,-11.90083,6.35,0.51],[1818,81.1925,-52.31639,6.27,0.07],[1819,82.145,13.67889,6.35,0.15],[1820,82.00667,1.29833,6.41,-0.18],[1821,82.31875,25.15056,5.47,-0.04],[1822,82.41917,29.18639,6.24,0.45],[1823,81.90208,-21.37556,6.07,1.04],[1824,82.7025,41.46194,6.0,1.11],[1825,82.68792,39.82583,6.37,0.97],[1826,82.23625,-3.3075,6.39,-0.01],[1827,81.77208,-40.94361,5.87,0.23],[1828,83.14083,57.22111,6.48,0.57],[1829,82.06125,-20.75944,2.84,0.82],[1830,82.34833,-3.44639,5.79,1.15],[1831,82.68083,22.4625,6.29,1.18],[1832,82.60875,15.36028,5.94,0.14],[1833,82.47833,1.78917,5.78,-0.2],[1834,82.43333,-1.09222,4.71,1.57],[1835,82.06375,-37.23056,5.57,0.02],[1836,81.58042,-58.9125,5.14,1.0],[1837,82.5825,4.20417,6.21,1.27],[1838,82.27792,-30.11667,6.75,1.06],[1839,82.69625,5.94806,4.2,-0.14],[1840,82.58625,-7.43472,6.33,-0.19],[1842,82.81042,3.29222,5.46,-0.18],[1843,83.18208,32.19194,4.76,0.34],[1844,84.93208,75.04389,6.17,1.57],[1845,83.05333,18.59444,4.38,2.07],[1846,83.36958,42.10889,6.55,-0.02],[1847,83.05917,17.05806,5.46,-0.04],[1848,82.83708,-6.70833,6.22,-0.17],[1849,82.78167,-20.86361,5.55,0.0],[1850,83.36458,32.80111,6.48,0.09],[1851,83.00208,-0.28444,6.85,-0.16],[1852,83.00167,-0.29917,2.23,-0.22],[1853,84.3175,66.69611,6.26,0.6],[1854,83.40833,34.72583,6.27,0.15],[1855,82.9825,-7.30139,4.62,-0.26],[1856,82.53958,-47.07778,5.46,0.62],[1857,84.31292,64.15472,6.15,0.01],[1858,83.38167,18.54028,5.69,0.01],[1859,81.75,-68.62278,6.03,0.34],[1860,83.41167,20.47417,6.18,-0.07],[1861,83.17208,-1.59194,5.35,-0.19],[1862,82.80292,-35.47056,3.87,1.14],[1863,83.28,-1.71833,6.46,-0.09],[1864,83.47625,14.30556,5.64,-0.14],[1865,83.1825,-17.82222,2.58,0.21],[1866,84.14667,54.42889,5.73,1.63],[1867,82.3225,-62.31444,6.59,1.53],[1868,83.38083,-1.15611,5.34,-0.18],[1869,84.06625,47.71528,6.11,0.26],[1870,82.90042,-45.92528,5.86,1.35],[1871,83.49,1.40778,6.59,-0.17],[1872,83.56958,3.76694,5.36,0.05],[1873,83.51625,-1.03556,6.22,-0.17],[1874,83.51667,-1.47056,5.93,1.55],[1875,83.86292,24.03944,5.38,-0.09],[1876,83.705,9.48944,4.41,-0.16],[1877,83.21375,-38.51306,5.48,1.22],[1878,83.98125,27.66222,6.27,1.54],[1879,83.78458,9.93417,3.54,-0.18],[1880,83.78542,9.935,5.61,0.04],[1881,83.28083,-35.13972,5.78,1.07],[1882,82.56625,-63.92778,6.19,0.22],[1883,83.80583,10.24,5.6,0.12],[1884,84.21833,40.18222,6.09,1.03],[1885,90.33417,85.18222,6.11,1.57],[1886,83.75375,-6.00917,5.67,-0.23],[1887,83.76125,-6.00194,4.78,-0.25],[1888,83.46708,-29.84889,6.53,-0.02],[1889,84.12583,25.93944,6.49,0.43],[1890,83.84083,-4.49333,6.56,-0.13],[1891,83.84375,-4.42528,6.24,-0.15],[1892,83.84667,-4.83833,4.59,-0.19],[1893,83.81625,-5.38722,6.73,0.02],[1894,83.81708,-5.38528,7.96,0.24],[1895,83.81875,-5.38972,5.13,0.02],[1896,83.82208,-5.38778,6.7,0.09],[1897,83.84542,-5.41611,5.08,-0.09],[1898,83.87958,-4.36472,6.38,-0.14],[1899,83.85833,-5.91,2.77,-0.24],[1900,83.89917,-3.25278,6.4,-0.12],[1901,83.91458,-4.85583,5.26,0.24],[1902,84.28667,26.92417,5.83,-0.07],[1903,84.05333,-1.20194,1.7,-0.19],[1904,84.44042,33.55917,6.33,1.31],[1905,84.26583,17.04028,5.54,0.22],[1906,84.0625,-5.64806,6.54,-0.18],[1907,84.22625,9.29056,4.09,0.95],[1908,84.26833,11.035,5.94,1.58],[1909,83.81417,-33.08,5.78,1.12],[1910,84.41125,21.1425,3.0,-0.19],[1911,84.14875,-6.065,5.72,-0.22],[1912,83.435,-54.90222,6.43,0.55],[1913,84.33042,8.95194,6.12,-0.17],[1914,84.65875,30.4925,5.4,0.45],[1915,84.04292,-28.70778,6.26,0.13],[1916,85.61,65.69778,5.6,1.24],[1917,83.24833,-64.2275,5.34,1.04],[1918,84.36417,-5.93833,6.05,-0.22],[1919,84.28667,-11.77556,6.11,0.05],[1920,84.50458,7.54139,5.88,-0.07],[1921,84.73917,26.61778,6.37,0.6],[1922,83.40625,-62.48972,3.76,0.82],[1923,84.4725,-4.81361,6.19,-0.04],[1924,84.82667,29.21528,5.96,0.16],[1925,85.33458,53.48111,6.23,0.84],[1926,84.31875,-27.87139,6.16,0.34],[1927,84.01125,-47.31389,6.11,1.16],[1928,84.93417,25.89694,5.18,-0.15],[1929,84.8625,21.76278,6.34,0.06],[1930,83.76,-58.87111,6.75,1.45],[1931,84.68667,-2.6,3.81,-0.24],[1932,84.69625,-2.59417,6.65,-0.19],[1933,84.6575,-6.57389,5.96,-0.23],[1934,84.79625,4.12139,4.57,-0.11],[1935,84.43583,-28.68944,5.31,0.46],[1936,83.74,-61.17583,6.32,0.85],[1937,84.72125,-7.21306,4.8,0.13],[1938,85.14958,31.35806,6.04,0.04],[1939,85.17542,31.92083,6.11,2.12],[1940,84.88,-3.56472,6.0,0.27],[1941,85.75667,56.58167,6.05,0.95],[1942,84.87833,-9.70667,6.5,-0.1],[1943,86.03583,61.47667,6.15,0.9],[1944,84.81792,-17.84944,6.38,-0.12],[1945,85.3375,29.4875,6.43,-0.11],[1946,85.32375,16.53389,4.86,-0.13],[1947,84.68167,-40.7075,5.82,-0.09],[1948,85.18958,-1.94278,2.05,-0.21],[1949,85.19,-1.94278,4.21,0.6],[1950,85.15542,-2.825,6.22,-0.2],[1951,85.4775,23.32639,6.59,-0.06],[1952,85.21083,-1.12889,4.95,-0.21],[1953,82.97042,-76.34111,5.19,1.13],[1954,85.51625,22.66028,6.36,0.6],[1955,85.27333,0.33778,5.93,0.3],[1956,84.91208,-34.07417,2.64,-0.12],[1957,85.19167,-10.40944,6.52,-0.16],[1958,84.9575,-32.62917,5.45,0.92],[1959,85.41792,-2.89611,6.42,0.3],[1960,84.22792,-66.56028,6.31,-0.07],[1961,85.83125,23.20417,6.21,-0.06],[1962,85.42292,-16.72556,6.21,-0.13],[1963,85.61917,1.47472,4.91,1.17],[1964,83.68625,-73.74139,5.78,1.71],[1965,85.55958,-17.53028,6.15,1.38],[1966,85.3625,-33.40056,6.34,-0.04],[1967,85.72417,-6.79611,6.02,0.4],[1968,85.55792,-22.37361,5.87,0.11],[1969,86.62667,56.11556,5.94,0.17],[1970,85.78875,-1.61306,6.31,1.47],[1971,86.475,49.82639,5.47,0.03],[1972,85.54833,-30.53556,6.19,0.01],[1973,85.56292,-34.66778,5.29,-0.05],[1974,86.45625,40.50722,6.58,0.25],[1975,85.84,-18.5575,5.73,-0.01],[1976,87.27042,62.80806,6.13,0.6],[1977,86.41417,20.695,6.95,3.03],[1978,86.25792,4.00806,6.09,0.31],[1979,86.81125,42.52667,6.29,1.35],[1980,86.11833,-20.12639,6.34,0.58],[1981,85.87583,-39.40694,6.25,0.37],[1982,86.11042,-22.42167,6.15,0.94],[1983,86.11583,-22.44833,3.6,0.47],[1984,85.92125,-45.83306,6.39,0.29],[1985,86.68958,15.8225,6.0,-0.06],[1986,86.51167,-4.26833,6.34,1.05],[1987,86.71708,9.52222,5.79,0.88],[1988,86.64583,1.16806,5.95,0.78],[1989,86.805,14.48833,5.72,0.04],[1990,86.85917,17.72917,5.49,0.3],[1991,83.90125,-78.82083,6.05,-0.02],[1992,87.64167,56.91889,6.54,0.6],[1993,86.92875,13.89972,5.29,-0.17],[1994,88.23125,68.47139,6.2,0.95],[1995,87.29375,39.18111,4.52,0.94],[1996,86.49958,-32.30639,5.17,-0.28],[1997,87.09333,20.86944,6.07,-0.08],[1998,86.73875,-14.82194,3.55,0.1],[1999,87.00083,6.45417,5.27,0.23],[2000,86.78167,-16.23778,6.17,0.89],[2001,86.86125,-10.53306,6.03,0.16],[2002,87.25417,24.5675,4.86,1.01],[2003,87.735,51.51472,6.29,1.05],[2004,86.93917,-9.66972,2.06,-0.17],[2005,86.76958,-28.63917,6.22,-0.15],[2006,88.0725,58.96417,6.14,-0.04],[2007,87.14542,-4.09472,5.97,0.64],[2008,86.61417,-46.59722,5.31,1.04],[2009,86.8275,-35.67472,6.32,1.18],[2010,87.38708,12.65111,4.91,-0.07],[2011,87.76,37.30556,4.74,1.62],[2012,87.8725,39.14861,3.97,1.13],[2013,87.74208,27.96778,5.56,0.97],[2014,87.51083,9.87111,5.8,0.87],[2015,86.19333,-65.73556,4.35,0.21],[2016,87.62042,14.30556,5.52,1.01],[2017,86.99208,-40.6525,6.61,1.12],[2018,87.85708,32.125,6.25,1.75],[2019,87.55458,4.42333,5.97,1.36],[2020,86.82125,-51.06639,3.85,0.17],[2021,87.40208,-14.48361,5.49,0.88],[2022,84.29083,-80.46917,5.65,0.6],[2023,86.80417,-54.36083,6.18,1.4],[2024,87.625,2.02444,5.98,0.91],[2025,88.16458,39.57444,6.45,0.09],[2026,87.47292,-22.97167,5.87,0.06],[2027,88.74083,59.88833,5.2,0.02],[2028,88.16708,33.9175,5.98,1.6],[2029,88.71167,55.70694,4.99,0.05],[2030,88.0975,19.86806,6.06,0.54],[2031,87.84167,-7.51806,5.35,-0.2],[2032,87.39208,-44.87528,6.38,1.27],[2033,88.09292,14.17167,5.59,-0.05],[2034,88.33167,27.61222,4.58,-0.02],[2035,87.83042,-20.87917,3.81,0.99],[2036,87.86917,-22.92611,6.17,1.02],[2037,88.11,1.855,4.78,1.38],[2038,88.32958,20.29917,6.71,-0.07],[2039,88.03167,-9.04139,5.97,0.1],[2040,87.74,-35.76833,3.12,1.16],[2041,89.39583,66.09611,6.25,1.36],[2042,87.45708,-56.16667,4.51,1.1],[2043,87.99792,-29.44861,6.45,1.48],[2044,87.61917,-52.76778,6.35,0.76],[2045,89.06,51.80389,6.49,0.6],[2046,88.74583,31.70167,5.9,0.14],[2047,88.59542,20.27611,4.41,0.59],[2048,88.55583,10.58694,6.12,1.47],[2049,87.72167,-52.10889,5.17,0.99],[2050,88.63417,11.7625,6.59,0.03],[2051,88.56542,3.22528,6.31,1.29],[2052,88.73625,19.74972,5.92,-0.17],[2053,88.13833,-37.63111,5.63,1.04],[2054,89.27042,49.02944,6.47,0.99],[2055,88.19875,-38.52583,6.7,1.08],[2056,88.27875,-33.80139,4.87,-0.15],[2057,88.68375,0.96833,6.0,1.34],[2058,88.64458,-4.06389,6.57,-0.18],[2059,82.55792,-84.785,6.2,-0.02],[2060,88.48917,-19.63833,6.69,0.1],[2061,88.79292,7.40694,0.5,1.85],[2062,86.95042,-72.70222,6.53,1.08],[2063,88.95542,20.175,5.4,0.99],[2064,87.47333,-66.90111,5.11,-0.14],[2065,88.68167,-11.77389,5.66,1.53],[2066,89.14083,28.94222,6.32,0.3],[2067,89.01458,13.92528,6.6,0.65],[2068,88.55875,-29.14778,6.36,0.37],[2069,88.34542,-42.92139,6.55,1.37],[2070,88.87625,-4.61639,5.87,1.18],[2071,88.8975,-4.78833,6.28,0.06],[2072,88.08458,-57.15611,5.94,0.66],[2073,87.84583,-64.03361,6.36,0.86],[2074,89.23375,24.24972,6.02,0.39],[2075,89.11667,9.50972,5.99,-0.07],[2076,89.20625,11.52111,5.87,1.1],[2077,89.88167,54.28472,3.72,1.0],[2078,91.28875,75.58583,6.4,0.6],[2079,89.94042,55.32083,6.44,0.31],[2080,89.95042,54.54722,6.14,1.2],[2081,89.84083,49.92444,5.89,1.23],[2082,88.71875,-39.95806,5.57,1.51],[2083,88.54458,-50.36194,6.52,0.9],[2084,89.49875,25.95389,4.82,-0.06],[2085,89.10125,-14.16778,3.71,0.33],[2086,89.05958,-22.84028,5.96,1.11],[2087,88.87458,-37.12083,4.97,1.11],[2088,89.88208,44.9475,1.9,0.03],[2089,88.67125,-49.62694,6.1,-0.13],[2090,89.14375,-23.21556,6.36,1.07],[2091,89.98375,45.93694,4.26,1.72],[2092,89.08708,-31.3825,5.5,0.6],[2093,89.47583,1.22444,6.22,1.48],[2094,88.70917,-52.63528,5.29,0.31],[2095,89.93042,37.2125,2.62,-0.08],[2096,90.07917,44.59194,6.22,0.6],[2097,89.54875,-0.99417,6.22,1.14],[2098,89.20417,-31.97611,6.44,1.07],[2099,89.72167,12.80861,5.7,0.89],[2100,89.60167,1.83694,5.9,0.21],[2101,90.24417,47.90194,5.73,-0.01],[2102,88.52542,-63.09,4.65,1.05],[2103,89.70667,0.55306,5.22,0.01],[2104,88.54958,-64.48222,6.63,0.38],[2105,90.42958,48.95944,5.96,1.45],[2106,89.38417,-35.28333,4.36,-0.18],[2107,89.75417,-9.38222,6.12,0.29],[2108,89.76792,-9.55833,5.03,0.19],[2109,89.90708,-1.44444,6.63,-0.07],[2110,90.2925,31.03472,5.98,0.08],[2111,90.25167,27.57222,6.05,0.25],[2112,90.70292,49.90556,6.05,-0.06],[2113,90.01417,-3.07417,4.53,1.22],[2114,89.31,-53.42611,6.45,1.48],[2115,90.72333,43.37861,6.42,0.6],[2116,90.42333,22.40083,6.37,-0.07],[2117,89.65667,-44.03444,5.81,1.07],[2118,90.07375,-12.89972,6.22,0.36],[2119,90.825,42.91167,6.1,0.97],[2120,89.78667,-42.81528,3.96,1.14],[2121,91.28458,59.39306,6.34,1.1],[2122,90.72958,32.63583,6.24,0.42],[2123,91.12125,51.57333,6.45,0.18],[2124,90.59583,9.6475,4.12,0.16],[2125,87.56958,-79.36139,5.47,-0.08],[2126,91.66333,63.45361,6.39,0.6],[2127,90.57125,1.69444,6.59,-0.05],[2128,90.46,-10.59806,4.95,-0.12],[2129,90.30458,-25.41778,6.05,0.02],[2130,90.86375,19.69056,5.14,-0.11],[2131,90.31833,-33.91167,5.55,1.58],[2132,91.26417,42.98167,5.87,0.3],[2133,90.85292,11.68083,6.08,-0.04],[2134,91.03,23.26333,4.16,0.82],[2135,90.98,20.13833,4.63,0.28],[2136,90.64083,-14.49722,6.2,0.96],[2137,91.26083,37.96417,6.34,0.6],[2138,90.205,-51.21639,5.67,0.2],[2139,91.39167,33.59917,6.23,-0.08],[2140,90.81458,-26.28444,5.04,1.34],[2141,91.53542,35.3875,6.12,0.6],[2142,91.05625,-6.70917,5.21,-0.06],[2143,91.64625,38.48278,5.36,0.25],[2144,91.2425,5.42,5.67,1.04],[2145,91.24333,4.15861,5.63,1.04],[2146,91.59375,29.5125,6.08,1.73],[2147,91.86208,41.85417,6.12,1.22],[2148,91.24625,-16.48444,4.93,0.24],[2149,91.08458,-32.1725,5.65,-0.19],[2150,91.3625,-10.24278,5.87,0.37],[2151,90.53833,-60.09694,6.45,1.58],[2152,92.49625,58.93583,5.36,1.09],[2153,92.09583,41.05556,6.36,1.05],[2154,91.66125,-4.19389,5.38,-0.13],[2155,91.53875,-14.93528,4.67,0.05],[2156,91.44042,-24.19556,6.95,1.63],[2157,91.11833,-45.03667,6.35,0.52],[2158,91.1675,-45.07889,5.93,0.49],[2159,91.89292,14.76833,4.42,-0.17],[2160,91.36292,-35.51361,5.8,0.02],[2161,91.71625,-11.17361,6.66,-0.15],[2162,91.19542,-48.45861,6.58,0.72],[2163,91.63333,-23.11056,5.47,0.08],[2164,91.52292,-29.75861,5.81,0.05],[2165,93.21292,65.71833,5.32,1.34],[2166,91.74,-21.81278,5.78,1.64],[2167,92.19667,8.67,6.55,-0.07],[2168,91.92333,-19.16583,5.31,1.68],[2169,92.385,22.19,5.93,1.63],[2170,91.76542,-34.31194,5.83,-0.13],[2171,91.67083,-42.29861,6.12,0.25],[2172,92.94167,52.64722,6.3,0.14],[2173,92.43333,23.11333,5.75,0.21],[2174,92.24125,2.49944,5.73,0.07],[2175,92.90208,48.71306,6.82,0.6],[2176,92.9025,48.71111,6.09,0.1],[2177,91.88167,-37.25306,5.02,-0.11],[2178,91.75792,-45.09139,6.51,1.16],[2179,92.40083,-5.71111,6.17,0.34],[2180,92.24125,-22.4275,5.5,-0.01],[2181,91.97042,-42.15389,5.5,0.0],[2182,92.33458,-18.12611,6.35,-0.03],[2183,92.39292,-14.58417,5.56,1.16],[2184,92.7575,18.12944,6.33,1.35],[2185,92.88458,24.42028,5.8,1.11],[2186,92.44958,-22.77417,5.71,0.44],[2187,92.14417,-44.35611,6.27,-0.15],[2188,93.43875,51.1725,6.04,1.06],[2189,93.08375,32.69333,5.78,1.66],[2190,92.96417,21.86861,6.56,2.25],[2191,92.86625,13.63861,6.04,0.0],[2192,92.44667,-26.70083,6.27,1.01],[2193,93.00542,19.79056,5.75,-0.07],[2194,91.53917,-66.03972,5.71,-0.03],[2195,92.75542,-6.75417,6.15,0.01],[2196,91.76417,-62.15472,5.05,1.25],[2197,93.07958,22.90833,6.39,2.24],[2198,93.01375,16.13056,4.95,-0.14],[2199,92.985,14.20889,4.48,-0.18],[2200,92.64417,-27.15417,5.72,1.07],[2201,93.91917,59.99917,5.35,1.34],[2202,92.93208,-4.66556,6.18,-0.08],[2203,92.54292,-40.35361,5.58,1.68],[2204,92.34708,-49.56278,6.49,0.52],[2205,92.96583,-6.55028,5.05,-0.2],[2206,92.80625,-26.48222,6.09,-0.04],[2207,93.38917,18.68028,6.58,-0.08],[2208,93.3025,10.6275,6.45,0.67],[2209,94.71167,69.31972,4.8,0.03],[2210,93.185,-2.50444,6.62,0.05],[2211,92.66625,-45.28194,6.31,-0.03],[2212,92.57458,-54.96861,4.81,-0.23],[2213,93.19292,-17.76306,6.52,-0.17],[2214,93.61917,17.90639,5.88,0.22],[2215,94.47833,61.51528,4.98,1.83],[2216,93.71917,22.50667,3.28,1.6],[2217,93.9125,36.14861,6.92,0.45],[2218,93.47625,-3.74139,5.83,0.94],[2219,93.84458,29.49806,4.35,1.02],[2220,93.71208,19.15639,5.2,0.44],[2221,92.18417,-68.84333,5.06,-0.08],[2222,93.78542,13.85111,5.91,-0.23],[2223,93.85458,16.14306,5.3,-0.14],[2224,93.65292,-4.56833,5.83,-0.17],[2225,93.43792,-23.86194,6.39,0.72],[2226,93.38875,-29.39611,6.54,-0.1],[2227,93.71375,-6.27472,3.98,1.32],[2228,94.39458,46.42417,6.52,0.27],[2229,93.9375,12.55111,5.33,-0.02],[2230,94.07917,23.97,6.08,0.9],[2231,93.91708,6.06611,6.07,-0.13],[2232,93.94583,4.28361,6.64,-0.17],[2233,93.89292,-0.51222,5.65,0.5],[2234,93.87375,-4.91528,5.99,0.09],[2235,94.09917,17.18139,6.39,1.58],[2236,93.975,1.16917,6.37,0.46],[2237,93.85833,-9.03528,6.1,-0.08],[2238,94.90583,59.01083,4.48,0.01],[2239,94.57042,46.36056,6.38,1.11],[2240,94.24458,23.74083,6.25,0.45],[2241,94.11083,12.27222,5.04,0.42],[2242,93.785,-20.27222,5.91,1.32],[2243,93.82292,-18.47667,5.99,1.06],[2244,93.93708,-13.71833,5.01,-0.08],[2245,92.8125,-65.58944,5.01,1.62],[2246,94.08833,1.08028,6.63,-0.05],[2247,94.2775,9.9425,5.39,0.1],[2248,94.24333,7.05306,6.57,-0.12],[2249,94.03208,-16.61778,5.92,-0.17],[2250,94.38875,14.05833,6.59,-0.03],[2251,94.31708,5.10028,5.71,0.61],[2252,93.98833,-29.78833,6.67,1.55],[2253,94.52333,14.38278,6.16,0.01],[2254,94.26458,-22.715,6.07,0.56],[2255,94.39667,-10.72528,6.75,0.35],[2256,94.13792,-35.14056,4.37,1.0],[2257,95.515,59.37222,5.94,0.6],[2258,94.7575,17.325,6.32,-0.07],[2259,94.66875,9.04722,6.24,0.87],[2260,94.42375,-16.81583,5.14,1.3],[2261,92.56,-74.75306,5.09,0.72],[2262,94.14833,-39.26444,6.0,0.16],[2263,94.255,-37.7375,5.53,1.14],[2264,95.44208,53.45222,5.36,0.43],[2265,94.28958,-37.25306,5.87,0.14],[2266,94.55708,-19.96694,5.52,-0.18],[2267,94.71083,-9.39028,5.36,1.24],[2268,94.70333,-15.02472,6.06,1.66],[2269,95.0175,14.65111,5.69,1.61],[2270,94.78292,-8.58639,6.22,-0.04],[2271,94.74583,-20.92611,5.81,-0.15],[2272,95.30042,29.54111,6.43,0.06],[2273,94.92833,-7.82306,5.27,-0.19],[2274,94.07708,-59.21361,6.43,0.59],[2275,94.99833,-2.94444,4.9,1.6],[2276,95.21792,11.75639,6.54,-0.1],[2277,95.35792,17.76361,6.35,0.6],[2278,94.46542,-52.73306,6.41,1.46],[2279,94.92083,-34.39667,5.78,-0.08],[2280,95.3575,2.26861,6.31,0.24],[2281,94.695,-50.35917,7.04,0.83],[2282,95.07833,-30.06333,3.02,-0.19],[2283,93.77458,-71.70278,6.64,0.56],[2284,95.35292,-11.77333,5.64,-0.02],[2285,97.06083,70.53556,5.97,0.6],[2286,95.74,22.51361,2.88,1.64],[2287,95.65208,12.57,6.0,0.6],[2288,95.15125,-34.14389,5.53,-0.19],[2289,96.22458,49.28806,4.91,1.97],[2290,95.02542,-48.74111,6.6,0.66],[2291,96.6075,56.285,5.64,0.24],[2292,95.82708,3.76444,6.4,-0.15],[2293,96.70375,58.41722,5.21,1.53],[2294,95.675,-17.95583,1.98,-0.23],[2295,95.84458,-4.68722,6.67,0.06],[2296,95.52833,-33.43639,3.85,0.88],[2297,96.21917,29.70722,6.71,-0.06],[2298,95.94208,4.59278,4.44,0.18],[2299,95.94375,4.59556,6.72,0.45],[2300,96.00958,8.88472,6.26,-0.08],[2301,95.9,-9.87444,6.19,1.84],[2302,96.22042,16.05694,6.33,1.08],[2303,95.94167,-15.07167,6.24,1.53],[2304,96.38708,23.32694,6.06,-0.03],[2305,96.04292,-11.53028,5.22,1.24],[2306,95.94833,-19.78528,6.6,-0.15],[2307,95.81,-31.79,6.34,0.89],[2308,96.36708,14.72194,6.24,2.34],[2309,96.08542,-12.9625,6.12,-0.08],[2310,96.30458,7.08583,5.98,1.22],[2311,95.98292,-25.57778,5.63,1.56],[2312,96.32667,1.50111,6.66,-0.04],[2313,96.31833,-0.94611,5.87,0.56],[2314,96.96292,47.40528,6.56,-0.04],[2315,96.44417,2.27222,6.51,-0.03],[2316,96.00417,-36.70778,5.62,1.04],[2317,96.44625,-3.88917,6.35,1.02],[2318,96.18292,-28.78,6.39,0.62],[2319,96.89792,32.56306,6.43,1.26],[2320,95.7325,-56.37,5.61,0.24],[2321,96.495,-7.89417,6.4,0.14],[2322,95.90708,-52.18111,5.98,1.04],[2323,96.18542,-40.28417,6.31,-0.05],[2324,96.665,-1.50722,5.87,0.08],[2325,96.64375,-4.59722,6.15,-0.14],[2326,95.98792,-52.69583,-0.72,0.15],[2327,96.74458,0.84083,6.71,0.04],[2328,96.68708,-7.51139,6.27,-0.04],[2329,96.37458,-35.06389,6.25,1.36],[2330,96.98583,20.49611,6.22,0.01],[2331,97.69667,58.16278,5.88,0.94],[2332,97.14208,30.49306,5.55,0.68],[2333,96.835,2.90806,5.55,1.04],[2334,96.8075,0.29917,5.2,1.18],[2335,96.815,-0.27611,5.55,1.38],[2336,95.94542,-58.54389,6.48,0.12],[2337,95.75542,-63.68306,6.27,1.6],[2338,97.5125,46.68556,5.9,1.44],[2339,97.23583,26.96778,6.47,0.6],[2340,97.11667,16.23833,6.23,0.9],[2341,96.20083,-52.80639,6.51,1.7],[2342,97.07833,10.30389,6.15,1.15],[2343,97.24083,20.21222,4.15,-0.13],[2344,96.99,-4.76222,5.06,-0.17],[2345,96.05708,-60.28111,5.8,0.0],[2346,100.07,79.59944,6.54,0.6],[2347,97.07,1.91222,6.48,-0.07],[2348,96.43167,-48.17722,5.76,-0.06],[2349,96.79667,-25.85667,6.07,0.53],[2350,101.12583,82.11528,6.65,0.17],[2351,97.25,11.01944,6.59,0.6],[2352,95.65917,-69.98417,5.56,1.51],[2353,96.78125,-37.89556,6.48,0.39],[2354,96.10958,-63.42889,6.46,0.66],[2355,97.31208,2.64611,6.16,1.54],[2356,97.20417,-7.03278,4.6,-0.1],[2357,97.20625,-7.03444,5.4,-0.07],[2358,97.20625,-7.03444,5.6,0.6],[2359,97.15542,-17.46611,5.77,1.12],[2360,96.23167,-63.82778,6.27,-0.13],[2361,97.04208,-32.58,4.48,-0.17],[2362,97.52292,9.02917,6.57,0.14],[2363,100.12,77.99583,5.73,1.47],[2364,97.16333,-32.37111,5.74,-0.17],[2365,99.47875,73.69556,6.24,0.38],[2366,97.79208,16.93861,6.2,1.16],[2367,97.54708,-10.08139,5.93,1.38],[2368,97.17625,-41.07444,6.32,0.4],[2369,96.76667,-58.00222,5.82,1.28],[2370,97.78958,11.25083,6.14,-0.08],[2371,97.90583,15.90333,6.4,0.6],[2372,98.11333,32.45472,5.87,0.14],[2373,97.64458,-13.14806,6.16,-0.15],[2374,97.91333,11.79222,6.65,-0.12],[2375,97.95125,11.54444,5.23,0.15],[2376,98.63667,55.35306,6.45,0.6],[2377,96.36917,-69.69028,5.38,0.97],[2378,98.09708,11.67361,6.03,1.07],[2379,97.84583,-12.39167,5.15,1.27],[2380,97.69292,-27.76944,5.93,-0.15],[2381,97.95875,-8.15806,5.43,1.38],[2382,98.08,4.85583,5.84,0.99],[2383,98.42792,33.02417,6.42,0.03],[2384,97.45458,-50.23917,5.27,0.41],[2385,98.22583,7.33306,4.5,0.0],[2386,98.09625,-5.86889,5.6,0.25],[2387,97.96375,-23.41833,4.33,-0.24],[2388,97.80417,-35.25917,5.84,0.81],[2389,97.36875,-56.85278,5.22,1.09],[2390,97.74917,-40.91639,6.2,1.4],[2391,98.40042,14.15528,5.53,1.11],[2392,98.19542,-11.16639,6.24,1.11],[2393,97.89583,-36.94,6.34,1.63],[2394,99.4225,61.48111,5.94,0.89],[2395,98.40792,-1.22028,5.1,-0.14],[2396,100.13417,71.74889,5.92,1.19],[2397,98.1625,-32.03056,5.69,-0.17],[2398,98.80042,28.02222,5.27,-0.03],[2399,98.08875,-37.69667,5.24,1.0],[2400,97.82625,-51.82611,5.6,0.54],[2401,101.55875,79.56472,5.45,0.5],[2402,99.41042,56.8575,5.85,0.6],[2403,98.36083,-20.92389,6.4,0.83],[2404,98.69333,7.5725,6.45,-0.02],[2405,99.13708,38.44528,5.29,2.61],[2406,98.82333,9.98833,5.88,1.51],[2407,98.29292,-38.62528,6.44,1.0],[2408,97.5125,-65.56833,6.29,0.33],[2409,98.81583,0.89,5.8,0.0],[2410,97.79417,-61.87972,6.15,-0.15],[2411,98.45625,-36.23222,5.42,1.44],[2412,97.99333,-58.75417,5.7,-0.06],[2413,99.0,4.4975,6.55,-0.06],[2414,98.76417,-22.96472,4.54,-0.05],[2415,98.64708,-32.71639,5.62,-0.08],[2416,98.35875,-52.32889,6.19,1.09],[2417,99.36333,24.59083,6.44,0.1],[2418,99.14708,-5.21111,5.52,-0.08],[2419,99.66458,39.39083,5.69,1.35],[2420,99.705,39.9025,5.2,-0.07],[2421,99.42792,16.39917,1.93,0.0],[2422,99.35042,6.13528,6.06,0.05],[2423,99.095,-18.66,5.7,0.85],[2424,98.85042,-36.78,5.59,-0.14],[2425,99.59583,28.98417,5.79,0.0],[2426,99.40375,10.85306,6.38,0.6],[2427,99.83292,42.48889,4.79,1.23],[2428,99.19458,-13.32083,5.97,1.56],[2429,99.17083,-19.25583,3.95,1.06],[2430,99.41792,2.70417,6.17,1.08],[2431,98.975,-36.08889,6.35,0.48],[2432,99.46958,4.95722,6.15,0.14],[2433,99.17042,-22.615,6.35,-0.11],[2434,99.99167,44.01389,6.41,0.6],[2435,98.74417,-52.97556,4.39,-0.02],[2436,99.77208,22.03083,6.04,1.03],[2437,99.42042,-12.985,6.12,1.0],[2438,99.88792,28.26306,6.03,-0.08],[2439,99.88083,24.6,6.38,0.53],[2440,99.58542,-2.54361,6.14,1.48],[2441,99.70625,4.70056,6.57,-0.07],[2442,99.65875,1.61361,6.21,0.15],[2443,99.4725,-18.2375,4.43,1.15],[2444,99.25792,-38.14667,6.04,1.03],[2445,99.21375,-41.55694,6.34,1.15],[2446,99.3075,-36.99056,5.71,-0.12],[2447,99.44833,-32.33972,5.27,1.18],[2448,99.6475,-16.87361,6.03,0.03],[2449,99.94833,12.98306,5.97,0.06],[2450,99.81958,-14.14583,4.82,1.5],[2451,99.44042,-43.19611,3.17,-0.11],[2452,100.40708,35.93194,6.46,0.49],[2453,100.3375,28.19639,6.42,1.09],[2454,100.1325,6.37167,6.51,-0.14],[2455,99.90125,-23.69556,6.05,-0.03],[2456,100.24458,9.89556,4.66,-0.25],[2457,100.34083,16.3975,6.28,-0.01],[2458,100.32167,11.00333,6.11,1.68],[2459,100.77083,44.52444,5.02,1.48],[2460,99.92792,-30.47028,5.71,1.14],[2461,100.2725,0.49528,5.79,-0.1],[2462,99.65667,-48.22028,4.93,0.87],[2463,101.04833,53.29639,6.27,1.08],[2464,100.8075,37.14694,6.19,1.03],[2465,99.98708,-38.15889,6.58,1.18],[2466,100.60125,17.64528,5.21,0.06],[2467,100.49708,6.345,6.37,-0.05],[2468,99.5025,-61.53306,6.18,0.62],[2469,100.485,-9.16722,5.19,1.53],[2470,101.55875,59.44167,4.87,0.08],[2471,101.0525,36.10972,6.31,0.06],[2473,100.98292,25.13111,2.98,1.4],[2474,100.77708,3.03333,6.19,1.37],[2475,100.30875,-40.34972,6.12,-0.14],[2476,100.20542,-47.67472,6.65,1.58],[2477,101.70625,57.16917,5.35,0.96],[2478,100.99708,13.22778,4.49,1.16],[2479,100.91125,3.93222,5.9,-0.02],[2480,101.18958,28.97083,5.44,1.45],[2481,100.69083,-22.44917,6.13,0.34],[2482,100.56833,-38.39861,6.29,0.34],[2483,101.68458,43.5775,5.25,0.56],[2484,101.3225,12.89556,3.36,0.43],[2485,102.05375,55.70444,6.33,0.6],[2486,102.05125,55.70444,6.28,0.47],[2487,101.915,48.78944,5.22,1.12],[2488,100.84708,-39.19333,6.3,0.26],[2489,101.47583,12.69361,6.46,0.6],[2490,102.73792,67.57194,5.14,-0.17],[2491,101.28708,-16.71611,-1.46,0.0],[2492,101.11833,-31.07056,5.2,-0.12],[2493,101.21625,-27.34139,6.45,0.54],[2494,101.635,8.58722,5.93,-0.17],[2495,101.34708,-23.46194,6.05,1.2],[2497,101.26,-30.58611,6.54,-0.11],[2498,101.49708,-14.79611,5.32,0.07],[2499,101.84792,18.19333,6.2,0.07],[2500,101.345,-31.79361,5.92,0.48],[2501,101.38042,-30.94889,5.8,-0.19],[2502,101.6625,-10.10722,5.66,-0.05],[2503,101.8325,8.03722,4.77,1.4],[2504,101.71292,-14.42583,5.29,-0.04],[2505,100.24083,-71.77556,6.51,1.11],[2506,101.965,2.41222,4.47,1.11],[2507,101.51375,-39.54,6.62,-0.13],[2508,101.90458,-8.99833,5.07,1.8],[2509,101.75625,-21.01556,6.08,-0.19],[2510,101.55042,-37.77556,6.21,-0.13],[2511,103.42583,68.88833,5.12,-0.13],[2512,102.42208,32.60667,5.71,1.29],[2513,101.35875,-52.20111,6.57,1.08],[2514,102.07917,-1.31917,5.75,0.28],[2515,101.47375,-52.41,5.8,1.53],[2516,102.69125,41.78139,5.02,1.27],[2517,102.26542,1.00194,6.15,-0.13],[2518,101.83917,-37.92972,5.26,-0.08],[2519,102.4575,16.20278,5.85,-0.13],[2520,103.27125,59.44861,5.33,0.65],[2521,102.31833,-2.27194,5.74,-0.1],[2522,102.24083,-15.14472,5.39,-0.1],[2523,101.72,-51.26583,5.4,1.34],[2524,101.67292,-54.69472,6.46,0.86],[2525,102.60625,13.41333,5.65,1.34],[2526,101.82792,-55.54,5.61,1.52],[2527,105.01667,76.9775,4.55,1.36],[2528,102.43333,-24.07583,6.33,0.04],[2529,102.8875,21.76111,5.27,-0.02],[2530,102.70792,-0.54083,5.77,0.39],[2531,100.90333,-73.11806,6.37,0.96],[2532,103.28167,44.83944,6.26,0.21],[2533,103.0,23.60167,5.65,1.45],[2534,102.67625,-8.04111,6.29,0.0],[2535,102.59125,-17.08389,5.79,1.44],[2536,101.23375,-70.43389,6.11,1.33],[2537,102.525,-27.33389,7.04,-0.18],[2538,102.46042,-32.50861,3.96,-0.23],[2539,103.25625,38.86917,6.12,0.37],[2540,103.19708,33.96111,3.6,0.1],[2541,103.30583,38.43806,6.3,0.49],[2542,103.26417,35.78861,6.01,1.45],[2543,102.91375,3.04167,6.38,0.04],[2544,102.65375,-25.77806,6.33,-0.18],[2545,102.59708,-31.70611,5.7,0.14],[2546,102.49083,-45.45,6.55,1.51],[2547,103.4875,38.505,6.48,-0.05],[2548,102.4775,-46.61472,5.14,0.45],[2549,102.71833,-34.36722,4.99,1.38],[2550,102.0475,-61.94139,3.27,0.21],[2551,103.20583,8.38028,5.77,0.26],[2552,103.09542,-5.31611,6.3,0.99],[2553,102.48417,-50.61472,2.93,1.2],[2554,102.46375,-53.62222,4.4,0.92],[2555,103.34375,10.99639,6.24,0.97],[2556,103.81333,45.82639,6.34,0.94],[2557,103.81125,43.91,6.13,0.32],[2558,102.92625,-36.23028,5.96,0.18],[2559,100.01125,-80.81361,5.64,0.2],[2560,104.31875,58.4225,4.35,0.85],[2561,104.305,57.56333,6.05,1.49],[2562,102.50458,-60.24917,6.11,0.46],[2563,102.88667,-48.2925,6.42,1.21],[2564,103.66125,13.17778,4.65,0.3],[2565,103.32833,-19.03278,5.64,0.28],[2566,103.34042,-18.93333,6.14,0.15],[2567,103.25042,-26.9575,6.4,1.53],[2568,104.13458,46.27417,5.87,-0.06],[2569,103.8275,25.37556,5.73,0.57],[2570,103.53542,-5.8525,6.41,0.17],[2571,103.38708,-20.22417,4.83,-0.21],[2572,103.6025,-1.12694,5.45,0.18],[2573,104.23333,46.705,5.86,1.08],[2574,103.5475,-12.03861,4.07,1.43],[2575,103.16542,-42.50444,6.52,0.42],[2576,103.39125,-28.53972,6.04,0.71],[2577,103.67542,-1.75639,6.21,0.56],[2578,103.48042,-24.53917,6.21,0.01],[2579,103.19625,-43.97583,6.46,-0.1],[2580,103.53292,-24.18389,3.87,1.73],[2581,105.33958,70.80806,5.68,1.33],[2582,103.745,-2.80361,6.04,1.1],[2583,103.55417,-23.92833,6.91,-0.28],[2584,103.89417,8.32472,6.29,0.04],[2585,104.40458,45.09417,4.9,0.03],[2586,104.25208,33.68111,5.89,0.88],[2587,103.19542,-54.09,6.57,1.08],[2588,103.76125,-20.40472,5.74,0.08],[2589,104.1075,9.95639,5.92,-0.08],[2590,103.90583,-20.13639,4.68,0.37],[2591,103.61125,-42.36556,6.32,2.24],[2592,103.18917,-59.34111,6.41,0.18],[2593,104.0275,-14.04361,5.0,1.18],[2594,103.50958,-50.61167,6.26,0.99],[2595,103.945,-22.94139,5.3,-0.18],[2596,104.03417,-17.05417,4.37,-0.07],[2597,104.35708,11.9075,6.27,0.34],[2598,103.97833,-31.79,6.36,0.6],[2599,104.25042,-8.17889,6.34,0.64],[2600,104.76167,38.05222,6.0,1.23],[2601,104.6975,26.08111,6.1,0.46],[2602,102.8625,-70.96333,5.4,-0.11],[2603,104.31167,-22.20333,6.61,-0.19],[2604,104.19042,-35.34167,6.29,1.29],[2605,104.86625,25.91417,6.4,-0.11],[2606,104.6625,7.62194,6.27,0.11],[2607,104.39125,-24.63056,5.46,0.36],[2608,104.06667,-48.72111,4.95,1.69],[2609,115.12708,87.02,5.07,1.63],[2610,104.7375,3.60222,5.97,1.06],[2611,104.42667,-27.5375,6.23,-0.14],[2612,104.32333,-35.5075,6.23,0.46],[2613,104.83375,7.31694,6.35,-0.11],[2614,104.53167,-27.16472,6.37,-0.19],[2615,105.06583,16.07889,5.68,1.66],[2616,104.64958,-25.41389,5.59,-0.16],[2617,106.46583,70.73194,6.5,0.6],[2618,104.65625,-28.97222,1.5,-0.21],[2619,104.60458,-34.11167,5.06,-0.16],[2620,105.32167,32.41444,6.59,0.27],[2621,104.6825,-30.99778,6.42,-0.14],[2622,105.075,-5.36694,6.3,0.57],[2623,104.91375,-21.60333,6.26,-0.15],[2624,105.09875,-8.40694,5.96,-0.08],[2625,105.03375,-20.15889,6.31,-0.15],[2626,104.67417,-45.76806,6.22,0.0],[2627,105.16375,-9.20306,6.49,0.21],[2628,105.08042,-22.11944,6.53,-0.17],[2629,105.4225,4.81806,6.63,0.06],[2630,105.60333,24.21528,5.18,0.94],[2631,105.60625,17.75556,5.94,1.63],[2632,105.5725,15.33611,5.74,0.6],[2633,105.47917,5.5575,6.59,-0.02],[2634,104.665,-55.72944,6.27,1.16],[2635,105.63958,16.67417,5.82,1.68],[2636,105.47042,-1.34556,6.17,1.28],[2637,105.1775,-28.48944,6.27,0.45],[2638,104.65083,-56.39472,6.45,0.39],[2639,105.485,-5.72222,5.2,1.68],[2640,105.27458,-25.21528,5.63,-0.17],[2641,105.2075,-33.46528,6.4,1.05],[2642,106.50542,59.80194,6.44,0.6],[2643,105.87667,29.33722,5.93,0.6],[2644,106.41583,52.75806,6.12,0.11],[2645,106.2875,47.775,6.38,-0.04],[2646,105.42958,-27.93472,3.47,1.73],[2647,105.82458,9.13833,5.97,0.12],[2648,105.72833,-4.23917,4.99,-0.2],[2649,105.90833,10.95167,5.13,1.39],[2650,106.02708,20.57028,3.79,0.79],[2651,105.965,12.59444,5.98,1.58],[2652,105.21458,-51.4025,5.14,1.61],[2653,105.75625,-23.83333,3.02,-0.08],[2654,106.08417,1.48833,6.57,0.01],[2655,106.02167,-5.32361,5.62,1.29],[2656,105.98875,-10.12417,6.45,-0.08],[2657,105.93958,-15.63333,4.12,-0.12],[2658,105.565,-43.40417,6.43,-0.04],[2659,106.32667,22.63722,6.02,-0.03],[2660,106.54833,34.47389,5.55,0.91],[2661,105.27125,-58.94,6.02,0.3],[2662,104.96042,-67.91611,5.17,1.4],[2663,106.41292,9.18583,5.78,1.52],[2664,106.19625,-22.03222,6.09,1.22],[2665,106.84292,34.00944,5.91,1.51],[2666,106.01167,-42.33722,5.2,0.2],[2667,105.98875,-43.60806,5.54,0.64],[2668,105.995,-43.61167,6.79,0.8],[2669,106.85417,28.17722,6.48,-0.09],[2670,106.45708,-10.66111,6.49,-0.05],[2671,106.83917,22.70361,7.68,2.21],[2672,105.97375,-49.58389,4.93,0.13],[2673,107.05542,33.83222,6.28,1.34],[2674,105.815,-59.17806,5.5,-0.11],[2675,107.15125,37.445,6.16,1.21],[2676,106.77667,4.91028,6.11,-0.13],[2677,106.38333,-34.77778,6.14,0.37],[2678,106.66958,-11.29417,5.39,0.05],[2679,106.64958,-12.39389,6.48,-0.1],[2680,106.5025,-30.65556,6.34,-0.16],[2681,108.49208,71.81667,6.35,1.12],[2682,106.95625,7.47111,5.75,1.18],[2683,106.07625,-56.74972,5.17,-0.04],[2684,107.09167,15.93083,5.44,1.03],[2685,106.50958,-38.38278,6.11,0.7],[2686,106.71792,-24.96056,6.08,1.34],[2687,106.31875,-50.36028,6.46,0.6],[2688,106.75042,-26.65778,6.62,-0.17],[2689,104.14333,-79.42028,5.45,0.05],[2690,106.84417,-23.84028,5.71,-0.1],[2691,106.77958,-40.89333,5.79,-0.17],[2692,107.52792,21.24694,6.43,0.89],[2693,107.09792,-26.39333,1.84,0.68],[2694,107.33458,-10.34722,6.21,0.03],[2695,107.20542,-24.04417,6.65,-0.19],[2696,107.91375,39.32056,4.9,1.45],[2697,107.785,30.24528,4.41,1.26],[2698,106.80542,-51.96778,5.96,1.0],[2699,107.38833,-16.23472,6.03,0.06],[2700,107.84625,26.85667,5.78,0.1],[2701,107.55708,-4.23722,4.92,1.03],[2702,107.21292,-39.65583,4.83,-0.18],[2703,108.3475,51.42889,5.47,1.67],[2704,107.42875,-25.23111,5.69,-0.16],[2705,107.53875,-18.68528,6.23,0.4],[2706,108.11,24.12833,5.85,0.36],[2707,107.84833,-0.30194,5.45,0.29],[2708,107.58083,-27.49139,5.46,1.0],[2709,111.34125,81.2575,6.31,-0.04],[2710,107.96375,5.65472,6.09,-0.02],[2711,108.20417,27.22472,6.43,0.49],[2712,106.55875,-68.83722,6.47,1.04],[2713,108.03083,5.47472,6.16,1.14],[2714,107.96625,-0.49278,4.15,-0.01],[2715,108.97875,59.6375,5.2,1.07],[2716,107.92333,-20.88306,5.84,-0.04],[2717,108.34292,16.15889,5.0,1.66],[2718,108.05083,-25.9425,5.92,-0.17],[2719,107.69792,-48.93222,5.14,1.24],[2720,108.01708,-30.82167,6.1,0.27],[2721,108.95875,47.24,5.58,0.58],[2722,108.61083,24.71083,6.89,-0.03],[2723,108.28,-11.25139,5.78,1.51],[2724,108.10042,-27.47417,6.59,0.19],[2725,108.67458,24.885,5.82,1.56],[2726,108.10708,-36.54444,5.96,-0.14],[2727,108.06583,-40.49889,5.31,0.06],[2728,108.63583,12.11583,5.62,1.01],[2729,108.58333,3.11139,5.35,1.19],[2730,108.34958,-22.67333,6.01,1.48],[2731,108.54583,-3.90139,5.75,1.58],[2732,108.56458,-9.9475,5.9,1.52],[2733,108.45125,-22.90639,6.36,-0.21],[2734,108.40125,-27.35639,6.12,-0.23],[2735,107.17583,-70.49722,5.69,0.4],[2736,107.18708,-70.49889,3.78,1.04],[2737,109.39042,52.13083,5.92,1.26],[2738,108.98792,27.8975,5.71,1.63],[2739,108.6175,-10.31667,6.03,-0.18],[2740,108.14,-46.75944,4.49,0.32],[2741,108.44625,-31.08389,6.6,-0.17],[2742,112.76833,82.41139,4.96,1.66],[2743,108.48833,-30.34,6.33,-0.2],[2744,108.83042,-0.16139,6.41,0.9],[2745,108.56333,-26.3525,4.66,-0.19],[2746,108.30583,-45.18306,4.89,-0.02],[2747,108.91417,7.97778,5.82,1.6],[2748,108.385,-44.63972,5.1,1.56],[2749,108.70292,-26.77278,3.85,-0.17],[2750,108.71292,-27.03806,5.58,1.22],[2751,109.63292,49.465,5.05,0.08],[2752,108.92958,-10.58389,5.95,1.18],[2753,109.50917,40.88333,5.78,0.17],[2754,108.00833,-63.19,6.02,-0.02],[2755,108.94792,-23.74056,6.32,0.6],[2756,108.8375,-30.68639,5.36,-0.17],[2757,109.51708,30.95583,6.24,-0.03],[2758,109.06042,-15.58583,5.46,0.08],[2759,108.73792,-41.42583,5.94,-0.16],[2760,109.32417,6.68056,6.65,-0.11],[2761,108.69125,-46.84972,5.72,-0.11],[2762,108.65917,-48.27167,4.76,-0.1],[2763,109.52333,16.54028,3.58,0.11],[2764,109.15333,-23.31556,4.79,1.71],[2765,109.38208,-6.68,6.29,1.62],[2766,109.14583,-27.88111,4.64,1.6],[2767,108.8375,-52.49972,5.97,1.1],[2768,109.23833,-30.89667,6.32,0.2],[2769,109.1325,-38.31889,5.8,-0.13],[2770,109.20625,-36.59278,5.03,-0.17],[2771,109.06458,-46.77444,5.66,1.44],[2772,110.57167,59.90194,6.35,0.6],[2773,109.28583,-37.0975,2.7,1.62],[2774,109.44958,-26.7975,6.46,-0.15],[2775,110.26292,42.65556,6.35,1.46],[2776,110.32292,45.22806,5.77,0.32],[2777,110.03083,21.98222,3.53,0.34],[2778,109.84333,2.74056,5.89,1.07],[2779,109.94833,7.14278,5.91,0.53],[2780,110.02875,15.14278,6.45,-0.02],[2781,109.66792,-24.55889,4.98,-0.15],[2782,109.67667,-24.95417,4.4,-0.15],[2783,110.71208,55.28444,6.53,0.6],[2784,110.71708,55.28139,5.45,0.6],[2785,109.75833,-19.28028,6.09,0.62],[2786,109.71333,-26.58583,5.28,0.96],[2787,109.57667,-36.73417,4.66,-0.1],[2788,109.86708,-16.395,5.7,0.35],[2789,109.5175,-43.98667,5.85,-0.12],[2790,109.65917,-36.74278,5.11,-0.16],[2791,109.64,-39.21028,5.25,0.01],[2792,110.55583,38.99611,6.4,1.22],[2793,110.51083,36.76056,5.13,1.08],[2794,109.80708,-33.72722,6.3,1.31],[2795,110.48667,20.44361,5.1,1.52],[2796,110.2425,-14.36,5.45,0.98],[2797,113.66542,80.89667,6.41,0.6],[2798,110.32042,-8.87833,6.55,0.54],[2799,110.22167,-22.85167,6.61,-0.15],[2800,110.22917,-26.96361,6.01,-0.17],[2801,110.51458,0.17722,5.99,-0.07],[2802,110.26792,-25.89139,5.87,1.64],[2803,109.2075,-67.95722,3.98,0.79],[2804,111.23833,51.88722,5.8,1.61],[2805,111.03542,40.67222,5.19,1.23],[2806,110.50833,-8.97917,6.43,-0.19],[2807,110.57708,-2.97889,6.23,0.68],[2808,110.86875,25.05056,5.03,0.9],[2809,111.8575,66.33167,6.47,-0.09],[2810,110.8675,22.94528,6.02,-0.01],[2811,110.60583,-5.98278,5.82,0.35],[2812,110.55625,-19.01667,4.96,-0.04],[2813,110.08917,-52.31167,6.05,0.42],[2814,110.09042,-52.30972,6.6,0.59],[2815,110.16125,-52.08611,5.39,-0.07],[2816,111.13917,27.63806,5.76,0.34],[2817,111.11542,15.51722,6.41,-0.18],[2818,111.67833,49.21139,4.64,-0.02],[2819,110.7525,-31.92389,5.43,-0.15],[2820,111.2425,11.66972,5.3,0.1],[2821,111.43167,27.79806,3.79,1.03],[2822,110.87125,-27.83417,5.38,1.53],[2823,110.88292,-32.20222,5.39,-0.18],[2824,110.97625,-30.21694,6.6,-0.2],[2825,111.16708,-16.20111,5.33,-0.05],[2826,111.07167,-22.91278,6.19,-0.09],[2827,111.02375,-29.30306,2.45,-0.08],[2828,111.41208,9.27611,4.99,1.01],[2829,110.99292,-35.83778,6.31,-0.15],[2830,112.71958,68.46556,5.64,1.11],[2831,111.21125,-19.01222,6.24,0.29],[2832,111.28458,-13.75194,5.78,0.42],[2833,111.4625,-5.775,5.97,0.92],[2834,111.1825,-31.80889,5.35,1.07],[2835,111.70917,21.53583,6.54,0.46],[2836,111.61625,10.60833,6.37,0.09],[2837,111.73458,20.25722,5.93,0.3],[2838,111.51458,-4.5375,6.76,-0.01],[2839,111.33292,-21.98278,6.05,0.23],[2840,111.67208,11.00917,6.41,-0.13],[2841,111.35542,-25.21778,5.78,-0.1],[2842,111.19667,-37.29,6.97,0.22],[2843,111.19708,-37.29083,6.84,0.27],[2844,112.215,48.18389,5.72,-0.1],[2845,111.7875,8.28944,2.9,-0.09],[2846,111.935,21.445,5.22,0.39],[2847,111.42917,-31.73861,6.31,-0.17],[2848,101.74458,-87.025,6.47,0.42],[2849,112.48333,49.6725,5.36,0.45],[2850,111.66958,-23.71222,6.56,0.01],[2851,112.00875,6.94194,5.25,0.22],[2852,112.27792,31.78444,4.18,0.32],[2853,111.78333,-17.86444,5.63,0.32],[2854,112.04083,8.92556,4.32,1.43],[2855,111.7475,-23.08611,5.61,-0.13],[2856,111.67625,-34.14083,5.9,-0.17],[2857,112.335,28.11806,5.05,0.11],[2858,112.19708,15.10944,6.22,-0.05],[2859,111.96542,-11.55694,5.79,0.58],[2860,111.92875,-22.85972,5.95,-0.09],[2861,112.45292,27.91611,5.01,1.11],[2862,111.59125,-51.01833,5.1,1.06],[2863,111.99667,-29.15583,5.54,-0.08],[2864,112.44917,12.00667,4.54,1.28],[2865,112.32792,-1.90528,5.59,1.5],[2866,112.35708,-7.55111,5.86,0.48],[2867,112.34208,-10.32667,5.75,1.62],[2868,112.34125,-14.99917,6.05,0.47],[2869,112.095,-37.81028,6.58,0.06],[2870,112.21375,-31.84833,6.38,-0.17],[2871,112.21458,-31.84694,7.13,-0.15],[2872,112.98208,38.89639,6.54,0.07],[2873,112.27042,-31.45639,5.77,-0.19],