371 lines
13 KiB
Go
371 lines
13 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 astronomicalUnitLightTimeDays = 0.0057755183
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type planetPhysicalModel struct {
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planetIndex int
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positiveEast bool
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equatorialRadius float64
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polarRadius float64
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poleRotation func(float64) (ra, dec, rotationEast float64)
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}
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type phaseAngleModel struct {
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base float64
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rate float64
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accelRate float64
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}
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// PlanetPhysicalInfo 行星物理观测参数 / planetary physical observing parameters.
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type PlanetPhysicalInfo struct {
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// SubEarthLongitude 子地经度，单位度；正方向遵循该天体当前 IAU/Horizons 制图约定。
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SubEarthLongitude float64
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// SubEarthLatitude 子地纬度，单位度。
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SubEarthLatitude float64
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// SubSolarLongitude 子日经度，单位度；正方向遵循该天体当前 IAU/Horizons 制图约定。
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SubSolarLongitude float64
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// SubSolarLatitude 子日纬度，单位度。
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SubSolarLatitude float64
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// NorthPolePositionAngle 天体北极位置角，单位度。
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NorthPolePositionAngle float64
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}
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var (
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mercuryPhysicalModel = planetPhysicalModel{
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planetIndex: 1,
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positiveEast: false,
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equatorialRadius: 2440.53,
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polarRadius: 2438.26,
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poleRotation: mercuryPoleRotation,
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}
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venusPhysicalModel = planetPhysicalModel{
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planetIndex: 2,
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positiveEast: true,
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equatorialRadius: 6051.8,
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polarRadius: 6051.8,
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poleRotation: venusPoleRotation,
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}
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marsPhysicalModel = planetPhysicalModel{
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planetIndex: 3,
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positiveEast: false,
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equatorialRadius: 3396.19,
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polarRadius: 3376.20,
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poleRotation: marsPoleRotation,
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}
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jupiterPhysicalModel = planetPhysicalModel{
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planetIndex: 4,
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positiveEast: false,
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equatorialRadius: 71492.0,
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polarRadius: 66854.0,
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poleRotation: jupiterPoleRotation,
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}
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saturnPhysicalModel = planetPhysicalModel{
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planetIndex: 5,
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positiveEast: false,
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equatorialRadius: 60268.0,
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polarRadius: 54364.0,
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poleRotation: saturnPoleRotation,
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}
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uranusPhysicalModel = planetPhysicalModel{
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planetIndex: 6,
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positiveEast: true,
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equatorialRadius: 25559.0,
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polarRadius: 24973.0,
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poleRotation: uranusPoleRotation,
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}
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neptunePhysicalModel = planetPhysicalModel{
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planetIndex: 7,
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positiveEast: false,
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equatorialRadius: 24764.0,
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polarRadius: 24341.0,
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poleRotation: neptunePoleRotation,
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}
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)
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// MercuryPhysical 水星物理观测参数 / physical observing parameters of Mercury.
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func MercuryPhysical(jd float64) PlanetPhysicalInfo {
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return MercuryPhysicalN(jd, -1)
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}
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// MercuryPhysicalN 水星物理观测参数（截断版） / truncated physical observing parameters of Mercury.
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func MercuryPhysicalN(jd float64, n int) PlanetPhysicalInfo {
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return planetPhysicalN(jd, n, mercuryPhysicalModel)
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}
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// VenusPhysical 金星物理观测参数 / physical observing parameters of Venus.
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func VenusPhysical(jd float64) PlanetPhysicalInfo {
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return VenusPhysicalN(jd, -1)
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}
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// VenusPhysicalN 金星物理观测参数（截断版） / truncated physical observing parameters of Venus.
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func VenusPhysicalN(jd float64, n int) PlanetPhysicalInfo {
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return planetPhysicalN(jd, n, venusPhysicalModel)
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}
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// MarsPhysical 火星物理观测参数 / physical observing parameters of Mars.
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func MarsPhysical(jd float64) PlanetPhysicalInfo {
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return MarsPhysicalN(jd, -1)
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}
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// MarsPhysicalN 火星物理观测参数（截断版） / truncated physical observing parameters of Mars.
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func MarsPhysicalN(jd float64, n int) PlanetPhysicalInfo {
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return planetPhysicalN(jd, n, marsPhysicalModel)
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}
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// JupiterPhysical 木星物理观测参数 / physical observing parameters of Jupiter.
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func JupiterPhysical(jd float64) PlanetPhysicalInfo {
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return JupiterPhysicalN(jd, -1)
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}
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// JupiterPhysicalN 木星物理观测参数（截断版） / truncated physical observing parameters of Jupiter.
