Commit `8592cd1a6d`

8592cd1a6de1ce83d21c53dd06f22c618d79d0e6

parent: 913cbaccdb

Verified · cmc

cmc <hello@cleberg.net> · 2026-10-19 06:15 UTC

3D solar system: moons, dwarf planets, spacecraft, comets and meteor showers

Layout: unified · split

App/Sources/SolarSystem3D.swift +481 −118

		@@ -2,6 +2,7 @@ import Feeds
2	2	import Library
3	3	import RealityKit
4	4	import SkyEngine
	5	import SkyRenderer
5	6	import SwiftUI
6	7	import UIKit
7	8
		@@ -32,6 +33,11 @@ struct SolarPlanet: Identifiable, Sendable {
32	33	return SolarPlanet(id: id, body: body, radiusKm: d.radiusKm ?? 6371, color: d.color ?? "#cccccc", tiltDeg: d.axialTiltDeg ?? 0, periodDays: period)
33	34	}
34	35
	36	/// Pluto, which Astronomy Engine covers, drawn with the dwarf planets.
	37	static let pluto: SolarPlanet? = Library.page(id: "pluto")?.drawing.map {
	38	SolarPlanet(id: "pluto", body: .pluto, radiusKm: $0.radiusKm ?? 1188, color: $0.color ?? "#cdb79e", tiltDeg: $0.axialTiltDeg ?? 0, periodDays: 90_560)
	39	}
	40
35	41	/// Heliocentric position on J2000 ecliptic axes, AU.
36	42	func position(at date: Date) -> SIMD3<Double> {
37	43	if let body { return (try? SkyEngine.heliocentricEcliptic(body, at: date)) ?? .zero }
		@@ -39,6 +45,36 @@ struct SolarPlanet: Identifiable, Sendable {
39	45	}
40	46	}
41	47
	48	/// A moon from its Library page: exact positions for Earth's Moon and Jupiter's four big moons,
	49	/// a circular orbit in the planet's equator plane (at an arbitrary starting point) for the rest.
	50	struct SolarMoon: Identifiable, Sendable {
	51	var id: String
	52	var parent: String
	53	var distanceKm: Double
	54	var periodDays: Double
	55	var radiusKm: Double
	56	var color: String
	57
	58	static let galilean = ["io", "europa", "ganymede", "callisto"]
	59
	60	static let all: [SolarMoon] = Library.pages(in: .moons).compactMap { p in
	61	guard let dist = p.facts.first(where: { $0.label.hasPrefix("Mean distance from") }),
	62	let period = p.facts.first(where: { $0.label.hasPrefix("Orbital period") }),
	63	let km = number(dist.value), let days = number(period.value) else { return nil }
	64	let parent = dist.label.replacingOccurrences(of: "Mean distance from ", with: "").lowercased()
	65	let retrograde = p.facts.contains { $0.value == "Retrograde" }
	66	return SolarMoon(id: p.id, parent: parent, distanceKm: km, periodDays: retrograde ? -days : days,
	67	radiusKm: p.drawing?.radiusKm ?? 100, color: p.drawing?.color ?? "#999999")
	68	}
	69
	70	/// 1070400 from "1,070,400 km"; 0.319 from "0.319 days (7 h 39 m)".
	71	static func number(_ s: String) -> Double? {
	72	s.split(separator: " ").first.flatMap { Double($0.replacingOccurrences(of: ",", with: "")) }
	73	}
	74
	75	var isExact: Bool { id == "moon" \|\| Self.galilean.contains(id) }
	76	}
	77
42	78	/// Maps ecliptic AU to scene metres (y up) and gives drawn radii for each scale.
43	79	struct SolarMapping {
44	80	var scale: SolarScale
		@@ -54,10 +90,20 @@ struct SolarMapping {
54	90	return SIMD3(Float(u.x), Float(u.z), Float(-u.y))
55	91	}
56	92
	93	/// Ecliptic axes to scene axes without changing length.
	94	static func axes(_ v: SIMD3<Double>) -> SIMD3<Float> { SIMD3(Float(v.x), Float(v.z), Float(-v.y)) }
	95
57	96	func radius(km: Double) -> Float {
58	97	scale == .compressed ? Float(0.09 * pow(km / 6371, 0.45)) : Float(km / Self.auKm)
59	98	}
60	99
	100	/// How far from its planet a moon is drawn: log-squeezed in compressed scale, true otherwise.
	101	func moonDistance(km: Double, planetRadiusKm: Double) -> Float {
	102	scale == .compressed
	103	? radius(km: planetRadiusKm) * Float(1.2 + 1.6 * log10(max(km / planetRadiusKm, 1.5)))
	104	: Float(km / Self.auKm)
	105	}
	106
61	107	var sunRadius: Float { scale == .compressed ? 0.35 : Float(Self.sunRadiusKm / Self.auKm) }
62	108	}
63	109
		@@ -116,16 +162,41 @@ struct SolarWeather: Equatable {
116	162	}
117	163	}
118	164
	165	/// Which optional layers are drawn.
	166	struct SolarLayers: Equatable {
	167	var moons = true
	168	var dwarfs = true
	169	var craft = true
	170	var comets = true
	171	}
	172
	173	/// Anything the scene draws and can label or fly to.
	174	struct SolarMarker {
	175	enum Kind { case sun, planet, moon, dwarf, craft, comet }
	176	var id: String
	177	var name: String
	178	var kind: Kind
	179	var scene: SIMD3<Float>
	180	/// Drawn radius in scene units (for dots, the dot's size at the current zoom).
	181	var radius: Float
	182	var visible: Bool
	183	}
	184
119	185	/// Entities created once and moved on each update.
120	186	@MainActor
121	187	final class SolarSceneEntities {
122	188	let root = Entity()
123	189	let camera = PerspectiveCamera()
124	190	let sun = ModelEntity()
125		var planets: [String: ModelEntity] = [:]
	191	var bodies: [String: ModelEntity] = [:]
126	192	var nights: [String: ModelEntity] = [:]
	193	var tails: [String: ModelEntity] = [:]
127	194	var orbits: [String: ModelEntity] = [:]
128	195	var orbitsBuilt: (SolarScale, Float)?
	196	var paths: [String: ModelEntity] = [:]
	197	var pathsBuilt: (SolarScale, Float, Int)?
	198	let debris = ModelEntity()
	199	var debrisBuilt: (SolarScale, Float, String)?
129	200	let flare = ModelEntity()
130	201	let aurora = Entity()
131	202	}
		@@ -147,8 +218,21 @@ struct SolarSystem3DView: View {
147	218	@State private var flight: Task<Void, Never>?
148	219	@State private var pulse = false
149	220	@State private var viewSize = CGSize(width: 400, height: 600)
	221	@AppStorage("solar.moons") private var showMoons = true
	222	@AppStorage("solar.dwarfs") private var showDwarfs = true
	223	@AppStorage("solar.craft") private var showCraft = true
	224	@AppStorage("solar.comets") private var showComets = true
150	225
151	226	private var mapping: SolarMapping { SolarMapping(scale: scale) }
	227	private var layers: SolarLayers { SolarLayers(moons: showMoons, dwarfs: showDwarfs, craft: showCraft, comets: showComets) }
	228
	229	private static let mainComets: Set<String> = ["halley", "encke", "67p"]
	230	private static let craftColor = UIColor(red: 0.88, green: 0.24, blue: 0.19, alpha: 1)
	231
	232	/// Meteor showers within a week of their peak, with a parent orbit to draw.
	233	private var activeShowers: [MeteorShower] {
	234	MeteorShower.major.filter { $0.parent != nil && abs($0.daysToPeak(from: date)) <= 7 }
	235	}
152	236
153	237	var body: some View {
154	238	GeometryReader { geo in
		@@ -165,12 +249,16 @@ struct SolarSystem3DView: View {
165	249	labels(size: geo.size).allowsHitTesting(false)
166	250
167	251	VStack(spacing: 8) {
168		if let s = selected, let planet = planetOrSun(s) { card(planet) }
	252	if let s = selected { card(s) }
169	253	Spacer()
170		Text(live ? weather.summary : "Live space weather is shown only for today.")
171		.font(.caption2).dimmed(0.75)
172		.padding(.horizontal, 10).padding(.vertical, 6)