[2874,112.46417,-23.02444,4.85,0.23],[2875,112.27375,-38.81222,5.43,-0.16],[2876,112.71292,-5.22639,6.24,1.18],[2877,112.95167,17.08611,5.42,1.13],[2878,112.3075,-43.30139,3.25,1.51],[2879,113.21083,22.88778,6.54,1.01],[2880,113.02458,1.91444,5.25,0.22],[2881,112.67708,-30.96222,4.65,0.93],[2882,112.67667,-37.33972,6.65,0.63],[2883,113.02417,-8.88083,5.9,0.54],[2884,112.49833,-52.65111,5.87,1.01],[2885,112.8575,-36.15278,6.68,-0.12],[2886,113.40208,15.82667,5.25,0.05],[2887,113.29833,3.29028,5.59,0.31],[2888,112.21375,-64.51,6.39,1.56],[2889,112.92833,-35.88778,6.61,-0.08],[2890,113.65,31.88861,2.88,0.04],[2891,113.65,31.88833,1.98,0.03],[2892,112.62875,-54.39944,5.96,1.56],[2893,113.52125,10.56833,6.28,-0.01],[2894,114.19583,55.75528,5.92,1.12],[2895,113.09292,-35.96139,6.3,-0.1],[2896,113.78625,30.96111,5.33,1.01],[2897,113.34208,-14.33833,6.21,-0.04],[2898,113.98333,43.03111,6.3,0.6],[2899,113.33125,-19.4125,5.66,1.12],[2900,113.29042,-24.71083,5.85,0.17],[2901,113.56583,3.37139,5.81,-0.02],[2902,113.44958,-14.52389,4.97,1.41],[2903,114.13167,46.18028,5.65,1.56],[2904,113.69167,2.725,6.55,0.22],[2905,113.98042,26.89583,4.06,1.54],[2906,113.51333,-22.29611,4.45,0.51],[2907,113.30625,-40.05889,6.26,-0.12],[2908,113.30542,-43.08639,6.52,0.92],[2909,113.5775,-23.47361,5.83,0.44],[2910,113.57958,-23.47472,5.87,0.6],[2911,113.4625,-36.33833,5.54,-0.06],[2912,113.62,-26.11667,6.65,-0.01],[2913,113.55333,-33.46333,6.11,0.29],[2914,114.47458,48.77361,5.92,0.22],[2915,114.32417,40.02528,6.38,0.6],[2916,113.64542,-27.01194,5.77,1.06],[2917,113.49375,-39.90583,6.76,1.13],[2918,114.14458,5.86167,5.91,0.6],[2919,111.40833,-79.09417,5.53,1.28],[2920,114.06917,-8.31139,6.27,1.54],[2921,114.01625,-14.49278,5.7,-0.12],[2922,113.845,-28.36944,4.64,-0.11],[2923,114.0325,-22.16056,6.34,0.99],[2924,114.63667,35.04861,5.56,0.93],[2925,113.66458,-51.47472,6.28,0.08],[2926,114.56042,24.36028,6.27,0.6],[2927,114.31958,-4.11111,5.13,0.44],[2928,114.17083,-19.70222,5.74,-0.19],[2929,115.20625,57.08278,6.06,1.46],[2930,114.79125,34.58417,4.9,0.4],[2931,114.79958,24.2225,6.17,0.01],[2932,114.41208,-14.44111,6.53,-0.01],[2933,114.32,-23.775,6.37,0.54],[2934,113.91542,-52.53389,4.94,1.4],[2935,115.06083,38.34444,5.73,1.63],[2936,114.97542,32.00972,6.17,0.35],[2937,114.34208,-34.96861,4.53,-0.09],[2938,114.86917,17.67472,5.05,1.56],[2939,115.30167,48.13167,5.56,1.01],[2940,114.18292,-48.83028,5.72,-0.06],[2941,114.00708,-55.8875,6.39,1.18],[2942,114.43667,-35.27722,6.6,1.14],[2943,114.82542,5.225,0.38,0.42],[2944,114.575,-25.36472,4.7,-0.11],[2945,114.43833,-38.01056,6.38,1.48],[2946,115.75167,58.71028,4.99,0.08],[2947,114.77958,-18.67917,6.72,-0.1],[2948,114.70542,-26.80167,4.5,-0.17],[2949,114.7075,-26.80361,4.62,0.6],[2950,115.02917,5.23083,6.02,-0.04],[2951,115.24375,23.01861,5.89,1.58],[2952,114.60083,-39.99139,6.59,-0.05],[2953,115.19708,13.77083,6.24,0.6],[2954,114.68292,-36.49694,5.8,-0.16],[2955,114.63583,-38.78111,6.19,1.02],[2956,114.86208,-26.86306,6.5,-0.1],[2957,114.57583,-48.60111,5.68,0.65],[2958,115.14792,-8.18583,6.01,0.15],[2959,115.09667,-15.26361,4.94,1.56],[2960,115.05667,-19.66083,5.93,1.16],[2961,114.86417,-38.30833,4.84,-0.19],[2962,115.68125,34.00028,6.02,0.6],[2963,114.9325,-38.13944,5.73,-0.12],[2964,114.94917,-38.26083,5.76,-0.07],[2965,115.46583,13.48056,5.77,1.67],[2966,115.39667,3.62472,5.94,-0.04],[2967,115.51333,14.20833,5.56,1.64],[2968,114.99167,-37.57944,6.0,-0.04],[2969,116.0175,50.43389,5.27,0.0],[2970,115.31167,-9.55111,3.93,1.02],[2971,114.75167,-53.27333,6.06,-0.11],[2972,115.18083,-27.94583,6.76,-0.16],[2973,115.82792,28.88361,4.28,1.12],[2974,115.21958,-31.66083,6.56,1.18],[2975,116.66708,65.45583,5.92,1.18],[2976,115.34833,-22.33722,6.18,1.62],[2977,116.61417,62.83056,6.49,0.26],[2978,115.8425,22.39944,6.21,0.93],[2979,113.84042,-74.27556,7.16,-0.02],[2980,113.84083,-74.27556,7.26,0.6],[2981,115.31583,-38.53361,5.42,-0.15],[2982,115.7725,0.18944,6.19,1.02],[2983,116.02875,25.78417,5.31,1.54],[2984,115.34083,-44.63222,6.41,0.0],[2985,116.11167,24.39806,3.57,0.93],[2986,115.49167,-38.52889,6.54,-0.09],[2987,116.05833,12.85944,6.43,0.6],[2988,115.70042,-26.35111,5.64,0.99],[2989,116.03083,2.405,6.47,0.2],[2990,116.32875,28.02611,1.14,1.0],[2991,116.28875,20.31639,6.33,0.0],[2992,115.91292,-25.50389,6.55,0.06],[2993,115.885,-28.41111,4.59,1.63],[2994,115.8,-36.05028,5.6,-0.13],[2995,115.77917,-38.86417,6.89,1.02],[2996,115.95208,-28.95472,3.96,0.18],[2997,119.07208,80.26556,6.56,0.73],[2998,115.73833,-45.17333,5.06,0.78],[2999,116.66375,37.5175,5.18,1.58],[3000,114.0175,-77.63417,6.18,1.73],[3001,115.92875,-38.20194,6.4,-0.16],[3002,115.92458,-40.93389,5.17,1.1],[3003,116.53083,18.51,4.88,1.45],[3004,116.14167,-24.67389,5.62,-0.19],[3005,115.77875,-49.99278,6.57,0.07],[3006,115.5425,-58.63083,6.43,-0.1],[3007,116.04,-36.06278,5.8,0.31],[3008,116.5675,10.76833,5.3,0.01],[3009,116.36958,-14.68611,6.89,0.6],[3010,116.37125,-14.69083,6.07,0.11],[3011,116.1425,-37.94306,5.88,-0.11],[3012,115.72208,-58.23,6.21,1.05],[3013,116.87625,33.41556,5.14,1.6],[3014,116.50917,-6.7725,5.49,1.38],[3015,116.48708,-14.56389,5.04,0.33],[3016,116.26917,-37.88778,6.54,-0.1],[3017,116.31375,-37.96861,3.61,1.73],[3018,116.39583,-34.17306,5.37,0.6],[3019,116.68708,-12.67528,6.39,-0.02],[3020,116.32542,-43.75222,6.03,-0.07],[3021,117.14,23.14111,6.18,0.6],[3022,116.54333,-37.93389,5.88,-0.11],[3023,116.80208,-22.51972,5.9,-0.19],[3024,115.455,-72.60611,3.95,1.04],[3025,116.63917,-40.05972,6.57,-0.13],[3026,116.91042,-15.99083,6.34,1.78],[3027,116.93833,-16.01444,6.43,1.7],[3028,117.77375,54.12917,6.02,0.46],[3029,116.98625,-12.19306,5.48,0.48],[3030,117.25833,13.37083,6.04,1.38],[3031,116.39833,-56.7225,6.12,0.39],[3032,116.77417,-39.33139,6.31,-0.17],[3033,117.24542,4.33278,6.53,0.78],[3034,117.02167,-25.93722,4.5,-0.05],[3035,116.85417,-38.51111,5.08,-0.1],[3036,116.18292,-66.07194,6.38,0.95],[3037,116.88125,-46.60861,5.23,-0.14],[3038,116.05417,-69.82139,6.18,-0.06],[3039,118.1525,55.20944,6.38,0.6],[3040,117.75958,33.23361,6.03,0.15],[3041,117.03542,-40.65222,6.14,1.58],[3042,117.36917,-13.35333,6.23,-0.09],[3043,117.25708,-24.91222,5.33,0.76],[3044,117.42167,-17.22833,5.18,1.28],[3045,117.32375,-24.85972,3.34,1.24],[3046,117.08458,-47.07778,4.71,1.06],[3047,117.54417,-9.18333,5.61,1.44],[3048,117.43833,-20.20694,6.56,0.58],[3049,117.31125,-35.24333,5.93,-0.05],[3050,117.6975,3.27722,6.18,1.12],[3051,117.52375,-19.52361,6.12,1.26],[3052,117.3975,-33.28889,5.6,1.61],[3053,117.98625,19.32528,5.99,1.13],[3054,117.73,-11.12861,6.16,1.13],[3055,117.30958,-46.37333,4.11,-0.18],[3056,117.08,-56.47111,6.33,1.01],[3057,117.3675,-44.75194,6.32,0.96],[3058,117.30375,-46.85778,5.84,-0.14],[3059,117.925,1.76694,5.14,-0.12],[3060,117.75,-24.52833,6.45,-0.01],[3061,118.03,3.27722,6.31,1.59],[3062,117.27792,-56.41056,5.59,1.13],[3063,117.92042,-12.81944,6.36,0.39],[3064,117.94292,-13.89806,5.17,0.6],[3065,118.62208,47.38611,6.25,1.15],[3066,118.67792,47.56472,5.45,1.46],[3067,118.37417,26.76583,4.97,0.09],[3068,117.92875,-21.17389,5.63,0.96],[3069,117.67667,-44.57972,6.45,0.9],[3070,117.30375,-60.28361,5.78,0.42],[3071,117.59958,-50.50972,5.91,1.09],[3072,118.19958,-5.42806,5.76,0.41],[3073,118.07875,-14.84639,5.69,0.37],[3074,117.83542,-43.09556,6.32,-0.17],[3075,120.04875,73.91806,5.41,1.42],[3076,117.47833,-60.05111,6.72,1.24],[3077,119.11167,56.50444,6.72,0.6],[3078,117.91792,-42.88833,6.04,-0.18],[3079,118.06542,-34.70528,5.01,0.44],[3080,118.05417,-40.57583,3.73,1.04],[3081,117.42083,-66.19583,5.79,-0.04],[3082,121.19625,79.47972,5.42,-0.06],[3083,118.92,35.41278,6.23,0.28],[3084,118.16125,-38.86306,4.49,-0.19],[3085,118.26458,-36.36389,5.43,1.16],[3086,118.91625,19.88389,5.35,-0.04],[3087,118.88083,8.86278,5.86,0.35],[3088,118.12375,-54.36722,5.7,-0.15],[3089,118.26542,-49.61306,4.63,-0.23],[3090,118.32583,-48.10306,4.24,-0.14],[3091,118.54583,-35.8775,5.49,-0.19],[3092,118.66625,-34.84694,6.15,1.53],[3093,119.09958,4.48583,6.17,0.98],[3094,119.56917,43.9775,6.34,1.06],[3095,119.2475,15.79028,5.78,1.28],[3096,118.80708,-30.9175,6.44,0.6],[3097,119.31625,8.64139,6.05,1.0],[3098,119.3175,1.12694,6.35,0.5],[3099,119.095,-30.28528,6.33,1.66],[3100,118.75208,-52.58306,6.38,-0.01],[3101,118.94375,-43.845,6.02,-0.11],[3102,119.21458,-22.88,4.2,0.72],[3103,119.52417,7.21361,6.41,-0.04],[3104,119.63125,16.51861,5.99,1.47],[3105,118.72167,-57.30306,5.63,1.3],[3106,120.33625,59.0475,5.77,0.39],[3107,119.10125,-40.73639,6.78,-0.18],[3108,124.22417,84.05778,6.49,0.03],[3109,120.42667,60.32444,6.01,0.14],[3110,119.58583,2.22472,5.29,0.92],[3111,119.24125,-42.40611,6.09,1.36],[3112,120.62833,63.09028,6.4,0.59],[3113,119.41708,-30.33472,4.79,0.15],[3114,119.24125,-43.50028,5.35,-0.18],[3115,119.89625,13.24222,6.02,1.32],[3116,119.32667,-44.10972,5.09,-0.17],[3117,119.19458,-52.98222,3.47,-0.18],[3118,119.33333,-47.89028,6.22,-0.1],[3119,120.64917,57.27361,6.49,0.62],[3120,119.0775,-60.52639,5.74,1.55],[3121,119.46583,-45.57778,5.17,1.27],[3122,119.93375,-3.67972,4.93,1.21],[3123,119.77375,-23.31056,5.11,1.12],[3124,120.23292,25.39278,5.83,1.02],[3125,120.2,19.81611,6.25,1.11],[3126,119.21125,-59.12639,6.25,2.08],[3127,120.25292,23.58306,6.34,0.6],[3128,120.19708,17.30861,5.55,1.32],[3129,119.56,-49.245,4.41,-0.17],[3130,120.47958,35.41306,6.34,1.56],[3131,119.96667,-18.39917,4.61,0.08],[3132,120.4325,25.08972,6.31,0.01],[3133,119.58917,-51.44861,6.44,0.25],[3134,120.37625,16.45528,5.99,-0.02],[3135,120.18375,-2.88167,6.51,-0.07],[3136,120.3075,4.87972,5.65,0.0],[3137,119.7575,-45.21611,5.99,-0.14],[3138,119.44542,-60.30333,5.6,0.57],[3139,119.30208,-63.29694,6.14,-0.1],[3140,119.86833,-39.29722,5.24,0.39],[3141,120.30542,-1.3925,4.68,1.49],[3142,119.80125,-49.97667,6.32,0.6],[3143,119.80583,-49.97361,6.34,0.6],[3144,120.46125,8.91389,6.22,0.57],[3145,120.56625,2.33444,4.39,1.25],[3146,120.08167,-45.45694,6.61,1.27],[3147,119.71042,-60.82444,5.81,-0.09],[3148,120.06208,-48.98139,6.02,0.04],[3149,120.87958,27.79417,4.94,1.12],[3150,120.60833,-6.33722,6.33,0.62],[3151,120.12042,-48.87139,6.12,-0.11],[3152,119.9175,-60.2075,6.33,-0.06],[3153,119.90667,-60.58694,5.17,1.74],[3154,120.40583,-37.28361,5.95,0.14],[3155,120.52583,-37.05056,6.34,1.62],[3156,120.20792,-54.15139,5.87,-0.14],[3157,120.34542,-54.515,6.1,-0.04],[3158,121.18833,18.84222,6.15,-0.05],[3159,120.08333,-63.5675,4.82,-0.17],[3160,120.76708,-32.46389,5.82,1.22],[3161,120.38125,-55.455,6.28,-0.15],[3162,120.68667,-41.31,5.52,-0.15],[3163,121.26875,13.11806,5.12,0.01],[3164,121.40417,27.52972,6.21,0.01],[3165,120.89625,-40.00333,2.25,-0.26],[3166,120.87292,-42.94861,6.29,1.01],[3167,121.79125,43.26028,6.26,-0.02],[3168,121.17292,-19.72806,6.13,-0.16],[3169,121.57667,22.63556,5.99,1.66],[3170,121.0675,-32.675,5.31,1.91],[3171,119.81708,-73.24472,6.34,0.14],[3172,121.45667,-0.57361,6.41,1.05],[3173,122.11417,51.50667,4.84,0.05],[3174,121.61458,-9.245,6.23,-0.07],[3175,122.51583,58.24806,5.93,1.39],[3176,121.94083,21.58167,5.3,0.63],[3177,121.43708,-33.56917,6.14,1.11],[3178,121.17667,-50.59056,5.95,1.21],[3179,121.335,-46.97889,6.19,-0.15],[3180,121.26667,-53.10806,5.53,1.34],[3181,122.34625,42.43056,6.27,1.27],[3182,123.20333,68.47417,5.32,1.04],[3183,121.825,-20.55472,5.38,0.1],[3184,122.17667,13.64083,6.27,0.43],[3185,121.88583,-24.30417,2.81,0.43],[3186,121.17875,-62.83611,6.3,-0.1],[3187,121.66833,-45.26639,5.05,1.5],[3188,122.14833,-2.98389,4.34,0.97],[3189,122.23708,-11.33972,6.32,0.01],[3190,122.18125,-20.36306,6.36,0.16],[3191,122.61333,25.50722,5.73,0.81],[3192,122.25667,-19.245,4.4,-0.15],[3193,122.84,38.73139,6.58,0.59],[3194,122.36875,-16.24889,5.68,-0.17],[3195,122.15667,-37.68139,6.37,-0.04],[3196,122.27792,-30.3225,6.65,1.4],[3197,126.13708,82.43083,6.32,0.01],[3198,122.745,14.62944,6.23,0.02],[3199,122.2925,-35.455,6.2,0.89],[3200,123.45917,56.45222,5.85,1.01],[3201,122.81917,9.82111,6.07,-0.1],[3202,122.66583,-13.79917,5.54,0.49],[3203,122.29,-48.68444,5.7,-0.12],[3204,122.39958,-44.12278,5.21,-0.19],[3205,122.44875,-42.64056,6.26,-0.04],[3206,122.37208,-47.34583,4.27,-0.23],[3207,122.38333,-47.33667,1.78,-0.22],[3208,123.05292,17.64778,5.63,0.54],[3209,123.05292,17.64778,6.02,0.54],[3210,123.05542,17.64778,6.2,0.6],[3211,122.81792,-12.92694,4.72,0.95],[3212,122.8875,-7.7725,5.36,0.89],[3213,122.43,-47.9375,5.23,-0.21],[3214,123.09208,14.00389,6.54,0.6],[3215,123.28708,29.65667,5.64,-0.07],[3216,124.88417,75.75694,5.54,0.9],[3217,122.10208,-63.80111,6.28,-0.06],[3218,122.39,-56.08556,5.66,0.21],[3219,122.75667,-37.29222,6.44,-0.01],[3220,122.25292,-61.3025,4.76,0.43],[3221,123.96042,60.38056,6.45,0.2],[3222,123.24917,16.51417,6.01,0.89],[3223,121.9825,-68.61722,4.35,-0.11],[3224,123.42375,23.13778,6.56,0.11],[3225,122.83958,-39.61861,4.45,1.62],[3226,122.85792,-42.98722,4.75,0.18],[3227,122.79625,-48.46194,5.82,-0.15],[3228,123.54625,17.67583,6.47,0.3],[3229,123.33333,-15.78833,4.99,1.07],[3230,123.19167,-29.91083,6.52,0.06],[3231,123.5875,13.04833,6.38,0.6],[3232,123.0,-46.64417,5.76,0.59],[3233,123.21458,-37.92444,6.43,0.1],[3234,123.12875,-46.26417,6.03,-0.11],[3235,124.46,59.57111,5.64,0.16],[3236,125.16792,72.40722,5.98,1.54],[3237,123.37333,-35.89972,4.78,-0.11],[3238,123.42125,-33.56917,6.37,1.14],[3239,123.54583,-32.14083,6.06,-0.16],[3240,123.49333,-36.3225,5.08,-0.19],[3241,123.495,-36.34111,6.11,-0.18],[3242,123.555,-35.49056,5.78,1.02],[3243,123.51208,-40.34806,4.44,1.17],[3244,123.40083,-46.99194,5.13,-0.14],[3245,124.82208,62.50722,5.71,0.89],[3246,124.56583,54.14361,6.27,1.54],[3247,123.39208,-50.19611,5.51,1.61],[3248,124.14125,11.72639,7.13,1.56],[3249,124.12875,9.18556,3.52,1.48],[3250,123.59958,-45.83444,5.83,-0.2],[3251,123.96875,-30.92583,6.21,0.78],[3252,124.38208,8.86611,6.29,0.98],[3253,123.99542,-35.90278,6.16,1.55],[3254,125.10875,57.74333,5.89,0.39],[3255,124.22583,-21.32028,6.6,0.02],[3256,123.84708,-50.44944,6.44,1.49],[3257,124.34625,-16.285,6.16,0.01],[3258,125.12125,53.57444,6.49,0.28],[3259,124.59958,-12.63194,5.98,0.76],[3260,123.81625,-62.91583,5.16,0.09],[3261,124.49292,-30.00333,6.45,1.04],[3262,125.01625,27.21778,5.14,0.47],[3263,125.68375,60.63111,6.41,0.97],[3264,125.0875,20.74778,5.83,1.13],[3265,124.81292,-10.16583,6.32,0.33],[3266,124.5725,-35.45167,5.58,1.24],[3267,124.5525,-37.37417,6.7,0.23],[3268,125.13375,24.02222,5.98,-0.03],[3269,124.95792,3.94778,6.05,0.97],[3270,124.63875,-36.65944,4.45,0.22],[3271,125.05458,-0.90944,6.18,0.6],[3272,125.07125,-5.32917,6.13,1.33],[3273,124.8725,-34.59028,6.43,-0.08],[3274,124.4825,-59.16694,6.42,0.39],[3275,125.70875,43.18806,4.25,1.55],[3276,125.11417,-22.92472,6.13,1.04],[3277,125.95208,53.21972,5.51,0.11],[3278,125.33417,-1.60222,6.5,0.02],[3279,125.33833,-20.07917,5.58,0.77],[3280,124.57875,-65.61333,5.07,1.15],[3281,125.4775,-17.58639,5.75,1.05],[3282,125.34583,-33.05444,4.83,1.45],[3283,125.3375,-36.48444,5.2,-0.19],[3284,125.84083,18.33222,5.95,0.17],[3285,125.62583,-6.17917,6.15,0.22],[3286,125.35083,-39.62083,6.16,0.17],[3287,126.17833,42.005,6.02,1.59],[3288,125.725,-7.54333,5.96,1.67],[3289,125.695,-13.05472,6.11,1.0],[3290,125.98,10.63194,6.08,1.49],[3291,125.70792,-26.34806,5.9,0.37],[3292,126.27042,35.01139,6.06,1.27],[3293,125.3,-57.97306,5.97,-0.09],[3294,125.63167,-48.49028,4.82,-0.15],[3295,126.15167,-4.71694,6.01,0.46],[3296,125.82167,-38.28583,6.32,1.63],[3297,126.14583,-3.75111,5.61,0.46],[3298,125.28208,-64.10611,6.12,0.93],[3299,126.45792,17.04611,6.14,0.41],[3300,125.73,-52.12389,5.85,0.01],[3301,124.95417,-71.515,5.37,-0.06],[3302,125.00292,-71.50528,5.65,-0.1],[3303,127.4425,67.2975,5.88,0.97],[3304,126.61542,27.89361,5.57,1.4],[3305,126.39792,2.10222,5.73,1.53],[3306,126.47833,7.56444,5.13,0.94],[3307,125.62833,-59.50972,1.86,1.28],[3308,126.22958,-23.15361,5.68,0.06],[3309,126.90333,45.65306,6.32,0.62],[3310,126.695,26.93444,6.32,0.18],[3311,126.69583,26.93528,6.3,0.18],[3312,126.66583,24.53417,7.02,0.32],[3313,126.66708,24.53528,7.81,0.52],[3314,126.415,-3.90639,3.9,-0.02],[3315,126.26542,-24.04611,5.28,1.48],[3316,126.32958,-21.04583,6.01,0.4],[3317,126.41417,-17.43944,6.44,0.6],[3318,124.63167,-76.91972,4.07,0.39],[3319,126.68292,12.65444,5.5,1.6],[3320,126.48167,-14.92972,5.98,0.17],[3321,126.61333,-3.9875,5.59,0.22],[3322,126.23833,-42.76944,5.98,-0.17],[3323,127.56625,60.71806,3.36,0.84],[3324,126.67458,-12.53444,5.54,1.19],[3325,126.82167,-6.40972,6.59,0.51],[3326,126.46625,-42.15333,5.47,-0.15],[3327,126.57333,-39.05944,6.53,-0.09],[3328,126.57583,-39.06028,7.25,0.08],[3329,127.15333,24.14472,6.1,0.24],[3330,126.37917,-51.72806,5.17,-0.16],[3331,126.71167,-29.21528,6.73,-0.05],[3332,128.2225,69.32,6.31,1.35],[3333,127.15542,14.21083,5.95,0.19],[3334,125.51833,-73.4,5.29,0.01],[3335,126.88875,-20.84389,6.56,0.04],[3336,126.81833,-31.67306,6.33,0.9],[3337,127.12167,-2.51722,6.39,0.33],[3338,127.08208,-8.81611,6.43,1.2],[3339,126.97292,-26.1325,6.62,0.11],[3340,125.16042,-77.48444,4.35,1.16],[3341,126.605,-52.8075,6.05,0.06],[3342,127.21208,-9.74833,6.0,0.42],[3343,126.99708,-35.11389,5.75,-0.15],[3344,127.14958,-23.07167,6.51,0.05],[3345,127.22208,-20.95028,6.67,-0.06],[3346,126.465,-64.60083,5.97,0.96],[3347,126.43417,-66.13694,3.77,1.13],[3348,127.83292,37.26583,6.18,-0.03],[3349,126.86417,-55.01167,6.53,-0.02],[3350,126.90208,-53.08861,5.09,0.25],[3351,128.13958,53.11472,6.24,1.01],[3352,129.20292,74.72361,6.31,0.6],[3353,127.365,-27.3325,6.7,-0.13],[3354,128.65083,65.145,5.47,0.18],[3355,127.87708,24.08111,5.75,0.28],[3356,127.28167,-44.16056,5.79,-0.16],[3357,127.89875,18.09444,5.35,1.56],[3358,127.26958,-47.92917,5.33,-0.14],[3359,127.365,-44.725,4.99,-0.16],[3360,128.22917,38.01639,5.9,1.11],[3361,127.9775,9.81444,6.83,-0.07],[3362,127.61917,-32.15944,5.65,1.49],[3363,127.44,-46.33194,5.99,-0.15],[3364,127.62333,-36.72111,6.69,1.95],[3365,128.34083,36.43639,6.24,0.36],[3366,128.17708,20.44111,5.33,1.25],[3367,127.87875,-19.5775,5.42,-0.06],[3368,127.40125,-55.19111,6.36,0.8],[3369,128.25042,24.08472,6.36,1.02],[3370,126.82042,-70.09333,5.53,-0.03],[3371,127.66333,-44.73722,6.3,-0.02],[3372,128.16625,10.06611,6.46,-0.02],[3373,127.8525,-39.06417,6.31,-0.15],[3374,128.13875,-15.02944,6.38,0.27],[3375,127.795,-47.86667,6.39,-0.15],[3376,128.43792,13.25722,6.28,1.17],[3377,128.6825,36.41944,5.78,0.04],[3378,128.43125,4.75667,5.87,1.07],[3379,129.9275,73.62972,6.15,1.02],[3380,128.55542,8.45194,6.03,0.33],[3381,128.27,-24.60639,6.19,0.27],[3382,127.87333,-54.39417,6.34,1.31],[3383,128.50667,-2.15167,5.81,0.0],[3384,128.21458,-31.50083,6.38,0.79],[3385,128.24417,-34.63389,6.36,0.95],[3386,128.02,-53.21222,5.69,0.58],[3387,128.83083,19.59,6.58,0.68],[3388,128.33292,-38.37111,6.49,-0.18],[3389,128.40958,-38.84889,5.96,-0.14],[3390,128.37667,-46.97111,6.24,1.56],[3391,129.79875,65.02083,5.64,0.62],[3392,128.85375,2.74361,6.33,1.02],[3393,126.0825,-80.91417,5.69,1.02],[3394,129.03208,15.31361,6.32,0.6],[3395,128.9625,6.62,5.99,0.52],[3396,128.96375,6.6225,7.25,0.71],[3397,128.63208,-32.59861,6.43,0.75],[3398,128.8675,-7.98222,5.72,-0.03],[3399,128.62208,-37.61139,6.3,1.56],[3400,129.5925,53.40139,5.66,0.96],[3401,129.7925,59.93944,6.48,0.6],[3402,128.87,-26.84361,5.96,0.37],[3403,130.05333,64.32778,4.6,1.17],[3404,128.8025,-39.97,6.47,0.58],[3405,129.75,52.925,6.42,0.6],[3406,129.27417,9.65556,5.88,0.09],[3407,128.68167,-49.94417,5.01,1.33],[3408,129.82333,52.71167,5.91,1.17],[3409,129.57917,32.80194,5.94,1.12],[3410,129.41417,5.70361,4.16,0.0],[3411,129.36292,-4.93361,6.19,1.05],[3412,129.52167,9.57472,6.53,-0.02],[3413,128.96708,-50.97,5.8,-0.13],[3414,128.83167,-58.00917,4.86,1.0],[3415,128.81417,-58.225,5.26,-0.14],[3416,129.58458,-6.6625,6.51,0.44],[3417,128.17583,-73.35667,6.12,0.95],[3418,129.68917,3.34139,4.44,1.21],[3419,129.37375,-33.74583,6.48,0.33],[3420,129.4675,-26.255,5.27,-0.04],[3421,129.33292,-40.1475,6.55,0.6],[3422,130.25458,45.83389,5.37,0.99],[3423,130.07625,31.94194,6.1,0.6],[3424,129.8525,8.01722,6.45,1.08],[3425,129.66792,-19.73694,6.33,1.59],[3426,129.41125,-42.98917,4.14,0.11],[3427,130.02667,20.00778,6.39,0.98],[3428,130.09208,19.67,6.44,1.02],[3429,130.1125,19.545,6.3,0.17],[3430,129.78333,-22.66194,5.05,0.73],[3431,130.00625,-12.47528,4.98,1.42],[3432,129.32833,-62.85361,5.47,1.02],[3433,129.92708,-29.56111,4.89,0.9],[3434,129.84208,-36.60694,6.13,0.42],[3435,129.68708,-53.09056,6.47,-0.1],[3436,130.75083,46.90111,6.22,0.96],[3437,130.25667,-9.05194,6.63,-0.02],[3438,130.02583,-35.30833,3.97,0.94],[3439,130.08042,-40.26417,5.2,-0.01],[3440,129.84917,-53.43972,5.48,-0.16],[3441,130.43042,-15.94333,4.88,1.06],[3442,129.99,-53.055,5.19,-0.14],[3443,129.805,-60.31722,6.36,0.0],[3444,130.14708,-45.19139,5.71,1.65],[3445,130.15667,-46.64889,3.84,0.71],[3446,130.54083,-11.96611,6.45,0.16],[3447,130.07333,-52.92194,3.62,-0.18],[3448,130.0725,-53.01528,5.61,-0.14],[3449,130.82125,21.46861,4.66,0.02],[3450,130.80125,12.68083,5.64,0.39],[3451,131.04208,36.91806,6.33,0.6],[3452,130.30458,-47.31694,4.77,0.12],[3453,130.27208,-48.9225,5.9,-0.21],[3454,130.80625,3.39861,4.3,-0.2],[3455,130.18167,-57.54528,6.34,0.2],[3456,130.48708,-45.41083,5.23,0.21],[3457,130.15417,-59.76111,4.33,-0.11],[3458,130.99875,4.33472,6.37,-0.06],[3459,130.91833,-7.23361,4.62,0.84],[3460,129.77167,-70.38694,5.2,0.01],[3461,131.17125,18.15417,3.94,1.08],[3462,130.56667,-48.09917,5.51,-0.18],[3463,130.7375,-35.94333,6.42,0.02],[3464,131.33917,30.69778,6.13,0.94],[3465,131.1875,10.08167,5.66,-0.11],[3466,130.57875,-53.1,5.52,-0.15],[3467,130.60625,-53.11389,4.86,-0.17],[3468,130.89792,-33.18639,3.68,-0.18],[3469,131.25542,5.68056,6.13,0.2],[3470,132.20583,66.70806,6.2,-0.11],[3471,130.58708,-55.77417,6.29,1.18],[3472,131.33667,-2.60083,6.41,0.52],[3473,131.23,-21.16778,6.11,0.22],[3474,131.66667,28.76528,6.57,0.04],[3475,131.67417,28.76,4.02,1.01],[3476,130.91792,-49.82278,5.16,-0.2],[3477,131.1,-42.64917,4.07,0.87],[3478,131.51042,-2.04889,5.7,1.1],[3479,131.21625,-37.14722,5.76,-0.15],[3480,131.52875,-11.00639,6.25,1.61],[3481,131.73333,12.11,5.87,0.11],[3482,131.69417,6.41889,3.38,0.68],[3483,131.45542,-25.3875,6.1,0.08],[3484,131.59375,-13.54778,4.32,0.9],[3485,131.17583,-54.70833,1.96,0.04],[3486,131.8125,-1.89722,5.29,0.04],[3487,131.50708,-46.04167,3.91,0.0],[3488,131.59917,-41.12556,6.21,-0.05],[3489,131.27208,-58.725,6.21,-0.09],[3490,131.705,-34.62278,6.37,-0.13],[3491,130.97625,-68.21167,6.32,1.5],[3492,132.10833,5.83778,4.36,-0.04],[3493,132.02042,-6.55861,6.09,1.28],[3494,131.6275,-45.91278,5.46,0.27],[3495,131.125,-65.82556,6.05,0.2],[3496,131.82875,-46.15556,5.75,0.56],[3497,131.91875,-41.73722,6.36,0.58],[3498,131.67708,-56.76972,4.49,-0.17],[3499,132.63417,33.28528,6.25,0.49],[3500,132.34042,-3.44306,5.31,-0.09],[3501,132.03667,-42.46389,6.43,-0.2],[3502,130.33125,-78.96333,5.47,-0.1],[3503,132.00083,-52.85056,6.3,-0.1],[3504,132.68792,18.83222,6.16,-0.01],[3505,133.34417,61.96222,5.73,0.28],[3506,133.27458,59.05611,6.25,0.6],[3507,132.43708,-21.04861,6.47,0.23],[3508,132.98667,43.72667,5.15,0.98],[3509,133.04833,45.3125,5.99,1.26],[3510,132.75625,15.35056,6.38,0.64],[3511,133.04167,42.0025,5.99,1.25],[3512,132.46458,-32.78056,5.21,0.87],[3513,132.50917,-29.46306,5.87,0.95],[3514,132.41333,-40.32056,5.48,0.06],[3516,132.59,-28.61806,6.17,-0.08],[3517,132.46833,-39.14167,6.39,0.23],[3518,132.63292,-27.71,4.01,1.27],[3519,133.14417,32.47417,5.66,0.22],[3520,132.44875,-45.30806,4.93,0.05],[3521,133.11917,28.25917,6.23,1.62],[3522,133.14917,28.33083,5.95,0.87],[3523,132.89375,-7.17722,5.54,0.15],[3524,130.80167,-79.06972,6.05,0.23],[3525,132.5875,-42.09,6.0,-0.1],[3526,133.10083,5.34,6.33,0.12],[3527,132.63958,-46.52917,5.1,-0.21],[3528,133.48208,35.53833,6.14,0.04],[3529,133.12792,-13.23361,6.13,1.14],[3530,132.86625,-42.50444,6.55,0.04],[3531,134.15625,64.60389,5.58,0.86],[3532,133.56125,30.57944,5.39,1.05],[3533,133.10875,-32.50917,6.5,1.46],[3534,133.16083,-36.54556,6.42,0.56],[3535,133.2,-38.72417,5.82,1.5],[3536,132.9025,-57.63361,5.59,-0.11],[3537,132.645,-66.79306,5.35,0.42],[3538,133.57458,-5.43444,6.0,0.67],[3539,133.16083,-48.35917,5.91,-0.15],[3540,133.91542,27.9275,5.22,1.0],[3541,133.84542,17.23139,6.64,3.36],[3542,133.17,-52.12917,6.39,0.0],[3543,131.48,-79.50444,5.79,1.6],[3544,132.45958,-72.55083,6.11,0.2],[3545,134.20833,45.63194,5.74,1.09],[3546,134.12708,40.20167,5.89,0.35],[3547,133.84833,5.94556,3.11,1.0],[3548,133.46125,-40.4475,6.47,0.96],[3549,133.26583,-56.64944,6.03,-0.02],[3550,133.98167,11.62611,5.41,1.46],[3551,133.46125,-47.52083,5.33,0.26],[3552,133.87292,-7.97028,6.91,0.6],[3553,133.87333,-7.97111,6.67,0.22],[3554,133.80167,-18.24139,5.75,1.32],[3555,134.23583,32.91028,5.45,0.12],[3556,133.88125,-27.68194,4.89,0.11],[3557,134.15375,4.23667,6.14,1.0],[3558,134.28417,17.14389,6.17,1.0],[3559,133.98292,-23.81833,6.39,0.16],[3560,133.45292,-60.35417,5.78,-0.08],[3561,134.31208,15.32278,5.2,0.15],[3562,133.83042,-45.04167,6.26,-0.16],[3563,134.49458,30.23361,6.29,0.43],[3564,134.14208,-16.70944,5.96,1.54],[3565,134.39667,15.58139,5.67,0.2],[3566,134.61458,35.8025,6.51,-0.01],[3567,134.425,9.38778,6.19,0.98],[3568,133.725,-58.24,6.38,-0.11],[3569,134.80167,48.04167,3.14,0.19],[3570,133.79958,-54.96556,5.71,0.48],[3571,133.76167,-60.64472,3.84,-0.1],[3572,134.62167,11.85778,4.25,0.14],[3573,134.53417,1.54167,6.59,0.06],[3574,134.08083,-52.72361,4.69,-0.12],[3575,134.88583,32.41861,5.2,0.93],[3576,135.63625,67.62972,4.76,1.53],[3577,134.795,18.13472,6.38,1.55],[3578,134.68292,-16.13278,5.86,0.53],[3579,135.16,41.78278,3.97,0.44],[3580,135.12833,37.60444,6.44,0.6],[3581,138.83833,84.18111,6.33,0.3],[3582,134.24333,-59.22944,4.92,-0.19],[3583,134.4825,-48.57333,5.87,1.07],[3584,134.91625,-19.20806,6.18,0.46],[3585,134.81542,-28.80611,6.25,1.0],[3586,135.41917,39.71333,6.36,0.3],[3587,135.35042,32.2525,5.82,0.0],[3588,134.71792,-47.23472,5.18,0.25],[3589,135.45375,27.90278,6.07,0.6],[3590,135.38083,5.64083,6.07,1.11],[3591,135.0225,-41.25389,4.45,0.65],[3592,136.00167,54.28389,5.75,0.02],[3593,135.0925,-43.17333,6.07,-0.16],[3594,135.90625,47.15667,3.6,0.0],[3595,135.68458,24.45278,5.45,-0.04],[3596,135.49167,-0.48278,5.67,1.15],[3597,135.2975,-26.66389,6.2,1.13],[3598,134.85042,-59.08361,5.16,0.42],[3599,135.68667,7.29806,5.85,1.11],[3600,135.33667,-41.86444,5.55,-0.14],[3601,136.04125,27.89833,6.38,0.0],[3602,135.52667,-39.4025,6.27,1.0],[3603,136.35042,48.53028,5.95,0.45],[3604,135.19042,-60.96389,5.79,1.21],[3605,135.43583,-52.18833,5.23,-0.12],[3606,136.23,32.37694,6.46,0.24],[3607,135.78667,-25.50444,6.74,-0.03],[3608,136.67958,59.34444,6.45,0.04],[3609,137.09833,66.87333,5.14,1.51],[3610,135.28542,-68.68389,5.88,1.63],[3611,135.77167,-53.54972,6.4,-0.09],[3612,136.6325,38.45222,4.56,1.04],[3613,136.49333,5.09222,4.97,1.22],[3614,136.03875,-47.09778,3.75,1.2],[3615,135.61167,-66.39611,4.0,0.14],[3616,137.59667,67.13472,4.8,0.49],[3617,136.86208,22.98111,6.4,0.6],[3618,136.74958,1.46278,6.17,1.65],[3619,137.21792,51.60472,4.48,0.27],[3620,137.01708,32.54056,6.5,0.36],[3621,137.00042,29.65417,5.43,0.89],[3622,136.2,-57.8525,6.44,0.25],[3623,136.93667,10.66806,5.24,-0.11],[3624,137.72958,63.51361,4.67,0.35],[3625,137.21292,33.88222,5.93,0.6],[3626,137.19708,26.62917,5.98,0.66],[3627,137.33958,22.04556,5.14,0.97],[3628,137.01208,-25.85833,4.58,1.59],[3629,136.64167,-55.80333,6.11,-0.15],[3630,137.17583,-8.58944,5.6,-0.06],[3631,136.81125,-51.21194,6.73,1.62],[3632,136.53167,-64.49972,6.37,1.35],[3633,138.51333,71.65583,6.55,0.96],[3634,136.99917,-43.4325,2.21,1.66],[3635,137.44333,11.56444,6.48,0.34],[3636,137.29792,-12.35778,5.77,0.94],[3637,137.18125,-26.76778,6.15,0.17],[3638,137.26792,-18.32861,5.73,0.0],[3639,137.66125,30.96306,5.95,1.67],[3640,137.58708,21.99639,6.01,0.9],[3641,137.39792,-8.78778,5.46,1.01],[3642,136.40958,-70.53889,4.71,-0.15],[3643,136.28667,-72.60278,4.48,0.61],[3644,137.485,-30.36528,5.59,0.19],[3645,138.96917,72.94611,5.96,0.18],[3646,137.59583,-23.17667,6.53,0.0],[3647,137.43792,-49.42472,6.48,0.17],[3648,138.58583,61.42333,5.13,0.58],[3649,137.98167,5.46833,6.35,0.32],[3650,138.07333,14.99611,6.51,0.73],[3651,138.05375,3.86722,6.14,-0.01],[3652,138.45083,43.21778,5.32,-0.14],[3653,137.99458,-19.74778,5.73,0.98],[3654,137.76833,-44.86806,5.0,0.23],[3655,138.10833,-7.10972,6.11,0.22],[3656,137.92083,-39.25889,6.0,-0.11],[3657,138.40542,21.28333,6.48,0.02],[3658,137.88833,-46.58389,5.79,-0.21],[3659,137.74167,-58.96694,3.44,-0.19],[3660,138.95792,56.74139,5.27,1.56],[3661,138.1275,-43.61361,5.57,-0.11],[3662,139.04708,54.02194,4.83,0.19],[3663,137.81917,-62.31722,3.97,-0.18],[3664,138.80958,34.63361,5.97,0.86],[3665,138.59125,2.31417,3.88,-0.06],[3666,139.9825,74.01639,6.5,0.6],[3667,138.35792,-38.61639,6.31,0.0],[3668,138.3275,-42.27361,6.29,1.25],[3669,138.8075,14.94139,5.34,1.32],[3670,138.39375,-47.33861,5.92,-0.05],[3672,138.53417,-44.14583,5.85,-0.12],[3673,138.23167,-59.41444,5.54,0.85],[3674,138.60208,-43.2275,5.25,-0.14],[3675,138.85375,-15.02472,6.35,0.02],[3676,139.38,46.81722,5.97,0.04],[3677,138.73833,-37.6025,5.86,0.83],[3678,134.17125,-85.66306,5.42,0.31],[3679,138.575,-55.56972,5.27,0.99],[3680,138.81083,-45.55556,6.25,-0.08],[3681,139.17375,-6.35306,5.24,1.17],[3682,138.90292,-38.57,4.94,1.11],[3683,139.17208,-8.74472,5.47,-0.09],[3684,138.93792,-37.41333,4.62,0.45],[3685,138.3,-69.71722,1.68,0.0],[3686,139.60833,35.36417,5.75,0.6],[3687,139.28125,-14.57361,5.84,1.06],[3688,139.0175,-44.89861,6.04,0.28],[3689,139.46417,11.50111,6.41,0.07],[3690,139.71125,36.8025,3.82,0.06],[3691,138.82292,-58.38861,6.02,-0.1],[3692,139.09625,-44.26583,5.12,1.67],[3693,138.89583,-57.57806,6.32,1.04],[3694,139.23833,-39.40139,5.33,1.17],[3695,138.05125,-76.66306,6.14,1.09],[3696,139.05083,-57.54139,4.34,1.63],[3697,140.1825,51.26611,6.13,0.42],[3698,140.43042,56.69917,5.47,1.61],[3699,139.2725,-59.27528,2.25,0.18],[3700,139.42625,-54.49528,6.33,1.41],[3701,140.24708,38.18833,6.12,0.38],[3702,139.89042,-11.31417,6.62,0.08],[3703,139.52417,-51.05111,5.26,-0.07],[3704,139.88833,-15.83444,5.78,1.29],[3705,140.26375,34.3925,3.13,1.55],[3706,139.94333,-11.975,4.79,0.93],[3707,140.36333,32.90194,6.16,1.09],[3708,139.67583,-51.56056,5.87,0.54],[3709,140.12083,-9.55583,4.8,0.93],[3710,139.94958,-34.10333,6.39,-0.1],[3711,140.31417,15.37111,6.53,-0.01],[3712,139.32167,-68.68944,5.39,0.42],[3713,139.46542,-67.05083,6.11,1.26],[3714,140.23125,-15.61778,6.33,0.46],[3715,140.18417,-31.76056,6.82,0.0],[3716,140.12333,-37.58139,6.05,1.39],[3717,139.88583,-55.18667,6.28,-0.1],[3718,140.37333,-25.96556,4.72,1.63],[3719,141.965,75.09833,6.29,0.07],[3720,139.35583,-74.89444,5.29,0.02],[3721,139.36417,-74.73472,5.86,-0.02],[3722,141.43417,63.94083,6.28,1.46],[3723,140.8825,25.18306,6.41,0.82],[3724,140.71208,-9.83889,6.53,0.22],[3725,141.23208,51.57389,6.31,0.75],[3726,140.46208,-42.195,5.58,1.63],[3727,141.09375,36.58694,6.67,0.21],[3728,140.23667,-62.40472,4.81,0.94],[3729,140.65292,-39.77472,6.54,1.13],[3730,140.6,-46.0475,5.75,0.92],[3731,141.16375,26.18222,4.46,1.23],[3732,140.45833,-55.515,5.63,0.19],[3733,140.80125,-28.83389,4.69,0.92],[3734,140.52833,-55.01083,2.5,-0.18],[3735,140.93667,-37.75722,6.48,0.18],[3736,141.38542,16.58556,6.29,0.97],[3737,141.06792,-39.42583,6.06,0.2],[3738,141.35,-5.1175,5.59,1.52],[3739,140.99792,-51.73722,6.08,0.57],[3740,140.86417,-60.3025,6.3,1.48],[3741,141.59292,-1.46389,6.01,1.32],[3742,141.02375,-61.64889,5.99,1.06],[3743,142.16667,45.60139,5.41,0.98],[3744,141.81083,-9.22361,6.54,0.05],[3745,141.68667,-28.7875,6.1,-0.1],[3746,141.61875,-40.50194,6.2,0.25],[3747,142.44833,55.74556,6.45,0.6],[3748,141.89667,-8.65861,1.98,1.44],[3749,141.82667,-22.34389,4.69,1.14],[3750,141.945,-6.07111,5.38,0.64],[3751,144.27167,81.32639,4.29,1.48],[3752,141.36292,-61.95028,5.77,0.15],[3753,141.57542,-53.37917,5.11,-0.11],[3754,142.11458,9.05667,5.41,0.6],[3755,142.12167,8.18833,5.71,1.04],[3756,141.91,-35.00778,6.65,0.2],[3757,142.88208,63.06194,3.67,0.33],[3758,142.25917,-1.25694,6.27,0.27],[3759,142.28708,-2.76889,4.6,0.46],[3760,142.35208,-2.20528,6.14,0.22],[3761,141.68417,-64.92972,6.05,0.15],[3762,142.385,-4.24722,6.26,0.84],[3763,142.3025,-20.74861,5.66,1.6],[3764,142.68,33.65556,5.85,1.05],[3765,142.31125,-35.95139,4.51,1.44],[3766,142.31792,-38.40389,6.19,0.22],[3767,142.45792,-23.34528,6.24,1.57],[3768,143.72333,72.20556,5.72,0.48],[3769,142.885,35.10306,5.37,1.53],[3770,142.47708,-26.58972,5.48,1.36],[3771,143.62042,69.83028,4.56,0.77],[3772,142.59417,-15.57722,5.85,1.2],[3773,142.93,22.96806,4.31,1.54],[3774,144.02833,74.31778,6.46,-0.1],[3775,143.21417,51.67722,3.17,0.46],[3776,142.19583,-62.27306,5.92,1.1],[3777,141.77667,-71.60222,5.47,1.08],[3778,143.28,49.43861,6.76,0.6],[3779,142.99,9.71583,5.07,1.37],[3780,142.68917,-31.89139,7.0,0.09],[3781,142.69208,-31.88944,6.18,0.03],[3782,142.98625,11.29972,4.97,1.05],[3783,142.1275,-66.70194,5.91,0.01],[3784,142.52167,-51.51722,5.45,-0.1],[3785,142.91208,-10.55222,6.14,0.24],[3786,142.675,-40.46667,3.6,0.36],[3787,142.99542,-1.185,4.57,0.1],[3788,142.9825,-10.37056,6.13,1.19],[3789,142.88417,-31.87194,5.93,0.26],[3790,142.88708,-35.715,5.87,1.29],[3791,143.37625,36.48694,6.18,1.27],[3792,143.32625,28.36806,6.53,0.12],[3793,142.5975,-58.36167,5.88,1.7],[3794,143.1725,1.86417,6.11,0.62],[3795,141.03792,-80.78694,5.36,0.45],[3796,143.085,-19.40028,5.74,0.14],[3797,143.58167,46.90222,6.52,0.22],[3798,143.07708,-28.62806,6.46,0.33],[3799,143.70625,52.05139,4.5,0.01],[3800,143.55583,36.3975,4.55,0.92],[3801,143.25875,-8.50528,6.12,0.98],[3802,143.2325,-13.51694,5.94,1.5],[3803,142.80542,-57.03444,3.13,1.55],[3804,143.49625,23.45389,6.25,1.46],[3805,143.33375,-7.19,6.24,1.17],[3806,144.48417,73.08056,6.42,0.6],[3807,143.08042,-40.64944,5.35,0.9],[3808,143.30208,-21.11583,5.01,1.02],[3809,143.76583,39.62139,4.81,0.99],[3810,143.35917,-22.86389,5.91,0.02],[3811,143.84333,39.96333,6.76,0.35],[3812,143.2825,-39.12889,6.43,0.33],[3813,142.88708,-66.71944,6.27,1.35],[3814,143.63625,-5.915,5.56,1.16],[3815,143.915,35.81028,5.41,0.77],[3816,143.06083,-62.78889,6.1,1.43],[3817,143.43542,-49.005,5.12,-0.12],[3818,143.97042,14.37972,6.36,0.01],[3819,143.53667,-51.25528,5.01,-0.18],[3820,144.17875,31.16167,5.56,1.59],[3821,142.90125,-73.08083,5.47,1.56],[3822,143.89042,-19.58361,6.31,0.06],[3823,143.79917,-35.82389,6.49,0.42],[3824,144.86625,67.27222,5.94,1.52],[3825,143.61125,-59.22944,4.08,0.01],[3826,144.26083,16.43778,5.69,1.25],[3827,144.30292,6.83583,5.0,1.05],[3828,144.14042,-24.70278,6.53,0.38],[3829,144.59042,40.23972,5.25,0.22],[3830,144.25083,-25.29667,5.7,1.12],[3831,144.10542,-48.75139,6.17,0.27],[3832,144.46458,-9.42444,6.4,-0.04],[3833,144.29125,-32.17861,5.63,1.02],[3834,144.61375,4.64917,4.68,1.32],[3835,144.36792,-36.09583,5.98,1.12],[3836,144.20667,-49.35528,4.35,0.17],[3837,144.19292,-52.94417,6.19,1.05],[3838,145.56167,69.2375,5.69,1.14],[3839,145.73833,72.2525,5.17,1.04],[3840,144.30125,-53.66861,5.45,0.15],[3841,144.02125,-64.95056,6.56,0.1],[3842,144.50625,-43.19111,5.5,1.0],[3843,146.37833,78.13472,6.23,1.35],[3844,144.66958,-39.61417,6.7,0.49],[3845,144.96417,-1.14278,3.91,1.32],[3846,144.9475,-10.57028,6.31,-0.03],[3847,146.825,79.13667,6.17,0.25],[3848,145.08375,-10.76917,6.37,0.08],[3849,145.07667,-14.33222,5.06,-0.15],[3850,145.39667,31.27806,5.89,1.6],[3851,145.50125,39.75778,5.62,0.95],[3852,145.2875,9.89222,3.52,0.49],[3853,145.41042,25.91278,6.24,1.25],[3854,145.67958,48.43111,6.39,-0.01],[3855,145.77917,54.36361,6.47,0.13],[3856,144.8375,-61.32806,4.52,-0.07],[3857,145.67792,35.09333,6.14,0.36],[3858,145.32083,-23.59167,4.77,-0.12],[3859,146.15292,64.98389,6.17,0.6],[3860,143.47167,-80.94139,5.11,-0.14],[3861,145.88875,29.97444,5.64,0.12],[3862,145.56,-23.91556,4.94,0.53],[3863,145.17708,-57.98361,5.32,0.2],[3864,145.25917,-57.25972,5.8,1.09],[3865,146.48083,63.65333,6.34,0.31],[3866,145.93292,14.02167,5.35,1.63],[3867,145.6725,-35.50167,6.41,-0.06],[3868,145.44917,-55.21417,6.0,-0.13],[3869,146.125,18.86361,6.5,0.6],[3870,146.63208,57.12806,5.2,1.62],[3871,146.05042,-27.76944,4.79,0.51],[3872,145.86458,-51.22833,6.15,-0.1],[3873,146.46292,23.77417,2.98,0.8],[3874,146.06583,-39.57111,6.82,0.3],[3875,145.92583,-53.89167,5.56,-0.04],[3876,146.54167,6.70861,5.79,1.64],[3877,146.59708,11.81,5.63,1.49],[3878,146.34083,-30.20278,6.45,-0.13],[3879,146.59833,1.78556,5.65,0.34],[3880,146.85792,11.56833,6.45,0.43],[3881,147.1475,46.02111,5.09,0.62],[3882,146.88958,11.42889,6.02,1.3],[3883,146.41875,-57.18556,6.46,-0.11],[3884,146.31167,-62.50778,3.69,1.22],[3885,147.59875,65.59333,6.31,0.28],[3886,146.62667,-44.755,5.55,-0.18],[3887,146.48083,-58.79417,6.22,0.46],[3888,147.7475,59.03861,3.8,0.29],[3889,147.45875,21.17944,6.09,0.25],[3890,146.77542,-65.07194,3.01,0.28],[3891,146.77792,-65.0725,6.26,0.08],[3892,147.36708,-37.18639,5.97,1.24],[3893,147.62542,4.34361,6.24,0.48],[3894,148.02667,54.06444,4.59,0.03],[3895,147.16667,-56.41194,6.06,0.94],[3896,147.75833,13.06611,6.46,1.58],[3897,147.46375,-36.26861,6.37,1.01],[3898,147.48792,-45.73278,5.08,-0.1],[3899,147.80833,-4.24333,6.01,0.17],[3900,147.97083,24.39528,5.32,0.23],[3901,147.84,-6.18167,6.42,0.58],[3902,146.58583,-76.77611,5.45,0.89],[3903,147.86958,-14.84667,4.12,0.92],[3904,147.675,-46.93444,5.73,1.08],[3905,148.19083,26.00694,3.88,1.22],[3906,148.05083,2.45417,6.02,-0.04],[3907,148.05,0.07556,6.35,0.94],[3908,147.99833,-16.53472,6.08,1.04],[3909,148.12667,