248 lines
6.9 KiB
Go
248 lines
6.9 KiB
Go
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package semianalytic
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import (
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"errors"
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"math"
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"sync"
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"b612.me/astro/internal/ephem"
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"b612.me/astro/planet/internal/semianalytic/lunar"
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"b612.me/astro/planet/internal/semianalytic/planets"
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)
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const (
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cKMPerDay = 299792.458 * 86400
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// 太阳史瓦西半径 2GM☉/c²，AU。
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srsAU = 1.97412574336e-8
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)
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var errInvalidObserver = errors.New("semianalytic: non-finite observer state")
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type observer struct {
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jd float64
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p, v [3]float64 // 地球日心位置 km、相对质心速度 km/日
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sunVel [3]float64 // 太阳相对质心速度 km/日
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}
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// 同一时刻常连续求多个天体，观测者状态缓存最近一次。
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var (
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observerMu sync.RWMutex
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observerCache observer
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observerSet bool
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)
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func observerAt(jd float64) (observer, error) {
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observerMu.RLock()
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c, set := observerCache, observerSet
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observerMu.RUnlock()
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if set && c.jd == jd {
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return c, nil
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}
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e, err := helio(ephem.Earth, jd)
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if err != nil {
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return observer{}, err
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}
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// 太阳质心速度只进光行差与光行时修正：快速档、只计四颗巨行星，内行星贡献 < 0.1 mas。
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var sv [3]float64
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_, total := planets.GM(1)
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for id := 1; id <= 4; id++ {
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gm, _ := planets.GM(id)
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total += gm
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}
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for id := 5; id <= 8; id++ {
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gm, _ := planets.GM(id)
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_, v, err := planets.Fast().HeliocentricState(id, jd)
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if err != nil {
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return observer{}, err
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}
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for i := range sv {
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sv[i] -= gm * v[i]
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}
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total += gm
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}
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o := observer{jd: jd, p: e.p}
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for i := range sv {
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sv[i] /= total
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o.sunVel[i] = sv[i]
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o.v[i] = e.v[i] + sv[i]
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// 坏表读出的非有限速度不得进缓存，否则同一时刻会一直返回 NaN 方向而 err 为 nil。
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if !finite(o.v[i]) || !finite(o.p[i]) {
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return observer{}, errInvalidObserver
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}
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}
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observerMu.Lock()
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observerCache, observerSet = o, true
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observerMu.Unlock()
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return o, nil
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}
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// targetHelio 目标日心位置；fast 用快速档，只作光行时初值与几何距离。
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func targetHelio(b ephem.Body, jd float64, fast bool) ([3]float64, error) {
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switch {
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case b == ephem.Sun:
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return [3]float64{}, nil
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case b == ephem.Moon:
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s, err := helio(ephem.Moon, jd)
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return s.p, err
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case b >= ephem.Mercury && b <= ephem.Neptune && b != ephem.EMB:
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if fast {
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return planets.Fast().Heliocentric(int(b), jd)
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}
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return planets.Default().Heliocentric(int(b), jd)
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}
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return [3]float64{}, ephem.ErrUnsupportedBody
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}
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type apparentEntry struct {
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jd float64
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dir [3]float64
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dist, tau float64
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set bool
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}
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var (
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apparentMu sync.RWMutex
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apparentCache [10]apparentEntry
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)
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func apparentStore(slot int, e apparentEntry) {
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e.set = true
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apparentMu.Lock()
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apparentCache[slot] = e
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apparentMu.Unlock()
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}
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// cacheSlot 天体对应的缓存槽；-1 表示不支持该天体。
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func cacheSlot(b ephem.Body) int {
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switch {
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case b == ephem.Sun:
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return 0
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case b == ephem.Moon:
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return 9
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case b >= ephem.Mercury && b <= ephem.Neptune && b != ephem.EMB:
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return int(b)
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}
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return -1
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}
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// Apparent 地心视方向（ICRF 单位矢量）、几何地心距 km、光行时 日 / geocentric apparent direction.