173		.background(Color.black.opacity(0.6), in: Capsule())
	254	HStack(alignment: .bottom) {
	255	Text(summary)
	256	.font(.caption2).dimmed(0.8)
	257	.padding(.horizontal, 10).padding(.vertical, 6)
	258	.background(Color.black.opacity(0.7), in: RoundedRectangle(cornerRadius: 10))
	259	Spacer(minLength: 8)
	260	layerMenu
	261	}
174	262	}
175	263	.padding(12)
176	264	}
		@@ -179,7 +267,7 @@ struct SolarSystem3DView: View {
179	267	.onChange(of: geo.size) { viewSize = geo.size }
180	268	}
181	269	.accessibilityElement(children: .contain)
182		.accessibilityLabel("3D solar system. Drag to turn, pinch to zoom, tap a planet to learn about it.")
	270	.accessibilityLabel("3D solar system. Drag to turn, pinch to zoom, tap a body to learn about it.")
183	271	.onChange(of: scale) { resetView() }
184	272	.task { await loadWeather() }
185	273	.task {
		@@ -190,6 +278,102 @@ struct SolarSystem3DView: View {
190	278	}
191	279	}
192	280
	281	private var summary: String {
	282	var lines: [String] = []
	283	if let s = activeShowers.first, let parent = KeplerOrbit.comets.first(where: { $0.id == s.parent }) {
	284	let d = s.daysToPeak(from: date)
	285	let when = abs(d) < 1 ? "peak today" : d > 0 ? "peak in \(Int(d.rounded())) days" : "peaked \(Int((-d).rounded())) days ago"
	286	lines.append("\(s.name) \(when): Earth is crossing debris from \(parent.name).")
	287	}
	288	lines.append(live ? weather.summary : "Live space weather is shown only for today.")
	289	return lines.joined(separator: "\n")
	290	}
	291
	292	private var layerMenu: some View {
	293	Menu {
	294	Toggle("Moons", isOn: $showMoons)
	295	Toggle("Dwarf planets", isOn: $showDwarfs)
	296	Toggle("Spacecraft", isOn: $showCraft)
	297	Toggle("Comets and meteor showers", isOn: $showComets)
	298	} label: {
	299	Image(systemName: "square.3.layers.3d").font(.body).frame(width: 44, height: 44)
	300	.background(Color.black.opacity(0.7), in: Circle())
	301	}
	302	.accessibilityLabel("Layers")
	303	}
	304
	305	// MARK: Markers
	306
	307	/// Every body's scene position and drawn size for the current date, scale, layers and camera.
	308	private func markers() -> [SolarMarker] {
	309	let map = mapping
	310	var out: [SolarMarker] = [SolarMarker(id: "sun", name: "Sun", kind: .sun, scene: .zero, radius: map.sunRadius, visible: true)]
	311	var parents: [String: (scene: SIMD3<Float>, radiusKm: Double, tiltDeg: Double)] = [:]
	312	func dot(_ p: SIMD3<Float>) -> Float { cam.distance(to: p) * 0.006 }
	313
	314	for p in SolarPlanet.all {
	315	let s = map.point(p.position(at: date))
	316	parents[p.id] = (s, p.radiusKm, p.tiltDeg)
	317	out.append(SolarMarker(id: p.id, name: Library.page(id: p.id)?.title ?? p.id, kind: .planet, scene: s, radius: map.radius(km: p.radiusKm), visible: true))
	318	}
	319	if let pluto = SolarPlanet.pluto {
	320	let s = map.point(pluto.position(at: date))
	321	parents["pluto"] = (s, pluto.radiusKm, pluto.tiltDeg)
	322	out.append(SolarMarker(id: "pluto", name: "Pluto", kind: .dwarf, scene: s, radius: map.radius(km: pluto.radiusKm), visible: layers.dwarfs))
	323	}
	324	for k in KeplerOrbit.dwarfPlanets {
	325	let r = Library.page(id: k.id)?.drawing?.radiusKm ?? 500
	326	out.append(SolarMarker(id: k.id, name: k.name, kind: .dwarf, scene: map.point(k.position(at: date)), radius: map.radius(km: r), visible: layers.dwarfs))
	327	}
	328
	329	// Moons appear when the camera is near their planet (or the planet or moon is selected).
	330	let galilean = SkyEngine.galileanMoons(at: date)
	331	let jd = date.timeIntervalSince1970 / 86_400 + 2_440_587.5
	332	var reach: [String: Float] = [:]
	333	var moonMarkers: [SolarMarker] = []
	334	for m in SolarMoon.all {
	335	guard let parent = parents[m.parent] else { continue }
	336	let dist = map.moonDistance(km: m.distanceKm, planetRadiusKm: parent.radiusKm)
	337	reach[m.parent] = max(reach[m.parent] ?? 0, dist)
	338	var dir: SIMD3<Float>
	339	if m.id == "moon" {
	340	dir = simd_normalize(SolarMapping.axes(SkyEngine.geocentricMoonEcliptic(at: date)))
	341	} else if let i = SolarMoon.galilean.firstIndex(of: m.id) {
	342	dir = simd_normalize(SolarMapping.axes(galilean[i]))
	343	} else {
	344	let phase = Double(m.id.unicodeScalars.reduce(0) { $0 + Int($1.value) } % 97) / 97
	345	let a = 2 * Double.pi * ((jd - 2_451_545) / m.periodDays + phase)
	346	let flat = SIMD3(Float(cos(a)), 0, Float(sin(a)))
	347	dir = simd_quatf(angle: Float(parent.tiltDeg * .pi / 180), axis: [1, 0, 0]).act(flat)
	348	}
	349	moonMarkers.append(SolarMarker(id: m.id, name: Library.page(id: m.id)?.title ?? m.id, kind: .moon,
	350	scene: parent.scene + dir * dist, radius: map.radius(km: m.radiusKm), visible: false))
	351	}
	352	for i in moonMarkers.indices {
	353	let m = SolarMoon.all.first { $0.id == moonMarkers[i].id }!
	354	guard let parent = parents[m.parent], let r = reach[m.parent] else { continue }
	355	let near = cam.distance(to: parent.scene) < r * 16
	356	let chosen = selected == m.id \|\| selected == m.parent
	357	let parentShown = m.parent != "pluto" \|\| layers.dwarfs
	358	moonMarkers[i].visible = layers.moons && parentShown && (near \|\| chosen)
	359	}
	360	out += moonMarkers
	361
	362	for craft in Spacecraft.all {
	363	guard let p = craft.position3(at: date) else { continue }
	364	let s = map.point(p)
	365	out.append(SolarMarker(id: "craft:\(craft.name)", name: craft.name, kind: .craft, scene: s, radius: dot(s), visible: layers.craft))
	366	}
	367
	368	let showerParents = Set(activeShowers.compactMap(\.parent))
	369	for c in KeplerOrbit.comets {
	370	let s = map.point(c.position(at: date))
	371	let shown = layers.comets && (Self.mainComets.contains(c.id) \|\| showerParents.contains(c.id))
	372	out.append(SolarMarker(id: "comet:\(c.id)", name: c.name, kind: .comet, scene: s, radius: dot(s), visible: shown))
	373	}
	374	return out
	375	}
	376
193	377	// MARK: Scene
194	378
195	379	private func build(_ content: RealityViewCameraContent) {
		@@ -210,37 +394,63 @@ struct SolarSystem3DView: View {
210	394	let a = CGFloat(0.09 * pow(0.78, Double(i - 1)))
211	395	var g = UnlitMaterial(color: UIColor(red: 1, green: 0.72, blue: 0.32, alpha: a))
212	396	g.blending = .transparent(opacity: .init(floatLiteral: Float(a)))
213		let shell = ModelEntity(mesh: .generateSphere(radius: r), materials: [g])
214		e.sun.addChild(shell)
	397	e.sun.addChild(ModelEntity(mesh: .generateSphere(radius: r), materials: [g]))
215	398	}
216	399
217
218		for p in SolarPlanet.all {
219		let planet = ModelEntity()
220		// Unlit, with a night-side shell turned away from the Sun, so day and night are exact
221		// without depending on scene lighting.
	400	// Planets, dwarf planets and moons: textured where there is a map, with a night side.
	401	var spheres: [(id: String, color: String, tilt: Double)] = SolarPlanet.all.map { ($0.id, $0.color, $0.tiltDeg) }