-8.105,5.05,0.04],[3910,147.8325,-46.19389,5.62,1.17],[3911,148.76417,61.11611,6.27,1.05],[3912,147.92,-46.54778,4.58,1.2],[3913,147.80042,-59.42583,5.79,1.36],[3914,147.73208,-62.74528,5.57,1.32],[3915,148.42875,5.95833,5.95,1.66],[3916,148.24167,-27.33222,6.3,0.62],[3917,148.92917,49.82,5.27,0.07],[3918,149.595,72.87944,5.83,1.14],[3919,148.55125,-25.9325,4.88,1.23],[3920,148.25,-55.37333,6.48,-0.14],[3921,148.63208,-22.48833,6.24,0.04],[3922,149.30667,57.41833,5.93,0.89],[3923,148.7175,-19.00944,4.94,1.57],[3924,148.45917,-51.14694,5.93,-0.15],[3925,148.57333,-45.28389,5.71,-0.11],[3926,149.10833,8.93306,5.85,1.13],[3927,148.71375,-50.24389,5.72,-0.01],[3928,149.42125,41.05556,5.14,0.46],[3929,149.48708,45.41444,6.3,1.11],[3930,149.0225,-40.82472,6.41,1.61],[3931,149.19375,-26.55028,6.28,0.22],[3932,149.14792,-33.41861,5.84,1.2],[3933,149.225,-27.475,6.32,0.17],[3934,152.14292,83.91833,6.37,1.52],[3935,149.09125,-51.33611,6.37,-0.17],[3936,149.60875,27.75889,6.3,0.6],[3937,149.55583,12.44472,5.26,-0.04],[3938,149.53167,8.31417,6.04,1.36],[3939,149.96542,56.81194,5.48,1.46],[3940,149.21583,-54.56778,3.54,-0.08],[3941,149.29542,-52.63889,6.12,-0.13],[3942,149.90083,29.64528,5.73,1.06],[3943,149.42708,-48.41444,6.05,-0.14],[3944,149.04042,-71.38944,6.35,-0.08],[3945,149.92958,3.38472,6.7,0.27],[3946,149.77542,-23.95028,6.21,-0.1],[3947,149.71792,-35.89111,5.23,0.31],[3948,149.31333,-64.48944,6.58,1.13],[3949,149.24875,-69.10194,6.2,-0.1],[3950,150.05333,8.04417,4.7,1.6],[3951,150.25292,31.92361,5.36,0.66],[3952,150.70375,21.94917,5.66,-0.19],[3953,150.14333,-56.94667,6.52,0.98],[3954,151.15125,53.89167,5.74,0.48],[3955,150.41875,-53.36444,6.2,-0.13],[3956,150.70542,-30.5775,6.54,1.19],[3957,150.49167,-57.34972,6.2,1.12],[3958,151.29375,52.37083,6.14,0.6],[3959,150.92083,-9.57389,6.12,1.66],[3960,150.5,-60.42083,5.94,0.26],[3961,151.035,3.20111,6.45,0.4],[3962,150.9225,-25.31667,6.7,0.0],[3963,151.01208,-18.10167,5.86,-0.06],[3964,150.83542,-46.63611,6.12,0.02],[3965,151.0875,-24.28556,5.7,0.3],[3966,150.74958,-60.17861,6.19,0.17],[3967,150.70583,-62.15639,6.42,1.72],[3968,151.0975,-39.97583,6.43,1.3],[3969,151.42042,15.7575,6.37,0.37],[3970,151.28125,-13.06472,4.6,-0.09],[3971,150.89292,-61.88389,6.14,-0.04],[3972,151.31333,-36.38389,6.27,1.11],[3973,151.6975,5.61139,6.21,0.94],[3974,151.8575,35.24472,4.48,0.18],[3975,151.83333,16.76278,3.52,-0.03],[3976,151.54708,-47.37,5.08,0.88],[3977,151.78958,-17.14167,5.6,1.5],[3978,151.52958,-52.18806,6.52,0.98],[3979,152.06625,31.60417,6.24,0.45],[3980,151.97625,9.9975,4.37,1.45],[3981,151.98458,-0.37167,4.49,-0.04],[3982,152.09292,11.96722,1.35,-0.11],[3983,150.18208,-82.21472,5.52,0.03],[3984,152.00708,-37.33361,6.36,0.98],[3985,152.19042,-10.88472,6.53,0.02],[3986,152.14792,-15.61167,6.27,-0.01],[3987,152.74542,40.66139,6.32,1.25],[3988,152.48542,-12.09583,6.24,0.18],[3989,152.53125,-8.40833,5.91,0.02],[3990,152.23458,-51.81111,4.86,-0.12],[3991,152.52458,-12.81611,5.31,0.36],[3992,152.3825,-35.85667,6.13,0.6],[3993,152.80333,37.40194,5.85,1.29],[3994,152.64708,-12.35417,3.61,1.01],[3995,152.1775,-65.81528,5.28,0.98],[3996,152.7325,-8.41833,5.65,1.3],[3997,151.03167,-81.56583,6.6,0.92],[3998,152.90917,13.355,6.44,0.46],[3999,152.34125,-61.54917,5.6,1.6],[4000,152.82417,-7.31667,6.25,0.01],[4001,152.65792,-41.715,5.98,1.24],[4002,152.37708,-68.68333,5.81,0.02],[4003,153.01208,-28.60639,6.28,0.01],[4004,153.20125,4.61472,5.77,1.18],[4005,153.1575,-19.15361,6.44,0.5],[4006,153.4575,27.13583,6.04,0.85],[4007,152.89667,-58.82806,6.4,1.66],[4008,153.78208,59.98556,6.25,1.6],[4009,152.94375,-58.06056,5.72,-0.08],[4010,153.09583,-52.16333,6.16,1.17],[4011,153.33083,-27.02889,6.25,0.31],[4012,153.62375,21.16778,6.02,0.56],[4013,153.35333,-33.03194,6.38,0.59],[4014,153.77625,31.46806,6.46,0.6],[4015,153.44125,-40.34583,5.9,1.21],[4016,154.50458,73.07333,6.4,0.23],[4017,153.345,-51.23333,5.28,0.25],[4018,153.25542,-59.91806,6.1,-0.08],[4019,153.48583,-40.31056,6.35,0.94],[4020,153.36667,-51.75611,5.78,0.14],[4021,154.46083,71.06056,6.66,0.32],[4022,153.33833,-61.65889,6.41,-0.11],[4023,153.68417,-42.12194,3.85,0.05],[4024,154.06,29.31056,5.35,0.01],[4025,153.3775,-66.37306,5.16,0.21],[4026,154.50833,65.10833,5.82,0.12],[4027,154.11708,28.6825,6.49,0.6],[4028,154.06708,17.74028,6.55,0.6],[4029,153.83708,-36.51806,6.19,1.06],[4030,154.13458,23.50306,5.97,0.67],[4031,154.1725,23.41722,3.44,0.31],[4032,154.17458,25.37139,5.84,1.2],[4033,154.27417,42.91444,3.45,0.03],[4034,154.03792,-11.20333,6.08,1.1],[4035,154.16958,13.72833,5.41,1.61],[4036,153.88125,-43.1125,5.6,1.52],[4037,153.43417,-70.03806,3.32,-0.08],[4038,153.81917,-54.97417,6.16,-0.17],[4039,154.31083,23.10611,5.82,0.5],[4040,154.19,-20.67056,6.57,0.48],[4041,154.54292,27.41528,6.52,-0.02],[4042,154.4075,-8.06889,5.24,0.31],[4043,154.01292,-59.90333,6.22,0.2],[4044,154.74583,46.76083,6.43,0.6],[4045,154.1675,-51.205,6.3,1.54],[4046,154.86167,48.39694,6.0,1.02],[4047,155.26417,68.7475,5.96,0.2],[4048,154.75292,24.71167,6.4,0.6],[4049,154.53167,-28.99194,5.34,0.24],[4050,154.27083,-61.33222,3.4,1.54],[4051,155.06167,53.77917,6.45,0.54],[4052,155.13,54.21694,6.0,1.13],[4053,154.6575,-36.80472,6.3,1.28],[4054,154.93375,19.47083,4.79,0.45],[4055,154.82,-12.52806,6.0,0.26],[4056,154.6175,-41.66833,5.96,-0.06],[4057,154.99292,19.84167,2.61,1.15],[4058,154.99417,19.84056,3.8,0.6],[4059,154.88417,-5.10583,6.37,0.9],[4060,154.9975,-9.05889,6.32,0.33],[4061,154.65667,-56.11,5.81,0.48],[4062,157.42292,84.25222,5.5,0.6],[4063,154.90333,-55.02944,4.57,1.62],[4064,155.25833,2.28972,6.66,-0.08],[4065,154.77,-64.67639,5.67,0.05],[4066,155.06958,-47.69917,5.65,1.67],[4067,155.54375,41.22944,5.76,0.54],[4068,155.2825,-17.985,6.51,0.4],[4069,155.58208,41.49944,3.05,1.59],[4070,155.45958,14.97556,6.12,0.02],[4071,155.36958,-23.71083,6.5,0.2],[4072,156.03292,65.56639,4.97,-0.06],[4073,155.4,-22.52833,6.51,0.07],[4074,155.22833,-56.04306,4.5,-0.12],[4075,155.77625,33.90806,5.9,0.14],[4076,155.55375,-19.86694,6.13,0.03],[4077,155.75167,6.5425,6.07,1.12],[4078,155.92417,29.61583,6.39,1.09],[4079,155.81083,5.69417,6.54,0.46],[4080,155.58167,-41.65,4.83,1.12],[4081,156.03583,33.71861,5.5,1.18],[4082,155.86042,-4.07417,5.97,-0.1],[4083,155.80458,-30.16222,6.27,0.31],[4084,157.76917,82.55861,5.26,0.37],[4085,156.05458,2.36806,6.32,1.0],[4086,155.87208,-38.01,5.33,0.25],[4087,155.91833,-41.95333,6.27,0.88],[4088,156.31333,8.78472,5.61,1.62],[4089,155.74208,-66.90167,4.99,-0.13],[4090,156.47875,33.79611,4.74,0.25],[4091,155.96208,-57.95389,6.35,1.52],[4092,156.43458,-7.05972,5.57,1.52],[4093,156.32167,-42.46806,6.18,1.0],[4094,156.5225,-16.83639,3.81,1.48],[4095,156.2475,-58.57639,5.95,0.32],[4096,156.86667,41.60083,6.02,0.17],[4097,156.75208,19.36444,6.15,1.14],[4098,157.01583,48.78472,6.44,0.6],[4099,156.53958,-42.73889,6.13,1.13],[4100,156.97083,36.70722,4.21,0.9],[4101,156.9125,9.7625,6.04,-0.06],[4102,156.09875,-74.03167,4.0,0.35],[4103,157.15208,45.21222,6.35,1.32],[4104,156.78792,-31.06778,4.25,1.45],[4105,156.18458,-73.97167,6.19,0.07],[4106,157.47625,65.62611,6.32,1.14],[4107,156.70417,-54.8775,5.58,1.56],[4108,157.61083,64.2575,6.12,0.16],[4109,157.18333,-3.7425,6.05,0.05],[4110,156.85167,-57.63889,4.66,0.51],[4111,157.00792,-49.40556,6.1,1.51],[4112,157.65667,55.98056,4.84,0.52],[4113,157.52667,38.92528,5.77,0.08],[4114,156.96958,-58.73944,3.82,0.31],[4115,156.85542,-65.70472,6.01,0.09],[4116,157.36958,-2.73917,5.21,-0.06],[4117,157.37083,-29.66361,5.58,1.42],[4118,157.3975,-30.60722,5.56,-0.04],[4119,157.57292,-0.63694,5.09,-0.14],[4120,157.21917,-64.17222,5.29,1.86],[4121,159.00708,80.49444,6.52,0.95],[4122,157.74458,-7.6375,6.2,1.38],[4123,157.74917,-13.58833,5.58,-0.04],[4124,157.96417,32.37944,5.9,0.11],[4125,157.71417,-26.48389,6.51,0.54],[4126,158.77292,75.71306,4.84,0.96],[4127,158.04917,14.13722,5.46,1.68],[4128,157.66333,-61.35611,6.43,1.76],[4129,157.53625,-66.985,6.19,0.01],[4130,157.9525,-28.2375,6.05,0.51],[4131,158.43167,53.4975,6.45,0.6],[4132,158.30792,40.42556,4.75,0.23],[4133,158.20292,9.30667,3.85,-0.14],[4134,157.84083,-53.71556,4.89,0.5],[4135,157.98958,-45.06667,5.74,-0.15],[4136,157.98583,-45.06944,6.09,-0.11],[4137,158.37875,34.98861,5.58,0.02],[4138,157.58375,-71.99306,4.74,0.04],[4139,158.14,-44.61889,5.91,0.92],[4140,158.00583,-61.68528,3.32,-0.09],[4141,158.79042,57.08278,5.16,0.34],[4142,157.75833,-73.22167,4.93,1.68],[4143,158.23708,-47.00333,5.02,1.04],[4144,158.19833,-58.66694,6.0,0.32],[4145,158.50375,-23.74528,5.08,1.6],[4146,158.7,6.95361,5.08,0.94],[4147,158.35542,-58.19028,6.14,0.35],[4148,158.75917,8.65028,5.67,0.05],[4149,158.74042,-23.17611,6.1,0.5],[4150,159.08917,36.32694,6.28,0.39],[4151,158.55375,-60.98778,6.23,1.4],[4152,158.91208,-18.56917,6.49,0.2],[4153,158.80375,-39.56278,5.38,2.88],[4154,158.79375,-43.66472,6.08,0.94],[4155,159.0725,-10.58333,6.57,0.29],[4156,159.06958,-16.34444,6.03,1.65],[4157,159.01917,-26.675,6.29,0.48],[4158,159.135,-12.23028,5.7,0.52],[4159,158.89708,-57.55778,4.45,1.62],[4160,159.29833,-11.74861,6.52,0.29],[4161,157.9625,-81.92111,7.07,-0.08],[4162,159.30708,-27.4125,4.89,1.62],[4163,159.38833,-13.38444,4.82,2.68],[4164,159.08458,-59.56472,5.08,1.18],[4165,159.77375,53.66833,5.52,1.27],[4166,159.68,31.97611,4.71,0.81],[4167,159.32542,-48.22583,3.84,0.3],[4168,159.78167,37.91,5.85,0.57],[4169,159.36167,-58.73333,5.45,0.5],[4170,158.85333,-76.30917,6.3,1.2],[4171,159.64583,-16.87667,4.91,0.92],[4172,159.71,-12.44361,6.04,0.0],[4173,159.51042,-57.25639,5.91,-0.14],[4174,158.86708,-78.60778,4.11,1.58],[4175,159.70958,-42.75361,6.11,0.66],[4176,160.45125,68.44333,5.75,1.3],[4177,159.68792,-59.18306,4.66,1.48],[4178,160.48583,65.71639,5.12,1.2],[4179,159.7475,-58.81694,5.92,1.65],[4180,159.82667,-55.60333,4.28,1.04],[4181,160.76708,69.07611,5.0,1.38],[4182,160.35083,-1.74167,6.26,0.88],[4183,160.215,-35.74167,6.37,0.92],[4184,160.54708,31.69694,6.02,1.62],[4185,160.04708,-65.10056,5.52,-0.16],[4186,159.81917,-74.49361,6.07,1.71],[4187,160.93042,57.19917,5.8,-0.02],[4188,160.32333,-59.67694,6.42,0.08],[4189,160.7575,26.32556,5.51,0.17],[4190,160.63042,-13.975,6.24,1.54],[4191,160.88708,46.20389,5.18,0.33],[4192,160.85417,23.18833,5.08,0.04],[4193,160.83708,4.74778,5.79,1.17],[4194,160.68,-32.71583,5.64,0.0],[4195,161.26667,67.41139,6.0,2.39],[4196,160.55833,-64.46639,4.82,-0.14],[4197,161.06042,19.75861,6.27,0.17],[4198,160.66917,-59.21583,5.38,0.26],[4199,160.73917,-64.39444,2.76,-0.22],[4200,160.88375,-60.56667,4.57,1.71],[4201,161.28917,2.48806,6.28,1.21],[4202,161.59375,57.36583,6.34,1.56],[4203,161.46625,30.68222,5.24,-0.06],[4204,160.96333,-64.24889,5.77,0.0],[4205,161.02875,-63.96111,4.82,-0.13],[4206,160.46375,-79.78333,5.97,-0.07],[4207,161.52375,6.37306,6.37,1.12],[4208,161.60208,18.89139,5.49,1.12],[4209,161.60542,14.19472,5.48,0.91],[4210,161.265,-59.68417,6.21,0.61],[4211,161.08083,-70.86,6.26,0.2],[4212,161.13375,-70.855,6.46,0.23],[4213,161.11042,-72.44389,6.27,0.49],[4214,161.71667,-17.29667,5.42,0.11],[4215,162.20833,65.13222,6.39,-0.02],[4216,161.6925,-49.42,2.69,0.9],[4217,161.57,-60.60333,6.25,0.04],[4218,161.90833,-15.26194,6.67,-0.01],[4219,161.56875,-64.515,5.34,-0.1],[4220,161.62375,-64.26333,5.23,-0.07],[4221,161.73958,-56.75722,5.23,-0.08],[4222,161.71333,-64.38333,4.85,-0.15],[4223,162.23833,29.41583,6.15,1.15],[4224,162.16917,-1.95889,5.93,1.6],[4225,162.05917,-31.68833,5.88,0.03],[4226,161.91125,-57.46778,6.36,1.62],[4227,162.31417,10.54528,5.34,0.03],[4228,162.0225,-59.91917,6.0,0.27],[4229,162.32208,-4.02417,6.61,0.22],[4230,162.47375,27.97389,6.04,0.37],[4231,161.31542,-80.46972,5.47,0.95],[4232,162.40625,-16.19361,3.11,1.25],[4233,162.43125,-9.85278,5.86,1.07],[4234,161.445,-80.54028,4.45,-0.19],[4235,162.79625,56.58222,5.67,1.12],[4236,162.84875,59.32,5.58,1.14],[4237,162.57542,-8.89778,5.79,0.16],[4238,162.4875,-34.05806,5.61,0.04],[4239,162.35042,-59.32361,5.91,0.0],[4240,162.7725,-3.0925,5.95,1.48],[4241,163.12833,52.56528,6.65,0.6],[4242,163.13292,52.50361,6.44,1.11],[4243,163.37792,69.85389,5.93,0.99],[4244,163.05708,1.02528,6.38,0.08],[4245,163.15042,-0.20139,6.31,1.5],[4246,163.39375,54.585,5.1,1.36],[4247,163.32792,34.215,3.83,1.04],[4248,163.49458,43.19,4.71,-0.05],[4249,163.35375,-2.25528,6.12,0.9],[4250,163.12875,-57.24056,5.25,0.16],[4251,163.37292,-20.13889,5.24,0.47],[4252,163.38708,-15.44556,6.38,1.16],[4253,163.43208,-2.12917,5.45,0.96],[4254,163.67583,25.49083,6.2,0.28],[4255,163.57417,-13.75806,5.66,0.83],[4256,163.7425,34.03472,5.72,1.01],[4257,163.37333,-58.85333,3.78,0.95],[4258,163.935,33.50694,5.03,1.1],[4259,163.90333,24.74972,4.5,0.01],[4260,163.90542,24.74889,6.3,0.6],[4261,163.79833,-20.665,6.44,1.1],[4262,163.425,-70.72028,5.99,-0.02],[4263,163.75417,-42.25111,6.11,-0.08],[4264,164.06042,42.00833,6.03,1.13],[4265,163.92667,0.73694,5.91,0.42],[4266,163.62333,-61.82667,5.93,1.75],[4267,164.00625,6.18528,5.81,1.45],[4268,163.11458,-79.55944,6.33,1.46],[4269,164.07042,22.35167,6.14,1.55],[4270,164.14333,25.5,6.35,1.03],[4271,163.82167,-60.51694,5.92,1.08],[4272,164.98667,77.77,6.2,0.97],[4273,164.17958,-37.13778,4.6,1.03],[4274,164.28292,-50.765,5.91,0.18],[4275,164.82458,51.88222,6.17,1.38],[4276,164.45167,-59.73194,6.11,1.1],[4277,164.86667,40.43028,5.05,0.61],[4278,164.88667,36.09306,6.0,1.59],[4279,164.31542,-75.09972,6.13,1.53],[4280,165.06125,45.52611,5.47,1.47],[4281,164.92125,11.70583,6.55,0.43],[4282,164.80792,-33.73722,5.71,0.37],[4283,165.10667,51.50194,6.43,0.6],[4284,164.87875,-16.35389,5.89,1.63],[4285,165.08583,42.91139,6.02,0.57],[4286,165.27417,63.42111,6.39,0.16],[4287,164.94375,-18.29889,4.08,1.09],[4288,165.21,39.21222,5.08,0.24],[4289,165.04833,-14.08333,5.88,1.5],[4290,164.80833,-61.32028,6.16,-0.06],[4291,165.14,3.6175,4.84,1.16],[4292,164.9975,-43.80722,5.81,-0.08],[4293,165.03875,-42.22583,4.39,0.11],[4294,165.18667,6.10139,4.99,0.16],[4295,165.46042,56.3825,2.37,-0.02],[4296,165.03583,-51.81778,6.15,0.18],[4297,165.23833,-15.79278,6.34,1.18],[4298,165.17,-31.83944,6.07,0.52],[4299,165.45708,-2.48472,4.74,1.62],[4300,165.5825,20.17972,4.42,0.05],[4301,165.93208,61.75083,1.79,1.07],[4302,165.60167,-26.83139,6.23,0.31],[4303,165.81083,-0.7525,6.14,0.26],[4304,164.80375,-81.55611,6.71,0.55],[4305,165.81208,-11.30361,5.5,0.94],[4306,165.9025,-0.00083,5.95,1.22],[4307,165.81708,-31.96083,6.46,1.62],[4308,165.90208,-13.43444,6.34,0.88],[4309,166.13,38.24139,6.0,0.16],[4310,166.25417,7.33611,4.63,0.33],[4311,166.13,-47.67917,5.67,0.24],[4312,164.8075,-84.59389,6.19,0.11],[4313,166.22583,-35.80472,5.43,0.03],[4314,166.33292,-27.29361,4.94,0.36],[4315,166.39167,-11.08889,6.09,0.3],[4316,166.2675,-49.3925,6.13,-0.02],[4317,166.49,-27.28778,5.71,-0.06],[4318,166.52417,-51.2125,6.3,0.95],[4319,166.72583,1.95556,5.52,0.97],[4320,166.66125,-28.72778,6.77,0.04],[4321,166.61417,-50.95667,6.32,1.16],[4322,166.91542,23.32361,6.46,0.16],[4323,166.62208,-58.67528,6.02,1.24],[4324,166.785,-32.58722,6.59,0.34],[4325,166.635,-62.42417,4.61,1.03],[4326,166.60083,-64.83972,6.41,0.12],[4327,166.81917,-42.63861,5.15,0.03],[4328,166.97667,-30.17472,6.54,0.6],[4329,166.70792,-70.87806,5.57,-0.05],[4330,167.41625,67.21028,6.06,0.22],[4331,167.06583,-29.97278,6.49,0.03],[4332,167.20458,24.65833,5.68,0.06],[4333,167.32958,36.30944,5.74,1.51],[4334,167.18292,-28.08056,5.44,0.07],[4335,167.41583,44.49861,3.01,1.14],[4336,167.41042,43.2075,5.89,1.57],[4337,167.1475,-58.975,3.91,1.23],[4338,167.14167,-61.94722,5.13,0.22],[4339,167.4725,-32.3675,5.81,0.04],[4340,168.04583,68.27194,6.4,0.6],[4341,167.93208,14.40028,6.3,0.21],[4342,167.72792,-58.45528,6.88,-0.08],[4343,167.91458,-22.82583,4.48,0.03],[4344,168.18542,54.89417,6.63,0.6],[4345,168.13417,35.81361,6.41,0.61],[4346,168.06167,-32.43389,6.38,1.7],[4347,168.12667,-18.5,6.13,-0.01],[4348,168.14417,-21.74917,6.4,1.38],[4349,167.87292,-71.43639,6.35,1.37],[4350,168.13792,-49.10111,5.36,0.18],[4351,168.4175,41.08861,6.33,1.15],[4352,168.15,-60.3175,4.6,0.55],[4353,168.23708,-49.73639,6.11,1.06],[4354,168.31125,-44.37222,5.8,1.66],[4355,168.18833,-64.16972,5.23,-0.06],[4356,168.44,-0.06972,5.42,-0.03],[4357,168.52708,20.52361,2.56,0.12],[4358,168.5075,8.06056,5.79,1.12],[4359,168.56,15.42944,3.34,-0.01],[4360,168.41375,-53.23167,5.76,1.32],[4361,168.37833,-59.61944,5.74,-0.1],[4362,168.80083,23.09556,4.63,1.66],[4363,169.01667,52.77306,6.5,0.43],[4364,168.725,-43.73417,6.21,1.61],[4365,168.96625,13.3075,5.32,1.2],[4366,168.99083,12.84472,6.67,0.27],[4367,169.17458,49.47639,5.88,1.08],[4368,169.16542,-3.65167,4.47,0.21],[4369,169.2425,-7.13472,6.14,0.2],[4370,169.11542,-45.88,6.31,0.4],[4371,169.3225,2.01056,5.18,1.52],[4372,169.29917,-38.01444,6.27,0.1],[4373,169.41333,-34.73722,6.45,0.4],[4374,169.54542,31.52917,4.87,0.6],[4375,169.54583,31.52917,4.41,0.59],[4376,169.42917,-36.53444,6.68,0.98],[4377,169.61958,33.09417,3.48,1.4],[4378,169.5875,11.98472,6.66,0.07],[4379,169.32917,-67.82361,6.06,1.76],[4380,169.78292,38.18556,4.78,0.12],[4381,169.72917,1.65056,5.91,1.04],[4382,169.83542,-14.77861,3.56,1.12],[4383,170.22417,67.10056,6.21,1.01],[4384,169.81875,-64.5825,5.99,0.46],[4385,169.64292,-79.66861,6.35,0.26],[4386,170.28417,6.02944,4.05,-0.06],[4387,169.90125,-75.1425,6.27,-0.03],[4388,170.45542,57.075,6.43,0.15],[4389,170.01625,-71.99444,6.41,0.05],[4390,170.25167,-54.49111,3.89,-0.15],[4391,170.71375,64.33056,6.02,0.09],[4392,170.70667,43.48278,4.99,0.99],[4393,170.59625,-44.64583,6.12,0.92],[4394,170.825,0.13167,6.05,1.46],[4395,170.84125,-18.78,5.09,0.42],[4396,170.80292,-36.16472,5.0,1.46],[4397,170.48792,-77.60833,6.43,0.2],[4398,170.78375,-56.77944,5.79,0.01],[4399,170.98125,10.52917,3.94,0.41],[4400,171.00958,1.40778,5.39,0.94],[4401,170.84083,-64.955,5.11,-0.08],[4402,171.1525,-10.85944,4.83,1.56],[4403,171.09208,-42.66917,6.12,-0.18],[4404,171.24542,11.43028,5.8,1.38],[4405,171.22042,-17.68389,4.08,0.21],[4406,171.04625,-72.25667,5.59,0.06],[4407,171.48792,55.85056,5.75,0.6],[4408,171.40167,16.45639,5.57,0.36],[4409,171.3725,-36.06306,5.22,0.99],[4410,171.45833,3.86,6.37,0.33],[4411,171.38792,-37.74778,5.89,1.54],[4412,171.60625,33.45056,6.32,0.43],[4413,171.43,-63.97278,5.17,0.5],[4414,171.68875,3.01306,6.5,0.79],[4415,171.64708,-61.11528,5.3,-0.08],[4416,171.78958,-12.35667,5.94,0.49],[4417,171.69708,-53.16,5.81,0.52],[4418,171.98417,2.85611,4.95,1.0],[4419,171.97375,-1.7,6.25,1.04],[4420,171.99375,-35.32861,6.45,0.6],[4421,172.26917,61.77833,5.83,0.36],[4422,172.2675,39.33694,5.31,0.01],[4423,172.14625,-42.67417,5.08,-0.03],[4424,172.43125,56.7375,6.28,0.15],[4425,172.07583,-72.47444,6.09,0.16],[4426,172.42458,15.41333,5.74,1.32],[4427,172.55375,54.36167,6.41,0.6],[4428,172.41083,-24.46333,5.76,0.07],[4429,172.96,81.12722,6.15,0.24],[4430,172.60417,46.6575,6.35,1.27],[4431,172.62958,43.17333,5.94,0.49],[4432,172.57875,-3.00361,4.77,1.54],[4433,172.62083,18.40972,5.52,1.05],[4434,172.85083,69.33111,3.84,1.62],[4435,172.72042,47.92917,6.42,0.88],[4436,172.7925,48.78917,6.56,0.93],[4437,172.93708,14.36444,6.2,0.57],[4438,172.8125,-61.27833,6.38,0.52],[4439,173.08667,61.0825,5.48,0.5],[4440,172.94833,-20.77667,6.24,0.54],[4441,172.94208,-59.44222,5.13,1.08],[4442,172.95333,-59.51583,5.15,0.49],[4443,173.06708,-29.26333,5.81,0.53],[4444,173.06792,-29.26111,5.64,0.53],[4445,173.09708,-26.74667,6.16,1.66],[4446,173.19792,-7.8275,5.95,1.38],[4447,173.20042,-40.43639,5.64,1.58],[4448,173.08292,-66.96222,5.9,1.13],[4449,173.22542,-31.08722,5.04,1.58],[4450,173.25042,-31.85778,3.54,0.94],[4451,173.31083,-16.28056,6.05,0.6],[4452,173.48458,36.81556,6.4,1.05],[4453,173.40542,-40.58694,5.39,0.12],[4454,173.54167,11.02361,6.55,0.18],[4455,173.59167,3.06,5.77,0.46],[4456,173.67708,16.79694,5.95,-0.16],[4457,173.77042,54.78528,5.63,1.02],[4458,173.62292,-32.83139,5.98,0.81],[4459,173.76583,20.44139,6.45,1.01],[4460,173.69042,-54.26417,4.62,-0.08],[4461,174.01167,69.32278,5.2,1.01],[4462,173.73667,-49.13667,5.5,1.04],[4463,173.805,-47.3725,5.71,1.66],[4464,173.93083,10.91111,6.56,0.13],[4465,174.07458,27.78111,5.8,0.23],[4466,173.98167,-47.64167,5.25,0.25],[4467,173.945,-63.01972,3.13,-0.04],[4468,174.17042,-9.80222,4.7,-0.08],[4469,174.14583,-33.57,5.74,1.02],[4470,174.17,-37.23778,6.31,0.06],[4471,174.23708,-0.82389,4.3,1.0],[4472,174.09292,-61.05222,5.83,-0.09],[4473,174.255,-32.98806,6.29,0.46],[4474,174.47083,50.61833,6.14,1.07],[4475,174.2525,-61.28333,5.15,1.12],[4476,174.39125,-47.74722,5.44,1.24],[4477,174.58583,43.62556,5.59,0.33],[4478,174.54083,8.88417,6.17,1.08],[4479,174.315,-75.89667,5.65,0.35],[4480,174.63958,46.83417,6.1,0.38],[4481,174.705,64.34694,6.46,0.6],[4482,174.63417,33.62556,6.27,1.32],[4483,174.615,8.13417,5.36,1.57],[4484,174.60042,-2.43611,6.22,1.12],[4485,174.45167,-67.62028,5.96,1.02],[4486,174.68708,45.10861,6.44,0.56],[4487,174.53042,-61.82639,5.15,-0.02],[4488,174.66708,-13.20194,5.48,0.52],[4489,174.75167,-24.72111,6.42,0.82],[4490,174.96292,-14.46861,6.21,0.0],[4491,174.96,-16.62028,6.19,1.62],[4492,174.8725,-65.39778,5.17,0.8],[4493,175.11417,57.97056,6.37,-0.12],[4494,175.05333,-34.74472,4.7,-0.07],[4495,175.19625,21.35278,5.26,0.98],[4496,175.2625,34.20167,5.33,0.72],[4497,175.1775,-53.96861,5.96,1.66],[4498,175.285,-29.19639,6.44,0.66],[4499,175.22333,-62.09,4.94,1.15],[4500,175.43167,55.1725,6.27,1.49],[4501,175.39292,31.74611,5.73,0.43],[4502,175.3325,-43.09583,5.55,0.6],[4503,175.43333,-32.49972,5.22,1.48],[4504,175.61833,66.745,5.3,1.28],[4505,175.52167,22.21083,6.59,0.6],[4506,175.51458,-20.29389,6.22,0.95],[4507,175.255,-83.1,6.33,1.08],[4508,175.86333,-37.19028,5.98,1.46],[4509,175.73083,-79.30639,6.39,0.9],[4510,175.97958,-6.67722,6.07,0.96],[4511,175.88,-62.48944,5.03,0.8],[4512,176.055,25.21833,6.02,1.53],[4513,175.97042,-62.87833,6.1,0.06],[4514,176.19083,-18.35083,4.73,0.97],[4515,176.32125,8.25833,4.85,0.18],[4516,176.3025,-49.06972,6.26,1.17],[4517,176.465,6.52944,4.03,1.51],[4518,176.5125,47.77944,3.71,1.18],[4519,176.43292,-45.69,5.29,-0.12],[4520,176.40167,-66.72861,3.64,0.16],[4521,176.73167,55.62833,5.27,1.27],[4522,176.62833,-61.17833,4.11,0.9],[4523,176.62958,-40.50056,4.91,0.66],[4524,176.77917,-35.90694,6.17,0.96],[4525,176.81542,-30.28694,6.48,0.68],[4526,176.82958,-57.69639,5.41,1.67],[4527,176.99625,20.21889,4.53,0.55],[4528,176.97875,8.24583,5.32,0.02],[4529,177.09792,-10.31333,6.26,0.58],[4530,177.05958,-66.81472,4.72,1.54],[4531,177.16125,14.28417,5.88,0.29],[4532,177.18792,-26.74972,5.11,1.6],[4533,177.255,-0.31861,6.15,0.52],[4534,177.265,14.57194,2.14,0.09],[4535,177.31208,16.24278,6.04,0.27],[4536,177.42375,34.93167,5.7,0.46],[4537,177.42125,-63.78833,4.32,-0.15],[4538,177.48583,-70.22583,4.97,1.4],[4539,177.58125,-15.86389,6.13,0.95],[4540,177.67375,1.76472,3.61,0.55],[4541,177.61333,-62.64944,5.7,0.26],[4542,177.65458,-27.27778,6.48,0.98],[4543,177.73042,12.27889,6.35,0.27],[4544,177.75917,-5.33333,5.64,1.06],[4545,177.78917,33.375,6.27,0.32],[4546,177.78625,-45.17361,4.46,1.3],[4547,177.84125,-12.18778,6.35,0.4],[4548,177.92333,-30.835,5.85,0.56],[4549,177.96333,-65.20611,4.9,-0.11],[4550,178.245,37.71861,6.45,0.75],[4551,178.04208,-56.98778,5.57,0.07],[4552,178.2275,-33.90806,4.28,-0.1],[4553,178.36167,-35.06667,6.17,0.08],[4554,178.4575,53.69472,2.44,0.0],[4555,178.45958,0.55194,6.3,0.2],[4556,178.54792,-57.41,6.06,0.05],[4557,178.6075,-37.74889,6.46,0.52],[4558,178.67708,-25.71389,5.3,0.88],[4559,178.76292,8.44389,5.58,0.94],[4560,178.77375,46.47694,6.54,0.1],[4561,178.79667,46.46972,7.03,0.01],[4562,178.80875,36.75639,6.49,1.58],[4563,178.74917,-63.27889,5.91,0.19],[4564,178.91875,15.64667,5.53,0.11],[4565,178.91708,-28.47694,5.93,1.5],[4566,178.99333,56.59861,5.84,1.1],[4567,179.00375,-17.15083,5.18,-0.02],[4568,178.97792,-39.68917,6.13,1.02],[4569,179.22167,61.54917,6.22,0.96],[4570,179.18292,-47.0725,6.26,0.4],[4571,179.26542,-33.31528,6.21,-0.04],[4572,179.31083,40.34361,6.62,0.46],[4573,179.41708,-62.44889,5.57,-0.15],[4574,179.53,32.27389,6.42,0.29],[4575,179.58583,61.46472,6.76,0.6],[4576,179.56333,-56.31722,5.44,-0.08],[4577,179.58458,-40.94722,6.79,0.97],[4578,179.69875,-64.33917,5.61,0.18],[4579,179.72667,-25.90889,6.43,0.03],[4580,179.76417,0.53056,6.17,1.26],[4581,179.82333,33.1675,5.96,1.15],[4582,179.79542,-51.69667,6.05,1.28],[4583,179.90542,-78.22194,4.91,-0.06],[4584,179.98833,34.035,6.5,0.22],[4585,179.98708,3.65528,5.37,0.0],[4586,180.0775,80.85306,6.17,1.61],[4587,180.18542,-10.44611,5.55,0.77],[4588,180.17708,-21.83722,6.28,1.22],[4589,180.21833,6.61417,4.66,0.13],[4590,180.21333,-19.65889,5.26,-0.2],[4591,180.2575,-1.76806,6.31,1.21],[4592,180.37083,-57.50361,6.16,0.0],[4593,180.41458,36.04194,5.59,1.01],[4594,180.52833,43.04556,5.21,0.26],[4595,180.58375,-85.63167,6.05,1.29],[4596,180.61917,-71.48889,6.42,1.17],[4597,180.65708,-69.19222,5.89,-0.08],[4598,180.715,-7.68361,6.22,1.49],[4599,180.75625,-63.31278,4.33,0.27],[4600,180.915,-42.43417,5.15,0.41],[4601,180.93458,-74.21389,6.44,1.23],[4602,181.06917,21.45917,5.87,0.22],[4603,181.08,-63.16556,4.72,-0.08],[4604,181.16125,-68.32917,5.35,-0.01],[4605,181.19375,-76.51917,5.04,1.49],[4606,181.11708,85.58722,6.27,0.59],[4607,181.23792,-60.96917,5.96,1.67],[4608,181.30208,8.73306,4.12,0.98],[4609,181.31292,76.90583,5.8,1.01],[4610,181.41542,62.93306,6.13,1.17],[4611,181.47167,-65.54722,6.33,0.22],[4612,181.48625,-35.69389,6.23,-0.08],[4613,181.49917,-3.13167,6.37,1.0],[4614,181.5825,-68.65083,6.23,1.24],[4615,181.59625,-65.70917,6.06,0.65],[4616,181.72042,-64.61361,4.15,0.34],[4617,181.9575,-75.36694,5.18,1.3],[4618,182.02167,-50.66139,4.47,-0.15],[4619,182.02,-50.76333,6.37,-0.05],[4620,182.06125,-48.69278,5.34,-0.01],[4621,182.08958,-50.7225,2.6,-0.12],[4622,182.1025,-60.84722,6.22,1.74],[4623,182.10333,-24.72889,4.02,0.32],[4624,182.22417,-44.32611,5.75,0.24],[4625,182.22708,-41.23139,5.48,-0.07],[4626,182.42208,1.89778,5.95,1.12],[4627,182.44708,74.66139,6.35,0.5],[4628,182.51042,-34.705,6.17,0.03],[4629,182.51417,5.80694,5.72,0.35],[4630,182.53125,-22.61972,3.0,1.33],[4631,182.64083,-37.87028,6.06,0.2],[4632,182.63167,16.80917,6.39,0.06],[4633,182.69208,27.28139,6.01,0.11],[4634,182.77042,-61.2775,6.08,0.39],[4635,182.76625,-23.6025,5.46,0.06],[4636,182.76208,-45.42278,6.61,1.08],[4637,182.88083,-51.35944,6.23,0.82],[4638,182.91292,-52.36861,3.96,-0.15],[4639,182.75,81.71,6.0,1.62],[4640,182.96333,25.87028,5.66,1.41],[4641,182.93708,57.05444,6.43,0.6],[4642,183.005,28.53611,6.49,0.36],[4643,183.03875,20.54194,5.57,0.95],[4644,183.09167,-62.95083,5.92,0.29],[4645,183.195,-70.15194,6.17,0.84],[4646,183.04958,77.61639,5.14,0.33],[4647,183.30417,-34.12556,6.5,1.66],[4648,183.35542,-38.92917,5.76,-0.13],[4649,183.48208,-78.57361,6.35,1.24],[4650,183.35792,10.26222,5.85,0.27],[4651,183.40292,-33.79278,6.33,0.08],[4652,183.51083,-45.72389,5.31,1.43],[4653,183.57,-64.40861,6.22,0.12],[4654,183.68083,53.43472,6.16,1.04],[4655,183.74833,-20.84417,5.83,1.05],[4656,183.78625,-58.74889,2.8,-0.23],[4657,183.79417,-10.3125,6.11,0.46],[4658,183.87708,-41.91306,6.26,1.01],[4659,183.78542,70.2,5.71,1.19],[4660,183.85667,57.0325,3.31,0.08],[4661,183.94583,-23.35361,6.54,0.45],[4662,183.95167,-17.54194,2.59,-0.11],[4663,184.00083,14.89889,5.1,0.06],[4664,184.09792,-72.61472,6.22,-0.01],[4665,183.9225,72.55083,6.29,1.14],[4666,184.03167,40.66028,5.66,1.55],[4667,184.08542,23.94528,4.95,0.97],[4668,184.12542,33.06139,5.0,1.14],[4669,184.275,-65.69278,6.06,0.03],[4670,184.26375,-16.69361,6.05,0.1],[4671,184.39208,-67.96083,4.11,1.58],[4672,184.37292,53.19111,5.81,1.3],[4673,184.37708,28.93722,5.7,0.16],[4674,184.58625,-79.31222,4.26,-0.12],[4675,184.44708,-36.09389,6.15,0.01],[4676,184.43458,15.14417,6.34,1.37],[4677,184.53792,-3.95444,6.99,0.36],[4678,184.54,-3.94861,6.54,0.33],[4679,184.60875,-64.00306,4.04,-0.17],[4680,184.63167,30.24917,6.23,0.3],[4681,184.66792,-0.78722,5.9,0.17],[4682,184.74875,-55.14306,5.0,1.59],[4683,184.21417,86.43611,6.33,0.43],[4684,184.75875,26.00778,6.48,0.18],[4685,184.82958,23.03472,6.27,0.17],[4686,183.83458,87.7,6.28,0.35],[4687,184.70792,75.16056,5.38,-0.02],[4688,184.87333,28.15694,6.33,0.5],[4689,184.97667,-0.66694,3.89,0.02],[4690,184.95292,48.98417,5.29,1.66],[4691,185.04458,-22.17556,5.97,0.82],[4692,185.11667,-65.84278,6.21,-0.04],[4693,185.08208,26.61944,5.54,1.09],[4694,185.07375,26.00194,6.15,0.3],[4695,185.0875,3.3125,4.96,1.16],[4696,185.14042,-22.21583,5.21,-0.1],[4697,185.17917,17.79278,4.74,1.01],[4698,185.17208,27.05472,7.13,0.36],[4699,185.23208,-13.56556,5.14,1.05],[4700,185.34,-60.40111,3.59,1.42],[4701,185.21167,57.86389,5.55,1.43],[4702,185.48958,-56.37472,5.92,1.57],[4703,185.53042,-67.52194,5.15,0.19],[4704,185.54958,-68.3075,5.74,1.04],[4705,185.545,24.77389,6.19,-0.01],[4706,185.70542,-57.67611,5.39,-0.1],[4707,185.62625,25.84611,4.81,0.49],[4708,185.63333,5.30556,6.4,0.6],[4709,186.40625,-86.15056,6.33,1.08],[4710,185.8075,-67.63167,6.36,0.89],[4711,185.84,-24.84056,5.68,1.16],[4712,185.8975,-35.41278,5.32,-0.08],[4713,185.90375,-39.30306,6.4,0.29],[4714,185.93708,-38.91111,5.79,-0.08],[4715,185.94583,42.54278,6.06,0.33],[4716,186.00625,51.56222,4.8,0.87],[4717,186.07708,26.09861,5.18,0.08],[4718,186.18625,-41.38417,6.25,1.18],[4719,186.11125,25.58278,6.42,0.27],[4720,186.32208,-65.77056,6.3,0.96],[4721,186.28542,-42.51444,6.11,0.65],[4722,186.29875,-11.61028,5.95,0.03],[4723,186.32667,-27.74917,6.09,1.27],[4724,186.34083,-35.18639,5.73,-0.06],[4725,186.31292,23.92611,6.03,1.1],[4726,186.26333,56.7775,5.81,1.62],[4727,186.27667,63.80278,6.32,0.91],[4728,186.46208,39.01861,5.02,0.96],[4729,186.62875,-63.1225,4.86,-0.12],[4730,186.64958,-63.09917,1.33,-0.24],[4731,186.65208,-63.09944,1.73,-0.26],[4732,186.63167,-51.45083,4.82,-0.14],[4733,186.60042,27.26833,4.95,0.27],[4734,186.70083,-48.91333,6.26,0.68],[4735,186.71542,-32.83,5.55,0.01],[4736,186.8525,-63.78917,6.0,0.07],[4737,186.73458,28.26833,4.36,1.13],[4738,186.74708,26.82556,5.0,0.08],[4739,186.86958,-58.99194,5.5,1.45],[4740,186.60083,71.92972,6.24,1.06],[4741,186.92542,8.61028,6.37,0.93],[4742,186.95583,-16.63194,6.35,0.84],[4743,187.01,-50.23056,3.91,-0.19],[4744,187.07875,-64.34139,6.04,0.02],[4745,186.89625,55.71278,5.7,1.55],[4746,186.965,-4.61528,6.22,0.44],[4747,187.10625,-61.79528,6.22,1.26],[4748,187.09375,-39.04139,5.44,-0.08],[4749,187.13917,-56.40778,6.15,0.92],[4750,187.15875,26.22667,6.54,0.17],[4751,187.18583,25.89917,6.65,0.22],[4752,187.22792,25.91278,5.29,-0.05],[4753,187.36208,24.10889,5.48,0.43],[4754,187.47458,-56.52472,5.8,1.56],[4755,187.49125,-41.73611,6.02,1.52],[4756,187.43,20.89611,5.69,0.07],[4757,187.46625,-16.51556,2.95,-0.05],[4758,187.52,-13.39306,6.35,0.56],[4759,187.57292,-23.69667,5.63,1.67],[4760,187.48875,58.40583,5.35,0.2],[4761,187.51208,51.53556,6.21,0.51],[4762,187.51792,58.7675,6.08,0.98],[4763,187.79125,-57.11333,1.63,1.59],[4764,187.81958,-57.08111,6.42,0.16],[4765,187.52792,69.20111,4.95,1.62],[4766,187.7525,24.56722,5.46,0.05],[4767,187.70875,53.07667,6.21,0.54],[4768,187.91792,-59.42389,5.48,0.63],[4769,188.04167,-73.00167,5.88,1.11],[4770,187.83917,7.60417,6.05,1.52],[4771,187.9825,-63.50611,5.95,0.27],[4772,187.91125,-5.0525,6.19,1.04],[4773,188.11667,-72.13306,3.87,-0.15],[4774,188.01875,-32.53361,6.46,0.2],[4775,188.0175,-16.19611,4.31,0.38],[4776,188.15,-13.85917,5.74,0.4],[4777,188.26208,10.29556,6.26,0.95],[4778,188.34333,-19.79194,6.26,0.29],[4779,188.39292,-12.83028,5.58,0.86],[4780,188.3925,24.28306,6.29,0.11],[4781,188.445,-9.45194,5.48,-0.03],[4782,188.49667,-49.90944,6.38,0.46],[4783,188.41208,33.2475,5.42,1.0],[4784,188.4475,33.38472,6.24,1.05],[4785,188.43542,41.3575,4.26,0.59],[4786,188.59667,-23.39667,2.65,0.89],[4787,188.37083,69.78833,3.87,-0.13],[4788,188.67625,-44.67333,5.77,0.7],[4789,188.71292,22.62917,4.81,0.0],[4790,188.87083,-61.84194,6.22,0.73],[4791,188.77625,18.37722,6.56,0.25],[4792,188.7825,18.37694,5.02,1.15],[4793,188.78375,21.88139,5.85,1.22],[4794,188.93958,-41.02194,5.13,0.22],[4795,188.68333,70.02194,4.94,1.31],[4796,189.005,-39.87,5.8,0.01],[4797,188.99417,-20.52722,6.2,0.33],[4798,189.29583,-69.13556,2.69,-0.2],[4799,189.1975,-5.83194,5.87,0.07],[4800,189.09708,59.48694,5.5,0.6],[4801,189.24292,17.08944,5.68,1.41],[4802,189.42583,-48.54111,3.86,0.05],[4803,189.42583,-27.13889,5.45,0.32],[4804,189.81042,-75.36944,6.49,0.08],[4805,189.51833,3.2825,6.33,0.01],[4806,189.71875,-67.19306,6.25,0.06],[4807,189.59333,1.85472,5.71,1.6],[4808,189.625,6.98833,7.08,1.44],[4809,189.68583,-18.25028,6.0,0.29],[4810,189.76458,-30.42222,5.89,1.21],[4811,189.69292,40.87444,6.37,0.18],[4812,189.75875,22.65944,6.38,1.1],[4813,189.81167,-7.99556,4.66,1.23],[4814,189.98167,-66.51167,6.26,-0.05],[4815,189.78042,21.0625,5.46,0.96],[4816,189.82042,35.95194,6.45,0.06],[4817,189.96875,-39.9875,4.64,-0.08],[4818,190.34583,-46.14556,5.84,1.52],[4819,190.37917,-48.95972,2.17,-0.01],[4820,190.52125,-69.4075,6.33,0.78],[4821,190.31667,-13.01361,6.08,0.6],[4822,190.3175,-13.015,5.98,0.42],[4823,190.48583,-59.68583,4.93,-0.04],[4824,190.39333,10.42639,6.19,0.19],[4825,190.415,-1.44944,3.65,0.36],[4826,190.415,-1.44944,3.68,0.6],[4827,190.455,-19.75861,6.03,0.39],[4828,190.47125,10.23556,4.88,0.09],[4829,190.48792,6.80667,5.59,0.0],[4830,190.70958,-63.05861,5.31,0.27],[4831,190.6475,-48.81306,4.66,1.09],[4832,190.70667,-55.94722,6.08,-0.03],[4833,190.39125,62.71306,6.07,0.01],[4834,190.78792,-56.17611,6.0,-0.08],[4835,190.8675,-58.90306,6.4,1.09],[4836,190.85958,-40.17778,6.44,0.25],[4837,190.90875,-1.57694,5.93,0.86],[4838,190.99458,-36.34917,6.39,-0.06],[4839,191.00208,-28.32389,5.48,1.34],[4840,190.7675,61.15556,6.38,1.26],[4841,191.25708,-68.83111,6.16,0.69],[4842,191.40792,-60.98111,4.69,1.05],[4843,191.11292,44.10306,6.33,0.43],[4844,191.57042,-68.10806,3.05,-0.18],[4845,191.24792,39.27889,5.95,0.55],[4846,191.2825,45.44028,4.99,2.54],[4847,191.40458,7.67333,5.22,0.33],[4848,191.59458,-56.48889,4.65,-0.16],[4849,191.59375,9.54,5.67,0.99],[4850,191.69167,-33.31556,5.86,1.34],[4851,191.66125,16.5775,5.12,1.35],[4852,191.10833,80.62111,6.4,0.12],[4853,191.93,-59.68861,1.25,-0.23],[4854,191.75958,5.95083,6.34,-0.05],[4855,191.80667,11.95806,6.07,0.12],[4856,191.88917,-6.30194,6.26,0.55],[4857,191.97375,-24.85167,6.44,-0.06],[4858,191.96417,3.57278,6.41,1.6],[4859,191.82875,62.78083,5.89,0.6],[4860,192.11,-27.5975,5.66,0.95],[4861,192.05958,13.55306,6.56,0.01],[4862,192.43708,-71.98639,5.55,1.17],[4863,191.89333,66.79028,5.43,1.56],[4864,192.19583,24.84028,6.31,0.7],[4865,192.22583,14.1225,5.7,0.02],[4866,192.17417,48.46694,6.27,0.18],[4867,192.16417,60.32,5.85,0.46],[4868,192.55,-60.40083,6.75,0.35],[4869,192.3225,27.55222,5.78,0.03],[4870,193.74417,-85.12333,5.46,1.02],[4871,192.58167,-48.45972,6.24,0.05],[4872,192.74125,-52.7875,5.73,0.13],[4873,192.5725,22.86333,6.43,1.0],[4874,192.67167,-33.99944,4.91,-0.04],[4875,192.54458,37.51694,5.89,0.15],[4876,192.82417,-60.32972,5.72,0.38],[4877,192.84542,-10.33833,6.41,1.02],[4878,192.90375,3.05667,6.02,1.29],[4879,192.98667,-39.68083,5.98,-0.1],[4880,193.02208,-48.09417,6.33,0.03],[4881,192.99125,-26.73806,6.15,0.23],[4882,193.1025,-53.82944,6.24,1.13],[4883,192.92458,27.54056,4.94,0.67],[4884,193.05125,17.07389,6.32,1.59],[4885,193.26625,-54.9525,5.93,1.31],[4886,193.115,16.1225,6.3,0.16],[4887,193.34083,-60.32861,5.76,0.33],[4888,193.27875,-48.94333,4.33,1.37],[4889,193.35917,-40.17889,4.27,0.21],[4890,193.45458,-60.37694,5.9,0.2],[4891,193.29667,-3.55306,6.11,0.5],[4892,192.2775,83.41806,5.85,-0.06],[4893,192.30667,83.41278,5.28,-0.03],[4894,193.32417,21.245,4.9,0.9],[4895,193.59167,-58.43056,6.58,0.76],[4896,193.40875,-4.22389,6.44,1.1],[4897,193.66333,-59.14667,4.62,-0.15],[4898,193.64833,-57.17778,4.03,-0.17],[4899,193.65333,-57.16833,5.17,-0.12],[4900,193.45708,12.41861,6.25,0.27],[4901,193.57792,-11.64861,6.0,0.08],[4902,193.58833,-9.53889,4.79,1.6],[4903,193.74375,-44.15194,5.89,0.64],[4904,193.55458,33.53444,6.26,0.2],[4905,193.50708,55.95972,1.77,-0.02],[4906,193.83083,-42.91583,5.47,1.68],[4907,194.13125,-72.18528,5.93,1.13],[4908,193.9875,-56.83611,5.32,0.01],[4909,193.73542,47.19667,5.84,1.55],[4910,193.90083,3.3975,3.38,1.58],[4911,193.97208,-15.32694,6.17,0.0],[4912,194.12542,-26.46028,6.62,0.68],[4913,194.26833,-51.19861,5.16,-0.06],[4914,194.00167,38.31472,5.6,0.34],[4915,194.00708,38.31833,2.9,-0.12],[4916,193.86875,65.43861,5.24,0.28],[4917,194.07333,54.09944,5.82,0.19],[4918,194.38833,-22.75389,6.31,1.07],[4919,194.28208,46.17694,6.12,1.01],[4920,194.73083,17.40944,4.78,1.56],[4921,194.91458,-3.81194,5.79,0.18],[4922,195.13583,-33.50528,6.02,0.38],[4923,195.5675,-71.54889,3.62,1.18],[4924,195.06875,30.785,4.9,1.17],[4925,195.14958,-3.36861,5.99,1.12],[4926,195.16167,18.37306,6.2,0.42],[4927,194.69708,75.4725,6.01,0.99],[4928,194.97958,66.59722,5.32,1.29],[4929,195.29,17.12306,5.96,0.96],[4930,195.77167,-71.47611,6.03,0.05],[4931,195.1825,56.36639,4.93,0.36],[4932,195.54417,10.95917,2.83,0.94],[4933,195.88833,-49.52722,4.85,0.02],[4934,195.445,63.61028,6.0,0.41],[4935,195.94208,-20.58306,5.58,0.56],[4936,195.66833,59.71611,6.53,0.05],[4937,195.97667,-3.66333,6.59,0.29],[4938,196.20042,-41.19667,6.26,1.68],[4939,196.37833,-52.115,6.43,1.7],[4940,196.56958,-48.46361,4.71,-0.14],[4941,196.64625,-41.58861,5.59,1.05],[4942,196.7275,-49.90611,4.27,-0.19],[4943,196.43542,35.79889,5.25,-0.08],[4944,196.85083,-59.86056,5.99,0.48],[4945,196.46792,45.26861,5.63,1.13],[4946,196.58833,21.15333,5.99,0.39],[4947