425 lines
15 KiB
Go
425 lines
15 KiB
Go
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package basic
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import (
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"math"
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"b612.me/astro/planet"
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. "b612.me/astro/tools"
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)
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const (
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jupiterGalileanReferenceJD = 2433282.5
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jupiterGalileanLongPeriodShift = 310910.16
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jupiterGalileanMinSolarLPYear = 1150.0
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jupiterGalileanMaxSolarLPYear = 2750.0
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jupiterGalileanEquatorialRadiusKM = 71492.0
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astronomicalUnitKM = 149597870.691
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)
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var (
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jupiterGalileanBaseMeanLongitudes = [4]float64{3.55155228618240, 1.76932271112347, 0.878207923589328, 0.376486233433828}
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jupiterGalileanMu = [4]float64{2.82489428433814e-07, 2.82483274392893e-07, 2.82498184184723e-07, 2.82492144889909e-07}
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)
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const (
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jupiterGalileanFrameNode = 6.24950183065715
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jupiterGalileanFrameTilt = 0.445094736497665
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)
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type jupiterGalileanL1Term struct {
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Amp float64
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Period float64
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Phase float64
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}
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// JupiterGalileanState 木星伽利略卫星原始状态 / raw Galilean-satellite state.
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//
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// 输入 jd 使用 TT/TDB 对应的儒略日；返回值为 IMCCE L1 理论的木心 J2000 平赤道直角坐标与速度，单位 AU / AU/day。
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// The input jd is a TT/TDB Julian day. Returned coordinates are Jovicentric J2000 mean-equatorial position and velocity from the IMCCE L1 theory, in AU and AU/day.
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type JupiterGalileanState struct {
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X float64
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Y float64
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Z float64
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VX float64
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VY float64
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VZ float64
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}
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// JupiterGalileanObservation 木星伽利略卫星视位置 / apparent Galilean-satellite geometry.
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//
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// 视位置相对木星中心定义：X 向天球东为正，Y 向天球北为正，Z>0 表示比木星更远、位于盘后。
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// Apparent offsets are relative to Jupiter's center: X is positive to celestial east, Y to celestial north, and Z>0 means farther than Jupiter and behind the disk.
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type JupiterGalileanObservation struct {
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State JupiterGalileanState
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RA float64
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Dec float64
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Distance float64
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OffsetXArcsec float64
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OffsetYArcsec float64
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OffsetXJupiterRadii float64
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OffsetYJupiterRadii float64
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OffsetZJupiterRadii float64
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InFrontOfJupiter bool
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}
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// JupiterGalileanSatelliteState 伽利略卫星木心 J2000 状态 / Jovicentric J2000 state of a Galilean satellite.
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//
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// satellite 取 1=Io, 2=Europa, 3=Ganymede, 4=Callisto。jd 为 TT/TDB 对应儒略日。
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// satellite is 1=Io, 2=Europa, 3=Ganymede, 4=Callisto. jd is a TT/TDB Julian day.
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func JupiterGalileanSatelliteState(jd float64, satellite int) JupiterGalileanState {
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if satellite < 1 || satellite > 4 || !isFinite(jd) {
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return invalidJupiterGalileanState()
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}
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et := jd - jupiterGalileanReferenceJD
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includeSolarLongPeriod := jupiterGalileanUseSolarLongPeriod(jd)
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return jupiterGalileanSatelliteStateAtET(et, satellite-1, includeSolarLongPeriod)
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}
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// JupiterGalileanSatelliteStates 四颗伽利略卫星木心 J2000 状态 / Jovicentric J2000 states of the four Galilean satellites.
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//
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// 返回次序固定为 Io、Europa、Ganymede、Callisto。
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// The returned order is Io, Europa, Ganymede, Callisto.
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func JupiterGalileanSatelliteStates(jd float64) [4]JupiterGalileanState {
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var states [4]JupiterGalileanState
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et := jd - jupiterGalileanReferenceJD
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includeSolarLongPeriod := jupiterGalileanUseSolarLongPeriod(jd)
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for i := range states {
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states[i] = jupiterGalileanSatelliteStateAtET(et, i, includeSolarLongPeriod)
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}
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return states
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}
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// JupiterGalileanSatelliteObservation 伽利略卫星视位置 / apparent geometry of a Galilean satellite.