	402	if let pluto = SolarPlanet.pluto { spheres.append(("pluto", pluto.color, pluto.tiltDeg)) }
	403	spheres += KeplerOrbit.dwarfPlanets.map { ($0.id, Library.page(id: $0.id)?.drawing?.color ?? "#999999", 0) }
	404	spheres += SolarMoon.all.map { ($0.id, $0.color, 0) }
	405	for s in spheres {
	406	let body = ModelEntity()
222	407	var m = UnlitMaterial()
223		if let url = GlobeView.mapURL(p.id), let texture = try? TextureResource.load(contentsOf: url) {
	408	if let url = GlobeView.mapURL(s.id), let texture = try? TextureResource.load(contentsOf: url) {
224	409	m.color = .init(texture: .init(texture))
225	410	} else {
226		m.color = .init(tint: UIColor(Color(hex: p.color) ?? .gray))
	411	m.color = .init(tint: UIColor(Color(hex: s.color) ?? .gray))
227	412	}
228		planet.model = ModelComponent(mesh: .generateSphere(radius: 1), materials: [m])
	413	body.model = ModelComponent(mesh: .generateSphere(radius: 1), materials: [m])
	414	body.orientation = simd_quatf(angle: Float(s.tilt * .pi / 180), axis: [1, 0, 0])
	415	if s.id == "saturn" { body.addChild(Self.annulus(inner: 1.24, outer: 2.27, color: UIColor(red: 0.85, green: 0.78, blue: 0.62, alpha: 0.7))) }
	416	e.bodies[s.id] = body
	417	e.root.addChild(body)
229	418	let night = Self.nightShell()
230		night.name = "night"
231		e.nights[p.id] = night
	419	e.nights[s.id] = night
232	420	e.root.addChild(night)
233		planet.orientation = simd_quatf(angle: Float(p.tiltDeg * .pi / 180), axis: [1, 0, 0])
234		if p.id == "saturn" { planet.addChild(Self.rings(inner: 1.24, outer: 2.27)) }
235		e.planets[p.id] = planet
236		e.root.addChild(planet)
237	421	}
238	422
	423	// Spacecraft and comet nuclei: dots sized each frame to stay visible.
	424	for craft in Spacecraft.all {
	425	let dot = ModelEntity(mesh: .generateSphere(radius: 1), materials: [UnlitMaterial(color: Self.craftColor)])
	426	e.bodies["craft:\(craft.name)"] = dot
	427	e.root.addChild(dot)
	428	}
	429	for c in KeplerOrbit.comets {
	430	let nucleus = ModelEntity(mesh: .generateSphere(radius: 1), materials: [UnlitMaterial(color: UIColor(white: 0.92, alpha: 1))])
	431	e.bodies["comet:\(c.id)"] = nucleus
	432	e.root.addChild(nucleus)
	433	// A soft tail: nested cones, wider and fainter outward.
	434	let tail = ModelEntity()
	435	for (radius, alpha) in [(0.025, 0.3), (0.06, 0.14), (0.11, 0.06)] as [(Float, Float)] {
	436	var t = UnlitMaterial(color: UIColor(red: 0.7, green: 0.88, blue: 1, alpha: 1))
	437	t.blending = .transparent(opacity: .init(floatLiteral: alpha))
	438	tail.addChild(ModelEntity(mesh: .generateCone(height: 1, radius: radius), materials: [t]))
	439	}
	440	e.tails[c.id] = tail
	441	e.root.addChild(tail)
	442	}
	443
	444	var debrisMaterial = UnlitMaterial(color: UIColor(red: 1, green: 0.88, blue: 0.65, alpha: 0.55))
	445	debrisMaterial.blending = .transparent(opacity: .init(floatLiteral: 0.55))
	446	debrisMaterial.faceCulling = .none
	447	e.debris.model = ModelComponent(mesh: .generateBox(size: 0.0001), materials: [debrisMaterial])
	448	e.root.addChild(e.debris)
	449
239	450	var flareMaterial = UnlitMaterial(color: UIColor(red: 1, green: 1, blue: 0.85, alpha: 0.9))
240	451	flareMaterial.blending = .transparent(opacity: .init(floatLiteral: 0.9))
241	452	e.flare.model = ModelComponent(mesh: .generateSphere(radius: 1), materials: [flareMaterial])
242	453	e.root.addChild(e.flare)
243		// Two faint bands per pole, a wider glow and a brighter core, just above the surface.
244	454	for y: Float in [0.86, -0.86] {
245	455	for (inner, outer, alpha) in [(0.36, 0.66, 0.22), (0.45, 0.56, 0.5)] as [(Float, Float, CGFloat)] {
246	456	let ring = Self.annulus(inner: inner, outer: outer, color: UIColor(red: 0.35, green: 1, blue: 0.55, alpha: alpha))
		@@ -248,37 +458,43 @@ struct SolarSystem3DView: View {
248	458	e.aurora.addChild(ring)
249	459	}
250	460	}
251		e.planets["earth"]?.addChild(e.aurora)
	461	e.bodies["earth"]?.addChild(e.aurora)
252	462	place()
253	463	}
254	464
255		/// Moves everything for the current date, scale and camera.
	465	/// Moves everything for the current date, scale, layers and camera.
256	466	private func place() {
257	467	let e = entities
258	468	let map = mapping
259	469	e.sun.scale = .init(repeating: map.sunRadius)
260		for p in SolarPlanet.all {
261		guard let planet = e.planets[p.id] else { continue }
262		planet.position = map.point(p.position(at: date))
263		planet.scale = .init(repeating: map.radius(km: p.radiusKm))
264		if let night = e.nights[p.id] {
265		night.position = planet.position
266		night.scale = .init(repeating: map.radius(km: p.radiusKm) * 1.004)
267		// The shell's open side (+y) faces the Sun.
268		let toSun = simd_normalize(-planet.position)
269		night.orientation = simd_quatf(from: SIMD3(0, 1, 0), to: toSun)
	470	for m in markers() where m.kind != .sun {
	471	guard let body = e.bodies[m.id] else { continue }
	472	body.isEnabled = m.visible
	473	body.position = m.scene
	474	body.scale = .init(repeating: m.radius)
	475	if let night = e.nights[m.id] {
	476	night.isEnabled = m.visible
	477	night.position = m.scene
	478	night.scale = .init(repeating: m.radius * 1.004)
	479	night.orientation = simd_quatf(from: SIMD3(0, 1, 0), to: simd_normalize(-m.scene))
	480	}
	481	if m.kind == .comet, let tail = e.tails[String(m.id.dropFirst(6))] {
	482	place(tail: tail, at: m, map: map)
270	483	}
271	484	}
272	485	rebuildOrbitsIfNeeded()
273		// Orbits are a guide at system scale; close to a planet they only cut across it.
	486	rebuildPathsIfNeeded()
	487	rebuildDebrisIfNeeded()
	488	// Planet orbits are a guide at system scale; close to a planet they only cut across it.
274	489	let farEnough = cam.distance > map.radius(km: 70_000) * 25
275		for o in e.orbits.values { o.isEnabled = farEnough }
	490	for (id, o) in e.orbits {
	491	o.isEnabled = farEnough && orbitShown(id)
	492	}
	493	for p in e.paths.values { p.isEnabled = farEnough && layers.craft }
276	494
277		// Flare: a bright bulge on the side of the Sun facing Earth, pulsing.
278		if live, weather.showsFlare, let earth = e.planets["earth"] {
	495	if live, weather.showsFlare, let earth = e.bodies["earth"] {
279	496	e.flare.isEnabled = true
280		let dir = simd_normalize(earth.position)
281		e.flare.position = dir * map.sunRadius * 1.02
	497	e.flare.position = simd_normalize(earth.position) * map.sunRadius * 1.02
282	498	e.flare.scale = .init(repeating: map.sunRadius * (pulse ? 0.22 : 0.16))
283	499	} else {
284	500	e.flare.isEnabled = false
		@@ -287,55 +503,148 @@ struct SolarSystem3DView: View {
287	503
288	504	e.camera.look(at: cam.target, from: cam.position, relativeTo: nil)
289	505	e.camera.camera.near = max(cam.distance * 0.001, 1e-9)
290		e.camera.camera.far = cam.distance * 100 + 200
	506	e.camera.camera.far = cam.distance * 100 + 400
	507	}
	508