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func JupiterPhysicalN(jd float64, n int) PlanetPhysicalInfo {
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return planetPhysicalN(jd, n, jupiterPhysicalModel)
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}
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// SaturnPhysical 土星物理观测参数 / physical observing parameters of Saturn.
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func SaturnPhysical(jd float64) PlanetPhysicalInfo {
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return SaturnPhysicalN(jd, -1)
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}
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// SaturnPhysicalN 土星物理观测参数（截断版） / truncated physical observing parameters of Saturn.
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func SaturnPhysicalN(jd float64, n int) PlanetPhysicalInfo {
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return planetPhysicalN(jd, n, saturnPhysicalModel)
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}
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// UranusPhysical 天王星物理观测参数 / physical observing parameters of Uranus.
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func UranusPhysical(jd float64) PlanetPhysicalInfo {
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return UranusPhysicalN(jd, -1)
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}
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// UranusPhysicalN 天王星物理观测参数（截断版） / truncated physical observing parameters of Uranus.
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func UranusPhysicalN(jd float64, n int) PlanetPhysicalInfo {
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return planetPhysicalN(jd, n, uranusPhysicalModel)
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}
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// NeptunePhysical 海王星物理观测参数 / physical observing parameters of Neptune.
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func NeptunePhysical(jd float64) PlanetPhysicalInfo {
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return NeptunePhysicalN(jd, -1)
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}
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// NeptunePhysicalN 海王星物理观测参数（截断版） / truncated physical observing parameters of Neptune.
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func NeptunePhysicalN(jd float64, n int) PlanetPhysicalInfo {
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return planetPhysicalN(jd, n, neptunePhysicalModel)
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}
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func planetPhysicalN(jd float64, n int, model planetPhysicalModel) PlanetPhysicalInfo {
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initialX, initialY, initialZ := planetXYZN(model.planetIndex, jd, n)
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targetVector := Vector3{initialX, initialY, initialZ}
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lightTimeDays := astronomicalUnitLightTimeDays * vectorMagnitude(targetVector)
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targetJD := jd - lightTimeDays
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geoX, geoY, geoZ := planetXYZN(model.planetIndex, targetJD, n)
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geocentricVector := Vector3{geoX, geoY, geoZ}
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observerDirection := normalizeVector(Vector3{-geocentricVector[0], -geocentricVector[1], -geocentricVector[2]})
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heliocentricLongitude := planet.WherePlanetN(model.planetIndex, 0, targetJD, n)
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heliocentricLatitude := planet.WherePlanetN(model.planetIndex, 1, targetJD, n)
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solarDirection := normalizeVector(eclipticCartesian(heliocentricLongitude+180, -heliocentricLatitude, 1))
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obliquity := EclipticObliquity(targetJD, false)
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observerEquatorial := normalizeVector(rotateEclipticToEquatorial(observerDirection, obliquity))
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solarEquatorial := normalizeVector(rotateEclipticToEquatorial(solarDirection, obliquity))
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poleRA, poleDec, rotationEast := model.poleRotation(targetJD)
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poleJ2000 := raDecToVector(poleRA, poleDec)
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nodeJ2000 := Vector3{-math.Sin(poleRA * rad), math.Cos(poleRA * rad), 0}
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eastJ2000 := normalizeVector(pxp(poleJ2000, nodeJ2000))
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primeMeridianJ2000 := normalizeVector(Vector3{
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nodeJ2000[0]*Cos(rotationEast) + eastJ2000[0]*Sin(rotationEast),
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nodeJ2000[1]*Cos(rotationEast) + eastJ2000[1]*Sin(rotationEast),
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nodeJ2000[2]*Cos(rotationEast) + eastJ2000[2]*Sin(rotationEast),
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})
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j2000ToDate := precessionMatrix(2451545.0, targetJD)
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poleDate := normalizeVector(applyMatrix3(j2000ToDate, poleJ2000))
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primeMeridianDate := normalizeVector(applyMatrix3(j2000ToDate, primeMeridianJ2000))
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eastDate := normalizeVector(pxp(poleDate, primeMeridianDate))
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poleRAOfDate, poleDecOfDate := vectorToRaDec(poleDate)
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planetRA, planetDec := vectorToRaDec(observerEquatorial)