,196.72625,-35.86194,6.54,-0.02],[4948,196.5425,29.02944,6.54,0.05],[4949,196.59417,22.61611,5.6,1.59],[4950,196.20708,73.02528,6.31,0.6],[4951,196.90958,-53.45972,5.71,-0.07],[4952,197.02917,-65.30639,5.51,-0.02],[4953,196.59458,62.04194,6.14,0.99],[4954,196.79458,27.62472,4.8,1.48],[4955,196.97417,-10.74028,5.19,1.14],[4956,196.97333,27.55583,6.19,1.36],[4957,197.13542,-8.98444,5.55,1.18],[4958,197.26375,-23.11806,4.95,1.05],[4959,197.31,-9.53833,6.32,1.02],[4960,197.30167,10.02222,5.78,1.0],[4961,197.43875,-10.32944,5.94,1.49],[4962,197.44917,16.84861,5.91,1.45],[4963,197.4875,-5.53889,4.38,-0.01],[4964,197.41125,37.42306,6.02,1.15],[4965,197.74333,-52.56694,6.06,-0.09],[4966,197.965,-69.94194,5.91,0.42],[4967,197.425,38.53389,6.28,-0.12],[4968,197.49708,17.52944,5.22,0.45],[4969,197.49708,17.52944,5.22,0.6],[4970,197.78667,-42.23306,5.79,0.52],[4971,197.51333,38.49889,5.91,0.29],[4972,197.97125,-63.30278,6.33,0.44],[4973,197.84667,-43.36889,5.25,1.05],[4974,197.45917,62.22917,6.54,-0.02],[4975,198.0725,-59.92083,4.6,-0.08],[4976,198.57167,-78.44722,5.85,1.07],[4977,198.20375,-66.22694,5.9,0.06],[4978,197.91333,-26.55167,6.5,0.19],[4979,198.01333,-37.80306,4.85,0.7],[4980,198.23333,-59.81667,6.16,0.6],[4981,198.01458,-16.19861,5.04,0.46],[4982,198.21208,-42.69972,6.22,1.06],[4983,197.96833,27.87806,4.26,0.57],[4984,198.035,24.25806,6.33,0.98],[4985,198.34792,-50.7,5.89,-0.02],[4986,198.13708,11.55611,5.77,1.51],[4987,198.14958,18.75167,6.53,0.88],[4988,198.55042,-58.68389,5.89,1.08],[4989,198.56167,-59.10333,4.92,0.48],[4990,198.36167,-18.82667,6.28,0.09],[4991,198.48958,-43.13889,6.16,1.38],[4992,198.30167,18.72694,6.11,1.2],[4993,198.81208,-67.89444,4.8,-0.08],[4994,198.85708,-69.67972,6.37,1.21],[4995,198.54542,-19.93083,5.33,0.87],[4996,198.67958,-48.95667,5.89,1.06],[4997,198.42917,40.15278,4.92,1.06],[4998,198.63042,11.33167,5.67,1.5],[4999,198.79042,-36.37111,6.19,0.97],[5000,199.18667,-65.13833,6.07,0.44],[5001,198.995,-19.94306,5.22,1.03],[5002,199.30417,-66.78361,4.87,1.5],[5003,198.38333,72.79889,6.59,0.08],[5004,198.88333,40.85528,5.79,0.19],[5005,199.10625,-1.39056,6.68,0.31],[5006,199.22125,-31.50611,5.1,0.96],[5007,199.05958,19.05167,6.45,0.98],[5008,199.30792,-43.97944,5.84,0.2],[5009,198.10583,80.47139,6.25,0.94],[5010,199.13458,19.78528,6.45,0.25],[5011,199.19375,9.42417,5.22,0.59],[5012,199.82875,-72.03556,6.04,1.35],[5013,199.315,13.67556,5.33,1.31],[5014,199.37458,-0.67667,6.37,0.26],[5015,199.40125,5.46972,4.8,1.67],[5016,199.64417,-51.28611,6.19,0.01],[5017,199.38542,40.5725,4.73,0.3],[5018,199.11917,68.40806,6.2,-0.06],[5019,199.60125,-18.31139,4.74,0.71],[5020,199.73042,-23.17167,3.0,0.92],[5021,199.71292,3.68778,6.62,0.06],[5022,199.61583,34.09806,5.82,1.35],[5023,199.56042,49.68194,5.15,-0.07],[5024,200.14542,-59.77333,6.18,0.43],[5025,199.7675,35.12806,6.02,0.24],[5026,200.1575,-52.74806,5.48,-0.13],[5027,200.20125,-55.80056,6.02,0.29],[5028,200.14917,-36.71222,2.75,0.04],[5029,200.24042,-46.88056,5.77,1.12],[5030,200.71917,-72.14667,6.05,0.09],[5031,200.17333,2.94167,6.26,0.1],[5032,200.07917,40.15056,5.6,1.2],[5033,200.37458,-19.48889,6.21,0.09],[5034,200.64875,-60.97222,6.18,0.01],[5035,200.65792,-60.98833,4.53,-0.13],[5036,200.5675,-52.18306,5.83,0.12],[5037,200.42333,2.08722,5.69,0.06],[5038,200.71958,-47.94306,6.16,0.18],[5039,200.76083,-48.56278,6.38,-0.07],[5040,200.54042,5.15472,5.87,0.12],[5041,201.00208,-64.53583,4.53,0.85],[5042,201.27958,-74.88778,5.05,1.11],[5043,200.78625,-33.19,6.22,1.65],[5044,200.75458,-17.73528,5.37,0.99],[5045,200.51583,43.90306,6.35,0.24],[5046,200.96792,-49.82306,6.48,0.96],[5047,200.82875,-4.92444,5.89,1.43],[5048,201.30792,-64.48528,5.31,0.4],[5049,201.45875,-70.6275,5.67,-0.03],[5050,201.13833,-5.16389,5.75,0.42],[5051,201.82625,-74.69194,6.63,-0.06],[5052,200.975,37.03389,6.07,1.68],[5053,201.12708,12.43194,6.44,1.06],[5054,200.98125,54.92528,2.27,0.02],[5055,200.985,54.92167,3.95,0.13],[5056,201.29833,-11.16139,0.98,-0.23],[5057,201.27792,23.85444,5.78,0.06],[5058,201.5325,-39.75528,5.09,1.2],[5059,201.5475,-1.1925,5.97,0.19],[5060,201.73375,-41.49806,5.69,1.47],[5061,201.77625,-49.14389,6.31,0.6],[5062,201.30625,54.98806,4.01,0.16],[5063,201.83667,-49.38083,6.28,-0.12],[5064,201.68,-12.70778,5.25,1.52],[5065,201.81125,-40.16306,6.4,0.98],[5066,202.19333,-69.62806,6.2,0.02],[5067,201.56917,46.02806,5.88,0.97],[5068,201.86333,-15.97361,4.76,1.09],[5069,202.28167,-64.67583,6.11,0.11],[5070,201.49958,63.26111,6.5,0.74],[5071,202.355,-51.16528,5.06,0.07],[5072,202.1075,13.77889,4.98,0.71],[5073,201.53375,72.39139,5.79,1.63],[5074,201.76917,64.73556,6.66,0.37],[5075,201.79458,64.71944,7.04,0.39],[5076,201.99792,52.74583,6.34,0.23],[5077,202.10917,40.72972,6.47,0.92],[5078,202.31208,-1.36444,6.43,1.11],[5079,202.04875,50.58722,6.8,0.6],[5080,202.42833,-23.28139,4.97,1.6],[5081,202.30417,10.81833,5.65,1.05],[5082,203.31167,-77.56833,6.48,0.48],[5083,202.19042,50.71833,6.43,0.37],[5084,205.23125,-85.78611,5.58,0.18],[5085,202.11292,59.94583,5.4,-0.01],[5086,202.50042,7.17889,6.17,1.47],[5087,202.49,6.01333,6.51,0.96],[5088,202.60708,-6.47028,6.09,0.33],[5089,202.76125,-39.4075,3.88,1.17],[5090,202.88875,-28.11278,6.47,0.1],[5091,201.73625,78.64389,5.77,0.77],[5092,203.02208,-38.39917,6.16,1.04],[5093,203.39875,-65.6325,6.37,-0.02],[5094,203.01167,-18.72889,6.01,0.18],[5095,202.99125,-6.25583,4.69,1.62],[5096,202.81583,42.10611,6.08,1.05],[5097,203.14958,-28.69278,5.69,0.04],[5098,203.14375,-29.56528,6.45,0.44],[5099,203.21542,-15.36306,5.55,1.23],[5100,203.24208,-10.165,5.21,0.96],[5101,203.25292,-7.195,6.68,1.28],[5102,203.20042,24.34639,6.11,0.96],[5103,203.62042,-48.27222,6.33,-0.05],[5104,203.68167,-33.31083,6.44,1.26],[5105,203.53292,3.65889,4.94,0.03],[5106,203.66875,-13.21444,5.91,0.02],[5107,203.67333,-0.59583,3.37,0.11],[5108,203.59083,38.78917,6.37,0.21],[5109,203.53042,55.34861,5.6,-0.03],[5110,203.69917,37.1825,4.98,0.4],[5111,203.88042,-5.39611,5.73,0.95],[5112,203.61375,49.01611,4.7,0.12],[5113,204.30083,-61.69194,5.63,0.5],[5114,203.88875,10.20472,6.49,1.03],[5115,204.79958,-75.68389,6.34,0.01],[5116,203.80875,44.19694,6.84,0.2],[5117,204.21042,-34.46778,6.5,1.03],[5118,204.275,-44.14333,5.98,0.94],[5119,204.69042,-70.445,6.1,1.42],[5120,204.20167,-26.495,5.78,0.22],[5121,204.34875,-46.42833,5.9,-0.12],[5122,204.53167,-58.415,6.42,1.12],[5123,204.24625,24.61333,5.74,1.55],[5124,204.70458,-57.62306,6.01,1.14],[5125,205.0025,-70.78833,6.59,1.3],[5126,204.16583,49.48667,6.49,0.6],[5127,204.365,36.295,4.82,0.23],[5128,204.675,-29.56083,5.83,0.4],[5129,204.53292,14.30167,6.52,0.25],[5130,205.04542,-64.57694,5.79,0.39],[5131,203.67833,76.54667,6.57,0.6],[5132,204.97167,-53.46639,2.3,-0.22],[5133,204.42917,50.71472,6.48,1.55],[5134,204.99875,-49.95028,6.0,1.5],[5135,204.92,-39.74806,6.27,1.66],[5136,204.9525,-40.05194,5.6,1.3],[5137,204.75958,18.26528,6.48,1.2],[5138,204.89417,10.74611,5.57,0.33],[5139,204.29583,71.24222,5.5,1.2],[5140,205.50458,-58.78722,5.38,-0.03],[5141,205.43625,-54.56,5.01,-0.05],[5142,204.87667,52.92139,5.46,0.1],[5143,205.065,31.01194,6.21,0.96],[5144,205.16875,19.95556,5.75,0.01],[5145,205.16292,28.06528,6.23,1.28],[5146,205.37875,-23.44972,6.59,0.06],[5147,205.44042,-33.59694,6.05,1.44],[5148,205.09667,50.51944,6.32,0.54],[5149,205.25958,22.49583,5.62,1.01],[5150,205.40333,-8.70306,5.01,1.63],[5151,205.73375,-56.76806,6.0,-0.08],[5152,205.7275,-50.79056,6.41,1.67],[5153,205.08875,57.2075,6.29,0.1],[5154,205.18458,54.68167,4.66,1.64],[5155,205.72917,-41.40111,5.98,1.02],[5156,205.55292,8.38833,6.16,0.42],[5157,205.91667,-42.0675,5.98,-0.08],[5158,206.06625,-51.01306,6.47,-0.13],[5159,205.76542,3.53806,5.36,1.11],[5160,205.62,41.67417,6.3,0.86],[5161,205.68083,34.98889,5.98,0.85],[5162,205.37458,64.8225,5.85,0.07],[5163,205.97625,-5.49889,6.51,0.05],[5164,205.93833,22.70028,6.13,1.42],[5165,206.12417,-16.17917,5.6,0.81],[5166,206.19042,-25.50083,6.21,1.38],[5167,206.40375,-26.11611,5.81,0.02],[5168,206.42167,-33.04389,4.23,0.38],[5169,205.97792,52.06444,6.02,0.0],[5170,206.39625,-15.7675,6.19,0.05],[5171,206.79458,-62.59,6.51,1.98],[5172,206.66375,-51.43278,4.65,0.96],[5173,206.48458,-12.42667,5.51,0.9],[5174,206.735,-36.25194,5.15,-0.02],[5175,206.865,-50.24944,5.91,0.29],[5176,206.91,-50.32111,5.45,1.36],[5177,206.305,55.87944,6.5,0.47],[5178,206.80625,-9.70917,6.05,1.42],[5179,206.55625,41.08861,5.87,0.21],[5180,206.57917,38.50389,5.94,0.94],[5181,206.85583,-17.86,5.43,1.62],[5182,206.68042,25.70222,5.95,0.49],[5183,206.73792,6.35056,6.33,0.63],[5184,205.66375,78.06444,5.91,1.01],[5185,206.81542,17.45667,4.5,0.48],[5186,206.74917,38.54278,5.5,1.03],[5187,206.64875,54.43278,5.7,-0.08],[5188,208.91125,-82.66611,5.95,1.46],[5189,207.22958,-35.70389,6.53,0.57],[5190,207.37625,-41.68778,3.41,-0.22],[5191,206.885,49.31333,1.86,-0.19],[5192,207.36125,-34.45083,4.19,1.5],[5193,207.40417,-42.47389,3.04,-0.17],[5194,207.9475,-69.40139,5.75,1.73],[5195,207.16125,31.19028,5.62,1.01],[5196,207.46792,-18.13417,4.97,1.06],[5197,207.52708,-29.08139,6.18,-0.03],[5198,207.58083,-39.90111,6.44,0.99],[5199,207.23833,39.54278,7.4,0.6],[5200,207.36917,15.79778,4.07,1.52],[5201,207.42833,21.26417,4.91,1.43],[5202,207.64375,-19.89722,6.53,0.51],[5203,205.59625,82.7525,5.98,1.01],[5204,207.4375,36.63278,6.38,0.6],[5205,207.60292,5.49722,6.01,0.9],[5206,207.94667,-46.89917,5.77,-0.16],[5207,208.02,-52.81167,5.25,-0.09],[5208,207.9025,-36.43333,6.35,0.48],[5209,207.835,-24.39083,6.45,0.69],[5210,207.95667,-32.99444,4.56,-0.13],[5211,207.95875,-32.99472,6.06,-0.04],[5212,208.00375,-31.61944,6.12,0.48],[5213,207.43958,61.48917,5.96,0.96],[5214,207.76875,34.7725,6.65,0.12],[5215,207.78833,34.66444,5.87,1.62],[5216,207.61542,58.53944,6.46,0.09],[5217,208.42958,-53.37361,5.89,0.01],[5218,208.70375,-67.6525,5.71,1.49],[5219,207.94792,34.44417,4.74,1.66],[5220,208.07667,12.16528,6.04,0.04],[5221,208.30208,-31.92778,4.73,-0.14],[5222,208.38667,-35.66417,5.54,0.44],[5223,208.48708,-47.12806,6.1,-0.07],[5224,208.4675,-35.31444,6.19,1.02],[5225,208.30375,17.93278,5.7,0.84],[5226,207.85792,64.72333,4.65,1.58],[5227,207.74667,68.31528,6.4,1.17],[5228,208.56917,-28.56972,6.04,1.13],[5229,208.29292,28.64806,5.9,0.2],[5230,208.80083,-52.16111,5.71,-0.08],[5231,208.885,-47.28833,2.55,-0.22],[5232,208.67542,-1.50306,5.15,1.08],[5233,208.7425,-8.05889,6.19,0.53],[5234,209.0825,-54.13194,6.14,0.07],[5235,208.67125,18.39778,2.68,0.58],[5236,209.1375,-54.70444,6.0,0.78],[5237,208.93542,-31.285,6.51,0.9],[5238,208.4625,53.72861,5.7,-0.05],[5239,209.08125,-46.5925,5.83,1.14],[5240,210.13667,-78.59,6.09,0.03],[5241,209.41208,-63.68667,4.71,1.11],[5242,209.63,-65.80056,6.2,1.05],[5243,208.95833,14.05639,6.16,0.5],[5244,209.11625,1.05056,5.91,0.2],[5245,209.04375,32.0325,6.32,0.37],[5246,209.36542,-23.02278,6.14,1.43],[5247,209.1425,27.49194,5.01,1.42],[5248,209.56792,-42.10083,3.83,-0.21],[5249,209.67,-44.80361,3.87,-0.2],[5250,209.62958,-24.97222,5.15,-0.1],[5251,209.82208,-50.37,5.91,0.96],[5252,210.07208,-61.48139,6.49,0.33],[5253,210.2175,-66.26861,5.97,0.35],[5254,209.66625,14.64944,6.0,1.44],[5255,209.66208,21.69611,5.76,-0.03],[5256,209.38375,61.49278,6.37,0.6],[5257,210.00042,-25.01028,5.77,0.48],[5258,209.95542,-3.54972,6.4,0.49],[5259,210.32917,-40.22222,6.13,1.25],[5260,210.43083,-45.60361,4.34,0.6],[5261,211.3325,-76.79667,5.5,1.55],[5262,210.335,8.89472,5.99,0.09],[5263,210.29375,27.38667,6.23,0.17],[5264,210.41167,1.54444,4.26,0.1],[5265,210.595,-27.43,5.48,1.34],[5266,210.85917,-56.21361,5.92,1.22],[5267,210.95583,-60.37306,0.61,-0.23],[5268,210.75708,-31.68389,6.18,0.48],[5269,210.86458,-41.42333,6.11,-0.11],[5270,210.6325,9.68639,6.2,0.9],[5271,210.55083,45.75361,6.27,1.32],[5272,210.97125,-22.42167,6.3,0.45],[5273,210.88458,10.78667,6.3,0.74],[5274,210.90333,7.54639,6.26,0.94],[5275,210.9825,4.90083,6.24,0.39],[5276,211.06083,-5.38139,6.39,1.32],[5277,211.1125,-14.97167,6.28,1.08],[5278,211.44375,-54.66944,6.17,0.23],[5279,212.11292,-74.85028,6.02,0.58],[5280,210.74875,50.97194,6.15,0.01],[5281,211.60458,-59.71556,6.42,0.12],[5282,210.46083,68.67861,6.34,1.4],[5283,211.15625,2.2975,6.28,1.02],[5284,211.30833,-16.33583,6.56,0.1],[5285,211.51167,-41.17972,4.36,-0.19],[5286,211.54542,-43.09194,6.2,0.98],[5287,211.59292,-26.6825,3.27,1.12],[5288,211.67083,-36.37,2.06,1.01],[5289,212.05958,-63.20806,6.4,1.02],[5290,211.67833,-9.31333,5.46,0.34],[5291,211.09708,64.37583,3.65,-0.05],[5292,212.23458,-59.27667,6.34,0.05],[5293,212.62875,-70.30556,6.05,1.74],[5294,212.21625,-43.47111,6.17,-0.06],[5295,212.75792,-69.71972,6.06,0.18],[5296,212.39583,-51.50472,6.0,-0.06],[5297,212.47833,-53.43917,4.75,0.94],[5298,212.2525,-10.33444,6.47,1.0],[5299,211.9825,43.85444,5.27,1.59],[5300,212.07208,49.45806,5.25,1.65],[5301,212.71042,-16.30194,4.91,1.72],[5302,212.19167,59.33778,6.46,1.02],[5303,214.5575,-81.00778,4.91,0.25],[5304,212.59958,25.09167,4.83,0.54],[5305,211.735,74.59361,6.45,0.14],[5306,214.22875,-77.66389,6.47,1.42],[5307,212.88,1.36222,6.43,0.48],[5308,213.31833,-53.66583,5.56,1.44],[5309,213.10208,-24.36417,6.34,1.35],[5310,212.81292,32.29556,6.11,1.26],[5311,213.41625,-54.62583,6.11,0.05],[5312,213.19167,-27.26111,5.08,1.16],[5313,213.06583,2.40944,5.01,-0.12],[5314,213.305,-26.61222,6.24,1.08],[5315,213.22417,-10.27361,4.19,1.33],[5316,213.7375,-57.08583,5.07,-0.08],[5317,213.42,-0.84556,5.91,0.47],[5318,213.6775,-41.8375,5.61,0.93],[5319,213.83833,-53.50972,6.39,1.57],[5320,214.16083,-66.58778,5.75,-0.06],[5321,212.21208,77.5475,4.82,1.36],[5322,213.58875,-5.9475,6.36,0.6],[5323,213.52167,12.95944,5.54,0.54],[5324,213.75542,-29.28194,6.08,0.6],[5325,213.91167,-45.00083,6.31,0.6],[5326,214.1425,-59.91389,6.39,2.04],[5327,216.09708,-82.84861,6.42,0.02],[5328,213.36542,51.78778,6.69,0.39],[5329,213.37083,51.79028,4.54,0.2],[5330,213.71167,10.10056,5.29,1.0],[5331,213.72083,3.33611,6.45,1.6],[5332,213.85042,-18.20083,5.43,-0.03],[5333,213.67083,21.87333,6.39,0.18],[5334,213.01667,69.4325,5.24,1.58],[5335,213.59792,41.51889,6.24,1.04],[5336,215.59458,-80.10889,5.06,-0.1],[5337,214.07625,-33.24139,6.55,0.3],[5338,214.00375,-6.00056,4.08,0.52],[5339,216.72875,-83.66778,4.32,1.31],[5340,213.91542,19.1825,-0.04,1.23],[5341,214.08958,-6.62194,6.44,0.28],[5342,214.12542,-3.19639,6.15,-0.01],[5343,214.0175,18.91194,5.98,0.26],[5344,214.26583,-18.58528,6.22,0.98],[5345,213.82042,52.53583,6.58,0.1],[5346,214.13667,20.12139,6.25,0.49],[5347,214.10083,39.74472,6.38,0.36],[5348,214.59917,-33.22056,6.54,0.27],[5349,214.96458,-61.27306,5.23,0.29],[5350,214.04125,51.36722,4.75,0.2],[5351,214.09583,46.08833,4.18,0.08],[5352,214.36833,15.26333,5.8,1.71],[5353,214.5025,-7.5425,6.47,0.73],[5354,214.85083,-46.05778,3.55,-0.18],[5355,214.65958,-18.71611,5.9,0.0],[5356,214.75333,-25.81556,5.87,0.5],[5357,214.84958,-37.00361,5.94,0.08],[5358,215.08125,-56.38667,4.33,0.12],[5359,214.7775,-13.37111,4.52,0.13],[5360,214.33792,51.30722,6.2,0.04],[5361,214.49917,35.50944,4.81,1.06],[5362,215.04042,-43.05889,5.56,0.92],[5363,214.455,48.00167,6.32,0.44],[5364,215.17708,-45.18722,4.77,0.31],[5365,214.81792,13.00417,5.41,0.38],[5366,214.88542,-2.26556,5.14,1.02],[5367,215.13917,-37.88528,4.05,-0.03],[5368,214.92042,0.38417,6.19,0.2],[5369,214.73208,38.7675,6.86,1.06],[5370,214.93833,16.30694,4.86,1.23],[5371,215.65417,-58.45944,4.92,0.86],[5372,214.7325,54.86417,6.53,0.6],[5373,214.94875,38.79389,6.33,0.05],[5374,215.03625,30.42917,6.44,0.15],[5375,215.66125,-48.32028,6.09,-0.13],[5376,215.58208,-34.78694,5.56,-0.09],[5377,215.83458,-50.77222,6.02,1.36],[5378,215.75917,-39.51222,4.42,-0.18],[5379,216.27625,-68.19528,5.61,0.49],[5380,215.95167,-53.17667,6.0,1.1],[5381,215.77417,-27.75389,4.77,1.31],[5382,216.41458,-66.17333,6.36,0.13],[5383,215.85667,-11.71417,6.21,0.99],[5384,215.81375,1.24167,6.27,0.63],[5385,215.84417,8.445,6.86,0.43],[5386,215.84458,8.44667,5.12,-0.02],[5387,215.77833,25.33806,6.22,0.37],[5388,216.00375,8.24361,5.95,0.06],[5389,217.40333,-76.72917,6.07,1.18],[5390,216.2025,-24.80639,5.32,0.96],[5391,216.77958,-65.82167,5.85,1.5],[5392,216.04708,5.82,5.1,0.12],[5393,216.17042,-11.66972,6.49,0.42],[5394,216.07625,8.085,6.19,1.2],[5395,216.53417,-45.22139,4.56,-0.15],[5396,216.545,-45.37944,4.35,0.43],[5397,216.37417,-19.96972,6.61,0.14],[5398,216.55583,-42.31917,6.32,1.19],[5399,216.44875,-26.8525,6.48,0.94],[5400,216.70792,-39.87389,6.35,-0.08],[5401,216.80083,-46.13444,5.83,0.31],[5402,216.37167,38.39306,6.27,1.23],[5403,217.18125,-59.19778,6.45,0.14],[5404,216.29917,51.85083,4.05,0.5],[5405,216.61417,19.22694,5.39,0.23],[5406,216.85167,-6.12028,6.17,0.09],[5407,217.04333,-29.49167,4.97,-0.07],[5408,217.81875,-67.71722,5.83,1.0],[5409,217.05042,-2.22806,4.81,0.7],[5410,217.17375,-6.90056,5.42,1.49],[5411,216.86375,41.025,6.63,0.37],[5412,217.53583,-45.32167,5.5,-0.08],[5413,217.58708,-49.51917,5.37,0.05],[5414,217.13125,28.28917,7.62,-0.01],[5415,217.13875,28.29083,7.12,-0.03],[5416,217.06833,36.19694,6.1,0.6],[5417,217.73542,-40.845,6.39,1.44],[5418,217.46042,0.82889,5.94,0.16],[5419,217.795,-38.86972,5.97,1.06],[5420,217.1575,49.84472,5.59,0.85],[5421,218.13708,-56.88778,6.93,0.91],[5422,217.45708,31.79111,6.06,-0.03],[5423,217.40333,41.79583,6.35,0.7],[5424,217.68917,4.77222,6.02,1.42],[5425,218.15375,-50.45694,4.42,-0.19],[5426,218.385,-54.99833,5.87,0.48],[5427,218.37458,-52.68,5.87,1.09],[5428,218.29,-30.71417,6.09,1.03],[5429,217.9575,30.37139,3.58,1.3],[5430,216.88125,75.69611,4.25,1.44],[5431,218.53333,-42.09972,6.6,0.06],[5432,218.82167,-60.01583,6.4,1.26],[5433,218.08417,26.67722,6.01,0.22],[5434,218.13542,22.26,5.92,0.35],[5435,218.01958,38.30833,3.03,0.19],[5436,217.69208,63.18556,6.09,0.41],[5437,217.92833,60.22556,6.27,0.24],[5438,218.71125,-20.43917,6.5,0.14],[5439,218.88125,-41.51722,5.87,-0.08],[5440,218.87667,-42.15778,2.31,-0.19],[5441,218.33458,36.95944,6.43,0.6],[5442,218.12875,55.39778,5.76,1.5],[5443,219.44292,-67.93222,6.04,0.5],[5444,219.07917,-46.24528,5.55,1.48],[5445,218.54875,32.53444,6.33,0.4],[5446,219.10083,-39.59722,6.13,1.05],[5447,218.67,29.745,4.46,0.36],[5448,218.66042,36.62583,6.03,1.38],[5449,219.18417,-40.21167,5.74,-0.12],[5450,219.33375,-46.13389,5.41,1.01],[5451,218.56625,57.06528,6.48,0.49],[5452,218.665,49.36833,5.74,1.56],[5453,219.47167,-49.42583,4.05,-0.15],[5454,219.02875,23.25028,6.38,1.06],[5455,219.24917,-12.30528,6.2,0.46],[5456,219.58167,-38.79417,6.02,1.43],[5457,219.79583,-46.58417,6.07,0.51],[5458,219.85292,-49.05556,6.39,0.44],[5459,219.89958,-60.83528,-0.01,0.71],[5460,219.90042,-60.83556,1.33,0.88],[5461,220.13667,-56.44083,6.3,1.18],[5462,219.55833,18.29833,5.91,1.1],[5463,220.62667,-64.97528,3.19,0.24],[5464,219.55208,43.64194,5.7,1.48],[5465,220.48208,-58.61611,6.22,0.45],[5466,220.25583,-36.135,5.67,-0.08],[5467,219.56333,54.02333,5.85,-0.01],[5468,219.70917,44.40444,5.39,0.0],[5469,220.4825,-47.38833,2.3,-0.2],[5470,221.965,-79.04472,3.83,1.43],[5471,220.49,-37.79361,4.0,-0.17],[5472,220.09125,21.97556,6.1,0.4],[5473,220.17667,13.53417,5.91,0.21],[5474,220.46292,-30.93333,6.37,-0.09],[5475,220.18167,16.41833,4.94,-0.03],[5476,220.18292,16.41778,5.88,0.24],[5477,220.28708,13.72833,4.83,0.6],[5478,220.28708,13.72833,4.43,0.05],[5479,218.40958,79.66028,6.26,1.3],[5480,220.41167,8.16167,4.86,1.0],[5481,220.43125,11.66056,5.56,0.94],[5482,221.32208,-62.87583,5.36,0.29],[5483,220.47583,21.12361,6.38,0.6],[5484,220.80667,-24.9975,5.73,-0.01],[5485,220.91417,-35.17361,4.05,1.35],[5486,221.23125,-58.47778,6.11,1.02],[5487,220.765,-5.65833,3.88,0.38],[5488,221.29542,-55.60194,6.1,-0.06],[5489,221.24667,-35.19194,4.92,0.01],[5490,220.85583,26.52778,4.81,1.66],[5491,232.07958,-88.13306,6.48,0.3],[5492,220.51333,61.26194,6.25,0.41],[5493,220.935,40.45917,5.73,1.39],[5494,221.62125,-47.44111,5.74,0.07],[5495,221.75542,-52.38361,5.21,0.98],[5496,221.29875,-1.41778,6.07,1.61],[5497,221.50042,-25.44306,4.94,0.35],[5498,221.80125,-52.20556,6.07,0.09],[5499,221.52833,-23.15306,5.81,0.98],[5500,222.185,-66.59389,5.91,-0.07],[5501,221.37583,0.71722,5.69,-0.03],[5502,221.31042,16.96444,4.6,0.98],[5503,221.49083,-15.45972,6.33,1.19],[5504,221.54542,-21.17611,6.4,0.58],[5505,221.24667,27.075,5.12,0.6],[5506,221.24667,27.07417,2.7,0.97],[5507,221.33625,18.88472,6.13,0.83],[5508,221.77125,-38.29083,5.94,1.33],[5509,221.88375,-43.5575,6.3,1.08],[5510,221.30708,32.78833,6.28,1.58],[5511,221.56208,1.89278,3.72,-0.01],[5512,221.525,15.13194,5.63,1.57],[5513,221.80708,-21.32472,6.06,1.65],[5514,221.84375,-25.62444,5.63,0.6],[5515,222.27875,-56.66778,6.23,1.13],[5516,221.93667,-26.0875,5.24,0.94],[5517,221.98958,-26.64639,5.77,-0.02],[5518,221.97875,-12.83972,6.35,1.1],[5519,222.15875,-36.63472,6.04,1.54],[5520,223.30708,-73.19,5.6,0.82],[5521,222.32792,-24.25167,5.68,1.3],[5522,222.22542,-0.84778,6.14,-0.04],[5523,222.32958,-14.14889,5.31,0.07],[5524,222.09708,24.36667,6.14,0.48],[5525,225.46167,-83.22778,5.65,0.95],[5526,222.57208,-27.96028,4.41,1.4],[5527,223.14583,-63.81,5.87,0.72],[5528,222.91,-43.57556,4.32,-0.15],[5529,222.27792,37.81111,6.16,0.36],[5530,222.67167,-15.99722,5.15,0.41],[5531,222.71958,-16.04167,2.75,0.15],[5532,222.49333,28.61583,5.8,0.05],[5533,222.32792,46.11611,5.74,0.48],[5534,222.56583,23.91194,5.85,0.56],[5535,222.75417,-2.29917,4.94,0.98],[5536,222.75042,-0.25722,6.18,1.4],[5537,222.38458,51.37472,6.51,0.4],[5538,222.42208,48.72056,5.69,0.47],[5539,223.67667,-65.99139,6.09,-0.06],[5540,224.47042,-76.66278,5.34,1.45],[5541,222.62333,37.27194,5.48,1.02],[5542,223.13792,-30.57694,6.29,0.6],[5543,223.21292,-37.80333,5.03,-0.16],[5544,222.84708,19.10111,4.55,0.76],[5545,226.19458,-83.03833,5.65,1.3],[5546,223.89417,-60.11417,5.2,1.16],[5547,225.04917,-77.16028,5.93,1.05],[5548,223.58375,-24.64222,5.3,1.32],[5549,223.65833,-33.30056,5.82,1.42],[5550,223.34708,15.70444,6.4,0.57],[5551,224.18333,-62.78083,5.11,0.0],[5552,222.86,59.29389,5.46,1.36],[5553,223.34875,19.15278,6.01,0.83],[5554,223.59542,-11.89833,5.8,0.97],[5555,224.98333,-75.0325,6.2,-0.04],[5556,224.07208,-52.80972,5.38,0.13],[5557,227.78458,-84.7875,5.91,-0.06],[5558,223.93625,-33.85583,5.32,0.04],[5559,224.13333,-47.87917,5.64,-0.04],[5560,224.25583,-51.44694,6.64,1.7],[5561,224.14917,-39.41611,6.36,0.06],[5562,224.12875,-32.63667,6.06,1.41],[5563,222.67625,74.15556,2.08,1.47],[5564,224.19208,-11.40972,5.46,1.49],[5565,224.30667,-29.15778,6.29,-0.04],[5566,224.53667,-48.86306,6.35,0.71],[5567,224.055,14.44639,5.77,-0.06],[5568,224.36667,-21.41556,5.74,1.11],[5569,223.99458,32.30028,6.12,0.1],[5570,224.29583,-4.34639,4.49,0.32],[5571,224.63292,-43.13389,2.68,-0.22],[5572,224.65333,-39.90667,6.15,1.23],[5573,224.38875,-0.1675,5.53,1.13],[5574,224.265,21.55528,6.49,-0.01],[5575,224.29875,16.38833,5.71,0.94],[5576,224.79042,-42.10417,3.13,-0.2],[5577,224.66333,-27.65722,5.65,0.24],[5578,224.55583,-11.155,6.6,0.01],[5579,224.80792,-37.88139,6.47,-0.08],[5580,224.86292,-43.16,6.1,0.6],[5581,224.09583,49.62861,5.63,0.5],[5582,224.72333,-11.14417,5.87,1.26],[5583,224.72,-4.98917,6.09,0.5],[5584,224.84625,4.56778,5.93,1.6],[5585,225.30417,-38.05833,5.89,1.24],[5586,225.24333,-8.51889,4.92,0.0],[5587,225.49208,-34.35889,6.22,0.24],[5588,224.90375,39.26528,5.64,0.31],[5589,224.39583,65.9325,4.6,1.59],[5590,225.3325,-2.755,5.52,1.68],[5591,225.52667,-28.06056,5.85,0.16],[5592,225.21833,22.04556,6.38,0.6],[5593,226.20083,-64.03167,5.17,0.93],[5594,225.45375,-0.14056,5.71,1.52],[5595,225.74708,-32.64333,5.44,-0.12],[5596,222.585,82.51194,5.64,0.68],[5597,225.16125,47.27778,6.37,-0.14],[5598,226.78625,-71.90528,6.52,1.59],[5599,225.68708,-3.03139,6.61,0.2],[5600,225.52708,25.00806,4.81,1.5],[5601,225.725,2.09139,4.4,1.04],[5602,225.48667,40.39056,3.5,0.97],[5603,226.0175,-25.28194,3.29,1.7],[5604,226.17875,-40.86139,6.41,1.46],[5605,226.28,-47.05111,4.72,-0.14],[5606,226.28,-47.05111,4.82,0.6],[5607,226.32958,-41.06722,5.15,1.01],[5608,225.36292,60.20444,5.93,0.09],[5609,225.77542,35.20583,5.51,1.02],[5610,226.02667,5.4925,6.5,0.31],[5611,226.98667,-65.27556,6.17,1.47],[5612,225.7775,44.64444,6.65,0.46],[5613,225.90208,34.56611,6.59,1.02],[5614,226.44875,-25.78972,6.67,-0.01],[5615,226.55792,-36.26417,6.27,1.65],[5616,226.11125,26.9475,4.54,1.24],[5617,226.85792,-49.08833,5.77,0.92],[5618,225.9475,47.65444,4.76,0.65],[5619,226.63875,-30.91889,5.96,-0.08],[5620,226.61292,-22.03194,6.17,1.05],[5621,227.37458,-67.08417,5.76,0.69],[5622,226.65667,-16.25694,5.2,1.58],[5623,227.35625,-63.64278,6.28,0.06],[5624,227.05042,-40.58389,5.79,-0.14],[5625,227.16292,-42.86778,5.85,-0.11],[5626,227.21083,-45.27972,4.05,-0.18],[5627,226.3575,48.15111,5.57,0.0],[5628,228.14083,-72.77028,6.01,0.0],[5629,225.99083,65.91972,6.13,0.6],[5630,226.64625,36.45556,6.35,0.52],[5631,226.91792,5.49806,6.16,0.94],[5632,227.68583,-61.4225,6.3,0.63],[5633,226.835,18.44167,6.02,0.06],[5634,226.82542,24.86917,4.93,0.43],[5635,226.56958,54.55639,5.25,0.96],[5636,227.53125,-38.7925,5.98,0.6],[5637,227.81667,-55.34611,5.54,1.14],[5638,227.09917,26.30111,5.67,1.24],[5639,227.2225,13.235,6.1,0.96],[5640,227.14792,25.10861,5.81,1.24],[5641,227.5775,-26.33278,5.76,1.05],[5642,227.89542,-45.2775,6.44,1.04],[5643,227.88292,-45.27944,7.39,1.08],[5644,228.57958,-70.07944,5.81,3.38],[5645,228.25417,-61.74389,6.32,1.9],[5646,227.98375,-48.73778,3.87,-0.05],[5647,227.99,-48.74361,5.69,0.14],[5648,227.08125,50.055,6.39,1.03],[5649,228.07125,-52.09917,3.41,0.92],[5650,228.13042,-48.21861,6.33,1.12],[5651,228.20625,-44.50056,4.82,-0.17],[5652,228.05542,-19.79167,4.54,-0.08],[5653,228.28083,-36.09139,6.1,-0.08],[5654,228.01792,18.97583,5.89,1.53],[5655,228.32292,-24.00833,6.47,-0.04],[5656,228.33,-19.6475,6.08,0.12],[5657,228.36958,-25.30917,6.45,0.7],[5658,228.47208,-26.19361,5.84,1.14],[5659,228.18125,19.28583,6.68,0.68],[5660,228.65542,-31.51917,4.91,0.37],[5661,229.15167,-60.90389,5.73,-0.08],[5662,228.64042,-17.76861,6.17,-0.05],[5663,228.97417,-48.07417,5.95,0.21],[5664,229.23625,-60.9575,5.09,-0.06],[5665,228.38292,22.98333,6.3,0.06],[5666,229.41208,-63.61056,4.86,1.25],[5667,229.01667,-41.49111,5.16,0.58],[5668,229.04375,-43.48472,6.04,-0.14],[5669,228.71125,-5.50278,6.28,1.47],[5670,229.37833,-58.80111,4.07,0.09],[5671,229.7275,-68.67944,2.89,0.0],[5672,227.68375,67.78139,6.17,0.6],[5673,228.39833,38.26472,6.2,1.2],[5674,228.52542,31.78806,5.99,1.52],[5675,228.7975,4.93944,5.33,1.09],[5676,228.62167,29.16417,5.26,0.03],[5677,228.54292,42.17139,6.13,1.66],[5678,229.09583,-22.39944,5.5,1.38],[5679,228.95458,0.37222,5.63,0.18],[5680,229.70375,-60.49639,5.46,-0.1],[5681,228.87583,33.31472,3.47,0.95],[5682,229.53917,-41.06083,6.28,0.18],[5683,229.63333,-47.875,4.27,-0.08],[5684,230.16958,-67.48139,6.28,-0.09],[5685,229.25167,-9.38306,2.61,-0.11],[5686,229.45792,-30.14889,4.34,1.1],[5687,229.735,-40.78833,5.59,-0.1],[5688,229.67208,-31.20944,6.18,1.23],[5689,229.88167,-37.09667,6.2,0.96],[5690,229.60917,-0.46139,5.89,1.51],[5691,228.65958,67.34667,5.13,0.53],[5692,229.60208,20.57278,5.7,0.97],[5693,228.71625,68.94528,6.51,0.6],[5694,229.82833,1.76528,5.06,0.54],[5695,230.34292,-40.6475,3.22,-0.22],[5696,230.39708,-40.74972,6.2,0.07],[5697,230.37542,-38.21917,6.48,-0.06],[5698,230.53458,-47.92778,5.0,0.5],[5699,230.45083,-48.31778,5.65,0.65],[5700,230.79333,-60.65694,5.67,0.48],[5701,230.22375,-18.15861,6.17,1.02],[5702,229.87583,32.51528,6.32,0.24],[5703,230.25583,-15.54833,6.3,0.41],[5704,230.84458,-59.32083,4.51,0.19],[5705,230.45167,-36.26139,3.56,1.54],[5706,230.19625,-2.41333,6.35,1.06],[5707,230.28167,-5.82472,5.54,1.04],[5708,230.67042,-44.68944,3.37,-0.18],[5709,230.03542,29.61611,5.51,1.02],[5710,230.25833,0.71528,5.35,1.19],[5711,230.27875,24.95778,6.39,1.23],[5712,230.78917,-36.85861,4.54,-0.15],[5713,231.56125,-68.30917,5.89,1.02],[5714,229.27458,71.82389,5.02,1.37],[5715,230.02167,51.95861,5.66,0.11],[5716,230.17333,44.43417,6.19,0.39],[5717,230.59667,12.5675,6.28,-0.02],[5718,230.4525,32.93389,5.37,-0.07],[5719,231.18708,-39.71028,5.37,-0.11],[5720,230.9675,-12.36944,5.72,1.04],[5721,230.93208,-1.0225,6.12,0.25],[5722,231.2775,-38.16944,7.03,0.09],[5723,231.04958,-10.32222,4.94,0.44],[5724,231.33417,-38.73361,4.6,0.0],[5725,231.88792,-64.53139,5.71,1.64],[5726,230.65583,39.58139,5.5,1.59],[5727,230.80125,30.28778,5.58,0.58],[5728,230.80125,30.28778,6.08,0.6],[5729,235.82,-84.46528,5.57,0.11],[5730,232.87833,-73.38944,5.49,-0.12],[5731,230.65542,62.04722,5.98,-0.03],[5732,231.02125,45.27111,6.01,1.2],[5733,231.1225,37.37722,4.31,0.31],[5734,231.12875,37.34778,6.5,0.59],[5735,230.18208,71.83389,3.05,0.05],[5736,231.82583,-36.76778,5.45,-0.15],[5737,230.66,63.34139,5.79,1.27],[5738,232.11333,-51.5975,6.1,1.09],[5739,231.4475,15.42806,5.17,1.66],[5740,231.47208,19.48083,6.27,0.6],[5741,231.5725,34.33583,5.46,1.4],[5742,232.35125,-46.73278,5.24,1.74],[5743,232.06417,-16.71639,5.64,1.55],[5744,231.2325,58.96611,3.29,1.16],[5745,231.91208,25.10167,6.02,1.62],[5746,232.15917,1.84222,5.17,0.23],[5747,231.95708,29.10583,3.68,0.28],[5748,231.63542,54.02,6.45,0.05],[5749,232.65125,-20.72833,6.22,0.17],[5750,232.66833,-16.60944,5.82,1.06],[5751,233.01833,-38.62306,6.25,0.2],[5752,232.18542,47.20139,6.15,0.1],[5753,232.95958,-32.88111,6.46,0.09],[5754,231.92,62.27556,6.5,0.14],[5755,231.96417,60.67028,5.9,1.44],[5756,232.93083,-20.16472,6.22,0.22],[5757,234.82625,-77.91806,6.18,1.2],[5758,232.73083,8.57917,6.57,0.37],[5759,232.23667,55.195,6.43,0.08],[5760,232.59458,31.28611,6.46,0.19],[5761,232.61625,36.80417,6.37,0.6],[5762,233.15292,-19.67056,5.52,0.18],[5763,232.7325,40.83306,5.02,1.59],[5764,233.23,-16.85278,5.5,-0.14],[5765,233.28792,-24.48944,7.0,0.27],[5766,234.0725,-65.61333,6.51,0.35],[5767,233.50667,-40.06611,5.82,1.68],[5768,232.33833,62.09972,6.38,0.6],[5769,232.84333,36.61639,6.38,0.5],[5770,233.04042,16.05611,6.22,-0.05],[5771,234.18,-66.31694,4.11,1.17],[5772,233.24125,-1.18639,5.51,1.09],[5773,233.58708,-39.34944,6.36,-0.03],[5774,232.94583,40.89944,5.02,0.07],[5775,233.65542,-28.04694,5.15,1.3],[5776,233.78542,-41.16694,2.78,-0.2],[5777,233.54458,-10.06444,4.62,1.01],[5778,233.2325,31.35917,4.14,-0.13],[5779,233.58667,-5.695,6.51,0.58],[5780,233.61083,-9.18333,5.17,-0.09],[5781,233.97167,-44.95861,4.54,-0.18],[5782,235.08833,-73.44667,5.65,-0.04],[5783,233.47,17.13778,6.45,0.6],[5784,234.05042,-44.39694,5.43,1.5],[5785,232.73208,64.20861,5.79,0.96],[5786,235.4775,-76.08194,5.95,-0.04],[5787,233.88167,-14.78944,3.91,1.01],[5788,233.70042,10.5375,3.8,0.26],[5789,233.70042,10.53917,3.8,0.26],[5790,234.0475,-33.09278,6.24,0.6],[5791,233.76917,1.66889,6.56,0.28],[5792,235.04792,-70.22778,6.44,0.08],[5793,233.67208,26.71472,2.23,-0.02],[5794,234.25625,-28.135,3.58,1.38],[5795,233.88833,17.65556,6.12,0.94],[5796,233.9725,11.26556,6.07,1.09],[5797,234.51333,-42.5675,4.33,1.42],[5798,234.70625,-52.37278,5.44,0.0],[5799,234.14042,-0.56167,6.51,0.72],[5800,233.8125,39.01,5.11,1.64],[5801,234.36875,-26.28,6.19,0.01],[5802,234.12333,10.01,5.26,0.95],[5803,234.98542,-59.90833,5.95,0.48],[5804,234.12208,16.11889,5.93,0.29],[5805,234.63625,-39.16083,6.57,-0.07],[5806,234.45042,-23.14167,5.78,1.1],[5807,234.67625,-39.12806,6.04,0.21],[5808,233.95542,38.37389,6.42,0.6],[5809,234.56542,-28.20667,6.32,1.17],[5810,234.56792,-21.01611,5.84,1.08],[5811,233.81792,53.92194,5.97,1.18],[5812,234.66417,-29.77778,3.66,-0.17],[5813,234.2225,29.99111,6.52,0.6],[5814,234.72708,-19.30194,5.38,0.86],[5815,234.66667,-8.79444,6.5,0.53],[5816,234.66708,-8.79111,6.48,0.52],[5817,234.01708,52.06972,6.74,0.32],[5818,233.98792,54.63056,5.74,0.6],[5819,234.83875,-23.15028,6.34,0.02],[5820,234.94167,-34.41194,4.67,0.99],[5821,235.24292,-47.73556,6.23,1.63],[5822,235.06417,-31.21361,6.34,1.43],[5823,234.45667,40.35333,5.24,0.88],[5824,235.07042,-23.81806,4.96,1.33],[5825,235.29708,-44.66111,4.64,0.4],[5826,232.85375,77.34944,4.96,1.58],[5827,234.70375,34.675,6.11,1.02],[5828,234.38333,54.50889,5.87,1.07],[5829,232.29583,80.44861,6.58,0.67],[5830,234.5675,46.79778,5.75,0.36],[5831,235.04333,12.05306,6.25,0.94],[5832,235.655,-49.48944,6.04,1.31],[5833,234.8425,36.63667,6.0,0.6],[5834,234.84458,36.63583,5.07,-0.12],[5835,234.64292,50.42333,5.84,0.83],[5836,235.97958,-60.28722,6.48,1.05],[5837,235.65958,-37.425,5.24,0.98],[5838,235.48667,-19.67889,4.74,1.57],[5839,235.67083,-34.71056,4.75,-0.14],[5840,235.24667,16.02472,6.01,0.9],[5841,234.78958,57.92444,6.45,1.09],[5842,235.38792,19.67028,4.52,0.04],[5843,235.4475,12.8475,5.33,0.04],[5844,234.41292,69.28333,5.62,1.35],[5845,235.47792,18.46389,5.81,0.2],[5846,236.09417,-41.81944,5.94,0.0],[5847,235.85375,-15.04333,6.31,1.16],[5848,236.01833,-15.67278,5.41,0.23],[5849,235.68583,26.29556,3.84,0.0],[5850,235.79417,13.66778,6.48,0.86],[5851,236.97333,-65.4425,6.18,0.22],[5852,236.97375,-65.4425,6.39,0.24],[5853,236.0075,2.515,5.88,0.68],[5854,236.06708,6.42556,2.65,1.17],[5855,235.99708,32.51583,5.56,1.06],[5856,236.55333,-28.06167,6.51,0.32],[5857,235.71125,52.36083,5.51,-0.07],[5858,236.17542,17.26417,6.14,0.0],[5859,236.34792,5.44694,5.58,0.04],[5860,236.68417,-34.6825,5.61,-0.11],[5861,236.41542,0.89139,6.33,1.19],[5862,236.85583,-40.19417,6.42,0.88],[5863,236.52333,-1.80444,5.4,-0.03],[5864,236.87083,-37.91639,6.01,0.72],[5865,237.20958,-52.43806,6.07,1.38],[5866,236.68917,-6.12028,6.24,1.17],[5867,236.54708,15.42194,3.67,0.06],[5868,236.61083,7.35306,4.43,0.6],[5869,237.52875,-53.20944,5.77,-0.08],[5870,236.82208,14.11528,5.71,0.09],[5871,237.48958,-48.91194,5.84,0.07],[5872,237.56792,-45.40167,6.12,0.29],[5873,237.77833,-55.05583,5.73,0.06],[5874,237.05542,13.78861,6.0,1.25],[5875,237.23667,-3.81861,5.53,0.12],[5876,238.23625,-65.1525,6.54,0.19],[5877,237.00833,31.73583,6.44,0.6],[5878,236.645,55.47472,5.92,1.39],[5879,237.185,18.14167,4.09,1.62],[5880,237.14333,28.15667,5.85,0.77],[5881,237.405,-3.43028,3.53,-0.04],[5882,237.88125,-47.06056,6.01,1.16],[5883,237.73958,-33.62722,3.95,-0.04],[5884,238.345,-62.60694,6.19,1.47],[5885,237.74458,-25.75139,4.64,-0.05],[5886,236.66667,62.59944,5.19,0.04],[5887,236.90833,55.37667,5.86,0.25],[5888,237.57292,2.19639,5.23,1.02],[5889,237.39875,26.06833,4.63,0.8],[5890,238.21458,-50.61528,6.6,1.53],[5891,238.87333,-68.60306,5.09,1.13],[5892,237.70417,4.47778,3.71,0.15],[5893,238.05333,-29.88667,6.4,0.98],[5894,237.67375,15.13361,5.2,0.6],[5895,237.815,-3.09056,5.11,0.12],[5896,237.91,-14.13361,6.19,1.0],[5897,238.78542,-63.43056,2.85,0.29],[5898,238.71917,-60.74333,6.15,0.1],[5899,237.81625,20.97778,4.76,1.54],[5900,238.88458,-60.17778,5.77,0.35],[5901,237.80792,35.6575,4.82,1.0],[5902,238.33375,-20.16722,5.03,-0.01],[5903,236.01458,77.79444,4.32,0.04],[5904,238.40292,-25.32722,4.59,-0.07],[5905,239.025,-60.48278,5.76,0.06],[5906,238.47417,-24.53306,5.39,-0.02],[5907,238.4825,-23.97806,5.42,-0.04],[5908,238.45625,-16.72944,4.15,1.02],[5909,238.23417,17.40361,6.36,0.6],[5910,238.625,-27.33861,6.14,-0.07],[5911,238.30042,13.19667,6.1,0.6],[5912,238.66458,-25.24361,5.87,-0.06],[5913,238.39542,16.075,6.09,0.6],[5914,238.16875,42.45167,4.62,0.56],[5915,238.75125,-19.38306,5.94,-0.01],[5916,238.87667,-31.08361,6.21,1.37],[5917,238.87542,-26.26583,5.62,0.15],[5918,239.02708,-39.86417,6.03,0.15],[5919,238.66792,8.58028,6.29,0.18],[5920,239.74208,-65.03778,5.75,-0.06],[5921,239.26583,-48.16222,6.31,0.38],[5922,238.06917,55.82667,5.81,0.96],[5923,239.05792,-31.78583,6.29,0.43],[5924,238.64417,20.31083,5.44,1.59],[5925,239.22292,-33.96639,5.12,0.12],[5926,239.22583,-33.96417,5.62,0.05],[5927,239.06,-14.39944,6.37,0.48],[5928,239.22125,-29.21417,3.88,-0.2],[5929,239.33875,-36.185,5.8,1.01],[5930,239.13917,-14.82917,6.13,0.23],[5931,238.91583,18.62056,6.26,-0.11],[5932,238.65792,43.13861,5.37,1.65],[5933,239.11333,15.66167,3.85,0.48],[5934,239.41833,-20.98306,5.85,0.02],[5935,239.62792,-37.50306,6.31,1.01],[5936,238.94833,37.94694,5.45,0.33],[5937,239.975,-54.02111,6.1,0.0],[5938,238.8775,42.56611,5.75,-0.11],[5939,240.29458,-63.77667,6.41,0.78],[5940,239.31083,14.41444,5.54,1.14],[5941,239.5475,-14.27944,4.88,-0.1],[5942,239.645,-24.83139,5.43,-0.09],[5943,239.87625,-41.74444,4.99,1.0],[5944,239.71292,-26.11417,2.89,-0.19],[5945,239.99167,-40.65278,6.49,1.52],[5946,240.27667,-54.57778,6.13,0.25],[5947,239.39708,26.87778,4.15,1.23],[5948,240.03042,-38.39694,3.41,-0.22],[5949,238.95708,58.91167,6.31,-0.02],[5950,239.37458,39.69528,6.31,1.07],[5951,240.71833,-62.54167,6.25,-0.04],[5952,240.22375,-40.43528,6.21,0.01],[5953,240.08333,-22.62167,2.32,-0.12],[5954,240.08167,-16.53333,5.47,0.52],[5955,241.4825,-72.40083,5.7,1.17],[5956,240.33125,-31.88944,6.33,1.45],[5957,239.74042,36.64389,5.62,1.49],[5958,239.87583,25.92028,2.0,0.1],[5959,240.19833,-8.41139,5.55,0.05],[5960,239.4475,54.74972,4.95,0.26],[5961,240.88292,-57.77528,4.63,0.24],[5962,240.80375,-49.22972,4.65,0.92],[5963,240.21292,4.4275,5.83,1.0],[5964,239.76833,49.88111,6.05,0.29],[5965,240.66417,-29.13583,6.03,1.31],[5966,240.30958,17.81833,5.12,0.99],[5967,240.85083,-38.6025,4.89,-0.14],[5968,240.26125,33.30361,5.41,0.6],[5969,240.83583,-25.86528,5.0,1.22],[5970,240.89292,-32.00056,6.01,0.47],[5971,240.36083,29.85111,4.99,-0.07],[5972,240.57375,22.80444,4.83,0.07],[5973,240.97792,-24.72639,6.21,1.38],[5974,241.07417,-33.21444,6.1,0.34],[5975,241.15292,-37.86306,5.9,0.4],[5976,240.94042,4.98667,6.08,0.96],[5977,241.09208,-11.37306,5.07,0.6],[5978,241.09208,-11.37306,4.77,0.47],[5979,241.85,-56.19139,6.16,0.58],[5980,241.6225,-45.17333,4.72,0.23],[5981,240.52292,52.91583,5.93,1.48],