	509	/// A comet's tail points away from the Sun and grows as the comet nears it; none beyond 4 AU.
	510	private func place(tail: ModelEntity, at m: SolarMarker, map: SolarMapping) {
	511	guard let c = KeplerOrbit.comets.first(where: { "comet:\($0.id)" == m.id }) else { return }
	512	let au = (c.position(at: date) * c.position(at: date)).sum().squareRoot()
	513	guard m.visible, au < 4 else { tail.isEnabled = false; return }
	514	tail.isEnabled = true
	515	let away = simd_normalize(m.scene)
	516	let length = (map.scale == .compressed ? 0.9 : 0.4) * Float(min(1 / au, 2.5))
	517	// The cone's apex is at +y: point it at the Sun so the tail widens away from it.
	518	tail.orientation = simd_quatf(from: SIMD3(0, 1, 0), to: -away)
	519	tail.scale = .init(repeating: length)
	520	tail.position = m.scene + away * length / 2
291	521	}
292	522
293		/// Orbit ribbons, rebuilt when the scale changes or the zoom changes enough that their width would look wrong.
	523	private func orbitShown(_ id: String) -> Bool {
	524	if id.hasPrefix("comet:") {
	525	let c = String(id.dropFirst(6))
	526	return layers.comets && (Self.mainComets.contains(c) \|\| activeShowers.contains { $0.parent == c })
	527	}
	528	if id.hasPrefix("dwarf:") { return layers.dwarfs }
	529	return true
	530	}
	531
	532	/// Orbit ribbons for planets, dwarf planets and comets; rebuilt when the scale changes or the zoom
	533	/// changes enough that their width would look wrong.
294	534	private func rebuildOrbitsIfNeeded() {
295	535	let e = entities
296	536	let width = cam.distance * 0.0022
297	537	if let (s, w) = e.orbitsBuilt, s == scale, w / width < 1.6, width / w < 1.6 { return }
298	538	e.orbitsBuilt = (scale, width)
299	539	let map = mapping
300		for p in SolarPlanet.all {
301		let steps = 240
302		let points = (0..<steps).map { i in
303		map.point(p.position(at: date.addingTimeInterval(Double(i) / Double(steps) * p.periodDays * 86_400)))
304		}
305		let ribbon = Self.ribbon(points, width: width)
306		if let existing = e.orbits[p.id] {
307		existing.model?.mesh = ribbon
	540	func set(_ id: String, _ points: [SIMD3<Float>], color: UIColor, opacity: Float) {
	541	let mesh = Self.ribbon(points, width: width, closed: true)
	542	if let existing = e.orbits[id] { existing.model?.mesh = mesh; return }
	543	var m = UnlitMaterial(color: color)
	544	m.blending = .transparent(opacity: .init(floatLiteral: opacity))
	545	m.faceCulling = .none
	546	let orbit = ModelEntity(mesh: mesh, materials: [m])
	547	e.orbits[id] = orbit
	548	e.root.addChild(orbit)
	549	}
	550	for p in SolarPlanet.all + [SolarPlanet.pluto].compactMap({ $0 }) {
	551	let pts = (0..<240).map { i in map.point(p.position(at: date.addingTimeInterval(Double(i) / 240 * p.periodDays * 86_400))) }
	552	set(p.id == "pluto" ? "dwarf:pluto" : p.id, pts, color: .white, opacity: p.id == "pluto" ? 0.12 : 0.22)
	553	}
	554	for k in KeplerOrbit.dwarfPlanets {
	555	set("dwarf:\(k.id)", k.orbitPath().map(map.point), color: .white, opacity: 0.12)
	556	}
	557	for c in KeplerOrbit.comets {
	558	set("comet:\(c.id)", c.orbitPath(steps: 400).map(map.point), color: UIColor(red: 0.6, green: 0.8, blue: 1, alpha: 1), opacity: 0.22)
	559	}
	560	}
	561
	562	/// Spacecraft paths from launch to the slider's date, rebuilt every 10 days of date change.
	563	private func rebuildPathsIfNeeded() {
	564	let e = entities
	565	let width = cam.distance * 0.0022
	566	let bucket = Int(date.timeIntervalSince1970 / 864_000)
	567	let built = e.pathsBuilt
	568	if let built, built.0 == scale, built.1 / width < 1.6, width / built.1 < 1.6, built.2 == bucket { return }
	569	e.pathsBuilt = (scale, width, bucket)
	570	let map = mapping
	571	let day = date.timeIntervalSince1970 / 86_400
	572	for craft in Spacecraft.all {
	573	var pts = craft.points.filter { $0[0] <= day }.map { map.point(SIMD3($0[1], $0[2], $0[3])) }
	574	if let now = craft.position3(at: date) { pts.append(map.point(now)) }
	575	let mesh: MeshResource = pts.count > 1 ? Self.ribbon(pts, width: width, closed: false) : .generateBox(size: 0.0001)
	576	if let existing = e.paths[craft.name] {
	577	existing.model?.mesh = mesh
308	578	} else {
309		var m = UnlitMaterial(color: UIColor(white: 1, alpha: 1))
310		m.blending = .transparent(opacity: .init(floatLiteral: 0.22))
	579	var m = UnlitMaterial(color: Self.craftColor)
	580	m.blending = .transparent(opacity: .init(floatLiteral: 0.4))
311	581	m.faceCulling = .none
312		let orbit = ModelEntity(mesh: ribbon, materials: [m])
313		e.orbits[p.id] = orbit
314		e.root.addChild(orbit)
	582	let path = ModelEntity(mesh: mesh, materials: [m])
	583	e.paths[craft.name] = path
	584	e.root.addChild(path)
315	585	}
316	586	}
317	587	}
318	588
	589	/// Debris along an active meteor shower's parent orbit: small specks, densest where it crosses Earth's orbit.
	590	private func rebuildDebrisIfNeeded() {
	591	let e = entities
	592	let showers = layers.comets ? activeShowers.compactMap(\.parent).sorted().joined(separator: ",") : ""
	593	let size = cam.distance * 0.0016
	594	if let (s, w, key) = e.debrisBuilt, s == scale, key == showers, w / size < 1.6, size / w < 1.6 { return }
	595	e.debrisBuilt = (scale, size, showers)
	596	guard !showers.isEmpty else { e.debris.isEnabled = false; return }
	597	e.debris.isEnabled = true
	598	let map = mapping
	599	var rng = SeededRandom(seed: 42)
	600	var positions: [SIMD3<Float>] = []
	601	var indices: [UInt32] = []
	602	for id in showers.split(separator: ",") {
	603	guard let c = KeplerOrbit.comets.first(where: { $0.id == id }) else { continue }
	604	for p in c.orbitPath(steps: 360) {
	605	let r = (p * p).sum().squareRoot()
	606	// More specks near 1 AU, where Earth meets the stream.
	607	let copies = abs(r - 1) < 0.15 ? 4 : 1
	608	for _ in 0..<copies {
	609	let jitter = SIMD3(rng.next() - 0.5, rng.next() - 0.5, rng.next() - 0.5) * 0.08 * max(r, 0.3)
	610	let c = map.point(p + jitter)
	611	let base = UInt32(positions.count)
	612	positions += [c + SIMD3(size, 0, 0), c + SIMD3(-size / 2, size, 0), c + SIMD3(-size / 2, -size / 2, size)]
	613	indices += [base, base + 1, base + 2]
	614	}
	615	}
	616	}
	617	var d = MeshDescriptor(name: "debris")
	618	d.positions = MeshBuffer(positions)
	619	d.primitives = .triangles(indices)
	620	if let mesh = try? MeshResource.generate(from: [d]) { e.debris.model?.mesh = mesh }
	621	}
	622
319	623	// MARK: Meshes
320	624
321		/// A closed flat ribbon through `points`, lying in the plane of the orbit.
322		private static func ribbon(_ points: [SIMD3<Float>], width: Float) -> MeshResource {
	625	/// A flat ribbon through `points`, lying in the plane of the orbit.
	626	private static func ribbon(_ points: [SIMD3<Float>], width: Float, closed: Bool) -> MeshResource {
323	627	var positions: [SIMD3<Float>] = []
324	628	var indices: [UInt32] = []
325	629	let n = points.count