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//
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// jd 为 TT/TDB 对应儒略日；返回卫星的天球视赤道坐标，以及相对木星中心的东/北平面偏移。
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// jd is a TT/TDB Julian day. The result contains the satellite's astrometric equatorial coordinates and its east/north sky-plane offsets relative to Jupiter's center.
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func JupiterGalileanSatelliteObservation(jd float64, satellite int) JupiterGalileanObservation {
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if satellite < 1 || satellite > 4 || !isFinite(jd) {
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return invalidJupiterGalileanObservation()
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}
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context := newJupiterGalileanObservationContext(jd)
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return context.observationForSatellite(satellite - 1)
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}
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// JupiterGalileanSatelliteObservations 四颗伽利略卫星视位置 / apparent geometry of the four Galilean satellites.
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//
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// 返回次序固定为 Io、Europa、Ganymede、Callisto。
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// The returned order is Io, Europa, Ganymede, Callisto.
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func JupiterGalileanSatelliteObservations(jd float64) [4]JupiterGalileanObservation {
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var observations [4]JupiterGalileanObservation
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context := newJupiterGalileanObservationContext(jd)
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for i := range observations {
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observations[i] = context.observationForSatellite(i)
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}
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return observations
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}
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type jupiterGalileanObservationContext struct {
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jd float64
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targetJD float64
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earthHelioJ2000 Vector3
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jupiterGeoJ2000 Vector3
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jupiterDistance float64
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jupiterLightTime float64
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sunDistanceAU float64
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east Vector3
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north Vector3
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lineOfSight Vector3
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earthDirection Vector3
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sunDirection Vector3
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sunLineOfSight Vector3
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sunEast Vector3
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sunNorth Vector3
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earthMinorRadius float64
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sunMinorRadius float64
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bodyX Vector3
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bodyY Vector3
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bodyZ Vector3
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}
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func newJupiterGalileanObservationContext(jd float64) jupiterGalileanObservationContext {
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context := jupiterGalileanObservationContext{jd: jd}
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if !isFinite(jd) {
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return context
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}
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context.earthHelioJ2000 = rotateEclipticToEquatorial(earthHeliocentricVectorJ2000(jd), orbitJ2000Obliquity)
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context.jupiterGeoJ2000, context.jupiterLightTime = jupiterAstrometricGeocentricVectorJ2000(jd, context.earthHelioJ2000)
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context.targetJD = jd - context.jupiterLightTime
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context.jupiterDistance = vectorMagnitude(context.jupiterGeoJ2000)
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if context.jupiterDistance == 0 {
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return context
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}
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context.lineOfSight = normalizeVector(context.jupiterGeoJ2000)
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context.earthDirection = Vector3{-context.lineOfSight[0], -context.lineOfSight[1], -context.lineOfSight[2]}
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ra, dec := vectorToRaDec(context.lineOfSight)
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context.east = Vector3{-Sin(ra), Cos(ra), 0}
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context.north = Vector3{-Cos(ra) * Sin(dec), -Sin(ra) * Sin(dec), Cos(dec)}