[5982,240.69958,46.03667,4.76,-0.11],[5983,240.83083,36.63167,5.83,0.56],[5984,241.35917,-19.80556,2.62,-0.07],[5985,241.36042,-19.80194,4.92,-0.02],[5986,240.47208,58.56528,4.01,0.52],[5987,241.64792,-36.80222,4.23,-0.17],[5988,241.52625,-23.60639,5.92,-0.08],[5989,241.43542,-6.29167,6.53,0.48],[5990,241.49917,-6.13944,6.41,1.03],[5991,241.81833,-36.75556,5.73,0.29],[5992,241.4075,8.09611,6.29,0.08],[5993,241.70167,-20.66917,3.96,-0.04],[5994,242.3275,-57.93444,5.57,-0.04],[5995,240.78875,59.41083,6.19,1.58],[5996,241.76417,-14.07083,6.32,0.66],[5997,241.85125,-20.86861,4.32,0.84],[5998,241.96625,-24.46194,6.33,-0.06],[5999,242.1425,-39.10528,7.05,0.36],[6000,242.14333,-39.09306,6.65,-0.07],[6001,242.03167,-26.32667,5.38,1.65],[6002,241.90167,-12.74556,5.78,0.01],[6003,242.18208,-23.68556,5.88,0.02],[6004,241.90625,9.89167,5.63,0.2],[6005,241.8425,21.8225,6.14,1.37],[6006,242.38208,-32.64972,6.19,0.79],[6007,242.46917,-33.54583,5.54,-0.1],[6008,242.01875,17.04694,5.0,0.95],[6009,242.02042,17.05444,6.25,1.14],[6010,242.11667,8.53417,5.73,1.61],[6011,242.24542,3.45444,5.91,1.47],[6012,242.48,-18.34083,6.47,0.44],[6013,242.19417,17.20583,6.14,0.0],[6014,242.29667,6.37889,5.97,1.0],[6015,242.82375,-41.11972,5.86,0.27],[6016,242.46042,-3.46694,5.37,1.45],[6017,242.75833,-29.41639,5.13,1.12],[6018,242.24292,36.49083,4.76,1.01],[6019,243.34417,-55.54083,5.81,0.34],[6020,245.08667,-78.69583,4.68,1.69],[6021,245.11167,-78.66722,5.27,1.41],[6022,243.32,-53.67167,5.83,1.96],[6023,242.1925,44.935,4.26,-0.07],[6024,243.36958,-54.63056,4.94,1.04],[6025,241.58208,67.81028,5.44,-0.02],[6026,242.99417,-19.44972,6.3,0.13],[6027,242.99875,-19.46056,4.01,0.04],[6028,243.07583,-27.92639,4.59,-0.16],[6029,243.06625,-28.4175,5.67,0.01],[6030,243.85958,-63.68556,3.85,1.11],[6031,243.0,-10.06417,4.94,0.09],[6032,242.87375,9.7125,6.53,0.24],[6033,243.03042,-8.5475,5.43,0.12],[6034,240.88042,76.79361,5.56,0.6],[6035,242.86958,16.66556,6.08,0.02],[6036,242.26208,57.93778,6.33,0.6],[6037,244.27292,-67.94139,5.75,0.15],[6038,242.35833,55.82889,6.49,0.6],[6039,242.90833,23.49472,5.7,1.56],[6040,243.95708,-57.91222,5.63,0.14],[6041,243.23542,-4.22083,6.25,0.13],[6042,243.44042,-24.42194,6.41,0.04],[6043,242.91542,33.3425,6.29,1.2],[6044,243.59292,-33.01139,5.92,1.02],[6045,243.81375,-47.37222,5.14,-0.13],[6046,242.95,36.425,5.63,1.34],[6047,243.31417,5.02111,5.48,1.47],[6048,243.46208,-11.8375,5.22,1.42],[6049,243.85,-42.89972,6.14,1.11],[6050,242.94833,42.37444,5.87,1.45],[6051,243.62,-21.1075,6.41,-0.01],[6052,243.18875,26.67083,6.5,0.39],[6053,243.66292,-18.53528,6.32,1.09],[6054,243.72333,-25.47694,6.05,0.04],[6055,244.17958,-53.81111,5.44,1.73],[6056,243.58625,-3.69444,2.74,1.58],[6057,243.55625,5.90194,6.31,1.15],[6058,244.25375,-50.06833,4.99,0.8],[6059,244.33708,-53.08667,6.33,0.27],[6060,243.90542,-8.36944,5.5,0.65],[6061,243.96458,-14.84917,6.09,0.06],[6062,244.71625,-57.89972,6.49,1.0],[6063,243.67,33.85861,5.64,0.51],[6064,243.67,33.85833,6.66,0.6],[6065,243.86958,18.80833,5.69,1.12],[6066,244.245,-21.30389,6.61,0.02],[6067,244.23042,-3.95333,6.18,0.31],[6068,243.9475,27.42222,6.14,1.31],[6069,243.10458,67.14417,6.21,0.99],[6070,244.57458,-28.61389,4.78,0.02],[6071,244.82375,-42.67389,5.45,0.1],[6072,244.96,-50.15556,4.02,1.08],[6073,245.105,-55.14,5.77,0.97],[6124,246.70875,2.3475,6.07,0.92],[6074,244.18667,29.15028,5.78,0.07],[6075,244.58042,-4.6925,3.24,0.96],[6076,244.78208,-20.21778,6.29,1.08],[6077,244.88625,-30.90667,5.49,0.47],[6078,244.75167,-14.8725,5.94,1.52],[6079,242.70625,75.8775,5.48,-0.11],[6080,245.13583,-39.43083,6.12,-0.07],[6081,245.15917,-24.16944,4.55,0.84],[6082,243.13417,75.21056,6.39,0.6],[6083,245.61667,-49.57222,5.33,-0.04],[6084,245.29708,-25.59278,2.89,0.13],[6085,245.62042,-43.91222,5.88,1.16],[6086,244.31375,59.755,5.4,1.63],[6087,245.01792,21.1325,6.05,0.94],[6088,243.63958,73.395,5.98,0.08],[6089,246.34167,-63.12472,6.15,0.03],[6090,244.79667,49.03806,5.91,1.37],[6091,244.97958,39.70861,5.46,0.4],[6092,244.935,46.31333,3.89,-0.15],[6093,245.51833,1.02917,4.82,0.34],[6094,246.00542,-39.19306,5.4,0.62],[6095,245.48,19.15306,3.75,0.27],[6096,245.66208,-2.07972,6.23,0.07],[6097,245.98625,-33.19944,6.47,0.01],[6098,247.11708,-70.08444,4.91,0.55],[6099,246.22583,-45.34917,6.33,0.19],[6100,246.13208,-37.56583,5.42,-0.11],[6101,244.53917,68.55444,6.41,0.6],[6102,248.3625,-78.89722,3.89,0.91],[6103,245.52417,30.89194,4.85,0.97],[6104,246.02583,-20.0375,4.5,1.01],[6105,246.165,-29.70333,6.63,0.59],[6106,246.16542,-29.70472,5.84,0.59],[6107,245.58917,33.79917,5.2,1.6],[6108,245.62167,33.70361,5.39,1.53],[6109,246.98875,-64.05806,5.27,0.36],[6110,245.73542,32.33306,6.4,0.08],[6111,246.045,6.94806,5.85,-0.01],[6112,246.39667,-23.44722,5.02,0.24],[6113,246.39625,-23.44611,5.92,0.6],[6114,247.06333,-58.59972,5.69,0.0],[6115,246.79625,-47.555,4.47,-0.07],[6116,244.37625,75.75528,4.95,0.37],[6117,246.35417,14.03333,4.57,0.0],[6118,246.75583,-18.45639,4.42,0.28],[6119,246.44875,18.8925,6.7,0.6],[6120,247.4375,-57.75583,6.06,1.48],[6121,246.54792,11.4075,6.11,1.03],[6122,247.06125,-37.17944,5.79,1.1],[6123,246.35083,37.39389,5.54,0.17],[6125,247.70583,-61.63361,5.2,1.23],[6126,245.45292,69.10944,5.25,1.12],[6127,246.10542,55.205,5.74,0.0],[6128,246.93125,-7.59806,5.23,1.72],[6129,246.95042,-8.37167,4.63,0.17],[6130,245.94583,61.69667,5.67,0.96],[6131,247.42625,-46.24333,5.35,0.56],[6132,245.99792,61.51417,2.74,0.91],[6133,258.99708,-87.56639,6.57,0.91],[6134,247.35167,-26.43194,0.96,1.83],[6135,248.58042,-70.98806,5.5,1.22],[6136,247.14167,0.665,5.39,1.46],[6137,247.20375,-8.12889,6.48,0.4],[6138,251.47333,-83.23889,6.57,1.57],[6139,255.24375,-86.36444,6.04,0.05],[6140,247.44542,-14.55083,5.68,0.82],[6141,247.55167,-25.115,4.79,-0.11],[6142,247.92375,-41.81694,5.33,0.33],[6143,247.84542,-34.70444,4.23,-0.16],[6144,247.62458,-7.515,6.5,0.37],[6145,247.845,-26.53778,6.1,1.08],[6146,247.16042,41.88167,5.04,1.52],[6147,247.78458,-16.61278,4.28,0.92],[6148,247.555,21.48972,2.77,0.94],[6149,247.72833,1.98389,3.82,0.01],[6150,247.18083,51.40778,6.29,1.05],[6151,248.93667,-65.49528,5.52,0.93],[6152,247.64,20.47917,5.25,1.29],[6153,248.03417,-21.46639,4.45,0.13],[6154,247.80583,22.19528,5.76,1.61],[6155,248.52083,-44.04528,4.94,0.05],[6156,247.525,48.96083,6.45,0.03],[6157,247.76167,35.225,6.25,1.64],[6158,248.14875,5.52111,5.63,-0.06],[6159,248.15125,11.48806,4.84,1.49],[6160,248.78292,-45.24472,6.46,1.34],[6161,246.99583,68.76806,5.0,-0.06],[6162,247.94708,45.59833,5.65,0.12],[6163,250.76917,-77.5175,4.24,1.06],[6164,249.09375,-42.85889,5.47,0.4],[6165,248.97083,-28.21611,2.82,-0.25],[6166,249.09375,-35.25556,4.16,1.57],[6167,249.71958,-60.99028,6.18,-0.08],[6168,248.52583,42.43694,4.2,-0.01],[6169,248.85958,17.05722,6.41,0.05],[6170,248.10708,60.82333,5.94,0.02],[6171,249.08958,-2.32472,5.75,0.82],[6172,250.34708,-68.29611,5.91,-0.08],[6173,246.42958,78.96389,5.56,0.26],[6174,249.60917,-43.39861,5.83,-0.02],[6175,249.28958,-10.56722,2.56,0.02],[6176,249.17917,15.49806,6.3,-0.11],[6177,250.21042,-60.44611,6.18,0.48],[6178,249.77167,-37.2175,5.91,0.0],[6179,249.50667,-6.53806,6.09,0.16],[6180,247.86708,72.61194,6.3,1.32],[6181,249.45,13.68694,6.31,0.41],[6182,250.84208,-67.4325,6.03,0.02],[6183,249.04667,46.61333,5.79,1.04],[6184,249.04792,52.90028,5.53,-0.07],[6185,249.05708,52.92444,5.08,-0.04],[6186,249.05875,52.92417,6.53,-0.06],[6187,250.33458,-48.76306,5.65,0.13],[6188,250.4175,-49.65167,5.65,-0.03],[6189,249.91292,-9.55444,6.35,0.48],[6190,250.14375,-20.40861,6.26,1.08],[6191,247.66167,77.44667,6.34,1.0],[6192,250.43958,-33.14639,5.87,0.65],[6193,250.40083,-24.46806,6.09,0.2],[6194,250.14625,4.20722,6.93,0.13],[6195,250.16125,4.21972,5.77,-0.02],[6196,250.39333,-17.74222,4.96,1.11],[6197,250.76417,-46.07056,6.23,0.85],[6198,249.22917,63.07278,6.16,1.53],[6199,249.50167,56.01556,5.29,1.08],[6200,249.68708,48.92833,4.9,1.55],[6201,250.29792,-1.00056,6.24,0.3],[6202,250.47375,-19.92444,5.57,0.43],[6203,250.21417,12.395,6.08,0.05],[6204,251.66667,-67.10972,5.13,-0.08],[6205,250.42708,1.18111,5.74,0.32],[6206,250.93958,-41.11889,6.2,0.14],[6207,251.16583,-53.1525,5.96,1.26],[6208,250.2525,24.85861,6.06,1.31],[6209,250.97458,-41.11306,6.12,-0.07],[6210,250.94833,-38.15667,6.05,-0.06],[6211,250.91125,-32.10611,6.46,-0.08],[6212,250.32167,31.60306,2.81,0.65],[6213,250.40292,26.91694,5.92,0.4],[6214,251.1775,-40.83972,5.71,-0.12],[6215,251.58833,-58.50361,5.74,-0.09],[6216,251.07208,-27.45611,6.58,0.1],[6217,252.16625,-69.02778,1.92,1.44],[6218,251.25083,-28.50972,6.02,0.09],[6219,251.83125,-58.34139,5.58,-0.08],[6220,250.72417,38.92222,3.53,0.92],[6221,251.69917,-39.37722,5.48,0.98],[6222,250.96542,34.03889,5.99,0.29],[6223,250.22958,64.58917,4.83,1.22],[6224,251.37375,1.02028,6.03,-0.02],[6225,251.71375,-25.52861,6.71,1.18],[6226,250.74333,55.69028,6.16,0.07],[6227,251.34375,15.74528,5.56,1.66],[6228,251.45792,8.5825,5.15,1.53],[6229,252.44625,-59.04139,3.76,1.57],[6230,251.29875,43.21722,6.05,1.4],[6231,253.0725,-67.68194,6.32,1.28],[6232,251.79083,2.06444,6.1,0.14],[6233,252.97458,-65.37556,6.13,-0.02],[6234,251.94333,5.24667,5.24,-0.02],[6235,252.1125,-14.90944,6.03,0.2],[6236,252.64958,-50.04556,6.47,0.31],[6237,251.32417,56.78194,4.85,0.38],[6238,249.47042,78.91833,6.32,1.14],[6239,252.03708,13.59056,6.35,0.87],[6240,252.36583,-15.6675,6.1,0.6],[6241,252.54083,-34.29333,2.29,1.15],[6242,251.8325,42.23889,5.87,1.61],[6243,252.45833,-10.78306,4.65,0.47],[6244,252.74917,-37.51444,6.11,0.12],[6245,252.89042,-41.23056,5.22,0.07],[6246,252.39417,13.26139,5.91,0.03],[6247,252.9675,-38.0475,3.08,-0.2],[6248,252.59292,-2.65389,6.32,0.42],[6249,253.07958,-41.85444,6.49,0.23],[6250,252.58083,7.24778,5.49,0.1],[6251,253.50208,-57.90944,5.94,1.59],[6252,253.08375,-38.0175,3.57,-0.21],[6253,253.85292,-63.26972,6.02,0.05],[6254,252.30917,45.98333,4.82,0.09],[6255,252.85375,1.21611,5.51,0.05],[6256,252.41875,43.43056,6.13,1.26],[6257,253.42708,-43.05083,5.96,1.73],[6258,252.6625,29.80667,5.72,1.6],[6259,252.67958,32.55361,6.13,1.01],[6260,253.5075,-41.80639,5.45,0.19],[6261,253.495,-41.99472,6.32,0.5],[6262,253.49875,-42.36222,4.73,0.49],[6263,253.54917,-41.85028,6.45,0.2],[6264,252.65042,41.89667,6.29,1.08],[6265,253.58167,-41.82,6.59,0.21],[6266,253.61208,-42.47889,5.88,0.64],[6267,250.775,77.51417,5.98,0.42],[6268,253.02042,14.97417,6.52,-0.05],[6269,253.355,-20.41556,5.88,0.68],[6270,252.93875,24.65639,5.04,1.25],[6271,253.64583,-42.36139,3.62,1.37],[6272,253.74333,-41.15111,5.77,0.15],[6273,253.65,-30.58722,6.35,0.21],[6274,254.03708,-50.675,6.33,-0.02],[6275,254.11958,-52.28389,5.94,-0.08],[6276,254.89083,-69.26833,5.79,-0.1],[6277,253.54417,-1.61222,6.25,0.28],[6278,253.66792,-11.7925,6.57,0.14],[6279,253.24208,31.70167,5.32,0.29],[6280,253.64875,-6.15389,5.25,1.08],[6281,253.50208,10.16528,4.38,-0.08],[6282,253.99083,-33.50722,6.37,1.71],[6283,254.15,-40.82361,6.15,0.26],[6284,254.0075,-16.80611,6.37,0.92],[6285,254.655,-55.99028,3.13,1.6],[6286,253.32333,47.41694,6.0,1.32],[6287,253.73,20.95861,5.41,0.97],[6288,254.29625,-33.25944,5.48,1.59],[6289,254.575,-50.64111,5.55,0.02],[6290,253.81667,13.61972,6.34,0.34],[6291,254.2,-23.15,5.58,-0.02],[6292,253.75875,25.73056,6.08,0.92],[6293,253.8425,18.43333,5.35,1.41],[6294,254.26667,-19.54,6.27,0.07],[6295,254.89625,-53.16056,4.06,1.45],[6296,254.35875,-10.96333,6.19,1.0],[6297,255.02583,-54.59694,5.65,0.19],[6298,254.71833,-37.62111,6.09,0.19],[6299,254.41708,9.375,3.2,1.15],[6300,255.11292,-48.64778,6.0,0.88],[6301,254.38333,13.88417,6.37,0.94],[6302,254.67333,-14.86972,6.59,0.4],[6303,255.13458,-45.45167,6.65,1.8],[6304,255.4475,-58.95833,6.11,-0.03],[6305,254.37917,25.35278,6.28,0.9],[6306,254.02667,50.03889,6.56,1.62],[6307,254.42625,24.38139,6.32,1.1],[6308,254.99,-25.09194,5.86,1.62],[6310,255.03958,-24.98917,5.75,0.41],[6311,255.15375,-35.93417,5.97,1.16],[6312,255.44208,-51.13083,6.45,0.27],[6313,254.45917,42.5125,6.34,1.28],[6314,255.78667,-53.23694,5.29,0.48],[6315,254.00708,65.13472,4.89,0.48],[6316,255.46958,-32.14361,5.03,-0.1],[6317,255.1225,6.58361,6.59,0.23],[6318,255.265,-4.2225,4.82,1.48],[6319,254.105,65.03917,6.41,0.38],[6320,256.10292,-57.71222,5.73,-0.1],[6321,255.46333,-18.88556,6.26,1.38],[6322,251.49208,82.03722,4.23,0.89],[6323,255.92375,-47.16,6.06,0.6],[6324,255.0725,30.92639,3.92,-0.01],[6325,255.24208,22.63222,5.65,1.33],[6326,255.3875,14.94944,6.31,0.04],[6327,255.96167,-38.15222,5.91,0.38],[6328,255.29,27.19639,6.55,0.41],[6329,255.49625,8.45056,6.33,0.09],[6330,254.83958,56.68861,6.03,1.16],[6331,256.27208,-45.50167,6.28,0.07],[6332,255.40167,33.56833,5.25,0.02],[6333,255.57792,25.50556,5.75,1.02],[6334,256.20583,-34.12278,4.87,0.26],[6335,254.07,73.12778,6.3,0.24],[6336,255.57167,31.88472,6.36,1.13],[6337,255.7825,14.09194,4.98,1.6],[6338,256.4525,-44.105,6.19,0.28],[6339,255.79333,14.51111,6.52,0.76],[6340,256.18875,-20.49472,6.3,-0.02],[6341,255.91375,13.60528,5.93,0.0],[6342,255.99167,13.5675,6.08,1.03],[6343,255.96958,19.69056,6.35,1.52],[6344,256.58458,-37.2275,5.98,0.07],[6345,254.76083,69.18639,6.4,0.6],[6346,255.87583,35.41417,6.69,0.6],[6347,256.61833,-35.45111,6.13,0.5],[6348,255.31958,60.64917,6.13,1.0],[6349,256.32042,0.7025,6.01,0.58],[6350,256.54917,-21.56472,6.3,0.13],[6351,255.97292,34.79028,6.04,0.22],[6352,256.17208,19.59917,6.17,-0.01],[6353,256.38458,-0.89194,5.64,0.16],[6354,256.72167,-26.51306,6.29,-0.04],[6355,256.34458,12.74083,4.91,0.12],[6356,257.52625,-61.67556,6.39,-0.04],[6357,258.0825,-70.72111,6.22,1.06],[6358,256.54042,9.73333,6.37,1.45],[6359,256.55458,10.45417,6.37,0.87],[6360,255.56375,64.60056,6.1,0.96],[6361,256.72042,-1.65639,6.38,0.2],[6362,256.27083,43.81222,6.43,0.09],[6363,256.2075,48.80417,6.09,1.09],[6364,256.57542,22.08417,5.56,1.3],[6365,257.06208,-17.60917,5.99,1.01],[6366,257.19792,-30.40361,5.97,0.25],[6367,257.05667,-1.07944,6.06,0.08],[6368,258.32292,-67.19667,5.89,1.06],[6369,256.3325,54.47028,5.83,0.6],[6370,256.33208,54.47028,5.8,0.48],[6371,257.67625,-44.5575,5.08,0.86],[6372,257.22708,-3.88278,6.36,0.69],[6373,259.14833,-74.53306,6.25,-0.01],[6374,257.91208,-48.87417,5.84,1.84],[6375,257.45,-10.52333,5.56,0.52],[6376,256.94458,40.51611,6.34,0.03],[6377,257.00833,35.93528,5.39,0.31],[6378,257.59458,-15.72472,2.43,0.06],[6379,255.4175,75.29722,6.21,0.6],[6380,258.03833,-43.23917,3.33,0.41],[6381,258.0675,-39.50694,5.67,0.04],[6382,258.06875,-38.82222,6.3,1.05],[6383,257.07125,50.84222,6.46,0.0],[6384,258.555,-56.88833,6.09,1.78],[6385,257.69083,12.46722,6.57,0.08],[6386,258.05667,-25.25472,6.54,-0.04],[6387,258.10417,-27.76194,6.14,-0.04],[6388,257.38875,40.77722,5.08,1.28],[6389,258.24458,-32.43861,6.01,0.07],[6390,257.93833,7.89472,6.33,1.04],[6391,257.76333,24.23778,6.19,0.23],[6392,258.61542,-39.76694,6.6,2.21],[6393,258.11583,10.58528,5.33,1.59],[6394,258.22667,0.35194,6.65,0.5],[6395,257.6275,52.40889,6.29,0.0],[6396,257.19667,65.71472,3.17,-0.12],[6397,258.83042,-33.54833,5.53,-0.01],[6398,258.89958,-38.59389,5.96,0.58],[6399,257.9175,49.74667,6.04,0.6],[6400,260.05333,-70.04556,6.53,0.6],[6401,258.8375,-26.60278,5.11,0.86],[6402,258.83667,-26.60139,5.07,0.85],[6403,258.96458,-30.21056,6.21,-0.03],[6404,258.83458,-14.58389,5.99,1.1],[6405,259.08958,-35.74944,6.12,0.48],[6406,258.66208,14.39028,3.48,1.44],[6407,258.66333,14.39,5.39,0.6],[6408,259.80167,-59.69444,5.91,1.37],[6409,259.26542,-32.66278,5.55,0.5],[6410,258.75792,24.83917,3.14,0.08],[6411,260.52458,-70.12333,5.41,-0.04],[6412,259.05917,2.18611,6.17,0.22],[6413,259.17833,-6.245,6.09,1.1],[6414,259.13208,1.21056,5.88,0.06],[6415,259.15292,-0.44528,4.73,1.14],[6416,259.76333,-46.63389,5.48,0.8],[6417,260.4975,-67.77056,4.78,1.21],[6418,258.76167,36.80917,3.16,1.44],[6419,258.92333,23.74278,5.96,1.31],[6420,259.7,-44.12972,5.76,-0.05],[6421,258.13583,62.87444,5.56,0.21],[6422,259.585,-32.55333,6.36,0.15],[6423,259.87625,-50.06333,6.27,0.41],[6424,259.50292,-24.28694,5.2,1.1],[6425,259.50208,-24.28417,6.8,0.51],[6426,259.73833,-34.98972,5.91,1.04],[6427,259.85208,-44.22306,6.65,0.2],[6428,259.58,-16.31194,6.43,1.66],[6429,262.86375,-80.85917,5.88,1.67],[6430,259.39958,23.09083,6.45,0.6],[6431,259.33125,33.1,4.82,-0.17],[6432,259.52083,17.31806,6.0,0.01],[6433,259.65417,10.86444,5.03,1.55],[6434,259.72,6.08528,6.51,0.39],[6435,259.97208,-17.75639,6.02,0.04],[6436,259.41792,37.29167,4.65,0.05],[6437,259.2025,49.69111,7.48,0.6],[6438,260.72917,-58.01028,5.88,1.07],[6439,259.99792,-5.91722,6.32,0.85],[6440,261.00458,-62.86417,5.7,-0.14],[6441,260.1425,-19.33278,6.52,0.58],[6442,260.77875,-56.52528,5.8,1.0],[6443,259.70208,28.82306,5.65,0.98],[6444,259.59708,38.81139,5.94,1.0],[6445,260.25083,-21.11278,4.39,0.39],[6446,260.20708,-12.84694,4.33,0.03],[6447,261.07792,-60.67361,5.77,-0.08],[6448,259.1225,60.67056,6.32,1.09],[6449,260.21958,-10.69611,6.46,0.33],[6450,260.66417,-37.805,6.41,0.64],[6451,260.81708,-47.46833,5.25,-0.11],[6452,260.07875,18.05722,5.0,1.62],[6453,260.5025,-24.99944,3.27,-0.22],[6454,260.65833,-35.91,6.47,0.54],[6455,260.04083,25.5375,5.38,0.03],[6456,260.72875,-37.22056,5.93,1.08],[6457,260.22583,24.49944,5.12,-0.03],[6458,260.165,32.46778,5.39,0.62],[6459,260.84,-28.14306,5.35,1.55],[6460,261.05417,-44.1625,5.12,-0.06],[6461,261.325,-55.53,2.85,1.46],[6462,261.34833,-56.3775,3.34,-0.13],[6463,260.38917,16.73083,6.35,1.61],[6464,260.08792,46.24083,5.59,1.57],[6465,260.71375,-2.38833,6.29,0.68],[6466,260.38,28.75806,6.35,0.7],[6467,260.14,48.18833,6.43,0.43],[6468,261.5,-50.63361,5.23,1.06],[6469,260.43167,39.97444,5.51,0.68],[6470,261.26125,-34.69639,6.16,0.02],[6471,262.03208,-63.03639,6.24,-0.09],[6472,261.175,-21.44167,5.85,0.93],[6473,261.15458,-18.44583,6.21,0.03],[6474,261.27583,-24.24361,6.19,1.1],[6475,261.73458,-51.94917,6.19,-0.03],[6476,260.99,8.85278,5.77,1.25],[6528,262.73083,31.15833,5.61,0.95],[6477,261.71458,-45.84361,5.29,-0.07],[6478,261.80167,-50.63028,5.92,0.08],[6479,260.43917,53.42056,5.67,1.47],[6480,261.0275,22.96028,5.74,0.21],[6481,261.13125,16.30111,5.71,0.07],[6482,261.14083,15.60611,6.35,-0.02],[6483,261.99,-52.29722,5.75,1.17],[6484,260.91958,37.14667,5.47,0.6],[6485,260.92083,37.14583,4.52,-0.03],[6486,261.5925,-24.17528,4.17,0.28],[6487,262.16125,-55.16972,5.94,1.11],[6488,261.00917,38.58278,6.49,0.73],[6489,261.49125,-1.65167,6.44,0.46],[6490,261.73,-25.94333,6.44,-0.06],[6491,261.11292,36.95194,6.28,0.88],[6492,261.83875,-29.86694,4.29,0.4],[6493,261.65792,-5.08667,4.54,0.39],[6494,261.90625,-29.72444,6.0,0.0],[6495,261.47667,16.9175,5.98,1.62],[6496,261.75875,-12.5125,6.21,0.51],[6497,261.57917,7.59556,6.06,0.58],[6498,261.62875,4.14028,4.34,1.5],[6499,261.50375,26.87889,6.41,0.1],[6500,262.77458,-60.68389,3.62,-0.1],[6501,262.23375,-36.77833,6.02,1.11],[6502,261.70458,20.08083,5.54,-0.13],[6503,262.35708,-38.51667,6.39,0.09],[6504,262.00958,-8.20833,6.37,0.58],[6505,262.84583,-56.92056,5.95,-0.08],[6506,261.6925,34.69583,5.94,-0.01],[6507,262.20708,0.33056,5.44,0.22],[6508,262.69083,-37.29583,2.69,-0.22],[6509,261.68417,48.26,5.85,0.12],[6510,262.96042,-49.87611,2.95,-0.17],[6511,261.42208,60.04833,5.65,0.03],[6512,262.4475,-5.91972,6.37,0.93],[6513,262.95458,-46.03639,6.03,0.83],[6514,261.52042,58.65194,6.51,0.14],[6516,262.59917,-1.0625,5.31,0.72],[6517,262.9475,-33.70278,6.44,1.19],[6518,261.25083,67.30639,6.43,0.76],[6519,262.85417,-23.96278,4.81,0.0],[6520,262.935,-26.26972,6.05,-0.06],[6521,262.59333,11.925,6.39,0.06],[6522,263.10208,-34.27972,6.17,0.35],[6523,263.28083,-41.17361,5.84,0.06],[6524,262.83875,2.72444,5.59,0.84],[6525,263.89542,-59.84611,6.28,-0.08],[6526,262.68458,26.11056,4.41,1.44],[6527,263.40208,-37.10389,1.63,-0.22],[6529,259.90417,80.13639,5.72,1.5],[6530,263.83333,-53.35278,6.1,0.02],[6531,262.66792,38.88222,6.43,0.49],[6532,263.0625,11.93028,6.42,-0.01],[6533,262.95667,28.4075,5.62,0.0],[6534,263.37458,-5.74472,5.62,0.18],[6535,263.67708,-32.58167,5.7,0.04],[6536,262.60833,52.30139,2.79,0.98],[6537,263.915,-46.50556,4.59,-0.03],[6538,263.00458,34.27083,6.56,0.65],[6539,263.92917,-37.44,6.48,0.01],[6540,262.6825,57.87639,6.4,0.6],[6541,263.345,19.25667,5.64,0.48],[6542,263.41417,16.3175,5.69,1.01],[6543,263.42833,14.84167,6.48,1.6],[6544,263.69333,-11.24194,5.55,0.02],[6545,263.82708,-22.04389,6.57,0.01],[6546,264.13667,-38.63528,4.29,1.09],[6547,264.36333,-50.06,5.93,1.1],[6548,263.65292,9.58667,5.81,0.02],[6549,264.52333,-54.50028,5.25,0.2],[6550,263.28042,41.24361,5.74,1.09],[6551,263.61333,16.50389,6.4,0.6],[6552,270.39208,-85.21472,6.45,0.44],[6553,264.33,-42.99778,1.87,0.4],[6554,263.04417,55.18417,4.88,0.26],[6555,263.06667,55.17306,4.87,0.28],[6556,263.73375,12.56,2.08,0.15],[6557,264.36167,-38.06556,6.26,1.25],[6558,264.53542,-42.88056,6.1,-0.06],[6559,263.99833,20.99611,6.1,0.19],[6560,263.38208,57.55889,6.17,0.59],[6561,264.39667,-15.39861,3.54,0.26],[6562,264.40083,-15.57111,5.94,0.37],[6563,263.92667,37.30167,6.1,0.98],[6564,264.03292,28.18472,6.38,0.6],[6565,266.08208,-72.22083,6.49,0.48],[6566,262.99125,68.135,5.05,1.08],[6567,264.46125,-8.11889,4.62,0.11],[6568,264.53958,-10.92639,5.75,1.23],[6569,265.09833,-49.41556,4.77,0.4],[6570,264.15292,30.78528,6.02,0.16],[6571,264.37958,24.31,5.77,0.11],[6572,265.31792,-46.92194,5.79,-0.01],[6573,263.74792,61.875,5.23,0.61],[6574,264.15667,48.58556,5.37,1.15],[6575,264.78542,2.02806,6.26,1.03],[6576,265.51625,-50.51056,6.24,1.76],[6577,264.74083,13.32917,6.12,0.56],[6578,265.04917,-2.1525,6.19,1.67],[6579,264.70708,32.73944,6.37,0.6],[6580,265.62208,-39.03,2.41,-0.22],[6581,265.35375,-12.87528,4.26,0.08],[6582,266.43333,-64.72389,3.62,1.19],[6583,265.7125,-36.94583,5.54,1.55],[6584,264.98958,31.2025,6.03,1.58],[6585,266.03625,-51.83417,5.15,0.7],[6586,266.2325,-57.54528,6.01,0.9],[6587,265.77875,-33.05111,6.4,1.81],[6588,264.86625,46.00639,3.8,-0.18],[6589,265.29583,15.17806,6.34,0.03],[6590,265.38458,6.31278,5.95,1.26],[6591,265.17167,31.2875,6.28,1.05],[6592,265.27292,24.51333,6.36,1.2],[6593,265.82417,-27.88417,6.36,0.47],[6594,265.49458,15.95194,5.52,0.38],[6595,265.8575,-21.68333,4.87,0.47],[6596,264.23792,68.75806,4.8,0.43],[6597,266.175,-42.72889,5.87,0.16],[6598,264.16542,69.57083,6.42,0.58],[6599,265.15667,43.47083,6.59,0.6],[6600,265.9525,-13.50861,6.39,0.37],[6601,265.94583,-7.07944,6.3,0.38],[6602,265.61833,24.56417,5.52,1.46],[6603,265.86833,4.56722,2.77,1.16],[6604,265.84167,14.295,6.24,0.42],[6605,265.15083,57.31028,6.77,0.92],[6606,264.28667,72.45583,5.86,1.01],[6607,265.34083,51.81806,5.99,1.05],[6608,265.84,24.32778,5.71,0.65],[6609,266.14167,2.57944,6.17,0.07],[6610,266.1475,2.57889,6.56,0.6],[6611,266.07208,14.41028,6.19,0.21],[6612,265.77333,44.08444,6.34,1.54],[6613,266.78042,-38.11167,6.43,-0.02],[6614,267.15875,-55.40167,6.11,0.28],[6615,266.89625,-40.12694,3.03,0.51],[6616,266.89,-27.83083,4.54,0.8],[6617,266.94,-22.47806,6.18,1.49],[6618,265.99708,53.80167,5.75,0.01],[6619,266.41792,31.50472,6.23,0.0],[6620,266.90333,-14.72583,5.94,0.05],[6621,267.11583,-26.975,6.35,0.12],[6622,267.6175,-53.61222,5.92,-0.08],[6623,266.61458,27.72056,3.42,0.75],[6624,267.89792,-60.16444,5.78,1.0],[6625,266.47375,38.88139,6.52,1.0],[6626,266.49375,39.3225,6.68,1.39],[6627,266.78333,17.69722,5.72,0.01],[6628,267.29375,-31.70333,4.83,-0.04],[6629,266.97333,2.70722,3.75,0.04],[6630,267.46458,-37.04333,3.21,1.17],[6631,267.54667,-40.09056,4.81,0.26],[6632,267.79583,-53.13056,6.09,0.0],[6633,267.08417,3.80417,6.22,0.16],[6634,268.32667,-65.48917,6.49,1.08],[6635,269.42417,-76.1775,6.07,1.2],[6636,265.48458,72.14889,4.58,0.42],[6637,265.49167,72.15694,5.79,0.53],[6638,267.10333,20.56556,5.69,0.94],[6639,267.32875,1.96111,6.47,1.24],[6640,267.93542,-45.60056,6.11,0.95],[6641,266.78375,47.61222,6.43,0.11],[6642,267.19958,19.25528,6.12,0.02],[6643,267.88667,-40.7725,5.96,1.59],[6644,267.205,25.62278,5.12,1.16],[6645,267.80208,-30.55722,6.66,0.04],[6646,271.36125,-81.48639,6.35,1.5],[6647,268.05667,-34.79917,5.9,-0.1],[6648,268.08208,-34.41667,5.84,1.13],[6649,268.21958,-41.99667,6.2,0.54],[6650,267.68125,11.94667,6.17,1.25],[6651,268.205,-34.11417,6.06,1.23],[6652,268.23292,-35.01861,6.45,0.02],[6653,268.24125,-35.62417,6.03,0.34],[6654,267.59542,29.32222,5.5,1.05],[6655,267.70167,22.31639,5.98,0.6],[6656,267.26792,50.78111,5.02,0.02],[6657,268.33167,-34.73056,6.17,-0.03],[6658,268.34708,-34.89528,5.6,1.14],[6659,267.99792,-1.23667,6.35,1.12],[6660,268.43958,-34.78583,6.38,0.0],[6661,268.16167,-6.14361,6.21,1.4],[6662,268.47875,-34.7525,5.96,-0.01],[6663,268.49208,-34.83167,6.42,0.01],[6664,267.51375,48.39417,6.68,-0.11],[6665,267.99375,15.32583,6.46,0.6],[6666,268.265,-10.89972,6.18,1.11],[6667,268.1475,1.305,5.95,1.58],[6668,268.61333,-34.46639,5.96,-0.01],[6669,267.80833,40.0725,6.46,0.6],[6670,268.30917,6.10139,5.77,0.42],[6671,268.78292,-36.47583,6.06,0.08],[6672,268.725,-24.88722,6.2,0.04],[6673,268.01958,39.98222,6.04,1.33],[6674,268.00417,46.64333,6.38,1.09],[6675,269.1975,-44.34222,4.86,1.21],[6676,268.55917,11.13056,6.38,0.45],[6677,268.32542,40.00806,5.16,1.18],[6678,269.2325,-40.30556,6.43,1.43],[6679,268.97917,-18.80222,6.52,0.05],[6680,269.17458,-28.06528,5.8,0.21],[6681,269.07917,-15.8125,5.89,0.05],[6682,269.44875,-41.71611,4.88,1.65],[6683,269.49083,-39.13694,6.29,0.01],[6684,269.07667,0.67028,5.82,0.09],[6685,268.855,26.05,5.46,0.34],[6686,269.19875,-4.08194,5.47,1.16],[6687,268.96167,22.46417,5.58,1.24],[6688,268.38208,56.87278,3.75,1.18],[6689,269.26792,0.06639,5.97,0.1],[6690,269.23333,6.48778,6.29,0.0],[6691,269.73167,-36.85833,5.74,0.9],[6692,269.66292,-28.75917,6.01,-0.08],[6693,269.77167,-30.25306,5.16,1.77],[6694,269.77292,-30.25333,7.04,1.06],[6695,269.06333,37.25056,3.86,1.35],[6696,269.36208,11.04417,6.36,0.11],[6697,269.30958,23.99583,6.3,0.63],[6698,269.75667,-9.77361,3.34,0.99],[6699,268.84875,55.97139,6.1,0.32],[6700,269.94833,-23.81611,4.76,-0.04],[6701,267.3625,76.96278,5.04,0.49],[6702,269.20167,45.35083,6.02,1.64],[6703,269.44125,29.24778,3.7,0.94],[6704,270.00042,-20.33917,6.21,1.4],[6705,269.15167,51.48889,2.23,1.52],[6706,269.90292,-4.82139,5.87,1.56],[6707,269.62583,30.18944,4.41,0.39],[6708,270.45125,-36.37778,6.3,-0.03],[6709,270.06458,0.62944,6.37,0.15],[6710,270.12083,-3.69028,4.62,0.38],[6711,269.67625,36.28778,6.0,0.94],[6712,270.06583,4.36861,4.64,-0.03],[6713,270.01417,16.75083,4.67,1.26],[6714,270.16125,2.93167,3.97,0.02],[6715,270.34625,-17.15694,6.28,1.8],[6716,270.47667,-22.78056,5.77,0.0],[6717,267.54375,78.30667,6.24,1.44],[6718,269.71792,45.47611,6.48,-0.08],[6719,270.22042,6.26833,6.34,-0.08],[6720,270.11542,19.50583,6.5,-0.06],[6721,283.69542,-87.60583,5.28,1.28],[6722,270.23833,15.09333,6.26,0.69],[6723,270.43833,1.30528,4.45,0.02],[6724,270.71292,-24.28222,5.34,0.52],[6725,268.79667,72.005,5.45,0.3],[6726,270.15167,33.21389,5.99,1.51],[6727,270.75708,-22.71833,6.74,-0.05],[6728,269.98417,45.50139,5.67,1.57],[6729,270.37458,21.59528,5.18,0.95],[6730,270.37667,21.59556,4.96,0.12],[6731,272.81542,-75.89139,5.86,1.24],[6732,270.69292,-5.35861,6.76,0.16],[6733,270.77083,-8.18028,5.94,0.6],[6734,270.77042,-8.18056,5.24,0.38],[6735,268.61083,75.17083,6.36,0.98],[6736,270.96833,-24.36056,5.97,0.0],[6737,270.39958,33.31139,6.15,1.55],[6738,270.59625,20.83361,5.28,-0.09],[6739,271.21,-35.90139,6.0,1.16],[6740,271.95125,-64.55,6.41,1.26],[6741,270.62542,22.92306,6.21,-0.1],[6742,271.25542,-29.58,4.69,0.78],[6743,271.65792,-50.09167,3.66,-0.08],[6744,270.81125,19.61306,6.5,0.01],[6745,272.145,-63.66833,4.35,0.22],[6746,271.45208,-30.42417,2.99,1.0],[6747,271.15542,1.91917,6.14,0.0],[6748,271.59875,-36.01972,5.95,0.62],[6749,271.7075,-43.42472,5.77,0.22],[6750,271.7075,-43.42472,5.77,0.6],[6751,273.14375,-73.67167,5.85,0.46],[6752,271.36375,2.49944,4.03,0.86],[6753,270.7875,48.46444,6.21,0.03],[6754,271.1675,23.9425,6.34,0.3],[6755,271.53083,-8.32389,5.85,0.21],[6756,271.56333,-4.75139,5.77,0.96],[6757,271.53083,-0.44667,6.34,1.06],[6758,271.43042,12.00389,7.04,0.3],[6759,272.12542,-45.76722,6.15,-0.08],[6760,272.49,-59.04,6.38,1.55],[6761,272.60875,-62.00222,5.49,0.58],[6762,271.7975,-21.44389,6.28,0.12],[6763,271.37583,21.64694,6.15,1.23],[6764,271.18,40.08417,6.52,0.46],[6765,271.50792,22.21889,5.06,1.58],[6766,272.02083,-28.45722,4.57,0.94],[6767,271.25333,41.94667,6.34,0.26],[6768,271.45667,32.23056,5.71,1.16],[6769,271.95167,-17.15417,5.52,1.11],[6770,271.82667,8.73389,4.64,0.96],[6771,271.8375,9.56389,3.73,0.12],[6772,272.34333,-36.6725,6.58,-0.03],[6773,272.22542,-25.4725,6.61,0.02],[6774,273.60042,-70.75139,6.73,-0.03],[6775,271.75625,30.56194,5.04,0.52],[6776,271.95167,13.07111,6.63,0.07],[6777,272.49958,-32.71972,6.43,1.02],[6778,272.76875,-47.51306,6.07,1.2],[6779,271.88583,28.7625,3.83,-0.03],[6780,272.52375,-30.72861,5.53,0.97],[6781,271.95625,26.10139,5.86,0.12],[6782,271.95625,26.0975,5.9,0.14],[6783,272.8075,-45.95444,4.53,1.01],[6784,272.14042,14.28472,6.37,0.17],[6785,272.43083,-13.93444,6.39,1.42],[6786,272.77333,-41.35917,5.86,0.29],[6787,272.18958,20.81444,4.36,-0.16],[6788,272.73,-33.79972,6.16,-0.14],[6789,263.05375,86.58639,4.36,0.02],[6790,271.72292,50.82278,6.29,1.04],[6791,271.87,43.46167,5.0,0.91],[6792,271.77625,49.71056,6.32,0.6],[6793,272.00917,36.40139,5.48,1.17],[6794,272.22042,20.04528,5.1,0.15],[6795,272.39083,3.99333,5.73,0.37],[6796,273.5675,-63.68944,6.47,1.41],[6797,272.475,3.11972,5.69,0.47],[6798,272.81167,-19.84222,6.36,0.16],[6799,272.2925,30.46944,6.38,1.19],[6800,272.66792,3.32417,5.51,1.19],[6801,272.93083,-23.70111,4.98,1.05],[6802,272.9925,-28.90139,6.51,-0.01],[6803,272.53625,16.47667,6.09,0.6],[6804,273.3025,-41.33611,5.47,-0.17],[6805,273.92042,-63.05556,5.6,0.92],[6806,272.40625,38.4575,6.4,0.87],[6807,272.49583,36.46639,5.58,0.91],[6808,274.50375,-68.22917,6.33,-0.04],[6809,270.01417,80.00083,6.04,0.51],[6810,270.03833,80.00417,5.68,0.5],[6811,262.7,86.96806,5.79,0.25],[6812,273.44083,-21.05889,3.86,0.23],[6813,273.29167,-4.01167,6.59,0.27],[6814,272.93792,33.44694,5.88,0.01],[6815,272.97583,31.40528,4.97,1.65],[6816,273.56625,-21.71306,5.44,1.52],[6817,272.63167,54.28667,5.95,0.94],[6818,273.96958,-44.20667,5.46,0.96],[6819,274.28125,-56.02333,5.33,-0.05],[6820,273.31875,21.88028,6.12,1.47],[6821,274.25375,-51.06833,6.06,-0.06],[6822,273.80375,-20.72833,5.38,0.07],[6823,273.80375,-20.38806,5.95,0.02],[6824,273.1775,41.14694,6.36,1.03],[6825,273.87833,-18.66139,6.07,0.2],[6826,273.27,38.77361,6.04,-0.08],[6827,272.77958,60.40944,6.49,0.0],[6828,274.9175,-63.88694,6.18,0.58],[6829,275.90042,-75.04417,5.47,0.02],[6830,273.99167,-3.6175,6.36,0.2],[6831,273.68333,29.20722,6.56,0.54],[6832,274.40667,-36.76167,3.11,1.56],[6833,274.40042,-34.10722,6.16,-0.11],[6834,274.02333,2.37778,6.01,1.59],[6835,274.35,-28.6525,6.19,0.18],[6836,274.34875,-28.28917,6.4,0.54],[6837,277.33125,-80.23278,5.95,1.16],[6838,274.29833,-17.37389,5.75,1.58],[6839,274.66667,-42.28833,6.3,-0.11],[6840,274.22125,-3.00722,6.0,0.89],[6841,274.36875,-18.46333,6.54,0.11],[6842,274.51333,-27.0425,4.65,1.66],[6843,274.35083,-9.75861,6.31,0.38],[6844,274.27,1.00583,6.63,0.31],[6845,273.91167,42.15944,5.59,-0.1],[6846,274.67375,-25.60472,6.51,1.34],[6847,273.88583,45.20944,6.29,0.62],[6848,274.68042,-18.61944,6.84,0.31],[6849,273.67125,56.58833,6.37,0.34],[6850,273.47417,64.39722,5.03,0.38],[6851,274.51208,13.77694,6.3,-0.03],[6852,274.53208,18.13139,5.99,0.03],[6853,274.27833,40.93667,6.11,0.99],[6854,274.53208,23.29667,6.63,0.6],[6855,275.80667,-61.49389,4.36,1.48],[6856,275.23042,-37.4875,6.45,1.31],[6857,274.78958,7.25972,5.39,1.07],[6858,275.03667,-15.83167,5.39,1.47],[6859,275.24875,-29.82806,2.7,1.38],[6860,274.79458,24.44611,5.27,1.53],[6861,275.38083,-24.915,6.25,1.84],[6862,275.5775,-38.65694,5.1,1.49],[6863,275.34625,-18.86,5.75,0.94],[6864,275.50083,-28.43,6.16,0.26],[6865,273.82083,68.75583,5.95,1.06],[6866,275.21708,3.37722,4.86,0.91],[6867,274.96708,29.66611,5.99,1.29],[6868,275.07458,21.96139,4.95,1.59],[6869,275.3275,-2.89889,3.26,0.94],[6870,275.72125,-36.66944,5.34,-0.14],[6871,276.38125,-63.02139,6.14,0.2],[6872,274.96542,36.06444,4.33,1.17],[6873,275.36875,5.43583,6.13,-0.04],[6874,275.87042,-36.23833,5.55,1.02],[6875,276.07583,-44.11028,5.25,-0.19],[6876,275.23792,29.85889,5.63,0.21],[6877,275.25417,28.87,5.12,0.2],[6878,275.75917,-10.21861,6.33,0.14],[6879,276.04292,-34.38472,1.85,-0.03],[6880,274.98375,51.34778,6.3,1.1],[6881,275.80083,-12.01472,5.73,0.01],[6882,275.53625,23.28528,5.41,1.6],[6883,275.64708,12.02889,5.89,0.04],[6884,275.91458,-8.93417,4.68,0.95],[6885,275.70417,17.82667,5.25,1.27],[6886,275.27958,49.72556,6.4,1.07],[6887,275.76208,16.68806,6.22,1.2],[6888,276.25625,-30.75667,5.6,1.14],[6889,276.34042,-35.99167,6.15,1.0],[6890,276.01458,-3.58333,6.38,0.34],[6891,275.38625,49.12167,5.05,1.66],[6892,276.17542,-7.07528,6.31,1.16],[6893,276.4775,-33.94528,6.3,-0.08],[6894,276.72458,-48.11694,5.46,0.84],[6895,275.92458,21.76972,3.84,1.18],[6896,276.3375,-20.54167,4.81,1.31],[6897,276.74333,-45.96833,3.51,-0.17],[6898,276.2375,-1.57944,6.15,0.37],[6899,278.23042,-73.96556,5.89,0.98],[6900,276.28667,5.08472,6.74,0.02],[6901,275.98917,38.73917,6.36,0.6],[6902,276.41167,8.03194,5.65,0.92],[6903,276.0575,39.50722,5.12,0.03],[6904,276.24375,27.39528,6.27,0.05],[6905,277.20792,-49.07083,4.13,1.02],[6906,276.48083,14.96667,6.37,0.01],[6907,276.95625,-29.81639,5.92,0.52],[6908,277.48625,-57.52306,5.76,0.98],[6909,276.9325,-26.63472,6.31,0.26],[6910,277.11292,-38.99556,5.64,0.13],[6911,275.94917,53.30083,6.32,0.16],[6912,280.55875,-81.80778,6.27,-0.13],[6913,276.9925,-25.42167,2.81,1.04],[6914,277.02583,-26.75722,6.27,0.16],[6915,277.30375,-43.84583,6.36,0.9],[6916,277.84333,-62.27833,4.64,-0.11],[6917,276.495,29.82889,5.83,0.06],[6918,276.80208,0.19611,5.21,0.5],[6919,276.98542,-17.8,6.2,0.01],[6920,275.18958,71.33778,4.22,-0.1],[6921,277.32,-38.85111,6.63,-0.02],[6922,277.4825,-47.22028,5.7,1.26],[6923,275.97708,58.80056,4.98,0.08],[6924,276.67042,26.44944,6.53,-0.11],[6925,276.95958,3.74861,6.07,1.62],[6926,277.23917,-26.58167,6.5,0.11],[6927,275.26417,72.73278,3.57,0.49],[6928,276.995,6.19417,5.73,-0.03],[6929,277.34167,-25.25639,6.59,0.07],[6930,277.29958,-14.56583,4.7,0.06],[6931,277.7625,-41.91361,6.04,0.14],[6932,277.445,-14.58167,5.96,-0.04],[6933,277.54958,-18.72889,5.66,1.06],[6934,277.93917,-45.915,4.96,-0.11],[6935,277.42083,-1.98528,5.39,0.96],[6936,277.77,-32.98917,5.34,0.16],[6937,277.98417,-43.50778,5.72,1.34],[6938,278.00833,-45.75722,5.07,-0.14],[6939,278.37292,-58.70917,6.44,0.68],[6940,277.55958,-5.72417,6.28,0.95],[6941,277.52125,4.06528,6.69,0.11],[6942,278.08917,-39.70389,5.16,0.08],[6943,277.39875,23.86611,5.9,-0.1],[6944,277.85958,-18.40278,5.14,0.0],[6945,276.49625,65.56361,4.82,1.19],[6946,277.85708,-10.79583,5.72,0.24],[6947,277.97208,-19.125,6.68,1.13],[6948,278.25375,-39.89222,6.22,0.42],[6949,276.92625,59.54917,6.43,0.6],[6950,277.67333,20.81528,6.5,0.79],[6951,278.37583,-42.3125,4.64,1.01],[6952,278.34708,-38.72028,6.32,0.6],[6953,278.34625,-38.72611,5.65,-0.06],[6954,278.63,-52.89194,6.22,1.25],[6955,277.76833,16.92861,5.77,0.04],[6956,278.08667,-14.64417,6.37,0.22],[6957,277.9875,-1.00306,5.94,0.16],[6958,278.02917,3.65972,6.43,-0.04],[6959,278.18042,-14.86556,5.5,1.97],[6960,278.49083,-33.01667,5.28,-0.11],[6961,278.47292,-24.0325,5.49,1.79],[6962,278.4125,-14.85361,5.76,0.04],[6963,278.34542,-5.91139,6.36,0.02],[6964,282.99125,-83.31639,7.16,1.26],[6965,278.63667,-24.2225,6.51,0.54],[6966,278.1925,23.61694,5.84,1.46],[6967,278.34708,8.26833,6.42,-0.03],[6968,278.20792,30.55417,5.48,-0.1],[6969,278.83875,-20.84083,6.48,0.28],[6970,278.76,-10.97722,5.14,0.92],[6971,278.34625,30.8925,6.59,-0.12],[6972,278.99875,-29.69917,6.37,1.27],[6973,278.80167,-8.24417,3.85,1.33],[6974,278.0475,52.11556,6.56,-0.07],[6975,278.58167,20.46639,6.57,0.11],[6976,278.69792,10.89167,6.4,0.08],[6977,278.8025,18.20333,5.78,0.0],[6978,278.14375,57.04556,4.77,0.61],[6979,277.81167,65.43611,6.59,0.3],[6980,278.87667,23.60556,5.61,1.0],[6981,278.97167,16.97556,6.21,0.53],[6982,280.75875,-71.42806,4.01,1.14],[6983,278.48625,52.35361,5.36,1.09],[6984,278.80625,34.45778,6.1,-0.11],[6985,279.11583,9.1225,5.39,0.37],[6986,279.80958,-47.90972,5.86,0.23],[6987,279.16292,6.67194,5.45,0.37],[6988,279.47667,-21.39778,5.94,0.19],[6989,279.51917,-14.00472,6.47,0.21],[6990,279.62792,-23.505,5.81,0.02],[6991,279.89583,-43.18611,5.37,1.68],[6992,279.3025,11.42167,6.42,-0.02],[6993,279.4,-0.30944,5.75,0.07],[6994,281.95583,-77.86722,6.39,0.6],[6995,279.2875,16.19833,6.29,0.9],[6996,280.59375,-64.64306,6.37,0.15],[6997,279.155,33.46889,5.42,-0.1],[6998,279.7225,-21.05194,5.86,0.68],[6999,279.59875,-3.19361,6.49,0.55],[7000,279.57958,-1.11333,6.66,0.42],[7001,279.23458,38.78361,0.03,0.0],[7002,279.5875,8.83389,6.4,1.32],[7003,279.19,43.22194,6.2,0.24],[7004,280.905,-64.55111,5.78,0.96],[7005,280.3775,-48.095,6.49,1.22],[7006,277.43708,77.54694,5.64,1.18],[7007,280.00208,-7.79056,5.84,1.55],[7008,279.90375,5.26417,6.38,0.78],[7009,279.52708,39.66806,6.04,1.65],[7010,279.965,7.35833,6.28,0.96],[7011,280.465,-23.83333,6.23,0.23],[7012,281.36208,-64.87139,4.79,0.2],[7013,279.05542,65.48861,6.06,0.28],[7014,280.42708,-14.56417,6.42,0.81],[7015,281.29792,-61.095,6.04,1.46],[7016,280.00833,30.84944,6.36,0.6],[7017,279.88792,40.935,6.25,-0.06],[7018,279.38958,62.52667,5.74,-0.06],[7019,280.05083,38.36722,6.45,0.21],[7020,280.56833,-9.0525,4.72,0.35],[7021,280.94542,-38.32361,5.13,0.09],[7022,281.34875,-56.88167,6.