326	630	for i in 0..<n {
327		let t = simd_normalize(points[(i + 1) % n] - points[(i + n - 1) % n])
328		var side = simd_cross(t, SIMD3(0, 1, 0))
	631	let next = closed ? points[(i + 1) % n] : points[min(i + 1, n - 1)]
	632	let prev = closed ? points[(i + n - 1) % n] : points[max(i - 1, 0)]
	633	var t = next - prev
	634	if simd_length(t) < 1e-12 { t = SIMD3(1, 0, 0) }
	635	var side = simd_cross(simd_normalize(t), SIMD3(0, 1, 0))
329	636	if simd_length(side) < 1e-6 { side = SIMD3(1, 0, 0) }
330	637	side = simd_normalize(side) * width / 2
331	638	positions += [points[i] - side, points[i] + side]
332		let a = UInt32(2 * i), b = UInt32(2 * ((i + 1) % n))
333		indices += [a, a + 1, b, b, a + 1, b + 1]
	639	if closed \|\| i < n - 1 {
	640	let a = UInt32(2 * i), b = UInt32(2 * ((i + 1) % n))
	641	indices += [a, a + 1, b, b, a + 1, b + 1]
	642	}
334	643	}
335	644	var d = MeshDescriptor(name: "orbit")
336	645	d.positions = MeshBuffer(positions)
337	646	d.primitives = .triangles(indices)
338		return (try? MeshResource.generate(from: [d])) ?? .generateBox(size: 0.001)
	647	return (try? MeshResource.generate(from: [d])) ?? .generateBox(size: 0.0001)
339	648	}
340	649
341	650	/// A flat ring in the local x-z plane, radii in units of the parent's radius.
		@@ -358,7 +667,7 @@ struct SolarSystem3DView: View {
358	667	return ModelEntity(mesh: (try? MeshResource.generate(from: [d])) ?? .generateBox(size: 0.001), materials: [m])
359	668	}
360	669
361		/// The half of a unit sphere below y = 0, drawn dark and mostly opaque over the planet's night side.
	670	/// The half of a unit sphere below y = 0, drawn dark and mostly opaque over a body's night side.
362	671	private static func nightShell() -> ModelEntity {
363	672	let rings = 24, segments = 64
364	673	var positions: [SIMD3<Float>] = []
		@@ -385,25 +694,12 @@ struct SolarSystem3DView: View {
385	694	return ModelEntity(mesh: (try? MeshResource.generate(from: [d])) ?? .generateBox(size: 0.001), materials: [m])
386	695	}
387	696
388		private static func rings(inner: Float, outer: Float) -> ModelEntity {
389		annulus(inner: inner, outer: outer, color: UIColor(red: 0.85, green: 0.78, blue: 0.62, alpha: 0.7))
390		}
391
392	697	// MARK: Labels, taps and the card
393	698
394		private func screenPoints(size: CGSize) -> [(id: String, point: CGPoint, radius: CGFloat)] {
395		let e = entities
396		var out: [(String, CGPoint, CGFloat)] = []
397		if let p = cam.project(.zero, in: size) { out.append(("sun", p, pixelRadius(mapping.sunRadius, at: .zero, size: size))) }
398		for planet in SolarPlanet.all {
399		guard let entity = e.planets[planet.id] else { continue }
400		let pos = mapping.point(planet.position(at: date))
401		if let p = cam.project(pos, in: size) {
402		out.append((planet.id, p, pixelRadius(mapping.radius(km: planet.radiusKm), at: pos, size: size)))
403		}
404		_ = entity
	699	private func screenPoints(size: CGSize) -> [(marker: SolarMarker, point: CGPoint, radius: CGFloat)] {
	700	markers().filter(\.visible).compactMap { m in
	701	cam.project(m.scene, in: size).map { (m, $0, pixelRadius(m.radius, at: m.scene, size: size)) }
405	702	}
406		return out
407	703	}
408	704
409	705	private func pixelRadius(_ r: Float, at p: SIMD3<Float>, size: CGSize) -> CGFloat {
		@@ -411,34 +707,53 @@ struct SolarSystem3DView: View {
411	707	return CGFloat(r / max(cam.distance(to: p), 1e-9) * k)
412	708	}
413	709
414		/// Points to label: larger bodies first, skipping a label that would sit on one already placed.
415		private func labelled(size: CGSize) -> [(id: String, point: CGPoint, radius: CGFloat, showName: Bool)] {
416		let order = ["sun", "jupiter", "saturn", "uranus", "neptune", "earth", "venus", "mars", "mercury"]
	710	/// Points to label, most important first, skipping a label that would sit on one already placed.
	711	private func labelled(size: CGSize) -> [(marker: SolarMarker, point: CGPoint, radius: CGFloat, showName: Bool)] {
	712	let planetOrder = ["jupiter", "saturn", "uranus", "neptune", "earth", "venus", "mars", "mercury"]
	713	func rank(_ m: SolarMarker) -> Int {
	714	switch m.kind {
	715	case .sun: 0
	716	case .planet: 1 + (planetOrder.firstIndex(of: m.id) ?? 9)
	717	case .craft: 20
	718	case .dwarf: 30
	719	case .comet: 40
	720	case .moon: 50
	721	}
	722	}
417	723	var placed: [CGPoint] = []
418		return screenPoints(size: size)
419		.sorted { (order.firstIndex(of: $0.id) ?? 99) < (order.firstIndex(of: $1.id) ?? 99) }
	724	let points = screenPoints(size: size)
	725	// Anything whose centre falls on the disc of a nearer body is hidden behind it.
	726	let discs = points.filter { $0.radius > 4 }.map { ($0.point, $0.radius, cam.distance(to: $0.marker.scene)) }
	727	return points
	728	.filter { item in
	729	let d = cam.distance(to: item.marker.scene)
	730	return !discs.contains { $0.2 < d && hypot($0.0.x - item.point.x, $0.0.y - item.point.y) < $0.1 }
	731	}
	732	.sorted { rank($0.marker) < rank($1.marker) }
420	733	.map { item in
421	734	let at = CGPoint(x: item.point.x, y: item.point.y - max(item.radius, 5) - 9)
422		let clear = item.id == selected \|\| placed.allSatisfy { abs($0.x - at.x) > 44 \|\| abs($0.y - at.y) > 14 }
	735	let clear = item.marker.id == selected \|\| placed.allSatisfy { abs($0.x - at.x) > 48 \|\| abs($0.y - at.y) > 14 }
423	736	if clear { placed.append(at) }
424		return (item.id, item.point, item.radius, clear)
	737	return (item.marker, item.point, item.radius, clear)
425	738	}
426	739	}
427	740
428	741	private func labels(size: CGSize) -> some View {
429	742	ZStack {
430		ForEach(labelled(size: size), id: \.id) { item in
431		let name = item.id == "sun" ? "Sun" : (Library.page(id: item.id)?.title ?? item.id)
432		let tiny = item.radius < 3
	743	ForEach(labelled(size: size), id: \.marker.id) { item in
	744	let m = item.marker
	745	let isSelected = m.id == selected
	746	let color: Color = isSelected ? accent : m.kind == .craft ? accent.opacity(0.9) : m.kind == .comet ? Color(red: 0.7, green: 0.85, blue: 1) : ink.opacity(m.kind == .moon ? 0.7 : 0.85)
433	747	ZStack {
434		if tiny {
435		Circle().stroke(item.id == selected ? accent : ink.opacity(0.7), lineWidth: 1.2).frame(width: 10, height: 10)
	748	if item.radius < 3, m.kind != .craft, m.kind != .comet {
	749	Circle().stroke(isSelected ? accent : ink.opacity(0.6), lineWidth: 1.2).frame(width: 10, height: 10)
436	750	}
437	751	if item.showName {
438		Text(name).font(.caption2.weight(item.id == selected ? .semibold : .regular))
439		.foregroundStyle(item.id == selected ? accent : ink.opacity(0.85))
440		.shadow(color: .black, radius: 2)
441		.offset(y: -max(item.radius, 5) - 9)
	752	Text(m.name).font(.caption2.weight(isSelected ? .semibold : .regular))
	753	.foregroundStyle(color)
	754	.shadow(color: .black, radius: 2)
	755	.fixedSize()