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return PlanetPhysicalInfo{
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SubEarthLongitude: bodyLongitude(observerEquatorial, primeMeridianDate, eastDate, model.positiveEast),
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SubEarthLatitude: bodyLatitude(observerEquatorial, poleDate, model.equatorialRadius, model.polarRadius),
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SubSolarLongitude: bodyLongitude(solarEquatorial, primeMeridianDate, eastDate, model.positiveEast),
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SubSolarLatitude: bodyLatitude(solarEquatorial, poleDate, model.equatorialRadius, model.polarRadius),
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NorthPolePositionAngle: northPolePositionAngle(planetRA, planetDec, poleRAOfDate, poleDecOfDate),
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}
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}
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func bodyLongitude(direction, primeMeridian, eastAxis Vector3, positiveEast bool) float64 {
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eastLongitude := Limit360(math.Atan2(vectorDot(direction, eastAxis), vectorDot(direction, primeMeridian)) * deg)
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if positiveEast {
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return eastLongitude
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}
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return Limit360(360 - eastLongitude)
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}
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func bodyLatitude(direction, pole Vector3, equatorialRadius, polarRadius float64) float64 {
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geocentricLatitude := ArcSin(vectorDot(direction, pole))
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if equatorialRadius == polarRadius {
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return geocentricLatitude
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}
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ratio := (polarRadius * polarRadius) / (equatorialRadius * equatorialRadius)
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return math.Atan2(math.Sin(geocentricLatitude*rad), math.Cos(geocentricLatitude*rad)*ratio) * deg
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}
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func northPolePositionAngle(planetRA, planetDec, poleRA, poleDec float64) float64 {
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y := math.Cos(poleDec*rad) * math.Sin((poleRA-planetRA)*rad)
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x := math.Sin(poleDec*rad)*math.Cos(planetDec*rad) -
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math.Cos(poleDec*rad)*math.Sin(planetDec*rad)*math.Cos((poleRA-planetRA)*rad)
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return Limit360(-math.Atan2(y, x) * deg)
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}
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func vectorDot(a, b Vector3) float64 {
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return a[0]*b[0] + a[1]*b[1] + a[2]*b[2]
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}
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func vectorMagnitude(vector Vector3) float64 {
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return math.Sqrt(vectorDot(vector, vector))
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}
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func normalizeVector(vector Vector3) Vector3 {
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normalized, magnitude := pn(vector)
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if magnitude == 0 {
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return Vector3{}
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}
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return normalized
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}
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func mercuryPoleRotation(jd float64) (ra, dec, rotationEast float64) {
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days := jd - 2451545.0
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julianCentury := days / 36525.0
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m1 := Limit360(174.7910857 + 4.092335*days)
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m2 := Limit360(349.5821714 + 8.184670*days)
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m3 := Limit360(164.3732571 + 12.277005*days)
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m4 := Limit360(339.1643429 + 16.369340*days)
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m5 := Limit360(153.9554286 + 20.461675*days)
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ra = 281.0103 - 0.0328*julianCentury
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dec = 61.4155 - 0.0049*julianCentury
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rotationEast = 329.5988 + 6.1385108*days +
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0.01067257*Sin(m1) -
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0.00112309*Sin(m2) -
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0.00011040*Sin(m3) -
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0.00002539*Sin(m4) -
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0.00000571*Sin(m5)
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return
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}
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func venusPoleRotation(jd float64) (ra, dec, rotationEast float64) {
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days := jd - 2451545.0
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return 272.76, 67.16, 160.20 - 1.4813688*days
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}
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// Mars/Jupiter orientation terms follow the official NAIF text PCK `pck00011.tpc`.