22,1.38],[7023,280.73,-19.28389,6.35,1.75],[7024,280.65042,-7.07333,6.15,1.0],[7025,276.03833,83.17528,6.17,0.05],[7026,281.03208,-36.71861,6.32,0.98],[7027,282.43125,-72.99472,6.06,0.0],[7028,279.97,52.19611,6.0,-0.07],[7029,281.08083,-35.64194,4.87,-0.18],[7030,280.42208,31.61778,6.41,-0.04],[7031,281.23833,-39.68639,5.43,0.87],[7032,280.88042,-8.27528,4.9,1.12],[7033,280.53375,34.74667,6.47,-0.13],[7034,280.96417,-6.81861,6.31,0.48],[7035,281.20667,-25.01111,5.83,0.05],[7036,282.1575,-65.07778,5.73,0.24],[7037,281.74625,-50.09444,6.54,0.28],[7038,281.32792,-21.00139,6.36,0.45],[7039,281.41417,-26.99083,3.17,-0.11],[7040,281.20792,2.06,5.02,-0.06],[7041,280.81958,39.30028,6.45,1.59],[7042,280.23458,62.74972,6.09,0.98],[7043,280.90042,36.55667,6.01,1.04],[7044,280.965,31.92667,5.7,0.34],[7045,281.505,-19.60639,6.42,1.65],[7046,281.58583,-22.39222,5.37,1.64],[7047,281.1675,23.58972,6.31,0.4],[7048,281.36833,5.49972,5.83,0.04],[7049,280.65792,55.53944,5.04,-0.09],[7050,281.93583,-40.40611,5.24,0.78],[7051,281.085,39.67,5.06,0.16],[7052,281.08458,39.67111,6.02,0.6],[7053,281.09542,39.61306,5.14,0.19],[7054,281.09542,39.61278,5.37,0.6],[7055,281.68042,-10.125,5.71,0.59],[7056,281.19333,37.605,4.36,0.19],[7057,281.20083,37.59444,5.73,0.28],[7058,281.39875,21.985,6.51,0.02],[7059,281.61875,-0.96167,5.9,0.13],[7060,280.87083,53.87194,6.11,0.12],[7061,281.41542,20.54639,4.19,0.46],[7062,282.21042,-43.68,5.49,0.13],[7063,281.79375,-4.74778,4.22,1.1],[7064,281.51875,26.66222,4.83,1.2],[7065,282.36417,-45.81028,5.81,0.9],[7066,281.87083,-5.705,5.2,1.47],[7067,281.6725,18.70583,6.17,1.59],[7068,282.39583,-43.43389,5.61,-0.08],[7069,281.75542,18.18139,4.36,0.13],[7070,282.32167,-34.74861,6.62,1.08],[7071,281.23083,54.89667,6.23,0.82],[7072,282.18875,-18.60139,6.47,0.6],[7073,281.55417,41.44167,6.07,-0.13],[7074,283.05417,-62.1875,4.22,-0.14],[7075,281.07583,61.04806,5.99,0.96],[7076,282.01125,4.24139,6.21,1.51],[7077,282.39792,-19.14222,6.75,0.2],[7078,282.41708,-20.32472,5.24,1.41],[7079,282.06833,23.51417,6.15,0.49],[7080,281.74583,46.315,6.52,0.07],[7081,281.98958,31.75694,6.06,-0.13],[7082,280.7925,70.79278,6.44,0.6],[7083,282.42083,-5.91278,5.99,1.6],[7084,281.67958,52.98806,5.88,-0.09],[7085,282.40458,0.83583,6.25,0.04],[7086,282.2225,19.32861,5.88,0.03],[7087,283.165,-52.1075,5.17,0.94],[7088,282.71042,-22.16222,6.61,0.38],[7089,282.58333,-7.9075,6.8,3.09],[7090,281.91667,49.075,6.4,0.6],[7091,282.31,25.04639,6.59,0.6],[7092,283.11292,-46.59528,5.54,1.63],[7093,283.30042,-51.93111,6.31,-0.09],[7094,282.74375,-9.77417,5.83,0.61],[7095,283.26042,-48.36,6.19,0.14],[7096,282.06708,48.7675,6.12,0.21],[7097,283.24833,-46.58583,6.19,0.03],[7098,282.43333,31.62917,6.64,0.02],[7099,282.69,10.97639,6.55,0.6],[7100,282.44125,32.81278,5.91,-0.16],[7101,282.84208,-3.31778,6.1,0.3],[7102,282.47042,32.55083,5.25,0.08],[7103,283.11875,-26.65028,6.29,0.94],[7104,283.15417,-29.37944,6.13,1.35],[7105,283.17375,-30.73417,6.63,-0.05],[7106,282.52,33.36278,3.45,0.0],[7107,284.2375,-67.23361,4.44,0.71],[7108,283.63458,-49.87861,6.6,0.08],[7109,283.00792,13.96556,6.14,0.0],[7110,283.25792,-9.57611,6.34,0.2],[7111,284.22792,-62.80111,6.48,1.53],[7112,282.89958,28.78361,6.18,1.18],[7113,283.06833,21.42528,5.48,-0.07],[7114,283.50042,-21.35972,5.69,1.23],[7115,282.90208,36.53861,6.09,-0.11],[7116,283.5425,-22.745,4.83,1.41],[7117,281.44458,74.08556,5.27,0.92],[7118,283.02958,41.38333,6.28,-0.09],[7119,283.67958,-15.60306,5.1,0.17],[7120,283.77958,-22.67139,4.99,1.33],[7121,283.81625,-26.29667,2.02,-0.22],[7122,284.07042,-42.71056,5.36,1.0],[7123,282.89583,52.975,5.51,0.84],[7124,281.5925,75.43389,5.35,0.05],[7125,282.80042,59.38833,4.66,1.19],[7126,283.87917,-16.37667,5.79,0.36],[7127,284.65167,-60.20056,5.14,1.37],[7128,284.0025,-23.17361,5.93,-0.02],[7129,284.16875,-37.34333,5.38,-0.14],[7130,285.01458,-66.65333,6.01,0.97],[7131,283.43167,36.97167,5.58,-0.15],[7132,283.555,27.90944,5.62,1.35],[7133,283.68708,22.645,4.59,0.78],[7134,284.61542,-52.93861,4.87,-0.05],[7135,283.86458,6.61528,5.57,1.04],[7136,284.39458,-39.82333,6.31,0.2],[7137,283.30667,50.70833,4.92,0.9],[7138,283.55958,41.22556,7.3,0.6],[7139,283.62583,36.89889,4.3,1.68],[7140,283.71875,33.96861,6.02,0.91],[7141,284.055,4.20361,4.62,0.17],[7142,284.06083,4.20194,4.98,0.2],[7143,284.09458,-1.8,6.22,-0.05],[7144,284.10667,2.47111,6.15,0.97],[7145,284.33542,-20.65639,5.08,0.13],[7146,283.7175,41.60278,5.44,1.03],[7147,284.01625,17.995,6.63,-0.04],[7148,284.02583,18.10528,5.69,1.09],[7149,284.26542,-5.84611,4.83,1.08],[7150,284.4325,-21.10667,3.51,1.18],[7151,284.58875,-31.03611,6.12,1.35],[7152,284.68083,-37.1075,4.87,0.41],[7153,283.44292,57.48694,6.22,1.23],[7154,283.69625,48.85972,5.77,0.43],[7155,284.58542,-24.87667,6.62,0.08],[7156,284.79625,-39.53472,6.49,-0.04],[7157,283.83375,43.94611,4.04,1.59],[7158,284.31917,2.53528,5.57,0.0],[7159,284.6025,-22.52944,6.14,0.09],[7160,281.40875,79.9425,6.39,0.28],[7161,285.87375,-68.75528,5.88,0.56],[7162,284.25667,32.90139,5.22,0.59],[7163,284.59917,6.24028,6.21,0.46],[7164,284.86167,-18.56694,6.37,0.99],[7165,284.56125,17.36083,5.38,0.8],[7166,284.84917,-12.84056,5.53,-0.04],[7167,284.69542,13.90667,5.89,0.25],[7168,285.10333,-24.94222,6.36,1.25],[7169,285.26333,-37.06083,6.69,0.6],[7170,285.26792,-37.06194,6.4,-0.03],[7171,284.68792,19.79417,6.5,-0.04],[7172,284.77375,13.6225,5.23,0.53],[7173,284.82292,10.14083,6.75,0.25],[7174,284.50792,38.26611,5.89,-0.17],[7175,284.1875,57.815,5.66,1.15],[7176,284.90583,15.06833,4.02,1.08],[7177,285.53625,-41.91,6.23,0.0],[7178,284.73583,32.68944,3.24,-0.05],[7179,284.69417,40.67917,6.22,-0.16],[7180,283.59958,71.29722,4.82,1.15],[7181,284.93958,26.23056,5.27,1.24],[7182,285.4075,-22.69556,6.24,1.66],[7183,284.99208,22.81472,6.29,1.75],[7184,284.36833,58.22528,6.46,0.08],[7185,284.80125,39.21778,6.41,-0.17],[7186,285.38958,-15.2825,6.32,1.0],[7187,284.10667,65.25806,5.63,0.95],[7188,285.77875,-42.09528,4.75,-0.02],[7190,285.98917,-51.01861,5.93,1.24],[7191,284.3225,62.39667,6.45,0.93],[7192,285.00375,32.14556,4.93,1.47],[7193,285.42,-5.73889,4.02,1.09],[7194,285.65292,-29.88028,2.6,0.08],[7195,285.61542,-24.84694,5.65,1.23],[7196,284.74833,50.80944,6.3,0.98],[7197,285.82375,-38.25333,5.74,0.32],[7198,285.27292,19.30972,6.39,0.6],[7199,283.38833,75.7875,6.22,0.6],[7200,285.34417,20.83361,6.69,0.02],[7201,285.07917,40.68417,6.65,0.6],[7202,285.3225,26.29139,5.69,-0.08],[7203,285.76583,-19.24528,6.05,1.29],[7204,285.23,33.80222,6.01,0.97],[7205,285.77917,-19.10333,6.37,0.48],[7206,285.39542,25.02583,6.72,0.6],[7207,285.45625,22.26389,6.4,0.16],[7208,285.59,8.37417,6.3,1.67],[7209,285.72708,-3.69889,5.42,0.0],[7210,285.05708,50.53361,5.38,-0.18],[7211,286.10458,-31.04694,5.5,0.03],[7212,285.45125,33.62139,6.39,-0.12],[7213,286.58292,-52.34083,5.16,0.53],[7214,285.88417,1.81889,5.83,0.18],[7215,285.36,46.93472,5.01,0.19],[7216,285.71917,19.66111,6.09,1.34],[7217,286.17083,-21.74167,3.77,1.01],[7218,285.18083,55.65833,5.48,0.86],[7219,286.04458,3.33056,6.73,0.13],[7220,286.10083,-5.685,6.9,4.19],[7221,287.46958,-68.42472,5.33,0.91],[7222,285.92708,21.26778,6.52,0.32],[7223,286.73167,-48.29917,5.97,-0.02],[7224,284.71917,69.53111,6.52,-0.15],[7225,286.24,-4.03139,5.42,1.12],[7226,286.60458,-37.06333,4.93,0.52],[7227,286.60458,-37.06333,4.99,0.52],[7228,317.1925,-88.95639,5.47,0.27],[7229,285.52917,52.26111,6.31,1.0],[7230,286.42167,-15.66028,5.97,-0.02],[7231,286.3275,-1.51278,6.53,0.35],[7232,286.71875,-37.81028,6.16,0.72],[7233,287.21708,-55.72028,6.49,1.1],[7234,286.735,-27.67056,3.32,1.19],[7235,286.3525,13.86333,2.99,0.01],[7236,286.56208,-4.8825,3.44,-0.09],[7237,286.24125,31.74444,5.56,1.54],[7238,286.24292,30.73333,6.06,1.55],[7239,286.71792,-16.22889,6.03,-0.04],[7240,286.87875,-28.63694,6.04,1.61],[7241,286.78542,-18.73778,6.29,-0.04],[7242,287.08708,-40.49667,4.59,1.09],[7243,286.5925,8.23,6.09,1.6],[7244,286.44625,29.92167,6.31,1.65],[7245,286.78792,0.64167,6.56,0.05],[7246,287.06083,-24.65694,6.3,0.04],[7247,284.48833,77.05083,6.54,0.38],[7248,286.74417,11.07139,5.09,-0.07],[7249,287.06958,-19.29,5.54,-0.11],[7250,286.66,24.25083,5.77,0.09],[7251,286.23,53.39667,5.38,-0.01],[7252,286.29125,49.92333,6.43,0.6],[7253,286.65708,28.62861,5.55,0.29],[7254,287.36792,-37.90444,4.11,0.04],[7255,287.41542,-39.82806,6.46,1.06],[7256,287.40167,-36.16472,6.56,-0.02],[7257,287.49083,-41.8925,5.88,-0.08],[7258,286.57083,41.41389,6.49,-0.15],[7259,287.50708,-39.34083,4.11,1.2],[7260,286.98875,16.85333,6.07,0.7],[7261,286.85667,32.50167,5.23,0.34],[7262,286.82542,36.10028,5.28,-0.11],[7263,287.015,21.69889,6.23,0.4],[7264,287.44083,-21.02361,2.89,0.35],[7265,287.45042,-19.80361,6.13,1.16],[7266,287.24958,6.07333,5.22,0.35],[7267,287.1675,16.85139,6.48,0.52],[7268,287.7575,-39.005,6.36,0.01],[7269,287.465,-0.42806,6.34,-0.04],[7270,287.82875,-29.50222,6.3,-0.04],[7271,288.19208,-50.48639,6.13,0.95],[7272,287.26833,34.60056,6.74,0.63],[7273,288.04083,-37.58278,6.57,1.02],[7274,289.11875,-69.19056,6.27,0.17],[7275,287.1075,52.42556,5.81,1.09],[7276,288.11667,-21.65806,6.41,1.13],[7277,288.30708,-25.90667,5.8,1.38],[7278,289.3,-66.66139,5.53,0.18],[7279,288.16958,-7.93944,5.34,0.13],[7280,287.87875,26.73583,6.36,0.41],[7281,288.66542,-45.19333,5.92,0.9],[7282,288.31458,-12.2825,5.51,1.44],[7283,287.94167,31.28333,5.98,-0.07],[7284,287.84625,40.42917,6.18,0.09],[7285,288.14333,16.84639,6.73,-0.01],[7286,288.15292,21.55444,5.93,0.03],[7287,288.42792,2.29361,5.15,-0.07],[7288,288.43375,5.51583,6.49,0.09],[7289,289.09042,-45.46639,5.4,1.35],[7290,287.44083,65.97861,6.25,0.0],[7291,288.88833,-24.17917,6.25,0.54],[7292,288.885,-25.25667,4.85,0.56],[7293,288.01917,49.85417,6.75,0.65],[7294,288.02083,49.85611,6.57,0.65],[7295,287.91875,56.85917,5.12,1.01],[7296,289.13667,-33.52167,6.25,0.02],[7297,289.53917,-53.38667,6.38,0.49],[7298,288.43958,39.14611,4.39,-0.15],[7299,288.76083,20.20333,6.0,0.88],[7300,288.83375,15.08361,5.57,1.07],[7301,288.8225,21.23222,5.64,0.11],[7302,288.85333,30.52639,5.85,1.67],[7303,289.12917,4.83472,5.59,0.08],[7304,289.40875,-18.95306,4.96,1.02],[7305,288.9875,27.45556,6.54,-0.06],[7306,289.05417,21.39028,4.77,-0.05],[7307,289.11167,14.54472,5.63,-0.02],[7308,288.9975,27.92694,6.16,0.61],[7309,288.48,57.705,4.99,1.16],[7310,288.13875,67.66167,3.07,1.0],[7311,288.83042,50.07083,6.27,0.6],[7312,287.29083,76.56056,5.13,0.31],[7313,289.45083,2.03167,6.19,0.02],[7314,289.09208,38.13361,4.36,1.26],[7315,289.45417,11.59528,5.28,0.2],[7316,289.91667,-35.42139,5.59,-0.13],[7317,289.75042,-15.53639,6.06,1.43],[7318,289.43167,23.02556,5.43,0.02],[7319,289.63542,1.08528,5.1,1.15],[7320,291.0225,-68.37111,6.34,1.23],[7321,289.71208,0.33917,6.41,1.05],[7322,289.21417,46.99917,6.0,0.44],[7323,290.10917,-31.81778,6.58,1.67],[7324,289.50333,31.02222,6.68,0.08],[7325,289.71958,9.61806,6.32,1.05],[7326,289.70208,19.61056,6.58,0.03],[7327,290.15875,-22.4025,5.58,0.27],[7328,289.27583,53.36861,3.77,0.96],[7329,290.71292,-54.42361,5.05,0.02],[7330,290.37458,-34.98389,6.48,0.63],[7331,289.91375,12.37472,5.53,0.26],[7332,289.97083,11.535,6.02,0.08],[7333,290.13708,-5.41583,5.01,0.92],[7334,290.54,-42.01611,6.34,1.14],[7335,289.76583,33.38889,6.6,-0.19],[7336,290.14875,-0.89222,5.49,-0.04],[7337,290.65958,-44.45889,4.01,-0.1],[7338,289.755,37.44528,6.22,-0.03],[7339,290.40458,-19.23417,6.26,-0.1],[7340,290.41833,-17.84722,3.93,0.22],[7341,289.65708,49.56972,6.31,1.12],[7342,290.43167,-15.955,4.61,0.1],[7343,290.805,-44.79972,4.29,0.34],[7344,290.46208,-18.30833,5.87,1.06],[7345,289.91208,37.33056,6.31,0.68],[7346,290.13792,35.18611,6.31,-0.12],[7347,290.58625,-8.20111,6.31,-0.1],[7348,290.97167,-40.61611,3.97,-0.1],[7349,290.58958,-0.2525,5.83,1.09],[7350,291.08917,-43.72306,6.17,1.6],[7351,289.90208,54.37611,6.26,0.03],[7352,288.8875,73.35556,4.45,1.25],[7353,290.76917,-7.40028,6.32,1.45],[7354,290.70167,9.91306,6.35,0.44],[7355,291.12542,-27.86556,6.04,-0.13],[7356,290.06708,57.64528,5.91,1.58],[7357,290.78417,14.92111,6.64,0.27],[7358,290.71208,26.2625,5.18,-0.12],[7359,290.63917,33.51806,6.06,1.03],[7360,291.26708,-29.30917,5.93,1.26],[7361,289.94208,64.39083,6.52,-0.04],[7362,291.31875,-24.50861,5.03,0.23],[7363,291.37375,-23.96222,5.43,1.43],[7364,290.94542,20.26444,6.4,0.01],[7365,290.35583,57.76694,6.43,0.6],[7366,291.25667,-4.88417,6.52,0.33],[7367,291.34,-13.89694,5.69,1.43],[7368,290.89167,33.22222,6.37,0.81],[7369,291.09208,16.93778,6.25,0.08],[7370,291.95042,-54.32528,5.69,1.4],[7371,290.16708,65.71472,4.59,0.02],[7372,291.03167,29.62139,4.97,-0.1],[7373,291.2425,11.94444,5.16,0.77],[7374,291.09333,28.08778,6.53,-0.08],[7375,291.58,-21.77667,5.59,1.22],[7376,291.02542,36.45194,6.36,0.6],[7377,291.37458,3.11472,3.36,0.32],[7378,291.54625,-15.05306,5.72,0.02],[7379,291.6025,-14.55111,6.7,0.05],[7380,291.73542,-29.74333,5.67,0.0],[7381,290.84917,50.27139,6.51,-0.08],[7382,290.98542,43.38806,5.84,0.92],[7383,292.79542,-68.43389,5.96,1.64],[7384,291.34333,20.27139,6.31,-0.02],[7385,291.36917,19.79861,5.16,0.98],[7386,291.3575,24.91278,6.19,0.51],[7387,291.62958,0.33861,4.66,0.6],[7388,292.46917,-55.44139,6.13,0.98],[7389,291.60042,13.02389,5.74,0.47],[7390,291.555,20.09778,5.63,-0.01],[7391,291.61958,19.89139,5.81,1.55],[7392,292.34958,-43.44583,5.71,0.22],[7393,292.64375,-55.11,6.3,0.45],[7394,259.23667,89.03778,6.38,1.57],[7395,291.53792,36.31778,5.15,-0.12],[7396,291.89125,14.2825,6.32,-0.06],[7397,292.08667,2.93028,5.85,0.01],[7398,292.4675,-26.98556,5.52,1.12],[7399,292.56125,-32.09222,6.6,0.39],[7400,292.25417,1.95028,5.8,0.08],[7401,291.44458,58.02722,6.6,-0.15],[7402,292.33958,-7.04389,6.61,1.1],[7403,291.90208,37.94111,6.34,-0.14],[7404,292.325,0.24611,6.25,1.32],[7405,292.17625,24.665,4.44,1.5],[7406,292.2375,24.76861,5.81,1.03],[7407,292.34208,14.59583,5.56,1.05],[7408,291.85792,52.32056,5.75,0.0],[7409,292.33708,20.27972,6.33,-0.1],[7410,292.725,-21.31222,6.13,0.12],[7411,293.22417,-53.18583,5.75,0.3],[7412,292.54375,2.90417,6.09,1.82],[7413,291.61042,62.55722,6.38,1.39],[7414,292.66583,-2.78889,5.03,1.75],[7415,292.63792,3.44444,6.05,0.01],[7416,293.34,-45.27194,5.61,-0.04],[7417,292.68042,27.95972,3.08,1.13],[7418,292.68875,27.96528,5.11,-0.1],[7419,292.69542,36.22861,6.25,-0.04],[7420,292.42625,51.72972,3.79,0.14],[7421,292.84083,26.61722,5.87,0.93],[7422,293.53542,-40.03472,5.89,0.09],[7423,290.4175,79.60278,6.05,0.07],[7424,293.80417,-48.09917,4.9,1.09],[7425,288.7825,83.46278,6.53,0.1],[7426,292.94292,34.45306,4.74,-0.14],[7427,292.83042,50.30667,5.53,1.25],[7428,292.80667,55.73194,6.37,1.16],[7429,293.5225,7.37889,4.45,1.17],[7430,293.78042,-10.56028,5.12,1.13],[7431,294.00708,-24.71917,5.65,0.19],[7432,293.87417,-7.46028,6.34,1.12],[7433,293.89,-12.25278,6.27,1.09],[7434,294.60792,-57.98333,6.18,0.97],[7435,294.96708,-66.68556,6.39,0.02],[7436,293.40167,38.76222,6.61,0.03],[7437,293.64542,19.77333,5.0,-0.09],[7438,293.855,2.91333,6.38,0.41],[7439,294.10875,-18.85278,6.11,0.27],[7440,294.17667,-24.88361,4.6,-0.07],[7441,293.71208,29.46306,5.38,0.55],[7442,293.42333,49.2625,5.96,1.64],[7443,294.26375,-18.23111,5.64,1.26],[7444,293.67167,42.41278,5.35,0.05],[7445,294.03333,11.15,6.68,0.6],[7446,294.22292,-7.0275,4.95,0.0],[7447,294.18042,-1.28639,4.36,-0.08],[7448,293.29208,60.15861,6.29,1.57],[7449,294.06583,14.39167,6.38,1.04],[7450,292.75083,70.98944,6.07,1.41],[7451,293.5825,51.23667,5.73,0.48],[7452,294.03458,22.58583,6.32,-0.07],[7453,293.66625,48.16472,6.67,0.24],[7454,294.39333,-14.30167,5.47,0.5],[7455,295.40625,-65.85417,6.09,1.55],[7456,294.21875,11.27333,5.98,0.88],[7457,293.95125,36.94444,6.05,-0.11],[7458,294.15708,20.33278,7.14,1.32],[7459,295.07625,-54.4175,6.26,1.0],[7460,294.44708,-4.6475,5.46,0.43],[7461,294.925,-45.27806,6.25,0.28],[7462,293.09,69.66111,4.68,0.79],[7463,294.3225,16.46278,5.66,1.02],[7464,294.98208,-39.43333,6.61,0.23],[7465,293.98292,50.23861,6.52,1.06],[7466,294.28917,29.33361,6.43,-0.09],[7467,294.23583,38.38389,6.5,-0.15],[7468,294.15792,44.695,5.17,0.93],[7469,294.11042,50.22111,4.48,0.38],[7470,294.95583,-23.42778,6.34,0.03],[7471,294.70417,3.38167,6.35,0.04],[7472,294.57292,20.78278,6.48,1.08],[7473,295.02958,-23.42861,5.97,1.04],[7474,294.79833,5.39778,5.17,0.03],[7475,294.85583,16.57139,6.38,2.07],[7476,295.18083,-16.29333,6.2,1.13],[7477,294.48625,49.28444,6.47,0.99],[7478,294.84417,30.15333,4.69,0.97],[7479,295.02417,18.01389,4.37,0.78],[7480,295.18042,-0.62111,5.67,0.11],[7481,294.9375,33.97917,6.1,0.08],[7482,295.11792,20.47667,6.5,0.39],[7483,294.86042,42.81833,5.4,-0.08],[7484,294.67167,54.97389,5.82,0.44],[7485,295.16542,23.7175,6.64,0.01],[7486,295.27292,13.81556,6.01,-0.08],[7487,294.89333,45.95806,6.2,0.9],[7488,295.26208,17.47611,4.37,1.05],[7489,295.62958,-16.12389,5.06,0.33],[7490,295.31208,22.45278,6.36,1.53],[7491,295.90667,-37.53889,6.16,0.01],[7492,295.17167,43.07778,6.16,1.56],[7493,295.55333,12.19333,6.34,-0.03],[7494,299.00625,-81.34972,6.39,1.4],[7495,295.20917,45.525,5.06,0.4],[7496,295.88958,-15.47,5.49,0.46],[7497,295.64167,11.82667,5.27,0.57],[7498,297.35542,-72.50333,5.41,0.22],[7499,295.48958,40.25389,6.23,0.18],[7500,295.05417,60.50722,6.51,0.22],[7501,295.70458,29.33167,6.49,0.33],[7502,295.68583,32.42667,5.94,0.11],[7503,295.45375,50.52528,5.96,0.64],[7504,295.46667,50.5175,6.2,0.66],[7505,295.78958,30.67861,6.05,0.0],[7506,295.92875,25.77194,5.49,0.93],[7507,296.505,-31.90861,5.52,0.02],[7508,295.98292,27.13556,6.28,1.1],[7509,295.51708,55.46333,6.48,1.61],[7510,297.005,-56.3625,5.35,0.2],[7511,296.14208,13.30278,6.26,-0.03],[7512,295.96417,34.1625,6.05,-0.06],[7513,297.47208,-66.81278,6.45,1.48],[7514,295.9375,41.77306,5.84,1.57],[7515,296.59042,-19.76111,4.86,0.93],[7516,296.4675,-2.88333,6.48,0.05],[7517,296.06917,37.35444,4.89,0.95],[7518,296.20292,29.26472,6.82,0.64],[7519,296.41625,7.61333,5.91,0.18],[7520,296.15917,34.41389,6.57,0.6],[7521,297.22958,-52.88806,6.25,1.13],[7522,295.81083,58.01639,6.22,0.56],[7523,296.20417,40.71667,6.34,1.64],[7524,297.75542,-65.605,6.05,0.3],[7525,296.565,10.61333,2.72,1.52],[7526,295.915,57.0425,6.27,0.88],[7527,297.59042,-61.06139,6.21,-0.14],[7528,296.24375,45.13083,2.87,-0.03],[7529,296.415,36.09111,6.43,-0.03],[7530,296.46417,35.01278,6.09,1.06],[7531,297.68667,-59.19306,5.42,0.08],[7532,297.0125,-13.70333,6.11,0.2],[7533,296.66458,25.13389,6.62,0.27],[7534,296.60667,33.72778,4.99,0.47],[7535,296.64583,32.88861,6.18,1.13],[7536,296.84708,18.53417,3.82,1.41],[7537,297.5575,-47.55722,5.94,1.7],[7538,297.29833,-28.78889,6.05,0.4],[7540,296.9525,25.38389,5.95,0.99],[7541,297.25917,-10.87083,6.04,1.24],[7542,297.12667,10.69417,6.44,0.96],[7543,296.86583,38.4075,5.77,-0.06],[7544,297.17542,11.81583,5.72,0.6],[7545,296.07708,69.33694,5.92,0.05],[7546,297.24458,19.14222,5.0,0.1],[7547,296.86167,47.90778,6.12,1.64],[7548,298.15667,-54.97111,5.74,0.92],[7549,298.1625,-54.97667,6.5,0.1],[7550,297.18292,35.31139,6.53,0.44],[7551,297.21083,33.43722,6.44,0.2],[7552,297.96083,-39.87444,5.33,-0.06],[7553,297.695,-10.76361,5.39,0.38],[7554,297.57292,7.9025,6.51,-0.1],[7555,297.36458,38.71,6.11,0.9],[7556,297.4775,28.44056,6.38,-0.06],[7557,297.69583,8.86833,0.77,0.22],[7558,298.66833,-61.17083,6.24,0.16],[7559,297.79625,-2.46083,6.13,1.57],[7560,297.75667,10.41556,5.11,0.55],[7561,298.05,-19.045,5.92,0.98],[7562,297.82375,9.63028,6.25,0.1],[7563,296.68625,68.43833,6.34,0.28],[7564,297.64125,32.91417,4.23,1.82],[7565,297.76708,22.61,4.95,-0.14],[7566,297.64167,38.7225,5.12,1.69],[7567,297.65542,40.59972,5.69,-0.04],[7568,297.69583,37.82639,6.06,1.7],[7569,298.01458,11.62889,6.13,0.65],[7570,298.11833,1.00556,3.9,0.89],[7571,298.27667,-14.60306,6.48,0.14],[7572,298.065,10.35139,6.54,-0.01],[7573,298.00667,24.99222,5.57,0.71],[7574,298.09083,18.67194,6.23,0.01],[7575,298.32792,-3.11444,5.65,0.2],[7576,297.65708,52.98806,5.03,1.28],[7577,297.83083,47.37722,6.2,0.36],[7578,298.57375,-23.94111,6.18,1.02],[7579,299.67208,-69.16389,5.75,0.23],[7580,298.34417,4.40056,6.53,0.02],[7581,298.81542,-41.86833,4.13,1.08],[7582,297.04333,70.26778,3.83,0.89],[7583,298.06792,36.43222,6.1,1.43],[7584,298.53417,-8.57417,5.79,1.64],[7585,298.77125,-33.04639,6.46,1.48],[7586,299.24042,-57.92556,6.53,1.53],[7587,299.27583,-58.90139,5.26,-0.01],[7588,299.72083,-68.76222,6.39,0.16],[7589,297.99625,47.0275,5.62,-0.07],[7590,300.14792,-72.91056,3.96,-0.03],[7591,298.03,47.93194,5.91,-0.18],[7592,298.36542,24.07972,4.58,-0.06],[7593,298.65667,-8.22722,5.71,-0.08],[7594,298.65875,-8.23722,6.49,-0.04],[7595,298.56208,8.46139,4.71,1.05],[7596,298.68667,0.27361,5.61,0.1],[7597,298.96,-26.29944,4.7,0.75],[7598,298.66792,7.14028,6.15,0.03],[7599,298.83167,-6.73417,6.51,0.39],[7600,298.255,47.8075,6.29,-0.11],[7601,298.62958,24.31944,5.52,-0.02],[7602,298.82833,6.40667,3.71,0.86],[7603,300.09583,-66.94944,5.76,1.04],[7604,299.23667,-27.17,4.52,1.46],[7605,299.42208,-38.05833,6.55,0.39],[7606,298.70125,36.99611,5.76,0.75],[7607,298.77708,30.19528,6.57,-0.08],[7608,298.3225,57.52361,5.14,-0.13],[7609,299.00542,16.63472,5.36,0.67],[7610,299.05958,11.42389,5.28,-0.01],[7611,298.3975,59.70889,6.06,0.02],[7612,300.46833,-66.94417,5.31,1.22],[7613,298.96542,38.48667,4.94,-0.08],[7614,299.4875,-15.49139,5.02,0.05],[7615,299.07667,35.08333,3.89,1.02],[7616,299.25083,20.99806,6.48,0.07],[7617,299.735,-30.53806,6.28,1.05],[7618,299.73833,-26.19556,4.83,0.9],[7619,298.9075,52.43889,4.92,0.12],[7620,299.18417,36.25083,6.02,-0.15],[7621,300.10542,-49.35111,6.17,1.06],[7622,299.43917,16.78917,5.53,-0.05],[7623,299.93417,-35.27639,4.37,-0.15],[7624,299.96375,-34.69778,5.3,0.17],[7625,300.43625,-59.37611,5.13,1.53],[7626,298.84208,58.25028,6.09,1.02],[7627,300.11042,-43.04333,6.14,1.64],[7628,299.30792,40.36806,5.45,-0.1],[7629,300.06625,-37.70222,5.95,1.0],[7630,300.20125,-45.11306,5.81,0.28],[7631,300.08458,-33.70389,5.66,0.49],[7632,299.18792,50.9025,6.43,-0.01],[7633,298.98083,58.84611,4.96,1.59],[7634,299.07917,56.68694,6.12,0.6],[7635,299.68917,19.49222,3.47,1.57],[7636,299.84458,1.37778,6.17,1.13],[7637,299.9475,-9.95833,5.88,0.58],[7638,299.48417,42.26083,6.43,0.6],[7639,300.36,-40.81417,6.29,0.11],[7640,299.65833,30.98361,5.49,-0.06],[7641,299.79375,23.10139,5.67,0.6],[7642,299.64333,38.10556,6.32,-0.09],[7643,300.34958,-22.73722,6.01,0.97],[7644,301.38667,-67.32083,6.07,0.64],[7645,300.01375,17.51667,5.37,1.67],[7646,299.83542,45.77222,5.92,0.16],[7647,299.98,37.04278,5.19,-0.17],[7648,300.24542,8.55806,5.91,1.52],[7649,300.49417,-13.63694,5.71,0.08],[7650,300.66458,-27.70972,4.58,1.65],[7651,299.81417,52.05583,6.15,-0.19],[7652,300.88958,-37.94083,4.77,1.41],[7653,300.27542,27.75361,4.64,0.18],[7654,299.61958,63.53417,5.96,0.09],[7655,300.31375,37.09889,6.2,1.31],[7656,300.43625,24.80028,5.88,-0.12],[7657,300.50583,24.93806,5.22,0.36],[7658,300.93458,-22.59556,6.45,0.5],[7659,301.08167,-32.05639,4.99,1.21],[7660,300.34,50.10472,5.05,1.11],[7661,301.005,-7.46972,6.72,0.35],[7662,300.81833,18.50056,5.96,1.42],[7663,302.08542,-66.35472,6.45,1.58],[7664,300.875,16.03139,5.67,-0.1],[7665,302.18167,-66.18194,3.56,0.76],[7666,299.67458,70.36694,6.33,0.88],[7667,301.09667,-0.70944,5.68,1.3],[7668,301.38375,-33.0,6.53,-0.08],[7669,301.03458,7.27806,5.52,1.06],[7670,300.90583,29.89667,5.71,0.73],[7671,301.2725,-11.59944,6.34,0.52],[7672,301.02583,17.07,5.8,0.61],[7673,301.84667,-52.88083,4.94,1.62],[7674,301.89625,-55.01639,6.26,0.53],[7675,301.36,-12.66528,6.55,0.04],[7676,300.36875,64.82111,5.27,1.56],[7677,301.24417,23.21028,6.45,0.6],[7678,301.15042,32.21861,5.64,0.54],[7679,301.28958,19.99111,5.1,1.06],[7680,301.36042,15.50028,6.34,1.64],[7681,301.55083,-4.07833,6.47,1.16],[7682,300.58458,64.63444,6.57,0.6],[7683,301.29083,38.47833,6.19,0.64],[7684,301.12,48.22972,6.16,0.04],[7685,300.70458,67.87361,4.51,1.32],[7686,299.9025,76.48139,6.2,1.61],[7687,301.27792,51.83944,6.14,1.6],[7688,301.7225,23.61444,5.07,-0.18],[7689,301.59083,35.9725,5.36,0.85],[7690,302.0075,-0.67833,5.99,1.02],[7691,302.78,-57.52389,6.37,0.06],[7692,301.33958,56.34139,6.21,0.43],[7693,301.95958,9.39972,6.43,0.46],[7694,302.13042,-10.06278,6.18,0.06],[7695,301.18583,63.89056,6.26,0.1],[7696,302.02708,16.66417,6.42,1.91],[7697,301.5575,53.16583,5.85,0.39],[7698,306.22667,-83.31056,6.17,0.2],[7699,301.9225,34.42306,6.11,0.16],[7700,302.15958,10.72583,6.31,-0.12],[7701,301.38667,61.99556,5.39,1.18],[7702,301.79792,50.22917,6.54,0.13],[7703,302.79958,-36.10111,5.32,0.87],[7704,301.22208,68.02722,6.28,1.65],[7705,302.48583,20.91528,6.48,0.38],[7706,303.09958,-42.78056,6.22,1.23],[7707,303.61208,-63.41583,6.09,0.31],[7708,302.35667,36.83972,4.93,-0.13],[7709,302.79208,-8.84222,6.49,-0.15],[7710,302.82625,-0.82139,3.23,-0.07],[7711,302.63958,26.90417,5.52,0.08],[7712,302.99125,-12.3925,6.34,1.21],[7713,302.76458,21.13472,6.22,0.9],[7714,303.57917,-52.44556,5.65,1.5],[7715,303.10792,-12.6175,5.85,0.48],[7716,302.83792,21.87556,6.26,-0.02],[7717,303.14667,0.8675,6.27,0.02],[7718,302.95,26.80889,5.49,1.41],[7719,303.00292,26.47889,5.92,-0.11],[7720,303.30792,-1.00944,5.47,1.43],[7721,303.01583,47.73694,6.92,-0.12],[7722,303.8225,-27.03278,5.73,0.88],[7723,303.41917,24.23889,6.56,0.29],[7724,303.56917,15.1975,4.95,0.08],[7725,303.96083,-30.00528,6.3,1.51],[7726,303.1325,51.46361,6.01,1.14],[7727,302.89542,62.07861,5.75,0.47],[7728,304.09875,-36.45444,6.39,1.54],[7729,304.11042,-35.19778,6.53,0.37],[7730,303.325,46.81583,4.83,0.09],[7731,303.56042,28.69472,5.18,0.18],[7732,304.7625,-63.23111,6.27,1.04],[7733,303.42833,43.37917,6.14,1.5],[7734,303.52083,36.60528,6.45,0.0],[7735,303.40792,46.74139,3.79,1.28],[7736,303.63333,36.80639,4.97,0.14],[7737,303.59,42.10361,6.71,-0.04],[7738,304.095,-12.33694,6.32,0.01],[7739,303.81625,25.59194,4.78,-0.18],[7740,303.34958,56.56778,4.3,0.11],[7741,303.87583,23.50861,5.15,1.04],[7742,303.36542,60.64056,5.79,1.47],[7743,303.84875,33.72944,5.66,0.91],[7744,303.94208,27.81417,4.52,1.26],[7745,304.73333,-47.71083,6.31,1.67],[7746,304.08208,21.59861,6.13,1.04],[7747,304.41208,-12.50833,4.24,1.07],[7748,304.50583,-21.81,5.87,1.0],[7749,304.82458,-47.58028,6.13,0.46],[7750,302.22208,77.71139,4.39,-0.05],[7751,303.86792,47.71444,3.98,1.52],[7752,304.01417,38.89778,6.27,0.01],[7753,304.19625,24.67111,5.32,0.95],[7754,304.51375,-12.54472,3.57,0.94],[7755,303.93083,50.23278,6.31,0.6],[7756,304.0025,45.57944,5.91,0.38],[7757,304.1175,37.05639,6.48,-0.09],[7758,305.13458,-55.05083,6.27,1.59],[7759,304.23042,40.365,5.24,1.65],[7760,304.38125,29.14806,6.22,1.01],[7761,304.84833,-19.11861,5.28,1.4],[7762,304.37125,42.72194,6.29,1.64],[7763,304.44667,38.03306,4.81,0.42],[7764,305.11708,-29.19722,6.3,0.17],[7765,305.21625,-35.67361,6.46,1.31],[7766,305.42083,-49.99944,6.27,0.55],[7767,304.52917,40.73222,5.84,0.1],[7768,304.93042,-1.07861,6.06,1.09],[7769,304.61917,37.0,5.58,0.06],[7770,304.66292,34.98278,5.17,0.65],[7771,304.87167,13.21694,6.21,1.63],[7772,305.10875,-6.36167,6.63,1.55],[7773,305.16583,-12.75917,4.76,-0.05],[7774,305.00083,13.54806,5.95,0.31],[7775,305.19417,-14.785,6.1,-0.02],[7776,305.25292,-14.78139,3.08,0.79],[7777,304.70667,46.32278,6.45,-0.13],[7778,305.08542,14.56917,6.13,0.91],[7779,305.61458,-42.04972,5.59,0.0],[7780,305.08917,17.79306,5.8,1.49],[7781,304.60333,55.39722,5.76,0.11],[7782,304.95125,37.1325,6.57,0.0],[7783,304.38042,66.85389,5.93,0.58],[7784,305.06333,39.40333,6.23,0.06],[7785,308.32292,-80.965,5.77,1.14],[7786,304.98375,46.8375,6.5,-0.06],[7787,305.97167,-42.42278,5.64,0.2],[7788,305.75333,-9.65472,6.3,0.91],[7789,305.51417,24.44611,5.54,-0.06],[7790,306.41208,-56.735,1.94,-0.2],[7791,305.12667,53.59611,6.18,1.56],[7792,304.90292,62.2575,5.72,-0.05],[7793,305.71792,14.55139,6.17,0.51],[7794,305.79458,5.34306,5.31,0.97],[7795,305.5125,41.13139,6.39,1.07],[7796,305.55708,40.25667,2.2,0.68],[7797,305.65583,31.265,6.09,1.35],[7798,305.5225,45.795,5.58,1.08],[7799,306.44958,-40.79639,6.09,1.36],[7800,305.68875,41.02611,5.93,1.6],[7801,306.36167,-28.66333,5.85,1.1],[7802,305.73125,42.98333,6.2,0.95],[7803,306.15625,1.06861,6.15,-0.04],[7804,305.025,68.88028,5.55,1.59],[7805,305.2975,63.98028,5.69,1.56],[7806,305.96542,32.19,4.43,1.33],[7807,305.935,37.47639,5.9,-0.2],[7808,306.72083,-37.40306,6.25,0.97],[7809,306.42708,-2.80028,6.11,1.19],[7810,306.43333,10.05639,6.33,1.56],[7811,306.41875,21.40972,5.66,0.93],[7812,309.5775,-81.28889,5.91,1.71],[7813,306.505,19.865,6.41,1.02],[7814,306.83,-18.21167,5.25,-0.07],[7815,306.135,53.55194,6.51,0.01],[7816,306.59667,17.31556,6.22,1.01],[7817,307.19458,-35.59583,6.1,-0.11],[7818,306.27125,59.6,6.44,0.09],[7819,307.18167,-15.74167,6.41,0.99],[7820,307.03125,8.4375,6.25,1.08],[7821,307.10375,-3.35778,6.13,-0.06],[7822,307.215,-17.81361,4.78,0.38],[7823,306.78208,34.32889,6.39,0.48],[7824,307.07,2.93694,6.21,0.9],[7825,307.38042,-22.39167,6.16,1.55],[7826,306.89292,38.44028,5.62,0.06],[7827,306.59792,56.63889,6.36,0.0],[7828,306.75958,49.38333,5.69,0.26],[7829,307.46875,-18.58667,6.74,0.22],[7830,307.47458,-18.58333,5.94,0.08],[7831,307.4125,-2.88556,4.91,1.15],[7832,307.73667,-29.1125,6.39,0.21],[7833,307.33792,20.08778,6.55,0.23],[7834,307.34875,30.36861,4.01,0.4],[7835,307.335,36.45472,5.88,0.52],[7836,307.575,10.89583,6.08,-0.03],[7837,307.76792,-15.05639,6.12,0.79],[7838,308.96542,-69.61111,6.11,1.29],[7839,307.74208,20.60583,6.18,0.15],[7840,307.80417,11.26056,7.11,0.03],[7841,307.49958,45.92861,6.41,1.13],[7842,308.21833,-24.94389,6.36,-0.01],[7843,307.36292,56.06806,5.91,-0.04],[7844,307.51458,48.95167,4.95,-0.09],[7845,308.09875,-9.85333,5.65,0.69],[7846,308.47958,-44.51611,5.11,1.01],[7847,307.74667,36.93583,6.19,1.01],[7848,308.895,-60.58167,4.76,0.28],[7849,307.9925,25.80444,6.34,0.26],[7850,307.39542,62.99417,4.22,0.2],[7851,307.82833,49.22028,5.44,1.55],[7852,308.30333,11.30333,4.03,-0.13],[7853,308.73125,-38.08972,6.44,0.26],[7854,307.83792,52.30972,6.18,1.01],[7855,308.54875,-13.72111,6.13,0.54],[7856,308.6975,-30.47361,6.4,-0.08],[7857,308.47333,10.05972,6.56,0.08],[7858,308.4875,13.02722,5.38,0.07],[7859,309.39708,-61.53,4.88,0.43],[7860,307.94375,56.78,6.14,1.43],[7861,308.21792,43.19167,6.6,-0.11],[7862,308.54167,20.98528,6.48,-0.14],[7863,310.51208,-76.18056,6.0,0.44],[7864,310.43208,-75.35056,6.55,0.62],[7865,308.88417,-16.52583,6.19,0.2],[7866,308.47583,35.25083,4.61,1.6],[7867,308.45167,41.77222,6.49,1.0],[7868,307.50292,72.53167,6.27,1.35],[7869,309.39167,-47.29139,3.11,1.0],[7870,308.47875,46.69389,5.78,-0.16],[7871,308.82708,14.67417,4.68,0.11],[7872,309.96417,-62.90778,6.22,1.1],[7873,309.18167,-2.55,4.89,1.6],[7874,309.03458,25.8825,6.41,0.21],[7875,310.01083,-60.54889,5.12,0.53],[7876,308.71,51.85417,6.11,0.41],[7877,309.46708,-25.10889,6.36,0.33],[7878,309.32625,0.09694,6.22,-0.08],[7879,307.87667,74.95472,5.2,0.07],[7880,309.26958,26.46194,5.59,-0.07],[7881,310.48792,-66.76083,5.15,-0.06],[7882,309.3875,14.59528,3.63,0.44],[7883,309.45458,11.37778,5.43,0.06],[7884,309.58458,-1.10528,4.32,0.95],[7885,309.3825,31.5725,6.32,-0.09],[7886,309.4775,18.26917,6.25,1.48],[7887,309.38583,31.52194,6.49,0.34],[7888,309.34833,38.32861,6.2,0.99],[7889,309.81833,-14.95472,5.22,-0.12],[7890,309.805,-2.41278,6.22,-0.1],[7891,309.63042,21.20111,4.82,-0.02],[7892,309.68292,13.315,5.72,1.53],[7893,310.0825,-33.43194,5.47,1.12],[7894,309.63292,24.11611,5.04,-0.14],[7895,309.64625,23.68056,5.91,0.98],[7896,309.7825,10.08611,5.05,0.72],[7897,309.85375,0.48639,5.16,1.06],[7898,310.04875,-23.77389,6.37,0.72],[7899,309.77083,15.83806,5.97,-0.14],[7900,310.0125,-18.13861,5.1,1.66],[7901,307.06083,81.42278,5.46,1.02],[7902,310.15,-26.645,6.51,0.57],[7903,309.79417,21.81722,6.08,-0.06],[7904,309.74792,30.33444,5.68,1.09],[7905,310.13542,-16.12417,5.8,1.0],[7906,309.90958,15.91194,3.77,-0.06],[7907,309.96583,11.24972,6.42,0.55],[7908,307.36458,81.09139,5.96,0.92],[7909,310.34875,-31.59833,5.76,1.53],[7910,310.35042,-26.0,6.28,1.22],[7911,309.88875,40.57944,6.06,-0.16],[7912,309.84625,45.66694,6.58,-0.06],[7913,311.23958,-66.20306,3.42,0.16],[7914,310.18833,19.93528,6.45,0.63],[7915,310.72083,-39.55861,6.29,1.08],[7916,309.75083,56.005,6.48,0.6],[7917,310.15083,29.80528,6.08,0.14],[7918,310.3175,14.58306,5.99,1.24],[7919,310.01292,43.45861,5.95,1.19],[7920,311.00958,-51.92111,4.51,0.27],[7921,310.26083,32.30722,5.51,0.88],[7922,310.25167,39.08222,6.51,-0.12],[7923,310.4925,17.52139,6.22,0.94],[7924,310.35792,45.28028,1.25,0.09],[7925,310.07458,60.50528,6.01,0.46],[7926,310.48542,41.71694,5.67,-0.12],[7927,310.5925,35.45611,6.66,-0.16],[7928,310.86458,15.07444,4.43,0.32],[7929,310.5525,50.34,5.39,-0.1],[7930,307.26292,83.62556,6.19,0.13],[7931,311.305,-27.24722,6.5,0.94],[7932,310.85083,35.58778,6.47,1.23],[7933,311.58375,-39.19917,5.5,-0.1],[7934,312.32542,-68.77639,5.41,1.12],[7935,311.5775,-36.12028,6.49,0.39],[7936,311.52375,-25.27083,4.14,0.43],[7937,311.54167,-21.51417,5.93,0.04],[7938,310.66542,60.60139,6.15,0.01],[7939,311.21875,25.27056,4.91,1.18],[7940,310.80625,57.11417,6.32,0.33],[7941,311.3675,18.09028,6.38,1.68],[7942,311.41542,30.71972,4.22,1.05],[7943,312.12167,-43.98861,5.11,0.35],[7944,311.09167,56.48806,5.78,1.67],[7945,310.79583,66.6575,5.58,0.22],[7946,311.765,-2.48667,6.27,1.55],[7947,311.66125,16.12444,5.14,0.49],[7948,311.66458,16.12417,4.27,1.04],[7949,311.55292,33.97028,2.46,1.03],[7950,311.91917,-9.49583,3.77,0.0],[7951,311.93417,-5.02778,4.42,1.65],[7952,312.37083,-46.22694,4.89,1.52],[7953,311.95125,6.00833,5.58,-0.02],[7954,311.94917,3.30667,6.4,-0.02],[7955,311.33792,57.57972,4.51,0.54],[7956,311.795,34.37417,4.92,1.32],[7957,311.3225,61.83889,3.43,0.92],[7958,311.66042,46.53167,6.3,0.03],[7959,312.90958,-62.42917,6.28,0.15],[7960,312.91167,-62.42917,6.59,0.17],[7961,312.32333,-25.78139,5.86,-0.07],[7962,311.58833,52.99528,6.33,1.12],[7963,311.85208,36.49083,4.53,-0.11],[7964,312.33542,-18.03583,6.21,1.42],[7965,312.49208,-33.77972,4.9,1.0],[7966,311.83667,45.57972,6.4,1.61],[7967,311.13792,69.75194,6.41,0.6],[7968,312.87542,-51.60833,5.05,1.13],[7969,311.95542,47.83194,5.57,1.46],[7970,312.69625,-32.05444,6.36,1.54],[7971,312.75292,-37.91333,5.52,1.38],[7972,311.97,52.40722,6.27,0.89],[7973,312.4075,12.54528,5.98,0.43],[7974,312.45125,7.86417,6.33,0.02],[7975,312.49625,5.54472,6.21,0.98],[7976,312.67417,-12.545,5.88,1.07],[7977,312.23458,46.11417,4.84,0.41],[7978,312.17792,51.91056,6.29,-0.07],[7979,312.995,-33.17722,6.04,0.03],[7980,312.95542,-26.91917,4.11,1.64],[7981,312.65417,18.05139,6.52,0.04],[7982,312.85708,-5.62639,5.99,0.46],[7983,312.47792,46.66111,6.33,-0.07],[7984,312.52042,44.05944,5.04,0.2],[7985,313.03625,-5.50694,5.55,-0.08],[7986,313.7025,-58.45417,3.65,1.25],[7987,313.4175,-39.81,5.35,1.32],[7988,312.8675,28.25056,5.77,0.72],[7989,313.255,-23.78306,6.33,0.88],[7990,313.16333,-8.98333,4.73,0.32],[7991,313.35417,-30.71861,6.35,1.09],[7992,313.64583,-50.72778,6.24,-0.12],[7993,312.3225,64.04222,6.45,0.07],[7994,313.27333,-11.57361,6.38,0.67],[7995,313.03208,27.09694,4.59,0.83],[7996,313.00125,32.84917,6.44,-0.15],[7997,313.52833,-27.92556,6.41,1.6],[7998,313.49333,-6.88972,6.44,0.37],[7999,313.28083,29.64944,6.34,1.09],[8000,313.69958,-17.92306,5.78,1.12],[8001,313.31167,44.38722,4.78,-0.14],[8002,310.64667,82.53111,5.75,0.0],[8003,313.3275,45.18194,5.45,1.1],[8004,313.36,42.41028,6.66,-0.04],[8005,313.47458,33.43778,5.47,1.52],[8006,313.78375,-1.37333,6.55,0.29],[8007,313.59333,28.52194,6.56,-0.13],[8008,313.64,28.0575,5.01,1.48],[8009,313.59292,40.70306,6.7,-0.07],[8010,313.91958,4.53278,6.05,0.82],[8011,313.90292,13.72139,5.17,1.12],[8012,313.91083,12.56861,5.58,0.12],[8013,314.19708,-26.29639,5.7,0.5],[8014,314.07625,-3.56139,6.57,-0.1],[8015,314.225,-9.6975,5.51,1.47],[8016,311.88917,80.55222,5.39,1.12],[8017,314.29417,0.46361,6.05,1.22],[8018,314.41917,-16.03167,5.87,0.18],[8019,315.36708,-68.20972,6.37,0.1],[8020,313.9575,47.41778,5.67,0.47],[8021,316.17917,-77.02389,5.15,0.49],[8022,314.05375,51.075,6.63,-0.1],[8023,314.14458,44.925,5.96,0.05],[8024,314.67458,-14.48278,6.01,0.23],[8025,314.10625,50.72861,5.81,0.3],[8026,314.10792,49.19583,5.9,1.04],[8027,315.08958,-51.26528,5.76,0.47],[8028,314.29333,41.16722,3.94,0.02],[8029,314.07083,56.8875,6.23,-0.18],[8030,314.60792,10.83917,5.48,0.93],[8031,314.99875,-36.12972,6.11,0.39],[8032,314.56833,22.32583,5.31,1.4],[8033,314.90042,-19.03528,6.25,-0.13],[8034,314.76833,4.29361,5.23,0.46],[8035,314.58125,44.47167,5.55,0.97],[8036,314.62833,41.94028,6.16,-0.08],[8037,314.96167,16.82417,6.66,0.38],[8038,315.01625,7.51639,5.99,0.26],[8039,315.32292,-32.25778,4.67,0.89],[8040,314.62542,50.46222,5.61,-0.15],[8041,315.14083,-4.73028,6.21,0.63],[8042,315.5525,-43.00194,6.64,0.68],[8043,313.68458,75.92556,6.05,0.93],[8044,315.11542,19.32944,5.65,1.61],[8045,315.43875,-26.88111,6.05,0.06],[8046,315.61333,-38.53056,5.94,1.11],[8047,314.95667,47.52111,4.74,-0.05],[8048,315.74167,-38.63167,5.3,0.41],[8049,314.85583,59.43861,5.51,1.4],[8050,315.7925,-27.73194,6.25,0.95],[8051,315.30375,36.02611,5.97,0.98],[8052,317.19958,-76.2125,6.58,1.23],[8053,315.29542,46.15583,5.37,-0.21],[8054,315.74833,-0.92472,6.5,-0.1],[8055,316.30917,-54.72722,5.16,1.21],[8056,315.7625,1.53194,6.25,0.48],[8057,315.7575,14.73,6.31,1.67],[8058,316.01917,-5.82333,7.31,0.6],[8059,316.01958,-5.82306,5.89,0.68],[8060,316.10125,-19.855,4.84,0.17],[8061,317.34292,-73.17306,5.68,0.59],[8062,315.60042,44.79111,6.19,1.69],[8063,315.77,38.6575,6.07,1.01],[8064,315.70208,45.84889,6.48,-0.15],[8065,315.53792,56.66972