	756	.offset(y: -max(item.radius, 5) - 9)
442	757	}
443	758	}
444	759	.position(item.point)
		@@ -448,7 +763,7 @@ struct SolarSystem3DView: View {
448	763
449	764	private func tap(_ location: CGPoint, size: CGSize) {
450	765	let hit = screenPoints(size: size)
451		.map { ($0.id, hypot($0.point.x - location.x, $0.point.y - location.y) - max($0.radius, 0)) }
	766	.map { ($0.marker.id, hypot($0.point.x - location.x, $0.point.y - location.y) - max($0.radius, 0)) }
452	767	.filter { $0.1 < 28 }
453	768	.min { $0.1 < $1.1 }
454	769	guard let id = hit?.0 else { selected = nil; return }
		@@ -456,14 +771,54 @@ struct SolarSystem3DView: View {
456	771	fly(to: id)
457	772	}
458	773
459		private func planetOrSun(_ id: String) -> LibraryPage? { Library.page(id: id) }
	774	/// The selected body's Library page, title, one-line description and position note.
	775	private func details(_ id: String) -> (page: LibraryPage?, title: String, subtitle: String, note: String?) {
	776	func fromSun(_ v: SIMD3<Double>) -> String {
	777	let au = (v * v).sum().squareRoot()
	778	return String(format: "%.2f AU from the Sun · sunlight takes %@", au, lightTime(au))
	779	}
	780	if id.hasPrefix("craft:") {
	781	let name = String(id.dropFirst(6))
	782	let page = Library.page(spacecraft: name)
	783	let pos = Spacecraft.all.first { $0.name == name }?.position3(at: date)
	784	return (page, name, page?.subtitle ?? "Spacecraft", pos.map(fromSun))
	785	}
	786	if id.hasPrefix("comet:"), let c = KeplerOrbit.comets.first(where: { "comet:\($0.id)" == id }) {
	787	let years = c.periodDays / 365.25
	788	let last = Date(timeIntervalSince1970: (c.perihelionJD - 2_440_587.5) * 86_400)
	789	var sub = String(format: "Goes round the Sun every %.0f years.", years)
	790	if years < 10 {
	791	sub += " Next closest to the Sun \(c.nextPerihelion(after: .now).formatted(.dateTime.month(.wide).year()))."
	792	} else {
	793	sub += " Last closest to the Sun in \(last.formatted(.dateTime.year()))."
	794	}
	795	if let shower = MeteorShower.major.first(where: { $0.parent == c.id }) {
	796	sub += " Its debris makes the \(shower.name)."
	797	}
	798	return (c.page.flatMap { Library.page(id: $0) }, c.name, sub, fromSun(c.position(at: date)))
	799	}
	800	let page = Library.page(id: id)
	801	let title = page?.title ?? id
	802	let subtitle = page?.subtitle ?? ""
	803	if let m = SolarMoon.all.first(where: { $0.id == id }) {
	804	let parentName = Library.page(id: m.parent)?.title ?? m.parent
	805	let note = "\(Int(m.distanceKm).formatted()) km from \(parentName)" + (m.isExact ? "" : " · position illustrative")
	806	return (page, title, subtitle, note)
	807	}
	808	if let p = SolarPlanet.all.first(where: { $0.id == id }) ?? (id == "pluto" ? SolarPlanet.pluto : nil) {
	809	return (page, title, subtitle, fromSun(p.position(at: date)))
	810	}
	811	if let k = KeplerOrbit.dwarfPlanets.first(where: { $0.id == id }) {
	812	return (page, title, subtitle, fromSun(k.position(at: date)))
	813	}
	814	return (page, title, subtitle, nil)
	815	}
460	816
461		private func card(_ page: LibraryPage) -> some View {
462		let planet = SolarPlanet.all.first { $0.id == page.id }
463		let au = planet.map { p -> Double in let v = p.position(at: date); return (v * v).sum().squareRoot() }
	817	private func card(_ id: String) -> some View {
	818	let d = details(id)
464	819	return VStack(alignment: .leading, spacing: 6) {
465	820	HStack {
466		Text(page.title).font(.headline)
	821	Text(d.title).font(.headline)
467	822	Spacer()
468	823	Button { selected = nil; resetView() } label: {
469	824	Image(systemName: "xmark").font(.footnote.weight(.semibold)).frame(width: 44, height: 44).contentShape(Rectangle())
		@@ -472,11 +827,11 @@ struct SolarSystem3DView: View {
472	827	.padding(-12)
473	828	.accessibilityLabel("Close")
474	829	}
475		Text(page.subtitle).font(.footnote).dimmed(0.75)
476		if let au {
477		Text(String(format: "%.2f AU from the Sun · sunlight takes %@", au, lightTime(au))).font(.footnote.monospacedDigit()).dimmed(0.85)
	830	if !d.subtitle.isEmpty { Text(d.subtitle).font(.footnote).dimmed(0.75).fixedSize(horizontal: false, vertical: true) }
	831	if let note = d.note { Text(note).font(.footnote.monospacedDigit()).dimmed(0.85) }
	832	if let page = d.page {
	833	Button("Read more") { onOpen(page) }.font(.subheadline.weight(.medium)).foregroundStyle(accent)
478	834	}
479		Button("Read more") { onOpen(page) }.font(.subheadline.weight(.medium)).foregroundStyle(accent)
480	835	}
481	836	.padding(14)
482	837	.background(Color(white: 0.06), in: RoundedRectangle(cornerRadius: 14))
		@@ -508,7 +863,7 @@ struct SolarSystem3DView: View {
508	863	.onChanged { g in
509	864	flight?.cancel()
510	865	if pinchStart == nil { pinchStart = cam.distance }
511		let limits: ClosedRange<Float> = scale == .compressed ? 0.25...60 : 1e-6...200
	866	let limits: ClosedRange<Float> = scale == .compressed ? 0.02...80 : 1e-6...400
512	867	cam.distance = min(max(pinchStart! / Float(g.magnification), limits.lowerBound), limits.upperBound)
513	868	}
514	869	.onEnded { _ in pinchStart = nil }
		@@ -526,17 +881,15 @@ struct SolarSystem3DView: View {
526	881	return neptune * 1.22 / min(tanV, tanH)
527	882	}
528	883
529		/// Centres on a body and zooms to a few times its drawn radius.
	884	/// Centres on a body and zooms to a few times its drawn radius (or a fixed distance for dots).
530	885	private func fly(to id: String) {
531		let target: SIMD3<Float>, radius: Float
532		if id == "sun" {
533		target = .zero
534		radius = mapping.sunRadius
535		} else if let p = SolarPlanet.all.first(where: { $0.id == id }) {
536		target = mapping.point(p.position(at: date))
537		radius = mapping.radius(km: p.radiusKm) * (p.id == "saturn" ? 2.3 : 1)
538		} else { return }
539		animateCamera(to: SolarCamera(target: target, yaw: cam.yaw, pitch: max(cam.pitch, 0.25), distance: radius * 7))
	886	guard let m = markers().first(where: { $0.id == id }) else { return }
	887	let distance: Float
	888	switch m.kind {
	889	case .craft, .comet: distance = scale == .compressed ? 1.2 : 0.6
	890	default: distance = m.radius * (m.id == "saturn" ? 2.3 : 1) * 7
	891	}
	892	animateCamera(to: SolarCamera(target: m.scene, yaw: cam.yaw, pitch: max(cam.pitch, 0.25), distance: distance))
540	893	}
541	894
542	895	/// Moves the camera over about a second, interpolating distance on a log scale.
		@@ -577,3 +930,13 @@ struct SolarSystem3DView: View {
577	930	}
578	931	}
579	932	}
	933
	934	/// A small deterministic generator, so debris looks the same each time it is rebuilt.
	935	private struct SeededRandom {
	936	var state: UInt64
	937	init(seed: UInt64) { state = seed }
	938	mutating func next() -> Double {
	939	state = state &* 6_364_136_223_846_793_005 &+ 1_442_695_040_888_963_407
	940	return Double(state >> 11) / Double(1 << 53)
	941	}
	942	}