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var (
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marsPoleRAAngles = [...]phaseAngleModel{
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{198.991226, 19139.4819985, 0},
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{226.292679, 38280.8511281, 0},
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{249.663391, 57420.7251593, 0},
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{266.183510, 76560.6367950, 0},
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{79.398797, 0.5042615, 0},
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}
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marsPoleRACoefficients = [...]float64{0.000068, 0.000238, 0.000052, 0.000009, 0.419057}
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marsPoleDECAngles = [...]phaseAngleModel{
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{122.433576, 19139.9407476, 0},
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{43.058401, 38280.8753272, 0},
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{57.663379, 57420.7517205, 0},
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{79.476401, 76560.6495004, 0},
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{166.325722, 0.5042615, 0},
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}
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marsPoleDECCoefficients = [...]float64{0.000051, 0.000141, 0.000031, 0.000005, 1.591274}
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marsPrimeMeridianAngles = [...]phaseAngleModel{
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{129.071773, 19140.0328244, 0},
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{36.352167, 38281.0473591, 0},
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{56.668646, 57420.9295360, 0},
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{67.364003, 76560.2552215, 0},
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{104.792680, 95700.4387578, 0},
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{95.391654, 0.5042615, 0},
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}
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marsPrimeMeridianCoefficients = [...]float64{0.000145, 0.000157, 0.000040, 0.000001, 0.000001, 0.584542}
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jupiterPoleAngles = [...]phaseAngleModel{
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{99.360714, 4850.4046, 0},
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{175.895369, 1191.9605, 0},
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{300.323162, 262.5475, 0},
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{114.012305, 6070.2476, 0},
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{49.511251, 64.3000, 0},
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}
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jupiterPoleRACoefficients = [...]float64{0.000117, 0.000938, 0.001432, 0.000030, 0.002150}
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jupiterPoleDECCoefficients = [...]float64{0.000050, 0.000404, 0.000617, -0.000013, 0.000926}
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)
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func marsPoleRotation(jd float64) (ra, dec, rotationEast float64) {
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days := jd - 2451545.0
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julianCentury := days / 36525.0
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ra = 317.269202 - 0.10927547*julianCentury + sumSinOrientationTerms(marsPoleRAAngles[:], marsPoleRACoefficients[:], julianCentury)
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dec = 54.432516 - 0.05827105*julianCentury + sumCosOrientationTerms(marsPoleDECAngles[:], marsPoleDECCoefficients[:], julianCentury)
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rotationEast = 176.049863 + 350.891982443297*days +
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sumSinOrientationTerms(marsPrimeMeridianAngles[:], marsPrimeMeridianCoefficients[:], julianCentury)
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return
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}
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func jupiterPoleRotation(jd float64) (ra, dec, rotationEast float64) {
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days := jd - 2451545.0
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julianCentury := days / 36525.0
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ra = 268.056595 - 0.006499*julianCentury + sumSinOrientationTerms(jupiterPoleAngles[:], jupiterPoleRACoefficients[:], julianCentury)
|
||
|
|
dec = 64.495303 + 0.002413*julianCentury + sumCosOrientationTerms(jupiterPoleAngles[:], jupiterPoleDECCoefficients[:], julianCentury)
|
||
|
|
rotationEast = 284.95 + 870.5360000*days
|
||
|
|
return
|
||
|
|
}
|
||
|
|
|
||
|
|
func saturnPoleRotation(jd float64) (ra, dec, rotationEast float64) {
|
||
|
|
days := jd - 2451545.0
|
||
|
|
julianCentury := days / 36525.0
|
||
|
|
ra = 40.589 - 0.036*julianCentury
|
||
|
|
dec = 83.537 - 0.004*julianCentury
|
||
|
|
rotationEast = 38.90 + 810.7939024*days
|
||
|
|
return
|
||
|
|
}
|
||
|
|
|
||
|
|
func uranusPoleRotation(jd float64) (ra, dec, rotationEast float64) {
|
||
|
|
days := jd - 2451545.0
|
||
|
|
return 257.311, -15.175, 203.81 - 501.1600928*days
|
||
|
|
}
|
||
|
|
|
||
|
|
func neptunePoleRotation(jd float64) (ra, dec, rotationEast float64) {
|
||
|
|
days := jd - 2451545.0
|
||
|
|
julianCentury := days / 36525.0
|
||
|
|
n := Limit360(357.85 + 52.316*julianCentury)
|
||
|
|
ra = 299.36 + 0.70*Sin(n)
|
||
|
|
dec = 43.46 - 0.51*Cos(n)
|
||
|
|
rotationEast = 249.978 + 541.1397757*days - 0.48*Sin(n)
|
||
|
|
return
|
||
|
|
}
|
||
|
|
|
||
|
|
func (model phaseAngleModel) at(julianCentury float64) float64 {
|
||
|
|
return Limit360(model.base + model.rate*julianCentury + model.accelRate*julianCentury*julianCentury)
|
||
|
|
}
|
||
|
|
|
||
|
|
func sumSinOrientationTerms(angles []phaseAngleModel, coefficients []float64, julianCentury float64) float64 {
|
||
|
|
sum := 0.0
|
||
|
|
for i, angle := range angles {
|
||
|
|
sum += coefficients[i] * Sin(angle.at(julianCentury))
|
||
|
|
}
|
||
|
|
return sum
|
||
|
|
}
|
||
|
|
|
||
|
|
func sumCosOrientationTerms(angles []phaseAngleModel, coefficients []float64, julianCentury float64) float64 {
|
||
|
|
sum := 0.0
|
||
|
|
for i, angle := range angles {
|
||
|
|
sum += coefficients[i] * Cos(angle.at(julianCentury))
|
||
|
|
}
|
||
|
|
return sum
|
||
|
|
}
|