,5.83,-0.07],[8066,316.14458,5.50278,5.61,1.65],[8067,316.17375,2.94194,6.42,1.05],[8068,316.18917,2.26972,6.33,0.97],[8069,316.60625,-41.38611,5.53,1.35],[8070,316.505,-30.125,5.68,1.03],[8071,315.96708,41.62806,6.33,0.38],[8072,315.85833,50.35194,6.37,0.98],[8073,317.13708,-63.92889,5.76,1.18],[8074,315.93042,46.86194,6.32,0.25],[8075,316.48667,-17.23278,4.07,-0.01],[8076,316.60292,-32.34167,5.18,1.1],[8077,316.36125,5.95833,5.94,0.54],[8078,315.94833,53.28611,5.9,0.99],[8079,316.23292,43.92778,3.72,1.65],[8080,316.78208,-25.00583,4.5,1.61],[8081,317.83625,-72.54417,6.2,1.08],[8082,316.59792,26.92444,6.12,1.05],[8083,316.93583,-17.45528,6.17,0.02],[8084,316.62625,31.18472,5.82,0.56],[8085,316.7275,38.74583,5.21,1.18],[8086,316.73042,38.74333,6.03,1.37],[8087,317.14,-21.19361,5.3,0.01],[8088,316.89,15.65861,6.34,1.01],[8089,316.65042,47.64833,4.55,1.57],[8090,317.1175,6.98944,6.15,1.66],[8091,317.3875,-20.55639,6.25,0.38],[8092,318.33542,-70.12639,5.02,1.58],[8093,317.39875,-11.37167,4.51,0.94],[8094,317.16208,30.20583,5.59,-0.1],[8095,317.49292,2.94333,6.45,0.37],[8096,317.69542,-9.35389,6.27,1.16],[8097,317.58542,10.13167,4.69,0.26],[8098,317.63,10.04889,6.07,0.02],[8099,316.59708,71.43194,5.87,0.4],[8100,318.05667,-40.26944,5.83,0.45],[8101,317.63333,22.45472,6.68,0.03],[8102,317.92208,-14.47222,6.48,0.28],[8103,317.49417,45.5025,6.63,-0.16],[8104,318.26292,-39.42528,5.26,0.44],[8105,317.76625,36.29917,6.54,-0.14],[8106,317.565,53.56333,5.73,-0.12],[8107,317.62917,47.69194,6.46,-0.01],[8108,318.32875,-36.42389,5.96,0.98],[8109,317.37042,63.29556,6.54,-0.13],[8110,318.32208,-27.61944,5.42,1.42],[8111,319.56708,-75.34667,6.63,0.03],[8112,316.37208,78.12639,5.91,-0.07],[8113,317.38333,68.49028,7.33,1.49],[8114,318.94125,-53.26306,5.75,0.19],[8115,318.23417,30.22694,3.2,0.99],[8116,318.37,15.9825,6.27,0.24],[8117,318.81125,-40.50639,6.21,1.14],[8118,318.56958,-10.60528,6.77,-0.08],[8119,317.95083,59.98639,5.64,0.11],[8120,318.35958,36.63361,6.05,0.21],[8121,318.65417,0.09222,6.38,1.61],[8122,318.7775,-17.345,6.04,0.96],[8123,318.62042,10.00694,4.49,0.5],[8124,318.945,-36.21083,6.12,1.37],[8125,319.50125,-64.68167,6.31,-0.07],[8126,318.54292,29.90111,6.17,1.09],[8127,318.90792,-20.65167,5.24,1.17],[8128,318.93708,-15.17139,5.28,1.64],[8129,323.0175,-84.81,6.45,1.4],[8130,318.69792,38.04556,3.72,0.39],[8131,318.95583,5.24778,3.92,0.53],[8132,319.165,-1.60778,6.48,0.98],[8133,318.4275,64.40389,6.39,0.6],[8134,319.30625,-13.27889,6.4,0.04],[8135,319.48458,-32.1725,4.71,0.06],[8136,318.90333,47.97361,6.46,-0.15],[8137,319.48875,-17.98528,5.43,-0.12],[8138,319.12333,42.25139,6.43,0.6],[8139,319.56542,-17.46222,7.05,0.34],[8140,319.96667,-53.44972,4.39,0.19],[8141,319.54625,-4.51944,5.82,-0.13],[8142,319.72667,-28.76556,6.4,0.97],[8143,319.35417,39.39472,4.23,0.12],[8144,319.34667,42.68333,6.19,-0.11],[8145,320.03958,-45.02222,6.0,2.33],[8146,319.47958,34.89694,4.43,-0.11],[8147,319.25833,53.9975,6.13,0.05],[8148,319.94083,-26.35306,6.56,0.73],[8149,319.71667,11.20333,5.96,1.65],[8150,319.30958,55.79806,5.98,1.45],[8151,320.19,-40.80972,4.82,0.02],[8152,320.31833,-49.93778,6.38,1.32],[8153,319.32833,58.61167,6.42,0.2],[8154,319.61333,43.94583,5.0,-0.01],[8155,319.73042,41.04083,6.15,0.3],[8156,321.06958,-69.73417,6.41,2.82],[8157,319.8425,38.2375,5.83,0.5],[8158,320.05833,22.02639,6.29,-0.08],[8159,321.32542,-71.79944,6.09,1.26],[8160,320.26792,-4.56,5.87,0.92],[8161,319.87,49.51028,5.76,-0.15],[8162,319.645,62.58556,2.44,0.22],[8163,320.27,7.35444,5.82,1.66],[8164,319.81583,58.62361,5.66,1.38],[8165,320.26833,23.85583,5.57,1.05],[8166,320.20875,32.45278,5.68,1.08],[8167,320.56167,-16.83444,4.28,0.9],[8168,318.92583,77.01222,5.95,1.5],[8169,320.34167,32.61278,6.04,0.03],[8170,320.25583,40.34556,6.4,0.53],[8171,319.8425,64.87194,5.18,-0.04],[8172,320.75208,-22.66889,5.6,1.63],[8173,320.52167,19.80444,4.08,1.11],[8174,318.33958,81.23083,6.15,0.09],[8175,320.73458,-9.31944,5.99,1.54],[8176,323.47667,-82.68306,6.38,0.13],[8177,321.08667,-46.615,6.31,0.2],[8178,320.72333,6.81111,5.16,0.05],[8179,320.13958,60.75694,6.11,1.0],[8180,321.10333,-41.00667,5.77,-0.05],[8181,321.61083,-65.36611,4.22,0.49],[8182,320.67458,30.30972,6.05,1.08],[8183,321.04,-20.85194,5.41,1.16],[8184,321.03292,-22.74694,6.38,1.02],[8185,320.50167,49.38889,5.69,1.1],[8186,320.69542,38.63417,6.63,0.01],[8187,321.04792,-12.87806,5.49,0.29],[8188,321.56417,-54.66056,6.12,0.34],[8189,320.84583,37.40667,6.58,0.6],[8190,320.995,24.27417,5.71,0.32],[8191,321.1025,10.17417,6.35,0.47],[8192,321.21542,-3.39833,6.36,0.33],[8193,320.95125,37.35139,6.47,0.6],[8194,321.03083,25.31222,6.15,0.6],[8195,321.30458,-9.74861,5.7,0.2],[8196,322.18708,-69.50528,5.34,1.55],[8197,321.09625,24.52889,6.32,1.04],[8198,321.14167,26.17444,5.68,0.31],[8199,321.32083,-3.55667,5.49,1.46],[8200,321.59542,-37.82944,5.63,1.19],[8201,323.33583,-80.03917,6.47,0.04],[8202,321.75667,-42.54778,5.51,0.39],[8203,321.46458,0.53444,6.46,0.16],[8204,321.66667,-22.41139,3.74,1.0],[8205,321.61708,1.10333,6.13,0.44],[8206,321.23125,49.32333,6.58,-0.03],[8207,321.81167,-21.19611,5.78,1.44],[8208,321.33167,46.71444,5.6,0.32],[8209,321.44583,36.6675,5.94,-0.08],[8210,321.61125,19.37556,6.07,0.22],[8211,322.25125,-53.70583,6.39,1.14],[8212,322.05792,-11.56833,6.61,0.49],[8213,322.18083,-21.80722,4.51,0.91],[8214,322.26583,-31.23861,6.5,0.03],[8215,321.83917,37.11667,5.31,-0.14],[8216,321.715,48.835,5.31,0.07],[8217,321.91708,27.60861,5.41,0.04],[8218,321.6875,52.89861,6.03,-0.12],[8219,322.10333,8.19556,6.4,1.64],[8220,322.03458,32.22528,5.8,0.32],[8221,322.24958,17.90583,6.44,1.39],[8222,322.49833,-19.14778,6.57,0.41],[8223,322.24958,22.17944,5.93,1.53],[8224,321.85542,59.75,6.1,1.75],[8225,322.48708,23.63889,4.57,1.62],[8226,322.21958,55.41861,6.12,0.14],[8227,321.94208,66.80917,5.44,-0.11],[8228,322.3625,46.54056,5.24,0.97],[8229,323.02458,-41.17917,5.29,1.1],[8230,323.06083,-33.94472,5.97,0.05],[8231,322.79,12.1375,6.08,-0.05],[8232,322.88958,-5.57111,2.91,0.83],[8233,323.32375,-52.7375,6.41,1.48],[8234,324.73417,-79.4425,6.18,0.46],[8235,323.13875,-24.59056,6.43,0.2],[8236,323.34792,-44.84861,5.57,1.04],[8237,322.585,52.95806,6.02,0.08],[8238,322.165,70.56083,3.23,-0.22],[8239,321.20708,80.52472,5.97,0.92],[8240,323.11292,23.39444,6.7,-0.09],[8241,323.57083,-42.925,6.32,1.09],[8242,322.86458,52.62,6.16,0.9],[8243,322.74708,60.45944,5.53,0.12],[8244,323.72083,-29.69611,6.41,-0.11],[8245,323.7125,-20.08444,5.69,0.4],[8246,323.23583,49.97778,5.75,-0.03],[8247,323.81625,-23.45417,6.4,1.1],[8248,323.32458,45.85417,6.25,1.81],[8249,324.51208,-64.82417,6.2,0.03],[8250,323.64167,22.75472,6.47,0.51],[8251,323.82333,-3.98306,5.77,1.11],[8252,323.49542,45.59194,4.02,0.89],[8253,324.04583,-26.17139,5.73,0.22],[8254,325.36875,-77.39,3.76,1.0],[8255,323.69417,38.53417,4.9,1.08],[8256,324.20375,-33.04806,6.11,0.22],[8257,323.82917,28.19722,6.31,0.35],[8258,323.8625,24.45222,6.11,0.6],[8259,323.61458,51.69833,6.15,0.02],[8260,324.27,-19.46611,4.68,-0.17],[8261,324.05792,30.05556,6.36,0.6],[8262,324.01,45.37472,5.53,1.58],[8263,324.39083,-0.39028,6.25,0.06],[8264,324.43792,-7.85417,4.69,0.17],[8265,324.43208,6.61833,6.18,0.02],[8266,324.2375,40.41361,5.01,0.18],[8267,324.43917,19.31861,5.45,0.3],[8268,324.77542,-33.67917,6.28,0.92],[8269,324.99875,-52.35917,6.21,0.6],[8270,324.63292,5.77167,5.67,0.25],[8271,325.14,-55.7375,6.33,1.06],[8272,324.36625,44.69667,6.2,0.19],[8273,324.86708,-10.57694,6.08,1.03],[8274,324.6875,25.49889,6.16,1.02],[8275,324.41125,54.04222,6.15,0.99],[8276,324.75458,20.26528,5.85,0.32],[8277,324.88875,2.24361,5.1,1.04],[8278,325.02292,-16.66222,3.68,0.32],[8279,324.48,62.08194,4.73,0.3],[8280,327.72625,-82.71917,5.29,0.75],[8281,324.74,57.48917,5.62,0.21],[8282,325.44208,-25.10194,6.49,1.19],[8283,325.38708,-14.0475,5.18,0.65],[8284,325.04625,43.27389,5.11,1.6],[8285,325.50333,-23.26278,5.24,0.95],[8286,326.37,-71.00889,6.01,-0.1],[8287,325.54208,1.28528,5.67,1.44],[8288,325.66458,-18.86639,4.73,0.88],[8289,325.56458,5.68,5.3,1.64],[8290,325.18042,54.87222,6.2,1.16],[8291,325.39292,40.80528,6.11,0.07],[8292,325.6375,10.82472,6.09,-0.11],[8293,325.80625,-19.62083,6.22,0.27],[8294,341.36917,-88.81833,6.57,0.28],[8295,325.76833,-14.39972,5.88,0.25],[8297,325.50458,35.51028,6.07,2.52],[8298,325.535,45.76583,6.17,1.55],[8299,326.12292,-38.5525,6.3,1.12],[8300,325.59542,41.07722,5.69,0.01],[8301,325.52375,51.18972,4.67,-0.12],[8302,326.00417,-14.74944,5.99,0.21],[8303,326.32917,-49.49861,6.45,1.15],[8304,325.66208,49.60028,6.09,1.0],[8305,326.23667,-33.02583,4.34,-0.05],[8306,325.77667,41.155,5.49,1.59],[8307,325.85708,38.28389,5.65,0.0],[8308,326.04667,9.875,2.39,1.53],[8309,326.03583,28.74278,4.73,0.48],[8310,326.03458,28.74306,6.08,0.36],[8311,326.25125,-9.0825,5.09,1.11],[8312,325.68917,59.27111,6.08,1.34],[8313,326.12792,17.35,4.34,1.17],[8314,326.13042,14.77194,5.94,0.59],[8315,326.16125,25.645,4.13,0.43],[8316,325.87667,58.78,4.08,2.35],[8317,325.48042,71.31139,4.56,1.1],[8318,326.56792,-9.27583,6.0,1.66],[8319,326.63375,-11.36583,5.58,-0.01],[8320,326.43542,35.85722,6.4,1.0],[8321,326.51833,22.94889,5.29,1.41],[8322,326.76,-16.12722,2.87,0.29],[8323,327.06583,-47.30361,5.58,0.6],[8324,325.76667,72.32028,5.17,1.05],[8325,326.6,25.56333,6.28,1.21],[8326,326.93417,-30.89833,5.01,0.04],[8327,326.22208,62.46056,5.95,0.31],[8328,326.80833,2.68611,5.64,0.0],[8329,326.56917,43.06083,6.54,0.28],[8330,326.76958,17.19417,6.21,0.34],[8331,327.50042,-64.7125,5.62,1.02],[8332,326.90875,-5.91722,6.17,0.22],[8333,327.69625,-69.62944,5.53,1.37],[8334,326.36208,61.12083,4.29,0.52],[8335,326.69833,49.30944,4.23,-0.12],[8336,327.03458,36.58056,6.47,0.6],[8337,327.42125,-12.72306,6.31,0.22],[8338,327.1225,38.64861,6.12,-0.08],[8339,326.85542,60.69278,5.52,1.52],[8340,327.55458,-16.84472,6.38,1.42],[8341,327.36208,20.4625,6.29,-0.1],[8342,326.75417,70.15083,6.29,0.6],[8343,327.46125,30.17417,5.04,-0.03],[8344,327.53625,17.28556,5.29,0.37],[8345,327.41708,41.14889,6.48,0.42],[8346,327.92417,-18.62306,6.16,0.36],[8347,327.32917,61.27278,6.17,1.67],[8348,327.8925,19.82667,5.77,-0.1],[8349,327.77042,39.53667,6.17,-0.08],[8350,328.07583,21.27306,6.89,0.6],[8351,328.32417,-13.55167,5.08,0.37],[8352,328.79792,-61.88639,5.9,0.39],[8353,328.48208,-37.365,3.01,-0.12],[8354,328.12458,28.79333,5.53,0.42],[8355,328.4,-10.31167,6.59,-0.12],[8356,328.26583,25.925,5.08,-0.17],[8357,328.00417,55.79694,5.71,-0.13],[8358,328.40583,19.66833,5.68,0.01],[8359,328.49083,6.86444,6.15,0.8],[8360,328.54333,-4.27611,5.71,1.18],[8361,327.90542,65.75278,6.37,0.6],[8362,329.05833,-57.89944,6.19,0.21],[8363,328.64958,-3.30111,6.2,0.48],[8364,328.5725,19.71833,6.39,0.97],[8365,328.98167,-30.60639,6.41,0.93],[8366,329.095,-37.25361,5.46,0.08],[8367,329.25917,-37.74694,6.18,0.33],[8368,329.47958,-54.9925,4.4,0.28],[8369,329.62542,-59.01222,6.12,0.46],[8370,330.46708,-77.6625,6.41,0.22],[8371,328.72167,56.61139,5.8,0.73],[8372,329.1,21.23972,6.4,1.7],[8373,329.235,12.07639,5.54,0.05],[8374,328.83625,61.54194,6.13,1.6],[8375,328.87958,65.32083,5.86,-0.06],[8376,329.55542,-5.42472,6.33,0.37],[8377,329.25917,48.66861,6.42,-0.08],[8378,329.6825,-21.18278,6.12,1.65],[8379,329.82458,-38.39528,5.5,1.0],[8380,330.76583,-76.11861,5.95,0.39],[8381,330.10042,-55.88278,6.01,-0.1],[8382,329.72917,-4.37306,6.22,1.0],[8383,329.16292,63.62556,4.91,1.77],[8384,329.29625,66.15611,6.43,-0.05],[8385,330.03292,6.7175,6.0,-0.12],[8386,330.20917,-28.45361,5.42,-0.09],[8387,330.84,-56.78611,4.69,1.06],[8388,329.7225,62.69833,5.93,1.67],[8389,329.84583,57.65833,6.59,0.03],[8390,330.27083,0.605,5.58,1.28],[8391,330.11167,33.00611,6.46,0.6],[8392,330.2725,13.11972,5.6,0.34],[8393,330.28833,8.25722,5.65,1.44],[8394,330.54958,-17.90361,6.28,1.01],[8395,329.4625,74.99667,6.35,1.56],[8396,330.61083,-16.96417,6.37,0.42],[8397,330.50583,10.97389,6.37,-0.1],[8398,330.82167,-29.90417,7.1,0.32],[8399,330.16375,62.48806,6.66,0.06],[8400,329.8125,73.18,5.03,0.44],[8401,330.81833,-6.5225,5.54,0.96],[8402,330.82875,-2.15528,4.69,-0.06],[8403,330.46083,52.88222,5.78,-0.11],[8404,330.82917,11.38639,5.8,-0.07],[8405,331.09958,-29.91667,6.47,1.63],[8406,330.51917,58.00056,5.56,0.06],[8407,330.73625,44.65,5.6,-0.03],[8408,331.15333,-26.8225,5.96,-0.14],[8409,331.46208,-59.63611,5.62,1.46],[8410,331.1975,-0.90667,5.3,0.23],[8411,331.52875,-39.54333,4.46,1.37],[8412,331.14333,32.94194,6.38,1.1],[8413,331.42,5.05861,4.84,1.44],[8414,331.44583,-0.31972,2.96,0.98],[8415,331.2975,26.67389,5.78,1.25],[8416,330.97042,63.11972,5.29,1.58],[8417,330.9475,64.62778,4.29,0.34],[8418,331.60917,-13.86972,4.27,-0.07],[8419,331.39458,28.96389,5.7,-0.06],[8420,332.67708,-75.88056,6.55,1.18],[8421,331.31833,46.74472,6.13,1.61],[8422,331.46083,45.11222,6.44,-0.03],[8423,329.55292,82.86972,6.98,0.52],[8424,331.50833,45.01444,5.14,1.57],[8425,332.05833,-46.96111,1.74,-0.13],[8426,331.25208,62.78556,5.27,1.41],[8427,331.46333,48.23167,6.27,-0.06],[8428,331.28708,62.28,5.11,0.08],[8429,331.55167,45.24861,6.19,0.09],[8430,331.75292,25.345,3.76,0.44],[8431,332.09583,-32.98861,4.5,0.05],[8432,332.98042,-76.11611,6.15,1.0],[8433,332.10833,-34.04389,4.99,1.48],[8434,331.55625,56.34306,6.39,-0.1],[8435,331.86917,19.47556,5.75,0.6],[8436,331.875,18.00056,6.35,1.64],[8437,332.17792,-33.12556,6.37,0.2],[8438,331.95958,21.70278,5.78,-0.1],[8439,332.24583,-18.51972,5.81,-0.17],[8440,332.49167,-48.10722,6.43,1.39],[8441,332.07167,25.54361,6.11,0.27],[8442,331.79,58.84083,6.32,0.88],[8443,331.85625,53.30722,6.14,0.43],[8444,332.48208,-34.01472,5.37,0.24],[8445,332.06875,49.79639,6.42,0.6],[8446,332.50042,-28.2925,6.44,0.15],[8447,332.53667,-32.54833,4.92,0.48],[8448,332.17083,45.74194,6.11,0.72],[8449,332.30667,33.17222,5.58,1.0],[8450,332.55,6.19778,3.53,0.08],[8451,332.58792,-3.89417,6.27,-0.01],[8452,332.65625,-11.565,5.46,-0.12],[8453,332.64083,-4.26722,6.01,0.98],[8454,332.49667,33.17833,4.29,0.46],[8455,332.57917,19.61694,6.18,0.69],[8456,332.5925,14.63,6.33,1.08],[8457,332.76,-21.2325,6.09,0.5],[8458,332.65583,11.62444,5.78,1.58],[8459,332.62583,20.97806,6.46,0.12],[8460,332.715,30.55306,6.32,0.18],[8461,332.96375,16.04056,5.95,0.95],[8462,333.1075,-14.19389,6.03,0.38],[8463,332.79125,50.82333,5.4,0.15],[8464,333.23958,-26.32778,6.17,0.17],[8465,332.71375,58.20111,3.35,1.57],[8466,333.03333,24.95,5.92,1.51],[8467,333.1825,-4.72083,6.39,0.5],[8468,332.45167,72.34111,4.79,0.92],[8469,332.87792,59.41444,5.04,0.25],[8470,333.435,-25.18083,5.58,0.49],[8471,334.46042,-77.51167,5.51,0.31],[8472,332.95333,56.83944,5.24,0.51],[8473,332.56375,72.11111,6.37,-0.06],[8474,332.66208,70.13278,5.5,0.38],[8475,333.19917,34.60472,5.33,1.13],[8476,332.98708,59.08472,6.3,1.13],[8477,333.66083,-41.38167,6.23,0.65],[8478,333.57833,-27.76694,5.43,-0.16],[8479,333.00792,60.75944,5.35,1.17],[8480,333.575,-21.07417,5.32,0.8],[8481,335.00625,-80.43972,5.1,1.47],[8482,333.41083,28.60833,5.89,1.15],[8483,333.09292,63.29139,5.79,1.67],[8484,333.89625,-44.45194,6.1,1.02],[8485,333.46958,39.715,4.49,1.39],[8486,333.90375,-41.34667,4.79,0.8],[8487,333.45542,45.44083,5.53,0.04],[8488,334.11083,-41.6275,5.1,0.92],[8489,333.685,42.95389,5.71,0.0],[8490,333.45625,63.1625,6.11,-0.08],[8491,333.99917,8.54944,6.21,0.02],[8492,334.15583,-25.89833,6.15,1.11],[8493,333.22042,73.30722,6.08,1.01],[8494,333.75833,57.04361,4.19,0.28],[8495,334.14,-1.59639,6.15,0.19],[8496,334.20042,-12.83139,5.34,1.14],[8497,334.24917,-23.14,6.17,1.05],[8498,333.9925,37.74889,4.13,1.46],[8499,334.20833,-7.78333,4.16,0.98],[8500,334.21917,-9.04,5.79,1.16],[8501,334.565,-53.62778,5.37,0.6],[8502,334.62542,-60.25972,2.86,1.39],[8503,334.12375,27.80417,6.37,0.99],[8504,334.27708,-5.38722,5.75,0.88],[8505,337.90583,-85.96722,5.77,1.02],[8506,334.11042,57.22028,5.88,0.93],[8507,334.51792,-0.23778,6.39,0.44],[8508,334.75333,-13.305,5.95,1.06],[8509,335.15083,-57.51,6.34,1.37],[8510,334.73417,37.76944,6.17,0.28],[8511,334.55292,62.80444,5.75,1.26],[8512,335.04958,-7.82111,5.37,-0.06],[8513,335.115,5.78944,5.37,-0.02],[8514,335.2325,8.18667,6.17,0.44],[8515,336.15333,-72.25556,5.29,0.65],[8516,335.39833,-21.59833,5.13,1.07],[8517,335.25042,26.93528,6.47,1.59],[8518,335.41417,-1.38722,3.84,-0.05],[8519,335.165,50.98083,6.42,0.6],[8520,335.37958,12.20528,5.01,-0.13],[8521,335.68292,-45.94778,6.62,2.01],[8522,335.33042,28.33056,4.81,0.0],[8523,335.25667,46.53667,4.57,-0.1],[8524,335.78333,-45.92861,5.62,0.36],[8525,334.585,76.48806,6.66,0.0],[8526,336.4625,-75.01556,6.04,0.64],[8527,336.29375,-70.43167,5.78,0.38],[8528,335.46208,42.07833,6.41,-0.08],[8529,335.87875,-24.7625,5.53,0.99],[8530,335.88375,-7.19444,5.93,1.0],[8531,336.235,-57.79722,5.32,0.67],[8532,335.915,20.84833,6.04,0.6],[8533,336.02875,-4.83694,5.78,-0.04],[8534,336.11292,-13.52944,5.76,0.97],[8535,335.75083,57.28444,6.16,-0.13],[8536,335.97583,38.57361,6.22,0.49],[8537,335.75083,62.42,6.04,0.05],[8538,335.89,52.22917,4.43,1.02],[8539,336.31917,1.3775,4.66,-0.03],[8540,336.83333,-64.96639,4.48,-0.03],[8541,336.12917,49.47639,4.57,0.09],[8542,336.54458,-23.6825,6.29,-0.03],[8543,336.41958,18.44444,6.26,1.22],[8544,336.6425,-16.74139,6.57,0.6],[8545,336.64333,-16.7425,6.35,0.61],[8546,333.29417,86.10806,5.27,-0.03],[8547,337.15708,-67.48917,5.55,0.2],[8548,336.65583,4.39361,5.75,0.52],[8549,336.69042,37.44389,6.46,-0.13],[8550,335.92208,78.24333,6.76,-0.06],[8551,336.96458,4.69556,4.79,1.05],[8552,337.16333,-39.13194,5.47,0.95],[8553,336.86042,39.80972,6.14,-0.14],[8554,336.74667,56.43333,6.57,-0.1],[8555,336.9425,31.84028,5.98,1.45],[8556,337.3175,-43.49556,3.97,1.03],[8557,336.50333,70.77083,5.47,1.2],[8558,337.20708,-0.02028,4.59,0.6],[8559,337.20875,-0.02,4.42,0.38],[8560,337.43958,-43.74944,4.11,1.57],[8561,336.77208,65.13222,5.46,0.37],[8562,337.28333,9.12889,5.58,1.55],[8563,337.44167,-27.10722,5.95,0.33],[8564,337.2925,26.76306,5.79,1.25],[8565,337.50625,-12.915,6.4,0.32],[8566,337.49167,4.43167,5.48,0.38],[8567,337.5725,-14.58583,6.37,-0.04],[8568,337.08208,64.08556,6.29,1.08],[8569,337.43292,35.72556,6.56,0.6],[8570,337.72375,-26.07361,6.43,1.08],[8571,337.29292,58.41528,3.75,0.6],[8572,337.3825,47.70694,4.36,1.68],[8573,337.66167,-10.67806,4.82,-0.06],[8574,337.5075,32.5725,5.65,-0.04],[8575,337.52708,49.35611,6.4,1.15],[8576,337.87625,-32.34611,4.29,0.01],[8577,338.86,-78.77167,6.15,1.38],[8578,336.67708,78.78583,5.83,0.15],[8579,337.62208,43.12333,4.51,-0.09],[8580,337.82667,-2.91111,6.16,1.08],[8581,337.82667,-6.555,6.14,0.56],[8582,338.25042,-61.98222,4.81,1.61],[8583,337.92208,-10.90556,6.38,0.28],[8584,337.8925,29.54278,6.35,0.19],[8585,337.82292,50.2825,3.77,0.01],[8586,338.14792,20.23,6.42,0.32],[8587,338.19542,15.86333,6.32,1.19],[8588,338.11,39.77972,5.88,0.16],[8589,338.07833,54.0375,6.35,0.6],[8590,338.51208,-1.57417,5.89,0.99],[8591,337.47042,78.82417,5.5,0.06],[8592,338.67333,-20.70833,5.2,0.44],[8593,338.97042,-57.88361,6.23,0.2],[8594,338.41917,56.625,5.71,0.96],[8595,338.26208,69.91361,6.6,0.32],[8596,338.90208,-23.99111,5.97,0.99],[8597,338.83917,-0.1175,4.02,-0.09],[8598,338.32083,70.37389,6.34,0.0],[8599,338.0675,76.22639,5.68,0.05],[8600,339.12208,-40.58278,6.28,0.12],[8601,339.1475,-31.66389,5.82,1.09],[8602,339.245,-40.59111,5.86,0.06],[8603,338.96792,39.63417,5.73,-0.15],[8604,339.03292,35.57722,6.1,1.0],[8605,339.15167,11.69694,6.4,0.0],[8606,338.9725,50.07111,6.29,-0.05],[8607,338.96583,56.07,6.38,0.12],[8608,339.26958,12.57722,6.3,0.6],[8609,339.20292,35.6525,6.3,1.37],[8610,339.43917,-4.22806,5.03,1.14],[8611,339.785,-52.69222,6.65,0.35],[8612,339.5925,-7.89778,6.23,0.78],[8613,339.34333,51.54528,4.63,0.24],[8614,339.68625,-28.74778,6.47,1.04],[8615,338.94208,73.64306,5.08,0.39],[8616,339.71458,-33.08139,5.66,0.05],[8617,339.57292,45.18306,6.4,0.6],[8618,339.71917,19.52222,5.82,0.92],[8619,339.93333,-28.32528,6.31,1.01],[8620,340.20375,-57.42222,5.97,1.46],[8621,339.65792,56.79583,5.21,1.58],[8622,339.81542,39.05028,4.88,-0.2],[8623,340.09292,-30.65889,5.87,1.3],[8624,339.94583,19.68111,6.21,0.0],[8625,339.30417,75.37167,5.79,1.57],[8626,339.89292,37.59278,6.03,0.86],[8627,339.6625,63.58444,5.19,0.06],[8628,340.16417,-27.04361,4.17,-0.11],[8629,340.2,-3.55417,6.31,0.52],[8630,341.51375,-81.38167,4.15,0.2],[8631,340.21958,14.54944,5.71,0.72],[8632,340.12875,44.27639,4.46,1.33],[8633,340.07667,53.84611,5.93,0.93],[8634,340.36542,10.83139,3.4,-0.09],[8635,340.65375,-47.21056,5.98,0.58],[8636,340.66708,-46.88472,2.1,1.6],[8637,340.59208,-29.36083,6.17,1.54],[8638,340.38083,30.96583,6.34,0.6],[8639,340.67958,-44.24778,6.07,0.98],[8640,340.36917,40.22556,5.25,-0.14],[8641,340.43917,29.3075,4.79,-0.01],[8642,340.48917,14.51639,5.9,1.11],[8643,340.40042,41.54944,5.94,0.6],[8644,340.875,-41.41444,4.85,1.03],[8645,340.76458,-8.31167,6.45,0.17],[8646,341.06875,-60.49944,6.3,0.56],[8647,340.80958,-6.96278,6.41,-0.04],[8648,340.58667,53.90889,6.12,1.62],[8649,340.89708,-18.83028,4.69,1.37],[8650,340.75042,30.22139,2.94,0.86],[8651,340.73125,37.80278,6.43,-0.09],[8652,340.76875,47.16861,6.39,0.47],[8653,340.92792,10.93917,6.51,0.46],[8654,341.02167,39.46556,5.95,1.48],[8655,341.40792,-53.50028,4.85,1.18],[8656,341.02292,41.81917,5.08,0.96],[8657,341.41958,-46.5475,5.51,1.32],[8658,341.53333,-48.97889,6.62,0.63],[8659,341.61792,-49.68583,6.48,1.14],[8660,341.3675,19.36667,6.25,1.05],[8661,341.205,52.51722,6.55,0.6],[8662,341.68208,-46.93944,6.56,0.3],[8663,342.59542,-80.12417,5.35,-0.15],[8664,342.42042,-77.05056,6.73,0.11],[8665,341.67333,12.17278,4.19,0.5],[8666,341.5425,44.54611,5.76,0.36],[8667,341.63292,23.56556,3.95,1.07],[8668,341.82958,-34.16111,6.28,1.16],[8669,342.08917,-61.68417,6.37,1.06],[8670,341.88792,-19.61333,5.26,0.94],[8671,341.94625,-38.22194,6.71,0.48],[8672,342.3225,-70.34778,6.34,0.07],[8673,341.92833,-14.05639,5.66,-0.05],[8674,341.98417,-25.91194,6.3,0.91],[8675,342.13875,-51.31694,3.49,0.08],[8676,342.12583,-10.55556,6.19,0.28],[8677,341.84667,58.48278,6.36,-0.04],[8678,342.04542,37.41667,5.9,1.03],[8679,342.39792,-13.5925,4.01,1.57],[8680,342.49625,-32.80528,6.33,0.31],[8681,342.38458,10.47889,6.54,0.29],[8682,342.19917,54.415,6.12,-0.07],[8683,342.18417,62.93833,6.06,1.2],[8684,342.50083,24.60167,3.48,0.93],[8685,342.75917,-39.15694,5.42,1.43],[8686,342.93708,-59.88139,6.46,1.13],[8687,342.25292,68.57028,6.19,0.6],[8688,342.4425,55.90278,5.43,1.17],[8689,343.04125,-63.18861,6.12,1.03],[8690,342.59083,41.95361,5.92,0.08],[8691,342.66292,19.14083,6.4,0.6],[8692,342.5425,50.67694,6.21,1.14],[8693,342.83708,-29.53611,5.97,0.91],[8694,342.42,66.20056,3.52,1.05],[8745,344.7875,59.81472,6.43,0.03],[8695,343.13167,-32.87556,4.46,-0.04],[8696,342.845,61.69694,5.6,0.78],[8697,343.10042,9.83556,5.16,0.48],[8698,343.15375,-7.57972,3.74,1.64],[8699,343.00833,43.3125,4.94,1.56],[8700,343.40792,-48.59806,6.04,0.62],[8701,343.66417,-70.07361,6.05,0.66],[8702,341.87083,83.15389,4.74,1.26],[8703,343.25958,16.84111,5.64,1.12],[8704,343.36958,-11.61667,5.8,-0.08],[8705,343.21792,50.41194,6.46,-0.04],[8706,343.29708,40.16722,6.34,-0.08],[8707,343.26583,60.10111,6.01,1.75],[8708,343.41708,44.74917,5.81,0.26],[8709,343.6625,-15.82083,3.27,0.05],[8710,343.64208,-7.20472,6.19,1.28],[8711,343.68958,-16.27194,5.56,1.14],[8712,343.52917,40.37694,5.81,1.13],[8713,343.81208,-36.38861,6.4,1.31],[8714,343.64875,16.94167,6.12,1.77],[8715,343.74792,1.06472,6.11,0.2],[8716,343.79583,-4.98778,5.72,0.88],[8717,343.80708,8.81583,4.9,0.0],[8718,343.76083,37.07694,5.91,0.42],[8719,343.96417,-31.63306,6.1,1.36],[8720,343.98708,-32.53972,4.21,0.97],[8721,344.1,-31.56556,6.48,1.1],[8722,344.19917,-47.96917,5.7,0.22],[8723,343.93542,36.35167,5.74,-0.05],[8724,344.21458,11.84833,6.51,0.18],[8725,344.09833,41.60389,5.59,-0.14],[8726,344.10833,49.73361,4.95,1.78],[8727,344.32167,-4.81,6.31,0.94],[8728,344.41292,-29.62222,1.16,0.09],[8729,344.36625,20.76889,5.49,0.67],[8730,344.38667,3.81028,6.28,1.12],[8731,344.26875,48.68417,5.43,-0.09],[8732,344.64583,-35.52306,6.13,0.58],[8733,344.41958,39.30889,6.18,-0.15],[8734,344.56458,-2.39528,6.16,0.74],[8735,344.59875,-1.41028,6.37,0.35],[8736,342.75917,85.37361,5.9,1.32],[8737,344.64625,9.35694,6.43,0.64],[8738,344.6775,7.33972,6.33,0.06],[8739,344.79917,11.72889,5.75,0.32],[8740,344.89917,-29.46222,5.51,0.25],[8741,344.89875,-13.07083,6.07,1.45],[8742,344.86417,0.96278,5.43,0.98],[8743,345.02417,-25.16417,5.65,1.25],[8744,344.79292,52.65444,6.29,1.42],[8746,345.1025,-25.62667,6.29,1.13],[8747,345.22,-52.75417,4.12,0.98],[8748,343.60333,84.34611,4.71,1.43],[8749,345.28125,-50.95,5.68,1.42],[8750,345.15792,0.18583,6.21,0.89],[8751,345.17875,3.01167,5.83,1.34],[8752,345.02125,56.94528,5.0,1.42],[8753,345.17708,31.08306,6.6,-0.04],[8754,345.33083,-28.85361,5.55,1.35],[8755,345.14333,45.375,6.5,0.6],[8756,345.34583,-22.79083,6.28,0.13],[8757,345.34833,-7.06111,6.21,1.41],[8758,345.22792,38.70806,6.54,-0.11],[8759,345.38208,-4.71139,5.94,1.0],[8760,345.64167,-36.42083,6.47,0.94],[8761,345.37792,57.10556,6.2,1.5],[8762,345.48042,42.32611,3.62,-0.09],[8763,345.63583,-6.57417,6.15,1.58],[8764,345.68458,-20.87056,5.97,0.94],[8765,345.63792,31.78056,6.57,0.35],[8766,345.65125,42.75778,5.1,0.09],[8767,345.87417,-34.74944,5.11,0.29],[8768,345.68833,44.05889,6.39,0.0],[8769,346.2175,-68.82028,5.52,0.36],[8770,345.6825,55.23639,6.5,-0.08],[8771,345.99792,-41.47833,5.79,1.08],[8772,345.98875,-4.79528,6.68,0.58],[8773,345.96917,3.82,4.53,-0.12],[8774,346.165,-53.965,5.37,1.45],[8775,345.94375,28.08278,2.42,1.67],[8776,346.00417,6.61667,6.41,0.39],[8777,345.84875,60.44528,6.74,-0.02],[8778,345.84,58.56472,6.43,0.9],[8779,345.88708,67.20917,5.24,1.26],[8780,346.04583,50.05222,4.65,1.06],[8781,346.19042,15.20528,2.49,-0.04],[8782,346.29083,-7.69361,5.43,0.3],[8783,346.30333,-17.07917,6.14,1.37],[8784,346.27625,16.56306,6.44,0.83],[8785,346.32333,1.30694,6.39,0.94],[8786,347.09875,-79.48083,6.12,0.14],[8787,346.72,-43.52056,4.28,0.42],[8788,346.57583,18.5175,6.13,0.44],[8789,346.67042,-23.74306,4.47,0.9],[8790,346.72333,-38.89222,5.61,0.01],[8791,346.78958,-49.60667,6.33,1.45],[8792,346.63292,19.91083,6.3,0.49],[8793,346.81125,-50.68639,5.83,0.48],[8794,347.14875,-73.58639,6.15,1.42],[8795,346.75125,9.40944,4.52,1.57],[8847,349.2075,-41.19444,6.47,1.08],[8796,346.77833,25.46833,4.76,1.34],[8797,346.65375,59.41972,4.85,-0.03],[8798,346.86542,32.82583,6.02,0.12],[8799,346.86958,21.13417,5.99,0.26],[8800,346.82542,46.06806,6.66,-0.05],[8801,346.79208,52.81639,6.11,1.05],[8802,347.0875,-28.82333,5.6,0.88],[8803,346.79333,59.7275,6.4,-0.01],[8804,346.91375,46.38722,5.33,1.41],[8805,346.93917,49.29583,5.7,0.44],[8806,347.05125,44.56167,6.56,0.17],[8807,347.17042,2.12778,5.4,0.91],[8808,346.94875,63.63333,6.26,-0.02],[8809,347.54875,-66.8575,6.47,0.95],[8810,348.05,-80.91278,6.41,1.5],[8811,346.98833,64.2225,6.21,1.1],[8812,347.36167,-21.1725,3.66,1.22],[8813,347.43583,-28.08861,5.87,1.31],[8814,347.48875,-42.86056,5.81,0.48],[8815,347.38125,8.67722,5.12,1.47],[8816,347.45667,-14.51056,6.42,0.01],[8817,347.47833,-22.4575,4.69,0.65],[8818,347.54083,-40.59167,5.83,1.62],[8819,346.97458,75.3875,4.41,0.8],[8820,347.59,-45.24667,3.9,1.02],[8821,347.50625,9.82194,5.39,-0.08],[8822,347.43375,59.33306,5.7,0.33],[8823,347.69417,-29.525,6.51,0.27],[8824,347.6775,17.59444,5.71,1.34],[8825,347.61333,43.54417,5.94,0.44],[8826,347.93417,8.72,5.16,0.13],[8827,347.955,26.84722,6.17,0.94],[8828,348.3125,-49.61889,6.8,0.92],[8829,348.5275,-62.7,6.12,0.79],[8830,348.1375,49.40639,4.52,0.29],[8831,348.26667,29.44167,6.35,0.93],[8832,348.32083,57.16833,5.56,1.01],[8833,348.36042,11.065,5.82,1.01],[8834,348.58083,-6.04889,4.22,1.56],[8835,348.74417,-41.10556,5.77,1.18],[8836,348.6675,-10.68861,6.12,1.49],[8837,348.55958,50.61778,6.31,0.6],[8838,348.59042,29.77167,6.41,0.45],[8839,348.65208,24.10306,6.36,0.6],[8840,348.89292,-3.49639,5.55,0.06],[8841,348.97292,-9.08778,4.21,1.11],[8842,348.94292,28.24778,6.49,0.85],[8843,349.24042,-62.00111,5.66,0.51],[8844,348.65542,74.23111,5.84,0.6],[8845,348.99125,24.77111,6.6,0.4],[8846,349.16542,-44.48917,5.92,1.06],[8848,349.3575,-58.23583,3.99,0.4],[8849,349.78375,-79.47278,6.33,0.91],[8850,349.21208,-7.72667,5.06,1.6],[8851,348.9075,70.88806,5.56,0.24],[8852,349.29125,3.28222,3.69,0.92],[8853,349.17625,53.21361,5.54,0.52],[8854,349.11167,61.96306,6.53,0.23],[8855,349.58333,-67.47111,6.13,1.35],[8856,349.41667,-11.71306,6.34,0.05],[8857,349.31917,45.16417,6.43,1.07],[8858,349.47583,-9.1825,4.39,-0.15],[8859,349.54125,-40.82444,5.53,0.44],[8860,349.43625,49.01528,4.85,1.67],[8861,349.48375,45.48889,6.48,-0.03],[8862,352.01542,-87.48222,5.49,1.27],[8863,349.70583,-32.53194,4.41,1.13],[8864,349.5975,41.77361,6.02,0.6],[8865,349.74042,-9.61083,4.98,-0.02],[8866,349.77792,-13.45889,5.08,0.8],[8867,349.32875,75.29917,6.38,0.03],[8868,349.85,-5.12444,5.55,0.39],[8869,349.85042,-18.07528,5.93,1.52],[8870,349.76,45.13722,6.5,0.6],[8871,349.93,-33.70806,6.37,1.3],[8872,349.65625,68.11167,4.75,0.84],[8873,349.86417,34.79333,6.32,-0.08],[8874,349.87417,48.62528,5.44,1.03],[8875,349.92333,48.38083,6.32,1.12],[8876,349.96833,42.07806,5.79,1.48],[8877,350.20833,-50.30667,6.05,0.42],[8878,350.08583,5.38139,5.05,1.2],[8879,350.17042,-5.90806,6.17,1.07],[8880,350.15917,23.74028,4.6,0.17],[8881,350.05958,61.97,6.45,0.6],[8882,350.20667,30.415,5.59,1.5],[8883,350.31458,-26.98667,5.64,0.82],[8884,350.18333,44.11639,6.13,0.17],[8885,350.22208,38.18222,5.77,0.46],[8886,350.14417,62.21306,6.39,1.61],[8887,350.47875,31.8125,5.32,-0.11],[8888,350.4925,26.60889,6.62,0.37],[8889,350.73708,-60.05583,6.09,1.6],[8890,350.66333,-15.03917,5.2,0.2],[8891,350.66875,20.82861,6.29,-0.04],[8892,350.7425,-20.10056,3.97,1.1],[8893,350.76917,12.31389,5.08,1.31],[8894,350.63542,60.13361,5.56,1.68],[8895,350.97625,-53.80833,6.15,0.26],[8896,350.93917,-43.12444,6.1,1.46],[8897,350.88292,0.29139,6.31,1.61],[8898,351.05458,-51.89139,5.75,1.59],[8899,350.94792,32.53139,6.69,0.45],[8900,351.0325,-18.6875,6.19,1.02],[8901,351.33083,-56.84917,5.59,1.07],[8902,351.14583,41.11278,6.72,0.06],[8903,351.21167,32.385,5.57,-0.11],[8904,351.20958,62.28278,4.98,1.68],[8905,351.345,23.40417,4.4,0.61],[8906,351.51167,-20.64194,4.39,1.47],[8907,351.6525,-52.72167,5.52,0.4],[8908,351.78,-66.58111,6.45,1.47],[8909,351.8125,-58.47611,5.63,0.98],[8910,351.78792,-50.15722,6.2,-0.08],[8911,351.73333,1.25556,4.94,0.03],[8912,351.81167,1.1225,6.25,1.02],[8913,351.78083,42.91194,5.75,0.0],[8914,352.00292,-35.54444,6.32,1.2],[8915,351.91833,25.16722,5.98,-0.06],[8916,351.99208,6.37889,4.28,1.07],[8917,352.02167,-11.44972,6.37,0.9],[8918,351.81917,70.35972,5.6,0.19],[8919,352.25417,-63.11083,5.68,-0.17],[8920,352.25333,-44.49778,6.43,1.18],[8921,352.2525,-9.26611,6.18,1.44],[8922,352.27333,23.04778,6.35,0.6],[8923,352.28875,12.76056,4.55,0.94],[8924,352.38375,-4.53278,6.25,1.09],[8925,352.53083,49.13306,6.17,1.46],[8926,352.50833,58.54889,4.91,-0.12],[8927,352.66542,38.66194,6.05,0.99],[8928,352.75458,-6.28833,6.39,1.26],[8929,352.8625,-44.84361,6.02,1.02],[8930,352.8225,39.23639,5.22,1.02],[8931,352.88125,-4.08722,6.49,0.54],[8932,352.92542,-21.36944,6.29,0.33],[8933,352.92958,28.40361,6.41,0.01],[8934,352.99,-1.08583,6.38,1.18],[8935,353.33125,-77.38528,5.81,0.68],[8936,353.1025,34.9525,6.65,-0.06],[8937,353.24292,-37.81833,4.37,-0.09],[8938,351.75333,87.3075,5.58,0.23],[8939,353.31917,-20.91444,4.71,0.02],[8940,353.36708,22.49889,5.32,1.6],[8941,353.42792,45.05806,6.24,0.98],[8942,353.48125,20.84083,6.06,1.73],[8943,353.48833,31.32528,4.98,1.38],[8944,353.5375,-1.2475,5.87,0.3],[8945,353.80292,-64.68944,7.4,0.6],[8946,353.70583,-15.24583,5.96,1.36],[8947,353.65625,40.23639,5.59,0.1],[8948,353.65917,33.49722,5.63,1.03],[8949,353.76917,-42.615,4.71,0.08],[8950,353.69458,38.02389,6.18,1.58],[8951,353.88375,-7.46444,6.39,0.88],[8952,353.74583,71.64222,5.84,1.8],[8953,353.98292,24.56111,6.45,1.73],[8954,354.09708,2.10222,5.68,0.44],[8955,354.12708,32.90417,6.35,0.46],[8956,354.2725,-31.87083,6.52,1.26],[8957,354.60042,-76.87,6.0,0.9],[8958,354.415,-13.06028,5.65,1.03],[8959,354.4625,-45.4925,4.74,0.08],[8960,354.41583,16.82556,6.26,0.0],[8961,354.39125,46.45806,3.82,1.01],[8962,354.38333,44.42917,5.8,-0.06],[8963,354.48667,18.40056,5.53,0.0],[8964,354.49417,46.19972,6.58,0.66],[8965,354.53417,43.26806,4.29,-0.1],[8966,354.86667,-46.63778,6.09,0.24],[8967,354.78458,50.47167,5.3,-0.06],[8968,354.94625,-14.22167,5.0,0.24],[8969,354.9875,5.62639,4.13,0.51],[8970,354.97958,9.67722,5.97,0.2],[8971,354.79333,75.29278,5.95,0.13],[8972,354.83792,74.00278,5.98,0.89],[8973,355.01167,37.6525,6.53,0.35],[8974,354.83667,77.6325,3.21,1.03],[8975,355.15917,-32.07306,5.31,0.97],[8976,355.10208,44.33389,4.14,-0.08],[8977,355.16917,36.72083,6.23,0.39],[8978,355.27917,-24.16028,6.6,1.57],[8979,355.28708,-11.68056,5.89,1.0],[8980,355.39375,-18.02722,5.34,1.57],[8981,355.36208,49.51222,6.26,0.19],[8982,355.44083,-17.81639,4.82,0.82],[8983,355.48625,7.25056,5.89,0.1],[8984,355.51167,1.78,4.5,0.2],[8985,355.47708,57.26,6.24,0.6],[8986,355.56167,44.99194,6.57,0.6],[8987,355.61625,-15.44778,5.28,1.37],[8988,355.68042,-14.545,4.49,-0.04],[8989,355.58667,64.51556,6.56,1.88],[8990,355.63125,61.67944,6.4,1.24],[8991,355.84333,10.33139,5.06,1.68],[8992,355.95625,-15.28444,6.36,1.58],[8993,356.00583,-45.08333,6.09,0.98],[8994,356.10583,-70.49028,6.07,0.91],[8995,356.16958,-78.79139,5.75,1.11],[8996,356.05,-64.40444,5.72,1.4],[8997,355.99792,29.36167,4.93,0.95],[8998,356.05042,-18.27694,5.24,-0.08],[8999,356.12042,-26.24639,6.17,0.5],[9000,356.20125,55.79972,6.51,0.6],[9001,356.505,-40.1825,6.31,0.2],[9002,356.50375,-18.67806,5.29,0.28],[9003,356.50875,46.42028,4.95,1.11],[9004,356.59792,3.48667,5.04,2.6],[9005,356.65292,66.78222,5.95,-0.04],[9006,356.81667,-50.22667,5.18,-0.19],[9007,356.84708,-68.39417,6.89,0.46],[9008,356.76458,58.65194,4.87,1.11],[9009,356.81625,-11.91083,5.73,1.08],[9010,356.75792,57.45139,5.51,1.65],[9011,356.88833,46.8325,6.07,-0.14],[9012,356.98542,-2.76167,5.49,0.94],[9013,356.97833,67.80694,5.04,-0.01],[9014,357.13542,-6.38056,6.07,1.45],[9015,357.20542,2.21417,6.46,0.44],[9016,357.23167,-28.13028,4.57,0.01],[9017,357.1625,64.87639,6.41,0.06],[9018,357.20917,62.21444,5.43,0.67],[9019,357.22458,59.97889,6.34,-0.01],[9020,357.3,58.96306,6.33,0.4],[9021,357.38167,-15.86111,6.24,1.22],[9022,357.36458,1.07611,5.77,0.16],[9023,357.43625,-62.83944,6.59,1.48],[9024,357.42083,36.42528,5.9,0.79],[9025,357.41417,28.8425,5.97,0.19],[9026,357.45667,-25.33139,6.42,0.12],[9027,357.56125,-9.97417,5.94,1.13],[9028,357.59292,51.62167,6.44,0.37],[9029,357.63875,-14.40194,5.72,1.51],[9030,357.83833,9.31333,5.79,1.66],[9031,357.83875,-18.90889,5.18,-0.14],[9032,358.02667,-82.01889,5.11,0.92],[9033,357.99125,2.93028,5.55,1.53],[9034,357.99,77.59944,6.55,0.44],[9035,358.0975,21.67083,6.11,1.59],[9036,358.12208,19.12028,5.08,1.6],[9037,358.125,-14.25111,5.87,1.28],[9038,358.10458,75.54472,6.39,0.98],[9039,358.15458,10.9475,5.3,0.18],[9040,358.21042,-8.99667,5.75,1.17],[9041,358.23167,-3.15556,5.93,1.07],[9042,358.27,2.09056,6.28,-0.01],[9043,358.33667,-24.22917,6.24,0.19],[9044,358.58917,-27.04222,6.35,0.2],[9045,358.59583,57.49944,4.54,1.22],[9046,358.66083,-40.3,6.03,0.57],[9047,358.69417,0.10917,5.61,1.59],[9048,358.7825,7.07111,6.21,-0.07],[9049,358.81917,-31.92167,6.1,-0.08],[9050,358.81917,-31.88417,6.83,-0.08],[9051,358.84583,25.955,6.54,0.6],[9052,358.89042,57.41222,6.0,0.21],[9053,358.89,47.35583,6.0,1.16],[9054,359.12458,-24.73722,6.31,0.92],[9055,359.17292,22.64806,6.15,1.6],[9056,359.11542,83.19111,6.59,0.05],[9057,359.265,42.65833,5.97,0.69],[9058,359.28458,-26.62361,6.26,1.45],[9059,359.28542,55.70583,5.55,0.49],[9060,359.33292,-62.95639,5.97,0.11],[9061,359.38625,-82.17,5.73,1.05],[9062,359.39667,-64.29833,5.0,0.06],[9063,359.38958,60.02361,6.47,0.01],[9064,359.43958,25.14139,4.66,1.59],[9065,359.58833,-15.8475,6.26,1.08],[9066,359.60333,51.38861,4.8,1.83],[9067,359.66833,-3.55611,4.86,0.93],[9068,359.705,32.38167,6.52,-0.11],[9069,359.7325,-52.74583,5.13,1.13],[9070,359.69375,46.41306,6.54,-0.09],[9071,359.75208,55.755,4.88,-0.07],[9072,359.82792,6.86333,4.01,0.42],[9073,359.86625,-29.485,5.62,1.6],[9074,359.87167,33.72444,6.58,0.55],[9075,359.87167,33.72444,6.58,0.6],[9076,359.97917,-65.57722,4.5,-0.08],[9077,0.08,-44.29056,6.29,0.76],[9078,0.09958,26.91833,6.46,0.5],[9079,0.12875,59.55972,6.19,1.01],[9080,0.18208,45.25333,6.38,-0.07],[9081,0.26875,-48.81,5.71,0.91],[9082,0.33333,-50.33722,5.53,1.6],[9083,0.33042,49.98167,6.22,0.97],[9084,0.39875,-77.06583,4.78,1.27],[9085,0.40375,61.22306,5.55,0.41],[9086,0.4325,42.36722,6.25,-0.03],[9087,0.45583,-3.0275,5.1,-0.12],[9088,0.5425,27.08194,5.75,0.67],[9089,0.49,-6.01417,4.41,1.63],[9090,0.53042,-14.67611,7.1,1.8],[9091,0.58292,-29.72028,5.01,-0.15],[9092,0.60083,8.95694,6.32,0.18],[9093,0.62375,8.48556,5.63,0.29],[9094,0.65042,66.09889,5.86,1.09],[9095,0.74,-20.04611,6.25,0.53],[9096,0.78208,-24.14528,6.44,1.18],[9097,0.85708,63.64194,6.24,0.33],[9098,0.935,-17.33611,4.55,-0.05],[9099,0.96625,66.71222,6.29,1.67],[9100,1.05667,62.28778,5.88,0.3],[9101,1.08208,-16.52889,5.78,1.1],[9102,1.08458,-29.26861,6.4,0.0],[9103,1.12542,-10.50944,4.94,1.63],[9104,1.175,67.16667,5.67,1.07],[9105,1.15292,42.09222,6.01,0.6],[9106,1.12792,-72.89778,7.31,0.44],[9107,1.22417,34.65972,6.12,0.62],[9108,1.17208,-71.43694,5.59,-0.12],[9109,1.23333,26.64889,6.25,1.4],[9110,1.27583,61.31417,5.8,-0.09]]\ No newline at end of file