App/Sources/SystemScreen.swift +1 −1

		@@ -59,7 +59,7 @@ struct SystemScreen: View {
59	59	}
60	60	.pickerStyle(.segmented)
61	61	Text(solarScale == .compressed
62		? "Distances squeezed and planets enlarged so everything fits. Drag to turn, pinch to zoom, tap a planet."
	62	? "Distances squeezed and bodies enlarged so everything fits. Drag to turn, pinch to zoom, tap anything. Moons appear as you zoom in to their planet."
63	63	: "Real distances and sizes: the planets are specks, so circles mark them. Tap one to fly to it.")
64	64	.font(.caption).dimmed(0.7).padding(.top, 8)
65	65	}

Packages/MoonriseKit/Sources/SkyEngine/Kepler.swift added +114

		@@ -0,0 +1,114 @@
	1	import CAstronomy
	2	import Foundation
	3
	4	/// A two-body orbit around the Sun from osculating elements (J2000 ecliptic), for small bodies the
	5	/// engine doesn't cover. Planetary perturbations are ignored, so positions drift away from the epoch:
	6	/// fine for drawing, not for observing.
	7	public struct KeplerOrbit: Sendable, Identifiable {
	8	public var id: String
	9	public var name: String
	10	/// Library page, if there is one.
	11	public var page: String?
	12	public var a: Double, e: Double, i: Double, node: Double, peri: Double
	13	/// Time of perihelion (TDB Julian date). Propagating from it rather than from the epoch's mean
	14	/// anomaly keeps comets right near perihelion, where they are worth drawing.
	15	public var perihelionJD: Double
	16	public var isComet: Bool
	17
	18	/// Orbital period in days.
	19	public var periodDays: Double { 365.256898 * pow(a, 1.5) }
	20
	21	/// Heliocentric position in AU on J2000 ecliptic axes.
	22	public func position(at date: Date) -> SIMD3<Double> {
	23	let jd = date.timeIntervalSince1970 / 86_400 + 2_440_587.5
	24	let n = 360 / periodDays
	25	let M = ((n * (jd - perihelionJD)).truncatingRemainder(dividingBy: 360) + 360).truncatingRemainder(dividingBy: 360) * .pi / 180
	26	var E = e < 0.8 ? M : .pi
	27	for _ in 0..<50 {
	28	let d = (E - e * sin(E) - M) / (1 - e * cos(E))
	29	E -= d
	30	if abs(d) < 1e-12 { break }
	31	}
	32	let x = a * (cos(E) - e), y = a * (1 - e * e).squareRoot() * sin(E)
	33	let r = Double.pi / 180
	34	let (cO, sO) = (cos(node * r), sin(node * r)), (cw, sw) = (cos(peri * r), sin(peri * r)), (ci, si) = (cos(i * r), sin(i * r))
	35	return SIMD3(
	36	(cO * cw - sO * sw * ci) * x + (-cO * sw - sO * cw * ci) * y,
	37	(sO * cw + cO * sw * ci) * x + (-sO * sw + cO * cw * ci) * y,
	38	(sw * si) * x + (cw * si) * y
	39	)
	40	}
	41
	42	/// One full orbit, sampled evenly in eccentric anomaly so long, thin comet orbits stay smooth near the Sun.
	43	public func orbitPath(steps: Int = 240) -> [SIMD3<Double>] {
	44	let r = Double.pi / 180
	45	let (cO, sO) = (cos(node * r), sin(node * r)), (cw, sw) = (cos(peri * r), sin(peri * r)), (ci, si) = (cos(i * r), sin(i * r))
	46	return (0..<steps).map { k in
	47	let E = Double(k) / Double(steps) * 2 * .pi
	48	let x = a * (cos(E) - e), y = a * (1 - e * e).squareRoot() * sin(E)
	49	return SIMD3(
	50	(cO * cw - sO * sw * ci) * x + (-cO * sw - sO * cw * ci) * y,
	51	(sO * cw + cO * sw * ci) * x + (-sO * sw + cO * cw * ci) * y,
	52	(sw * si) * x + (cw * si) * y
	53	)
	54	}
	55	}
	56
	57	/// The next perihelion after `date`.
	58	public func nextPerihelion(after date: Date) -> Date {
	59	let jd = date.timeIntervalSince1970 / 86_400 + 2_440_587.5
	60	let k = ((jd - perihelionJD) / periodDays).rounded(.up)
	61	return Date(timeIntervalSince1970: (perihelionJD + k * periodDays - 2_440_587.5) * 86_400)
	62	}
	63
	64	/// JPL Small-Body Database osculating elements (full precision), fetched 2026-10-19.
	65	public static let dwarfPlanets: [KeplerOrbit] = [
	66	KeplerOrbit(id: "ceres", name: "Ceres", page: "ceres", a: 2.765552595034094, e: 0.07969229514816586, i: 10.58802780183462, node: 80.24862682043221, peri: 73.29421453021587, perihelionJD: 2461599.841466614, isComet: false),
	67	KeplerOrbit(id: "haumea", name: "Haumea", page: "haumea", a: 43.06029023650952, e: 0.1944430148898797, i: 28.20847393040364, node: 121.7860561329425, peri: 240.6905472508661, perihelionJD: 2500416.599615283, isComet: false),
	68	KeplerOrbit(id: "makemake", name: "Makemake", page: "makemake", a: 45.57093317300052, e: 0.1588889953992523, i: 29.02785603743067, node: 79.2948338209406, peri: 297.0922733397207, perihelionJD: 2408158.6940986165, isComet: false),
	69	KeplerOrbit(id: "eris", name: "Eris", page: "eris", a: 67.93394687853566, e: 0.4382385347971672, i: 43.9258279471791, node: 36.00477044417249, peri: 150.7949235840312, perihelionJD: 2545407.716847013, isComet: false),
	70	]
	71
	72	public static let comets: [KeplerOrbit] = [
	73	KeplerOrbit(id: "halley", name: "Halley's Comet", page: nil, a: 17.92863504856923, e: 0.9679359956953211, i: 162.1905300439129, node: 59.09894720612437, peri: 112.2414314637764, perihelionJD: 2446469.9736161465, isComet: true),
	74	KeplerOrbit(id: "encke", name: "Comet Encke", page: nil, a: 2.218624763741819, e: 0.846940430888432, i: 11.33675914978793, node: 334.0171400057891, peri: 187.2881998732444, perihelionJD: 2460240.0285326503, isComet: true),
	75	KeplerOrbit(id: "67p", name: "67P/Churyumov–Gerasimenko", page: "rosetta", a: 3.462249490129549, e: 0.6409081308996354, i: 7.040294937543767, node: 50.13557377155012, peri: 12.79824970228189, perihelionJD: 2457247.588657812, isComet: true),
	76	KeplerOrbit(id: "swift-tuttle", name: "Comet Swift–Tuttle", page: nil, a: 26.0920694978266, e: 0.963225755046038, i: 113.453816997171, node: 139.3811920815948, peri: 152.9821676305871, perihelionJD: 2448968.499784556, isComet: true),
	77	KeplerOrbit(id: "tempel-tuttle", name: "Comet Tempel–Tuttle", page: nil, a: 10.3383382297577, e: 0.905552720972412, i: 162.486575379434, node: 235.270989149082, peri: 172.5002736828059, perihelionJD: 2450872.5977341123, isComet: true),
	78	KeplerOrbit(id: "phaethon", name: "3200 Phaethon", page: nil, a: 1.271464620762422, e: 0.8896722844001859, i: 22.31052728977475, node: 265.0988060326684, peri: 322.3001684954223, perihelionJD: 2461285.6164380596, isComet: true),
	79	KeplerOrbit(id: "tuttle", name: "Comet 8P/Tuttle", page: nil, a: 5.700291361749948, e: 0.8197876162331501, i: 54.98196882510133, node: 270.3421615706648, peri: 207.5115175085094, perihelionJD: 2454492.5180154694, isComet: true),
	80	]
	81	}
	82
	83	extension MeteorShower {
	84	/// The comet (or asteroid) whose debris Earth passes through, by KeplerOrbit id.
	85	public var parent: String? {
	86	switch name {
	87	case "Perseids": "swift-tuttle"
	88	case "Leonids": "tempel-tuttle"
	89	case "Orionids", "Eta Aquariids": "halley"
	90	case "Geminids": "phaethon"
	91	case "Ursids": "tuttle"
	92	default: nil
	93	}
	94	}
	95
	96	/// Days from `date` to the nearest peak (negative once it has passed), in the given calendar.
	97	public func daysToPeak(from date: Date, calendar: Calendar = .current) -> Double {
	98	let year = calendar.component(.year, from: date)
	99	return (year - 1...year + 1).compactMap { y in
	100	calendar.date(from: DateComponents(year: y, month: month, day: day, hour: 12)).map { $0.timeIntervalSince(date) / 86_400 }
	101	}
	102	.min { abs($0) < abs($1) } ?? .infinity
	103	}
	104	}
	105
	106	extension SkyEngine {
	107	/// Io, Europa, Ganymede and Callisto relative to Jupiter, AU on J2000 ecliptic axes.
	108	public static func galileanMoons(at date: Date) -> [SIMD3<Double>] {
	109	lock.lock()
	110	defer { lock.unlock() }
	111	let m = Astronomy_JupiterMoons(time(date))
	112	return [m.io, m.europa, m.ganymede, m.callisto].map { ecliptic(SIMD3($0.x, $0.y, $0.z)) }
	113	}
	114	}

