89 lines
2.9 KiB
Go
89 lines
2.9 KiB
Go
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package ephem
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import "math"
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const (
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genericCKMPerDay = 299792.458 * 86400
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genericAUKM = 149597870.7
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// 太阳史瓦西半径 2GM☉/c²，AU。
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genericSunSchwarzschildAU = 1.97412574336e-8
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)
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// genericApparent 用 Engine.State 求地心视方向：迭代光行时、太阳引力偏折、相对论光行差，均在 ICRF 中进行。
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// 引擎不能给出相对太阳系质心的地球、太阳或目标状态时返回 ErrUnsupportedApparent。
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func genericApparent(engine Engine, target Body, jdTT float64) (dir [3]float64, distKM, tauDays float64, err error) {
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earth, earthVel, err := engine.State(Earth, SSB, jdTT)
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if err != nil {
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return dir, 0, 0, ErrUnsupportedApparent
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}
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now, _, err := engine.State(target, SSB, jdTT)
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if err != nil {
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return dir, 0, 0, ErrUnsupportedApparent
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}
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g := genericSub(now, earth)
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distKM = genericLen(g)
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if !(distKM > 0) || math.IsInf(distKM, 0) {
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return dir, 0, 0, ErrUnsupportedApparent
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}
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tauDays = distKM / genericCKMPerDay
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var retarded [3]float64
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for k := 0; k < 3; k++ {
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if retarded, _, err = engine.State(target, SSB, jdTT-tauDays); err != nil {
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return dir, 0, 0, ErrUnsupportedApparent
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}
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g = genericSub(retarded, earth)
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tauDays = genericLen(g) / genericCKMPerDay
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}
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q := genericScale(g, 1/genericLen(g))
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if target != Sun && target != Moon && target != Earth {
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sunThen, _, sunErr := engine.State(Sun, SSB, jdTT-tauDays)
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sunNow, _, sunNowErr := engine.State(Sun, SSB, jdTT)
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if sunErr == nil && sunNowErr == nil {
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q = genericDeflect(q, genericSub(retarded, sunThen), genericSub(earth, sunNow))
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}
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}
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return genericAberrate(q, earthVel), distKM, tauDays, nil
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}
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// genericDeflect 太阳引力偏折；p 目标方向，t 目标日心位置，e 地球日心位置。
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func genericDeflect(p, t, e [3]float64) [3]float64 {
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el, tl := genericLen(e), genericLen(t)
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if el <= 0 || tl <= 0 {
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return p
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}
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eu, qu := genericScale(e, 1/el), genericScale(t, 1/tl)
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qpe := genericDot(qu, eu) + 1
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if qpe < 1e-9 {
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return p
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}
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w := genericSunSchwarzschildAU / (el / genericAUKM) / qpe
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pe, pq := genericDot(p, eu), genericDot(p, qu)
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for i := range p {
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p[i] += w * (eu[i]*pq - qu[i]*pe)
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}
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return genericScale(p, 1/genericLen(p))
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}
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// genericAberrate 相对论光行差；v 观测者相对质心速度 km/日。
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func genericAberrate(p, v [3]float64) [3]float64 {
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b := genericScale(v, 1/genericCKMPerDay)
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bm := 1 / math.Sqrt(1-genericDot(b, b))
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pdv := genericDot(p, b)
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w1 := 1 + pdv/(1+1/bm)
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w2 := 1 / (1 + pdv)
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var r [3]float64
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for i := range p {
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r[i] = (p[i]/bm + w1*b[i]) * w2
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}
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return genericScale(r, 1/genericLen(r))
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}
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func genericDot(a, b [3]float64) float64 { return a[0]*b[0] + a[1]*b[1] + a[2]*b[2] }
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func genericLen(a [3]float64) float64 { return math.Sqrt(genericDot(a, a)) }
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func genericSub(a, b [3]float64) [3]float64 {
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return [3]float64{a[0] - b[0], a[1] - b[1], a[2] - b[2]}
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}
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func genericScale(a [3]float64, k float64) [3]float64 {
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return [3]float64{a[0] * k, a[1] * k, a[2] * k}
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}
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