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func Apparent(target ephem.Body, jd float64) (dir [3]float64, distKM, tauDays float64, err error) {
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slot := cacheSlot(target)
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if slot < 0 {
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return dir, 0, 0, ephem.ErrUnsupportedBody
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}
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if !finite(jd) {
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return dir, 0, 0, ephem.ErrOutOfRange
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}
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apparentMu.RLock()
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c := apparentCache[slot]
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apparentMu.RUnlock()
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if c.set && c.jd == jd {
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return c.dir, c.dist, c.tau, nil
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}
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o, err := observerAt(jd)
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if err != nil {
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return dir, 0, 0, err
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}
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if target == ephem.Moon {
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e, err := apparentMoon(jd, o)
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if err != nil {
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return dir, 0, 0, err
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}
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apparentStore(slot, e)
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return e.dir, e.dist, e.tau, nil
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}
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now, err := targetHelio(target, jd, true)
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if err != nil {
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return dir, 0, 0, err
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}
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g := vsub(now, o.p)
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dist := vlen(g)
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tau := dist / cKMPerDay
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// 迭代光行时，每次误差缩小约 v/c 倍：先用快速档收敛 τ，末次用全表；太阳在 τ 内相对质心的位移按线性计入。
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var r [3]float64
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for k := 0; k < 2; k++ {
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if r, err = targetHelio(target, jd-tau, k == 0); err != nil {
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return dir, 0, 0, err
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}
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for i := range g {
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g[i] = r[i] - o.p[i] - o.sunVel[i]*tau
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}
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tau = vlen(g) / cKMPerDay
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}
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q := vscale(g, 1/vlen(g))
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if target != ephem.Sun && target != ephem.Moon {
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q = deflect(q, r, o.p)
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}
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q = aberrate(q, o.v)
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e := apparentEntry{jd: jd, dir: toICRF(q), dist: dist, tau: tau}
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apparentStore(slot, e)
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return e.dir, e.dist, e.tau, nil
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}
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// apparentMoon 月球地心视方向。光行时仅约 1.3 s，若像行星那样在 jd 与 jd−τ 各求一次地月质心
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// 日心位置（~1.5e8 km）再与地球相减，远历元表求值的舍入噪声（2981 年约 2e-4 km）会原样进入
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// 地心矢量，超过下游牛顿迭代的残差容差。这里全程用地心量：
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// 月球日心(jd−τ) − 地球日心(jd) = EMB(jd−τ) − EMB(jd) + f·m(jd−τ) + m(jd)/(1+μ)，
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// 其中 EMB 在 τ 内的位移按 jd 时刻速度线性外推，二阶项 ½aτ² < 1e-5 km。
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// 月球地心位置同样按 jd 时刻解析速度外推（½aτ² ≈ 2e-6 km）：直接求 m(jd−τ) 时，jd−τ 的舍入
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// （~4.7e-10 日）乘月球地心速度（~8.8e4 km/日）给出 ~1e-5 km 的逐点抖动，有限差分导数会把它放大。
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func apparentMoon(jd float64, o observer) (apparentEntry, error) {
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emb, err := planetHelio(int(ephem.EMB), jd)
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if err != nil {
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return apparentEntry{}, err
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}
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now, vel := lunar.Default().PositionVelocityJ2000(jd)
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dist := vlen(now)
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tau := dist / cKMPerDay
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f := emrat / (1 + emrat)
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g := now
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for k := 0; k < 2; k++ {
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for i := range g {
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g[i] = f*(now[i]-vel[i]*tau) + now[i]/(1+emrat) - (emb.v[i]+o.sunVel[i])*tau
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}
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tau = vlen(g) / cKMPerDay
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}
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q := aberrate(vscale(g, 1/vlen(g)), o.v)
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return apparentEntry{jd: jd, dir: toICRF(q), dist: dist, tau: tau}, nil
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}
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// deflect 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 deflect(p, t, e [3]float64) [3]float64 {
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em := vlen(e) / auKM
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eu := vscale(e, 1/vlen(e))
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q := vscale(t, 1/vlen(t))
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qpe := vdot(q, 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 := srsAU / em / qpe
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pe, pq := vdot(p, eu), vdot(p, q)
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// p × (e × q) = e(p·q) − q(p·e)
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for i := range p {
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p[i] += w * (eu[i]*pq - q[i]*pe)
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}
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return p
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}
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// aberrate 相对论光行差；v 观测者相对质心速度 km/日。
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func aberrate(p, v [3]float64) [3]float64 {
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b := vscale(v, 1/cKMPerDay)
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bm := 1 / math.Sqrt(1-vdot(b, b))
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pdv := vdot(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 vscale(r, 1/vlen(r))
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}
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func vdot(a, b [3]float64) float64 { return a[0]*b[0] + a[1]*b[1] + a[2]*b[2] }
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func vlen(a [3]float64) float64 { return math.Sqrt(vdot(a, a)) }
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func vsub(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 vscale(a [3]float64, k float64) [3]float64 { return [3]float64{a[0] * k, a[1] * k, a[2] * k} }
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