Packages/MoonriseKit/Tests/SkyEngineTests/KeplerTests.swift added +52

		@@ -0,0 +1,52 @@
	1	import Foundation
	2	import Testing
	3	@testable import SkyEngine
	4
	5	private func jd(_ jd: Double) -> Date { Date(timeIntervalSince1970: (jd - 2_440_587.5) * 86_400) }
	6	private func auDist(_ a: SIMD3<Double>, _ b: SIMD3<Double>) -> Double { ((a - b) * (a - b)).sum().squareRoot() }
	7
	8	@Test func ceresMatchesHorizons() throws {
	9	// JPL Horizons, heliocentric J2000 ecliptic, 2026-10-19 00:00 TDB.
	10	let ceres = try #require(KeplerOrbit.dwarfPlanets.first { $0.id == "ceres" })
	11	let p = ceres.position(at: jd(2461332.5))
	12	#expect(auDist(p, SIMD3(0.09160098, 2.65726102, 0.06724773)) < 0.003)
	13	}
	14
	15	@Test func halleyMatchesHorizons() throws {
	16	let halley = try #require(KeplerOrbit.comets.first { $0.id == "halley" })
	17	// At its 1986 perihelion: within 0.05 AU, about a day of its motion there (Horizons uses a perturbed solution).
	18	#expect(auDist(halley.position(at: jd(2446470.5)), SIMD3(0.34233380, -0.44659254, 0.16779698)) < 0.05)
	19	// ...and near aphelion now, where two-body drift is a few tenths of an AU at 36 AU.
	20	#expect(auDist(halley.position(at: jd(2461332.5)), SIMD3(-19.34593976, 27.47052259, -9.85160687)) < 1)
	21	}
	22
	23	@Test func showersFindParentsAndPeaks() {
	24	let perseids = MeteorShower.major.first { $0.name == "Perseids" }!
	25	#expect(perseids.parent == "swift-tuttle")
	26	var cal = Calendar(identifier: .gregorian)
	27	cal.timeZone = TimeZone(identifier: "UTC")!
	28	let aug10 = cal.date(from: DateComponents(year: 2027, month: 8, day: 10, hour: 12))!
	29	#expect(abs(perseids.daysToPeak(from: aug10, calendar: cal) - 2) < 0.01)
	30	let dec30 = cal.date(from: DateComponents(year: 2026, month: 12, day: 30, hour: 12))!
	31	let quadrantids = MeteorShower.major.first { $0.name == "Quadrantids" }!
	32	#expect(abs(quadrantids.daysToPeak(from: dec30, calendar: cal) - 4) < 0.01)
	33	}
	34
	35	@Test func galileanMoonDistances() {
	36	let km = SkyEngine.galileanMoons(at: Date(timeIntervalSince1970: 1_792_400_000)).map { ($0 * $0).sum().squareRoot() * 1.495978707e8 }
	37	// Mean distances 421,800 / 671,100 / 1,070,400 / 1,882,700 km; orbits are nearly circular.
	38	for (d, mean) in zip(km, [421_800.0, 671_100, 1_070_400, 1_882_700]) { #expect(abs(d - mean) / mean < 0.02) }
	39	}
	40
	41	@Test func enckeReturnsFeb2027() throws {
	42	// Short periods are where two-body prediction holds; JPL lists Encke's next perihelion as 2027-02-10.
	43	let encke = try #require(KeplerOrbit.comets.first { $0.id == "encke" })
	44	let next = encke.nextPerihelion(after: Date(timeIntervalSince1970: 1_792_400_000))
	45	#expect(abs(next.timeIntervalSince(Date(timeIntervalSince1970: 1_802_217_600)) / 86_400) < 3)
	46	}
	47
	48	@Test func halleyPathSpansItsOrbit() throws {
	49	let halley = try #require(KeplerOrbit.comets.first { $0.id == "halley" })
	50	let r = halley.orbitPath().map { ($0 * $0).sum().squareRoot() }
	51	#expect(abs(r.min()! - 0.575) < 0.001 && abs(r.max()! - 35.28) < 0.01)
	52	}

THIRD_PARTY.org +1

		@@ -9,6 +9,7 @@
9	9	\| Hipparcos main catalogue positions (used only to match HIP to HR when building skycultures.json; not bundled) \| — \| ESA \| https://cdsarc.cds.unistra.fr/viz-bin/cat/I/239 \|
10	10	\| Global maps for globes (Mercury PIA15063; Venus Magellan C3-MDIR colourised topography; Earth Blue Marble Next Generation, December 2004; Moon SVS 4720 LROC colour 2K; Mars Viking MDIM 2.1 colour; Jupiter PIA07782; Pluto New Horizons global mosaic; Io, Europa, Ganymede, Callisto USGS Galileo/Voyager mosaics; Titan PIA22770; Enceladus Schenk 2024), downscaled to at most 2048 px \| =App/Globes/*.jpg= \| Public domain (NASA, USGS); credit per map in =App/Sources/GlobeMaps.swift= \| https://science.nasa.gov/photojournal, https://svs.gsfc.nasa.gov/4720/, https://astrogeology.usgs.gov \|
11	11	\| Sun texture for the 3D solar system (=App/Globes/sun.jpg=) \| generated noise, made for this app \| — \| — \|
	12	\| Orbital elements for Ceres, Haumea, Makemake, Eris and seven comets (=Packages/MoonriseKit/Sources/SkyEngine/Kepler.swift=) \| JPL Small-Body Database, fetched 2026-10-19 \| NASA/JPL, no published restrictions \| https://ssd.jpl.nasa.gov/tools/sbdb_lookup.html \|
12	13	\| 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 \|
13	14	\| Natural Earth 1:110m coastline v5.1.2 \| =Packages/MoonriseKit/Sources/SkyRenderer/Resources/coastline.json= \| Public domain \| https://www.naturalearthdata.com \|
14	15	\| Launch Library 2 (The Space Devs) \| fetched at runtime by =server/= \| Free API; credit shown in the app \| https://thespacedevs.com/llapi \|

Commit 8592cd1a6d

Commit `8592cd1a6d`