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jupiterHelio := rotateEclipticToEquatorial(jupiterHeliocentricVectorJ2000(context.targetJD), orbitJ2000Obliquity)
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context.sunDistanceAU = vectorMagnitude(jupiterHelio)
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context.sunDirection = normalizeVector(Vector3{-jupiterHelio[0], -jupiterHelio[1], -jupiterHelio[2]})
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context.sunLineOfSight = Vector3{-context.sunDirection[0], -context.sunDirection[1], -context.sunDirection[2]}
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sunRA, sunDec := vectorToRaDec(context.sunLineOfSight)
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context.sunEast = Vector3{-Sin(sunRA), Cos(sunRA), 0}
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context.sunNorth = Vector3{-Cos(sunRA) * Sin(sunDec), -Sin(sunRA) * Sin(sunDec), Cos(sunDec)}
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poleRA, poleDec, _ := jupiterPoleRotation(context.targetJD)
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context.bodyZ = raDecToVector(poleRA, poleDec)
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context.bodyX = normalizeVector(Vector3{-math.Sin(poleRA * rad), math.Cos(poleRA * rad), 0})
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context.bodyY = normalizeVector(pxp(context.bodyZ, context.bodyX))
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context.earthMinorRadius = jupiterProjectedMinorRadius(context.earthDirection, context.bodyZ)
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context.sunMinorRadius = jupiterProjectedMinorRadius(context.sunDirection, context.bodyZ)
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return context
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}
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func (context jupiterGalileanObservationContext) observationForSatellite(index int) JupiterGalileanObservation {
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if index < 0 || index >= 4 || context.jupiterDistance == 0 {
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return invalidJupiterGalileanObservation()
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}
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state, geocentric := jupiterGalileanSatelliteAstrometricGeocentric(index, context.jd, context.jupiterLightTime, context.earthHelioJ2000)
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direction := normalizeVector(geocentric)
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ra, dec := vectorToRaDec(direction)
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distance := vectorMagnitude(geocentric)
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relative := Vector3{
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geocentric[0] - context.jupiterGeoJ2000[0],
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geocentric[1] - context.jupiterGeoJ2000[1],
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geocentric[2] - context.jupiterGeoJ2000[2],
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}
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zAU := vectorDot(relative, context.lineOfSight)
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radiusAU := jupiterGalileanEquatorialRadiusKM / astronomicalUnitKM
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offsetXRad, offsetYRad := tangentPlaneOffsetAngles(direction, context.lineOfSight, context.east, context.north)
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jupiterSemidiameterArcsec := math.Atan2(radiusAU, context.jupiterDistance) * deg * 3600
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return JupiterGalileanObservation{
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State: state,
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RA: ra,
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Dec: dec,
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Distance: distance,
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OffsetXArcsec: offsetXRad * deg * 3600,
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OffsetYArcsec: offsetYRad * deg * 3600,
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OffsetXJupiterRadii: offsetXRad * deg * 3600 / jupiterSemidiameterArcsec,
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OffsetYJupiterRadii: offsetYRad * deg * 3600 / jupiterSemidiameterArcsec,
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OffsetZJupiterRadii: zAU / radiusAU,
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InFrontOfJupiter: zAU < 0,
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}
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}
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func tangentPlaneOffsetAngles(target, center, east, north Vector3) (float64, float64) {
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denominator := vectorDot(target, center)
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return math.Atan2(vectorDot(target, east), denominator), math.Atan2(vectorDot(target, north), denominator)
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}
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func jupiterGalileanSatelliteAstrometricGeocentric(index int, jd, initialLightTime float64, earthHelioJ2000 Vector3) (JupiterGalileanState, Vector3) {
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lightTime := initialLightTime
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state := JupiterGalileanState{}
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result := Vector3{}