Packages/MoonriseKit/Sources/SkyRenderer/Resources/constellations.json added +1

	@@ -0,0 +1 @@
		1	[{"id":"And","lines":[[8961,8976,8965,8762,8965,68,165,15,165,163,215,163,165,337,603,337,464,337,269,226]]},{"id":"Ant","lines":[[4273,4104,3871,3765]]},{"id":"Aps","lines":[[5470,6020,6102,6163]]},{"id":"Aql","lines":[[7602,7557,7525,7377,7235,7377,7570,7710,7570,7377,7236,7193]]},{"id":"Aqr","lines":[[8812,8841,8834,8597,8518,8698,8709,8698,8518,8499,8418,8499,8518,8414,8232]]},{"id":"Ara","lines":[[6743,6510,6461,6462,6500,6462,6285,6229,6285,6295,6510]]},{"id":"Ari","lines":[[951,888,838,617,553,546]]},{"id":"Aur","lines":[[1708,2088,2095,1791,1577,1612,1641,1605,1708]]},{"id":"Boo","lines":[[5435,5429,5340,5506,5681,5602,5435,5351,5404,5329,5351]]},{"id":"CMa","lines":[[2596,2574,2657,2596,2491,2294,2429,2580,2618,2646,2693,2827,2693,2653,2491]]},{"id":"CMi","lines":[[2943,2845]]},{"id":"CVn","lines":[[4915,4785]]},{"id":"Cae","lines":[[1443,1502,1503]]},{"id":"Cam","lines":[[1040,1035,1155,1148,1542,1603,1568]]},{"id":"Cap","lines":[[7754,7776,7936,7980,8204,8278,8322,8278,8167,8075,7776]]},{"id":"Car","lines":[[2326,2554,3117,3307,3699,4050,4140,4199,4037,3685,3890]]},{"id":"Cas","lines":[[542,403,264,168,21]]},{"id":"Cen","lines":[[4467,4522,4390,4638,4621,4743,4802,4819,5132,5267,5132,5459,5132,5231,5193,5190,5028,5190,5288,5190,5248,5440,5576]]},{"id":"Cep","lines":[[8974,8238,8162,8465,8694,8974]]},{"id":"Cet","lines":[[804,718,813,896,911,804,779,681,539,402,334,188,433,585,539]]},{"id":"Cha","lines":[[3318,3340,4231,4674,4174,3318]]},{"id":"Cir","lines":[[5670,5463,5704]]},{"id":"Cnc","lines":[[3572,3461,3249,3461,3449,3475]]},{"id":"Col","lines":[[2296,2256,2106,2040,2120,2040,1956,1743]]},{"id":"Com","lines":[[4968,4983,4737]]},{"id":"CrA","lines":[[7152,7226,7254,7259,7242,7188]]},{"id":"CrB","lines":[[5971,5947,5889,5849,5793,5747,5778]]},{"id":"Crt","lines":[[4567,4514,4405,4343,4287,4382,4405,4382,4402,4468]]},{"id":"Cru","lines":[[4730,4763],[4853,4656]]},{"id":"Crv","lines":[[4623,4630,4662,4757,4786,4630]]},{"id":"Cyg","lines":[[7417,7615,7796,7949,8115,7949,7796,7924,7796,7528,7420]]},{"id":"Del","lines":[[7852,7882,7906,7948,7928,7882]]},{"id":"Dor","lines":[[1338,1465,1674,1922,2015,1922,2102]]},{"id":"Dra","lines":[[6688,6705,6536,6554,6688,7310,7582,6927,6636,6396,6132,5986,5744,5291,4787,4434,3751]]},{"id":"Equ","lines":[[8131,8178,8123,8097]]},{"id":"Eri","lines":[[1666,1560,1520,1463,1298,1231,1136,1084,874,811,818,919,1003,1088,1173,1213,1240,1464,1393,1347,1195,1190,1106,1008,898,794,789,721,674,566,472]]},{"id":"For","lines":[[963,841,612]]},{"id":"Gem","lines":[[2134,2216,2286,2473,2343,2473,2697,2852,2890,2852,2697,2540,2697,2821,2905,2990,2905,2985,2905,2777,2650,2421,2650,2777,2763,2484]]},{"id":"Gru","lines":[[8353,8411,8556,8636,8425,8636,8675,8747,8675,8820,8787]]},{"id":"Her","lines":[[6324,6418,6695,6588,6695,6418,6220,6168,6092,6168,6220,6212,6148,6212,6324,6410,6623,6703,6779]]},{"id":"Hor","lines":[[909,934,802,778,810,868,1326,1302]]},{"id":"Hya","lines":[[3492,3482,3410,3418,3454,3492,3547,3665,3845,3748,3903,3994,4094,4232,4450,4552,5020,5287]]},{"id":"Hyi","lines":[[591,806,1208,98,591]]},{"id":"Ind","lines":[[7869,8140,8368,8387,8368,8140,8055,7986]]},{"id":"LMi","lines":[[4247,4100,3974]]},{"id":"Lac","lines":[[8498,8485,8579,8632,8579,8523,8579,8572,8541,8538,8585,8572]]},{"id":"Leo","lines":[[3873,3905,4031,4058,3975,3982,3852,3982,4359,4399,4386,4399,4359,4534,4357,4058]]},{"id":"Lep","lines":[[1654,1829,1865,1702,1865,1998,2085]]},{"id":"Lib","lines":[[5908,5787,5685,5531,5603,5685,5603,5794,5812]]},{"id":"Lup","lines":[[5987,5948,5776,5708,5646,5649,5469,5571,5695,5776,5695,5705,5883]]},{"id":"Lyn","lines":[[3705,3690,3612,3579,3275,2818,2560,2238]]},{"id":"Lyr","lines":[[7001,7056,7106,7178,7139,7056]]},{"id":"Men","lines":[[2261,1953,1629,1677]]},{"id":"Mic","lines":[[8151,8135,8039,7965]]},{"id":"Mon","lines":[[2385,2298,2506,2714,2356,2227,2356,2714,2970,3188]]},{"id":"Mus","lines":[[4844,4798,4923,4798,4773,4798,4671,4520]]},{"id":"Nor","lines":[[6115,6072,5962]]},{"id":"Oct","lines":[[8630,5339,8254,8630]]},{"id":"Oph","lines":[[6556,6299,6149,6056,6075,6175,6378,6603,6556]]},{"id":"Ori","lines":[[1948,2004,1713,1852,1790,1879,2061,2124,2199,2159,2047,2135,2199,2124,2061,1948,1903,1852,1790,1543,1552,1567,1601,1567,1552,1543,1544,1580,1638,1676]]},{"id":"Pav","lines":[[7790,7913,8181,7913,7590,6982,6582,6745,6855,7074,7665,7913]]},{"id":"Peg","lines":[[8454,8650,8775,15,8775,8781,39,15,39,8781,8634,8450,8308]]},{"id":"Per","lines":[[936,941,1017,915,1017,1122,1220,1228,1203]]},{"id":"Phe","lines":[[99,322,429,440,429,322,338,191,25,99]]},{"id":"Pic","lines":[[2550,2042,2020]]},{"id":"PsA","lines":[[8728,8628,8478,8386,8326,8305,8431,8576,8695,8720,8728]]},{"id":"Psc","lines":[[360,383,352,360,437,510,596,489,294,224,9072,8969,8916,8878,8852,8911,8984,9004,8969]]},{"id":"Pup","lines":[[3185,3045,2948,2922,2773,2451,2553,2878,3165,3185]]},{"id":"Pyx","lines":[[3438,3468,3518]]},{"id":"Ret","lines":[[1336,1355,1247,1264,1175,1336]]},{"id":"Scl","lines":[[280,9016,8863,8937]]},{"id":"Sco","lines":[[5985,6084,5953,6084,5944,6084,6134,6165,6241,6247,6271,6380,6553,6615,6580,6527,6508]]},{"id":"Sct","lines":[[7063,6973,6930,6973,6884]]},{"id":"Ser","lines":[[6446,6561,6581,6869,7142],[5867,5879,5933,5867,5788,5854,5892,5881,6446]]},{"id":"Sex","lines":[[4119,3981,3909]]},{"id":"Sge","lines":[[7635,7536,7479,7536,7488]]},{"id":"Sgr","lines":[[7348,7581,7337,7581,7623,7650,7604,7440,7234,7121,7217,7264,7340,7342,7340,7264,7217,7150,7217,7121,7039,7194,7234,7194,7039,6913,6859,6746,6859,6879,6832]]},{"id":"Tau","lines":[[1910,1457,1346,1239,1030,1239,1346,1373,1409,1791]]},{"id":"Tel","lines":[[6783,6897,6905]]},{"id":"TrA","lines":[[6217,5671,5771,5897,6217]]},{"id":"Tri","lines":[[622,664,544,622]]},{"id":"Tuc","lines":[[8540,8502,8848,9076,77,126,8848]]},{"id":"UMa","lines":[[5191,5054,4905,4660,4554,4518,4377,4375,4377,4518,4335,4069,4033,4069,4335,4518,4554,4295,4301,4660,4301,3757,3323,3888,4295,3888,3775,3594,3569]]},{"id":"UMi","lines":[[424,6789,6322,5903,5563,5735,6116,5903]]},{"id":"Vel","lines":[[3206,3485,3734,3940,4216,4167,4023,3786,3634,3477,3426,3206]]},{"id":"Vir","lines":[[5056,4963,4826,4910,5107,5056]]},{"id":"Vol","lines":[[3615,3347,3223,2803,2736,3024,3223]]},{"id":"Vul","lines":[[7306,7405,7592]]}]\ No newline at end of file

Packages/MoonriseKit/Sources/SkyRenderer/SkyScene.swift added +72

@@ -0,0 +1,72 @@
	1	import Foundation
	2	import SkyEngine
	3
	4	public struct Star: Sendable {
	5	public var hr: Int
	6	public var ra: Double
	7	public var dec: Double
	8	public var magnitude: Double
	9	public var colorIndex: Double
	10	}
	11
	12	public struct Constellation: Sendable, Decodable {
	13	public var id: String
	14	/// Polylines of HR numbers.
	15	public var lines: [[Int]]
	16	}
	17
	18	public enum Catalog {
	19	/// Yale Bright Star Catalogue, 5th ed. (VizieR V/50): HR, RA and Dec (J2000, degrees), V, B−V.
	20	public static let stars: [Star] = {
	21	let url = Bundle.module.url(forResource: "bsc5", withExtension: "json")!
	22	let rows = try! JSONDecoder().decode([[Double]].self, from: Data(contentsOf: url))
	23	return rows.map { Star(hr: Int($0[0]), ra: $0[1], dec: $0[2], magnitude: $0[3], colorIndex: $0[4]) }
	24	}()
	25
	26	public static let constellations: [Constellation] = {
	27	let url = Bundle.module.url(forResource: "constellations", withExtension: "json")!
	28	return try! JSONDecoder().decode([Constellation].self, from: Data(contentsOf: url))
	29	}()
	30	}
	31
	32	public struct PlacedStar: Sendable {
	33	public var star: Star
	34	public var position: Horizontal
	35	}
	36
	37	public struct PlacedBody: Sendable {
	38	public var body: Body
	39	public var position: Horizontal
	40	public var magnitude: Double
	41	public var phaseFraction: Double
	42	}
	43
	44	/// Everything above (and just below) the horizon for one place and time.
	45	public struct SkyScene: Sendable {
	46	public var date: Date
	47	public var observer: Observer
	48	public var stars: [PlacedStar]
	49	public var starsByHR: [Int: Horizontal]
	50	public var bodies: [PlacedBody]
	51	/// Moon's elongation east of the sun, degrees (0 new, 180 full).
	52	public var moonPhase: Double
	53
	54	public init(date: Date, observer: Observer, magnitudeLimit: Double = 6.5) throws {
	55	self.date = date
	56	self.observer = observer
	57	let visible = Catalog.stars.filter { $0.magnitude <= magnitudeLimit }
	58	let positions = SkyEngine.horizontal(j2000: visible.map { ($0.ra, $0.dec) }, at: date, from: observer)
	59	stars = zip(visible, positions).map { PlacedStar(star: $0, position: $1) }
	60	starsByHR = Dictionary(uniqueKeysWithValues: stars.map { ($0.star.hr, $0.position) })
	61	bodies = try ([.moon] + Body.planets).map { body in
	62	let i = try SkyEngine.illumination(body, at: date)
	63	return PlacedBody(
	64	body: body,
	65	position: try SkyEngine.horizontal(body, at: date, from: observer),
	66	magnitude: i.magnitude,
	67	phaseFraction: i.phaseFraction
	68	)
	69	}
	70	moonPhase = try SkyEngine.moonPhase(at: date)
	71	}
	72	}

Packages/MoonriseKit/Sources/SkyRenderer/SkyView.swift added +173

@@ -0,0 +1,173 @@
	1	import SkyEngine
	2	import SwiftUI
	3
	4	/// Stereographic projection of the sky centred on a viewing direction.
	5	public struct Projection: Sendable {
	6	public var centerAzimuth: Double
	7	public var centerAltitude: Double
	8	/// Horizontal field of view in degrees.
	9	public var fieldOfView: Double
	10	public var size: CGSize
	11
	12	public init(centerAzimuth: Double, centerAltitude: Double, fieldOfView: Double, size: CGSize) {
	13	self.centerAzimuth = centerAzimuth
	14	self.centerAltitude = centerAltitude
	15	self.fieldOfView = fieldOfView
	16	self.size = size
	17	}
	18
	19	/// Screen point, or nil when the direction is behind the viewer.
	20	public func point(_ h: Horizontal) -> CGPoint? {
	21	let r = Double.pi / 180
	22	let alt = h.altitude * r, alt0 = centerAltitude * r
	23	let dAz = (h.azimuth - centerAzimuth) * r
	24	let cosC = sin(alt0) * sin(alt) + cos(alt0) * cos(alt) * cos(dAz)
	25	guard cosC > -0.2 else { return nil }
	26	let k = 2 / (1 + cosC)
	27	let x = k * cos(alt) * sin(dAz)
	28	let y = k * (cos(alt0) * sin(alt) - sin(alt0) * cos(alt) * cos(dAz))
	29	let scale = Double(size.width) / (4 * tan(fieldOfView * r / 4))
	30	return CGPoint(x: Double(size.width) / 2 + x * scale, y: Double(size.height) / 2 - y * scale)
	31	}
	32	}
	33
	34	public struct SkyStyle: Sendable {
	35	public var background = Color(red: 0.043, green: 0.078, blue: 0.141)
	36	public var ground = Color(red: 0.02, green: 0.035, blue: 0.06)
	37	public var line = Color(red: 0.30, green: 0.36, blue: 0.45)
	38	public var label = Color(red: 0.95, green: 0.95, blue: 0.93)
	39	public var muted = Color(red: 0.60, green: 0.64, blue: 0.70)
	40	public var moonLight = Color(red: 0.93, green: 0.91, blue: 0.85)
	41	public var moonDark = Color(red: 0.16, green: 0.20, blue: 0.27)
	42
	43	public init() {}
	44
	45	/// Star tint from B−V colour index, kept pale.
	46	func starColor(_ bv: Double) -> Color {
	47	let t = min(max((bv + 0.3) / 2.0, 0), 1)
	48	return Color(red: 0.80 + 0.20 * t, green: 0.86 - 0.06 * t, blue: 1.0 - 0.32 * t)
	49	}
	50	}
	51
	52	public struct SkyView: View {
	53	public var scene: SkyScene
	54	public var centerAzimuth: Double
	55	public var centerAltitude: Double
	56	public var fieldOfView: Double
	57	public var style = SkyStyle()
	58
	59	public init(scene: SkyScene, centerAzimuth: Double = 180, centerAltitude: Double = 55, fieldOfView: Double = 110) {
	60	self.scene = scene
	61	self.centerAzimuth = centerAzimuth
	62	self.centerAltitude = centerAltitude
	63	self.fieldOfView = fieldOfView
	64	}
	65
	66	public var body: some View {
	67	Canvas { context, size in
	68	let p = Projection(centerAzimuth: centerAzimuth, centerAltitude: centerAltitude, fieldOfView: fieldOfView, size: size)
	69	context.fill(Path(CGRect(origin: .zero, size: size)), with: .color(style.background))
	70	drawConstellations(&context, p)
	71	drawStars(&context, p)
	72	drawBodies(&context, p)
	73	drawHorizon(&context, p, size: size)
	74	}
	75	}
	76
	77	func drawConstellations(_ context: inout GraphicsContext, _ p: Projection) {
	78	var path = Path()
	79	for c in Catalog.constellations {
	80	for line in c.lines {
	81	for (a, b) in zip(line, line.dropFirst()) {
	82	guard let ha = scene.starsByHR[a], let hb = scene.starsByHR[b],
	83	ha.altitude > -5 \|\| hb.altitude > -5,
	84	let pa = p.point(ha), let pb = p.point(hb) else { continue }
	85	path.move(to: pa)
	86	path.addLine(to: pb)
	87	}
	88	}
	89	}
	90	context.stroke(path, with: .color(style.line), lineWidth: 0.6)
	91	}
	92
	93	func drawStars(_ context: inout GraphicsContext, _ p: Projection) {
	94	for s in scene.stars where s.position.altitude > 0 {
	95	guard let pt = p.point(s.position) else { continue }
	96	let r = max(0.3, 2.6 - 0.42 * s.star.magnitude)
	97	let opacity = min(1, max(0.25, 1.15 - 0.13 * s.star.magnitude))
	98	context.fill(Path(ellipseIn: CGRect(x: pt.x - r, y: pt.y - r, width: 2 * r, height: 2 * r)), with: .color(style.starColor(s.star.colorIndex).opacity(opacity)))
	99	}
	100	}
	101
	102	func drawBodies(_ context: inout GraphicsContext, _ p: Projection) {
	103	// Naked-eye bodies only; Neptune (about mag 7.8) is left out.
	104	for b in scene.bodies where b.position.altitude > 0 && b.magnitude <= 6 {
	105	guard let pt = p.point(b.position) else { continue }
	106	if b.body == .moon {
	107	drawMoon(&context, at: pt, radius: 14, fraction: b.phaseFraction, waxing: scene.moonPhase < 180)
	108	label(&context, "Moon \(Int((b.phaseFraction * 100).rounded()))%", at: CGPoint(x: pt.x - 20, y: pt.y), anchor: .trailing)
	109	} else {
	110	let r = max(2.0, 3.6 - 0.35 * b.magnitude)
	111	context.fill(Path(ellipseIn: CGRect(x: pt.x - r, y: pt.y - r, width: 2 * r, height: 2 * r)), with: .color(Color(red: 0.95, green: 0.84, blue: 0.60)))
	112	var tick = Path()
	113	tick.move(to: CGPoint(x: pt.x + r + 3, y: pt.y))
	114	tick.addLine(to: CGPoint(x: pt.x + r + 15, y: pt.y))
	115	context.stroke(tick, with: .color(style.muted), lineWidth: 0.6)
	116	label(&context, b.body.rawValue.capitalized, at: CGPoint(x: pt.x + r + 18, y: pt.y), anchor: .leading)
	117	}
	118	}
	119	}
	120
	121	func drawMoon(_ context: inout GraphicsContext, at c: CGPoint, radius r: Double, fraction: Double, waxing: Bool) {
	122	let disc = CGRect(x: c.x - r, y: c.y - r, width: 2 * r, height: 2 * r)
	123	context.fill(Path(ellipseIn: disc), with: .color(style.moonDark))
	124	// Lit limb: a half disc plus or minus the terminator ellipse.
	125	let side: Double = waxing ? 1 : -1
	126	let e = r * abs(1 - 2 * fraction)
	127	var lit = Path()
	128	lit.move(to: CGPoint(x: c.x, y: c.y - r))
	129	lit.addArc(center: c, radius: r, startAngle: .degrees(-90), endAngle: .degrees(90), clockwise: side < 0)
	130	lit.addEllipseArc(center: c, rx: e, ry: r, gibbous: fraction > 0.5, side: side)
	131	lit.closeSubpath()
	132	context.fill(lit, with: .color(style.moonLight))
	133	}
	134
	135	func drawHorizon(_ context: inout GraphicsContext, _ p: Projection, size: CGSize) {
	136	var edge: [CGPoint] = []
	137	var az = centerAzimuth - fieldOfView
	138	while az <= centerAzimuth + fieldOfView {
	139	if let pt = p.point(Horizontal(altitude: 0, azimuth: az)) { edge.append(pt) }
	140	az += 1
	141	}
	142	guard let first = edge.first, let last = edge.last else { return }
	143	var ground = Path()
	144	ground.move(to: first)
	145	for pt in edge.dropFirst() { ground.addLine(to: pt) }
	146	ground.addLine(to: CGPoint(x: last.x, y: size.height + 10))
	147	ground.addLine(to: CGPoint(x: first.x, y: size.height + 10))
	148	ground.closeSubpath()
	149	context.fill(ground, with: .color(style.ground))
	150	for (name, az) in [("SE", 135.0), ("S", 180.0), ("SW", 225.0), ("E", 90.0), ("W", 270.0)] {
	151	guard let pt = p.point(Horizontal(altitude: 0, azimuth: az)), pt.x > 0, pt.x < size.width else { continue }
	152	label(&context, name, at: CGPoint(x: pt.x, y: pt.y + 18), anchor: .center, color: style.muted)
	153	}
	154	}
	155
	156	func label(_ context: inout GraphicsContext, _ text: String, at point: CGPoint, anchor: UnitPoint, color: Color? = nil) {
	157	let t = Text(text).font(.system(size: 11, weight: .regular)).foregroundStyle(color ?? style.label)
	158	context.draw(t, at: point, anchor: anchor)
	159	}
	160	}
	161
	162	extension Path {
	163	/// Half of the terminator ellipse, from the moon's bottom to its top.
	164	mutating func addEllipseArc(center c: CGPoint, rx: Double, ry: Double, gibbous: Bool, side: Double) {
	165	// Gibbous: terminator bulges into the dark half; crescent: into the lit half.
	166	let direction = gibbous ? -side : side
	167	let steps = 24
	168	for i in 0...steps {
	169	let a = Double.pi / 2 - Double.pi * Double(i) / Double(steps)
	170	addLine(to: CGPoint(x: c.x + direction * rx * cos(a), y: c.y + ry * sin(a)))
	171	}
	172	}
	173	}

Packages/MoonriseKit/Tests/SkyEngineTests/HorizonsTests.swift added +67

@@ -0,0 +1,67 @@
	1	import Foundation
	2	import Testing
	3	@testable import SkyEngine
	4
	5	// Reference values from JPL Horizons (ssd.jpl.nasa.gov/api/horizons.api), fetched 2026-10-17.
	6	// Observer table: site -87.6298 E, 41.8781 N, 0 km; 2026-10-17 02:00 UT; quantities 2 (apparent
	7	// RA/Dec, degrees) and 4 (airless apparent azimuth/elevation).
	8	// Vector table: CENTER 500@10, REF_PLANE FRAME, 2026-10-17 00:00 UT, AU.
	9
	10	let chicago = Observer(latitude: 41.8781, longitude: -87.6298)
	11	let observed = Date(timeIntervalSince1970: 1_792_202_400) // 2026-10-17T02:00:00Z
	12	let vectorEpoch = Date(timeIntervalSince1970: 1_792_195_200) // 2026-10-17T00:00:00Z
	13
	14	struct HorizonsRow {
	15	var body: Body
	16	var raDegrees: Double
	17	var dec: Double
	18	var azimuth: Double
	19	var altitude: Double
	20	}
	21
	22	let observerRows: [HorizonsRow] = [
	23	HorizonsRow(body: .moon, raDegrees: 276.63979, dec: -28.01156, azimuth: 223.832359, altitude: 5.580273),
	24	HorizonsRow(body: .mars, raDegrees: 133.60867, dec: 18.78232, azimuth: 15.406574, altitude: -27.902306),
	25	HorizonsRow(body: .jupiter, raDegrees: 144.84484, dec: 14.69461, azimuth: 3.616329, altitude: -33.353920),
	26	HorizonsRow(body: .saturn, raDegrees: 10.55474, dec: 1.59612, azimuth: 124.822854, altitude: 34.510943),
	27	]
	28
	29	/// One arcminute, Astronomy Engine's stated accuracy.
	30	let arcminute = 1.0 / 60
	31
	32	func angularDifference(_ a: Double, _ b: Double) -> Double {
	33	abs(remainder(a - b, 360))
	34	}
	35
	36	@Test(arguments: observerRows)
	37	func apparentEquatorialMatchesHorizons(_ row: HorizonsRow) throws {
	38	let eq = try SkyEngine.equatorial(row.body, at: observed, from: chicago)
	39	let raError = angularDifference(eq.rightAscension * 15, row.raDegrees) * cos(row.dec * .pi / 180)
	40	#expect(raError < arcminute, "\(row.body) RA off by \(raError * 60)'")
	41	#expect(abs(eq.declination - row.dec) < arcminute, "\(row.body) Dec off by \(abs(eq.declination - row.dec) * 60)'")
	42	}
	43
	44	@Test(arguments: observerRows)
	45	func horizontalMatchesHorizons(_ row: HorizonsRow) throws {
	46	let hor = try SkyEngine.horizontal(row.body, at: observed, from: chicago)
	47	let azError = angularDifference(hor.azimuth, row.azimuth) * cos(row.altitude * .pi / 180)
	48	#expect(azError < arcminute, "\(row.body) azimuth off by \(azError * 60)'")
	49	#expect(abs(hor.altitude - row.altitude) < arcminute, "\(row.body) altitude off by \(abs(hor.altitude - row.altitude) * 60)'")
	50	}
	51
	52	@Test(arguments: [
	53	(Body.jupiter, SIMD3(-3.581981680856141, 3.573182031399209, 1.618755638647523)),
	54	(Body.saturn, SIMD3(9.237054585455835, 1.860186986025053, 0.3705349659085789)),
	55	])
	56	func heliocentricMatchesHorizons(_ body: Body, _ expected: SIMD3<Double>) throws {
	57	let v = try SkyEngine.heliocentric(body, at: vectorEpoch)
	58	let d = v - expected
	59	let error = (d * d).sum().squareRoot()
	60	let angle = error / (expected * expected).sum().squareRoot() * 180 / .pi
	61	#expect(angle < arcminute, "\(body) off by \(error) AU (\(angle * 3600)\")")
	62	}
	63
	64	@Test func moonPhaseIsWaxing() throws {
	65	let phase = try SkyEngine.moonPhase(at: observed)
	66	#expect(phase > 0 && phase < 180)
	67	}

Packages/MoonriseKit/Tests/SkyRendererTests/SkyRenderTests.swift added +44

@@ -0,0 +1,44 @@
	1	import Foundation
	2	import SkyEngine
	3	import SwiftUI
	4	import Testing
	5	@testable import SkyRenderer
	6
	7	let chicago = Observer(latitude: 41.8781, longitude: -87.6298)
	8	let evening = Date(timeIntervalSince1970: 1_792_202_400) // 2026-10-17T02:00:00Z, 21:00 CDT
	9
	10	@Test func catalogLoads() {
	11	#expect(Catalog.stars.count > 9_000)
	12	#expect(Catalog.stars.contains { $0.hr == 2491 && $0.magnitude < -1 }) // Sirius
	13	}
	14
	15	@Test func sceneHasSaturnUpAndMarsDown() throws {
	16	let scene = try SkyScene(date: evening, observer: chicago)
	17	let saturn = try #require(scene.bodies.first { $0.body == .saturn })
	18	let mars = try #require(scene.bodies.first { $0.body == .mars })
	19	#expect(saturn.position.altitude > 30)
	20	#expect(mars.position.altitude < 0)
	21	}
	22
	23	/// Renders the sky to a PNG and reports timings. Set SKY_RENDER_OUT to keep the image.
	24	@MainActor
	25	@Test func renderStaticSky() throws {
	26	let clock = ContinuousClock()
	27	var scene: SkyScene!
	28	let build = try clock.measure { scene = try SkyScene(date: evening, observer: chicago) }
	29
	30	let renderer = ImageRenderer(content: SkyView(scene: scene).frame(width: 393, height: 852))
	31	renderer.scale = 3
	32	var image: CGImage?
	33	let render = clock.measure { image = renderer.cgImage }
	34	let cg = try #require(image)
	35
	36	print("scene: \(scene.stars.count) stars, build \(build); render \(cg.width)x\(cg.height) in \(render)")
	37
	38	if let out = ProcessInfo.processInfo.environment["SKY_RENDER_OUT"] {
	39	let url = URL(fileURLWithPath: out)
	40	let dest = try #require(CGImageDestinationCreateWithURL(url as CFURL, "public.png" as CFString, 1, nil))
	41	CGImageDestinationAddImage(dest, cg, nil)
	42	#expect(CGImageDestinationFinalize(dest))
	43	}
	44	}

THIRD_PARTY.org added +7

@@ -0,0 +1,7 @@
	1	#+title: Third-party code and data
	2
	3	\| Component \| Path \| Licence \| Source \|
	4	\|-
	5	\| Astronomy Engine v2.1.19, Copyright (c) 2019-2025 Don Cross \| =Packages/MoonriseKit/Sources/CAstronomy= \| MIT (=LICENSE= alongside) \| https://github.com/cosinekitty/astronomy \|
	6	\| Yale Bright Star Catalogue, 5th rev. ed. (Hoffleit & Warren 1991) \| =Packages/MoonriseKit/Sources/SkyRenderer/Resources/bsc5.json= \| See VizieR policy; licence statement pending \| https://cdsarc.cds.unistra.fr/viz-bin/cat/V/50 \|
	7	\| ConstellationLines v1.4, Copyright (c) 2005-2026 Marc van der Sluys \| =Packages/MoonriseKit/Sources/SkyRenderer/Resources/constellations.json= \| CC BY 4.0 \| https://github.com/MarcvdSluys/ConstellationLines, doi:10.5281/zenodo.10397192 \|

spikes/apns-worker/README.org added +34

@@ -0,0 +1,34 @@
	1	#+title: apns-worker spike
	2
	3	Checks that a deployed Cloudflare Worker can send APNs pushes. APNs only
	4	speaks HTTP/2; =wrangler dev= does not (workerd issue #4841), so test
	5	deployed.
	6
	7	* probe (no Apple credentials)
	8	#+begin_src sh
	9	wrangler deploy
	10	curl https://moonrise-apns-spike.<subdomain>.workers.dev/probe
	11	#+end_src
	12
	13	Sends from a throwaway key to a dummy token on the sandbox host. Any APNs
	14	JSON reason (expected: 403 =InvalidProviderToken=) means the HTTP/2
	15	connection worked. A network error means it did not.
	16
	17	* real push
	18	Needs an APNs auth key (.p8), its key ID, the team ID, the app's bundle ID,
	19	and a sandbox device token from a development build.
	20
	21	#+begin_src sh
	22	# set APNS_KEY_ID, APNS_TEAM_ID, APNS_TOPIC in wrangler.jsonc
	23	wrangler secret put APNS_KEY < AuthKey_XXXXXXXXXX.p8
	24	wrangler secret put SPIKE_SECRET
	25	wrangler deploy
	26	curl -X POST https://moonrise-apns-spike.<subdomain>.workers.dev/push \
	27	-H "authorization: Bearer $SPIKE_SECRET" \
	28	-d '{"token":"<device token hex>","sandbox":true}'
	29	#+end_src
	30
	31	* test
	32	#+begin_src sh
	33	node --test test/
	34	#+end_src

spikes/apns-worker/package.json added +9

@@ -0,0 +1,9 @@
	1	{
	2	"name": "moonrise-apns-spike",
	3	"private": true,
	4	"type": "module",
	5	"scripts": {
	6	"test": "node --test test/",
	7	"deploy": "wrangler deploy"
	8	}
	9	}

spikes/apns-worker/src/apns.ts added +78

@@ -0,0 +1,78 @@
	1	// APNs provider-token auth and sending, using only Web APIs (Workers, Node).
	2
	3	export interface ApnsConfig {
	4	keyId: string;
	5	teamId: string;
	6	/** Contents of the .p8 key file (PKCS#8 PEM). */
	7	privateKey: string;
	8	/** App bundle ID. */
	9	topic: string;
	10	}
	11
	12	export interface ApnsResult {
	13	status: number;
	14	apnsId: string \| null;
	15	reason: string \| null;
	16	}
	17
	18	const encoder = new TextEncoder();
	19
	20	function base64url(bytes: Uint8Array): string {
	21	let s = "";
	22	for (const b of bytes) s += String.fromCharCode(b);
	23	return btoa(s).replace(/\+/g, "-").replace(/\//g, "_").replace(/=+$/, "");
	24	}
	25
	26	function pemToDer(pem: string): Uint8Array {
	27	const body = pem.replace(/-----[^-]+-----/g, "").replace(/\s+/g, "");
	28	return Uint8Array.from(atob(body), (c) => c.charCodeAt(0));
	29	}
	30
	31	export async function importKey(pem: string): Promise<CryptoKey> {
	32	return crypto.subtle.importKey("pkcs8", pemToDer(pem), { name: "ECDSA", namedCurve: "P-256" }, false, ["sign"]);
	33	}
	34
	35	/** ES256 provider token. WebCrypto returns the raw r\|\|s signature JWS expects. */
	36	export async function providerToken(keyId: string, teamId: string, key: CryptoKey, issuedAt = Math.floor(Date.now() / 1000)): Promise<string> {
	37	const header = base64url(encoder.encode(JSON.stringify({ alg: "ES256", kid: keyId })));
	38	const claims = base64url(encoder.encode(JSON.stringify({ iss: teamId, iat: issuedAt })));
	39	const input = `${header}.${claims}`;
	40	const sig = await crypto.subtle.sign({ name: "ECDSA", hash: "SHA-256" }, key, encoder.encode(input));
	41	return `${input}.${base64url(new Uint8Array(sig))}`;
	42	}
	43
	44	/** Apple accepts a token for up to 60 minutes and rejects refreshes more often than every 20. */
	45	let cached: { token: string; issuedAt: number; keyId: string } \| null = null;
	46
	47	async function token(config: ApnsConfig): Promise<string> {
	48	const now = Math.floor(Date.now() / 1000);
	49	if (cached && cached.keyId === config.keyId && now - cached.issuedAt < 50 * 60) return cached.token;
	50	const t = await providerToken(config.keyId, config.teamId, await importKey(config.privateKey), now);
	51	cached = { token: t, issuedAt: now, keyId: config.keyId };
	52	return t;
	53	}
	54
	55	export async function send(config: ApnsConfig, deviceToken: string, payload: unknown, sandbox: boolean): Promise<ApnsResult> {
	56	const host = sandbox ? "api.sandbox.push.apple.com" : "api.push.apple.com";
	57	const res = await fetch(`https://${host}/3/device/${deviceToken}`, {
	58	method: "POST",
	59	headers: {
	60	authorization: `bearer ${await token(config)}`,
	61	"apns-topic": config.topic,
	62	"apns-push-type": "alert",
	63	"apns-priority": "10",
	64	"content-type": "application/json",
	65	},
	66	body: JSON.stringify(payload),
	67	});
	68	let reason: string \| null = null;
	69	if (!res.ok) {
	70	const text = await res.text();
	71	try {
	72	reason = (JSON.parse(text) as { reason?: string }).reason ?? text;
	73	} catch {
	74	reason = text;
	75	}
	76	}
	77	return { status: res.status, apnsId: res.headers.get("apns-id"), reason };
	78	}

spikes/apns-worker/src/index.ts added +58

@@ -0,0 +1,58 @@
	1	// Spike: does a deployed Worker reach APNs over HTTP/2? APNs rejects HTTP/1.1,
	2	// so any APNs response with an apns-id answers yes.
	3
	4	import { send } from "./apns";
	5
	6	interface Env {
	7	APNS_KEY_ID: string;
	8	APNS_TEAM_ID: string;
	9	APNS_TOPIC: string;
	10	APNS_KEY: string;
	11	SPIKE_SECRET: string;
	12	}
	13
	14	interface PushRequest {
	15	token: string;
	16	sandbox?: boolean;
	17	title?: string;
	18	body?: string;
	19	}
	20
	21	export default {
	22	async fetch(request: Request, env: Env): Promise<Response> {
	23	const url = new URL(request.url);
	24	if (request.method === "GET" && url.pathname === "/probe") return probe();
	25	if (request.method !== "POST" \|\| url.pathname !== "/push") return new Response("not found", { status: 404 });
	26	if (request.headers.get("authorization") !== `Bearer ${env.SPIKE_SECRET}`) return new Response("unauthorized", { status: 401 });
	27
	28	const req = (await request.json()) as PushRequest;
	29	if (!/^[0-9a-f]{64,200}$/i.test(req.token ?? "")) return new Response("bad token", { status: 400 });
	30
	31	const result = await send(
	32	{ keyId: env.APNS_KEY_ID, teamId: env.APNS_TEAM_ID, privateKey: env.APNS_KEY, topic: env.APNS_TOPIC },
	33	req.token,
	34	{ aps: { alert: { title: req.title ?? "Moonrise", body: req.body ?? "Push from a Cloudflare Worker" } } },
	35	req.sandbox ?? true,
	36	);
	37	return Response.json(result, { status: result.status === 200 ? 200 : 502 });
	38	},
	39	} satisfies ExportedHandler<Env>;
	40
	41	/** Sends with a throwaway key and token. Needs no Apple credentials: an APNs JSON
	42	* error (e.g. 403 InvalidProviderToken) still proves the HTTP/2 connection worked. */
	43	async function probe(): Promise<Response> {
	44	const pair = (await crypto.subtle.generateKey({ name: "ECDSA", namedCurve: "P-256" }, true, ["sign"])) as CryptoKeyPair;
	45	const der = new Uint8Array((await crypto.subtle.exportKey("pkcs8", pair.privateKey)) as ArrayBuffer);
	46	const pem = `-----BEGIN PRIVATE KEY-----\n${btoa(String.fromCharCode(...der))}\n-----END PRIVATE KEY-----`;
	47	try {
	48	const result = await send(
	49	{ keyId: "PROBE00000", teamId: "PROBE00000", privateKey: pem, topic: "org.example.probe" },
	50	"0".repeat(64),
	51	{ aps: { alert: "probe" } },
	52	true,
	53	);
	54	return Response.json({ http2: result.apnsId !== null \|\| result.reason !== null, ...result });
	55	} catch (e) {
	56	return Response.json({ http2: false, error: String(e) }, { status: 502 });
	57	}
	58	}

spikes/apns-worker/test/apns.test.ts added +25

@@ -0,0 +1,25 @@
	1	import assert from "node:assert/strict";
	2	import { test } from "node:test";
	3	import { importKey, providerToken } from "../src/apns.ts";
	4
	5	function b64urlDecode(s: string): Uint8Array {
	6	const b64 = s.replace(/-/g, "+").replace(/_/g, "/") + "=".repeat((4 - (s.length % 4)) % 4);
	7	return Uint8Array.from(atob(b64), (c) => c.charCodeAt(0));
	8	}
	9
	10	test("provider token is a valid ES256 JWT signed by the .p8 key", async () => {
	11	const pair = await crypto.subtle.generateKey({ name: "ECDSA", namedCurve: "P-256" }, true, ["sign", "verify"]);
	12	const der = new Uint8Array(await crypto.subtle.exportKey("pkcs8", pair.privateKey));
	13	const pem = `-----BEGIN PRIVATE KEY-----\n${btoa(String.fromCharCode(...der)).replace(/(.{64})/g, "$1\n")}\n-----END PRIVATE KEY-----\n`;
	14
	15	const jwt = await providerToken("ABC123DEFG", "TEAM123456", await importKey(pem), 1_792_202_400);
	16	const [h, c, s] = jwt.split(".");
	17
	18	assert.deepEqual(JSON.parse(new TextDecoder().decode(b64urlDecode(h))), { alg: "ES256", kid: "ABC123DEFG" });
	19	assert.deepEqual(JSON.parse(new TextDecoder().decode(b64urlDecode(c))), { iss: "TEAM123456", iat: 1_792_202_400 });
	20
	21	const sig = b64urlDecode(s);
	22	assert.equal(sig.length, 64);
	23	const ok = await crypto.subtle.verify({ name: "ECDSA", hash: "SHA-256" }, pair.publicKey, sig, new TextEncoder().encode(`${h}.${c}`));
	24	assert.ok(ok);
	25	});

spikes/apns-worker/wrangler.jsonc added +11

@@ -0,0 +1,11 @@
	1	{
	2	"name": "moonrise-apns-spike",
	3	"main": "src/index.ts",
	4	"compatibility_date": "2026-10-01",
	5	"vars": {
	6	"APNS_KEY_ID": "",
	7	"APNS_TEAM_ID": "",
	8	"APNS_TOPIC": ""
	9	}
	10	// Secrets: APNS_KEY (.p8 contents), SPIKE_SECRET. Set with `wrangler secret put`.
	11	}

@@ -0,0 +1,7 @@
	1	#+title: Third-party code and data
	2
	3	\| Component \| Path \| Licence \| Source \|
	4	\|-
	5	\| Astronomy Engine v2.1.19, Copyright (c) 2019-2025 Don Cross \| =Packages/MoonriseKit/Sources/CAstronomy= \| MIT (=LICENSE= alongside) \| https://github.com/cosinekitty/astronomy \|
	6	\| Yale Bright Star Catalogue, 5th rev. ed. (Hoffleit & Warren 1991) \| =Packages/MoonriseKit/Sources/SkyRenderer/Resources/bsc5.json= \| See VizieR policy; licence statement pending \| https://cdsarc.cds.unistra.fr/viz-bin/cat/V/50 \|
	7	\| ConstellationLines v1.4, Copyright (c) 2005-2026 Marc van der Sluys \| =Packages/MoonriseKit/Sources/SkyRenderer/Resources/constellations.json= \| CC BY 4.0 \| https://github.com/MarcvdSluys/ConstellationLines, doi:10.5281/zenodo.10397192 \|

Commit 94470ad726

Commit `94470ad726`