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includeSolarLongPeriod := jupiterGalileanUseSolarLongPeriod(jd)
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for i := 0; i < 8; i++ {
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targetJD := jd - lightTime
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jupiterHelio := rotateEclipticToEquatorial(jupiterHeliocentricVectorJ2000(targetJD), orbitJ2000Obliquity)
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state = jupiterGalileanSatelliteStateAtET(targetJD-jupiterGalileanReferenceJD, index, includeSolarLongPeriod)
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result = Vector3{
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jupiterHelio[0] + state.X - earthHelioJ2000[0],
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jupiterHelio[1] + state.Y - earthHelioJ2000[1],
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jupiterHelio[2] + state.Z - earthHelioJ2000[2],
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}
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nextLightTime := lightTimeDaysPerAU * vectorMagnitude(result)
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if math.Abs(nextLightTime-lightTime) < 1e-12 {
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break
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}
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lightTime = nextLightTime
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}
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return state, result
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}
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func jupiterAstrometricGeocentricVectorJ2000(jd float64, earthHelioJ2000 Vector3) (Vector3, float64) {
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lightTime := 0.0
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result := Vector3{}
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for i := 0; i < 8; i++ {
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jupiterHelio := rotateEclipticToEquatorial(jupiterHeliocentricVectorJ2000(jd-lightTime), orbitJ2000Obliquity)
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result = Vector3{
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jupiterHelio[0] - earthHelioJ2000[0],
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jupiterHelio[1] - earthHelioJ2000[1],
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jupiterHelio[2] - earthHelioJ2000[2],
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}
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nextLightTime := lightTimeDaysPerAU * vectorMagnitude(result)
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if math.Abs(nextLightTime-lightTime) < 1e-12 {
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return result, nextLightTime
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}
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lightTime = nextLightTime
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}
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return result, lightTime
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}
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func jupiterHeliocentricVectorJ2000(jd float64) Vector3 {
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return eclipticVectorAtReferenceEpoch(
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eclipticCartesian(
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planet.WherePlanet(4, 0, jd),
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planet.WherePlanet(4, 1, jd),
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planet.WherePlanet(4, 2, jd),
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),
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jd,
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orbitReferenceJD,
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)
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}
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func jupiterGalileanSatelliteStateAtET(et float64, index int, includeSolarLongPeriod bool) JupiterGalileanState {
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elements := jupiterGalileanElementsAtET(et, index, includeSolarLongPeriod)
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pv := jupiterGalileanElementsToPV(jupiterGalileanMu[index], elements)
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cosNode, sinNode := math.Cos(jupiterGalileanFrameNode), math.Sin(jupiterGalileanFrameNode)
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cosTilt, sinTilt := math.Cos(jupiterGalileanFrameTilt), math.Sin(jupiterGalileanFrameTilt)
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return JupiterGalileanState{
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X: pv[0]*cosNode - pv[1]*sinNode*cosTilt + pv[2]*sinTilt*sinNode,
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Y: pv[0]*sinNode + pv[1]*cosNode*cosTilt - pv[2]*sinTilt*cosNode,
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Z: pv[1]*sinTilt + pv[2]*cosTilt,
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VX: pv[3]*cosNode - pv[4]*sinNode*cosTilt + pv[5]*sinTilt*sinNode,
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VY: pv[3]*sinNode + pv[4]*cosNode*cosTilt - pv[5]*sinTilt*cosNode,
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VZ: pv[4]*sinTilt + pv[5]*cosTilt,
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}
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}
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type jupiterGalileanElements struct {
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A float64
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L float64
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K float64
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H float64
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Q float64
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P float64
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}
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func jupiterGalileanElementsAtET(et float64, index int, includeSolarLongPeriod bool) jupiterGalileanElements {
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longPeriod := jupiterGalileanEvaluateSeries(jupiterGalileanL1LongPeriodTerms[index], et+jupiterGalileanLongPeriodShift, et, includeSolarLongPeriod, index)
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crossPeriod := jupiterGalileanEvaluateSeries(jupiterGalileanL1CrossPeriodTerms[index], et, et, false, index)
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combined := jupiterGalileanElements{
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A: longPeriod.A + crossPeriod.A,
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L: longPeriod.L + crossPeriod.L + jupiterGalileanBaseMeanLongitudes[index]*et,
|
|||
|
|
K: longPeriod.K + crossPeriod.K,
|
|||
|
|
H: longPeriod.H + crossPeriod.H,
|
|||
|
|
Q: longPeriod.Q + crossPeriod.Q,
|
|||
|
|
P: longPeriod.P + crossPeriod.P,
|
|||
|
|
}
|
|||
|
|
combined.L = math.Atan2(math.Sin(combined.L), math.Cos(combined.L))
|
|||
|
|
if combined.L < 0 {
|
|||
|
|
combined.L += 2 * math.Pi
|
|||
|
|
}
|
|||
|
|
return combined
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func jupiterGalileanEvaluateSeries(blocks [4][]jupiterGalileanL1Term, angleTime, et float64, includeSolarLongPeriod bool, index int) jupiterGalileanElements {
|
|||
|
|
vals := [5]float64{}
|
|||
|
|
if includeSolarLongPeriod {
|
|||
|
|
x := (et/365.25 - 0.5*(812.721806990360-819.727638594856)) / (0.5 * (812.721806990360 - -819.727638594856))
|
|||
|
|
tn := [9]float64{1, x}
|
|||
|
|
for i := 2; i < len(tn); i++ {
|
|||
|
|
tn[i] = 2*x*tn[i-1] - tn[i-2]
|
|||
|
|
}
|
|||
|
|
for variable := 0; variable < len(vals); variable++ {
|
|||
|
|
sum := 0.0
|
|||
|
|
for term := 0; term < len(tn); term++ {
|
|||
|
|
sum += jupiterGalileanL1Chebyshev[index][variable][term] * tn[term]
|
|||
|
|
}
|
|||
|
|
vals[variable] = sum - 0.5*jupiterGalileanL1Chebyshev[index][variable][0]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
result := jupiterGalileanElements{}
|
|||
|
|
for blockIndex, terms := range blocks {
|
|||
|
|
realPart, imagPart := 0.0, 0.0
|
|||
|
|
for _, term := range terms {
|
|||
|
|
angle := term.Phase
|
|||
|
|
if term.Period != 0 {
|
|||
|
|
angle += 2 * math.Pi * angleTime / term.Period
|
|||
|
|
}
|
|||
|
|
realPart += term.Amp * math.Cos(angle)
|
|||
|
|
imagPart += term.Amp * math.Sin(angle)
|
|||
|
|
}
|
|||
|
|
switch blockIndex {
|
|||
|
|
case 0:
|
|||
|
|
result.A = realPart
|
|||
|
|
case 1:
|
|||
|
|
result.L = realPart + vals[0]
|
|||
|
|
case 2:
|
|||
|
|
result.K = realPart + vals[1]
|
|||
|
|
result.H = imagPart + vals[2]
|
|||
|
|
case 3:
|
|||
|
|
result.Q = realPart + vals[3]
|
|||
|
|
result.P = imagPart + vals[4]
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
return result
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func jupiterGalileanElementsToPV(mu float64, elements jupiterGalileanElements) [6]float64 {
|
|||
|
|
k := elements.K
|
|||
|
|
h := elements.H
|
|||
|
|
q := elements.Q
|
|||
|
|
p := elements.P
|
|||
|
|
a := elements.A
|
|||
|
|
al := elements.L
|
|||
|
|
an := math.Sqrt(mu / math.Pow(a, 3))
|
|||
|
|
ee := al + k*math.Sin(al) - h*math.Cos(al)
|
|||
|
|
for {
|
|||
|
|
ce := math.Cos(ee)
|
|||
|
|
se := math.Sin(ee)
|
|||
|
|
de := (al - ee + k*se - h*ce) / (1 - k*ce - h*se)
|
|||
|
|
ee += de
|
|||
|
|
if math.Abs(de) < 1e-12 {
|
|||
|
|
break
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
ce := math.Cos(ee)
|
|||
|
|
se := math.Sin(ee)
|
|||
|
|
dle := h*ce - k*se
|
|||
|
|
rsam1 := -k*ce - h*se
|
|||
|
|
asr := 1 / (1 + rsam1)
|
|||
|
|
phi := math.Sqrt(1 - k*k - h*h)
|
|||
|
|
psi := 1 / (1 + phi)
|
|||
|
|
x1 := a * (ce - k - psi*h*dle)
|
|||
|
|
y1 := a * (se - h + psi*k*dle)
|
|||
|
|
vx1 := an * asr * a * (-se - psi*h*rsam1)
|
|||
|
|
vy1 := an * asr * a * (ce + psi*k*rsam1)
|
|||
|
|
f2 := 2 * math.Sqrt(1-q*q-p*p)
|
|||
|
|
p2 := 1 - 2*p*p
|
|||
|
|
q2 := 1 - 2*q*q
|
|||
|
|
pq := 2 * p * q
|
|||
|
|
return [6]float64{
|
|||
|
|
x1*p2 + y1*pq,
|
|||
|
|
x1*pq + y1*q2,
|
|||
|
|
(q*y1 - x1*p) * f2,
|
|||
|
|
vx1*p2 + vy1*pq,
|
|||
|
|
vx1*pq + vy1*q2,
|
|||
|
|
(q*vy1 - vx1*p) * f2,
|
|||
|
|
}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func jupiterGalileanUseSolarLongPeriod(jd float64) bool {
|
|||
|
|
year := 2000.0 + (jd-2451545.0)/365.25
|
|||
|
|
return year >= jupiterGalileanMinSolarLPYear && year <= jupiterGalileanMaxSolarLPYear
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func invalidJupiterGalileanState() JupiterGalileanState {
|
|||
|
|
nan := math.NaN()
|
|||
|
|
return JupiterGalileanState{X: nan, Y: nan, Z: nan, VX: nan, VY: nan, VZ: nan}
|
|||
|
|
}
|
|||
|
|
|
|||
|
|
func invalidJupiterGalileanObservation() JupiterGalileanObservation {
|
|||
|
|
nan := math.NaN()
|
|||
|
|
return JupiterGalileanObservation{
|
|||
|
|
State: invalidJupiterGalileanState(),
|
|||
|
|
RA: nan,
|
|||
|
|
Dec: nan,
|
|||
|
|
Distance: nan,
|
|||
|
|
OffsetXArcsec: nan,
|
|||
|
|
OffsetYArcsec: nan,
|
|||
|
|
OffsetXJupiterRadii: nan,
|
|||
|
|
OffsetYJupiterRadii: nan,
|
|||
|
|
OffsetZJupiterRadii: nan,
|
|||
|
|
InFrontOfJupiter: false,
|
|||
|
|
}
|
|||
|
|
}
|