77 lines
2.5 KiB
Go
77 lines
2.5 KiB
Go
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package semianalytic
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import (
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"math"
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"testing"
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"b612.me/astro/internal/ephem"
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)
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// 视月球方向在远历元也必须是光滑函数：下游中心带牛顿迭代的残差容差约 2e-10，
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// 求值噪声需留出一个量级。二阶差分 RMS 按月地距折算成 km，h=1e-7 日时真实曲率项可忽略。
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func TestApparentMoonSmoothAtDistantEpochs(t *testing.T) {
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const h, n, limitKM = 1e-7, 200, 6e-5
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for _, jd0 := range []float64{2451545.0, 2460680.5, 2288000.5, 2810139.6097} {
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var prev [2][3]float64
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var sum float64
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for i := 0; i < n; i++ {
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d, _, _, err := Apparent(ephem.Moon, jd0+float64(i)*h)
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if err != nil {
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t.Fatal(err)
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}
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p := [3]float64{d[0] * 3.844e5, d[1] * 3.844e5, d[2] * 3.844e5}
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if i >= 2 {
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for k := range p {
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dd := p[k] - 2*prev[1][k] + prev[0][k]
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sum += dd * dd
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}
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}
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prev[0], prev[1] = prev[1], p
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}
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if rms := math.Sqrt(sum / (n - 2)); rms > limitKM {
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t.Errorf("jd %.1f: apparent Moon second-difference rms %.2e km, want <= %.0e", jd0, rms, limitKM)
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}
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}
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}
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// 地心化的光行时链与"两次日心相减"的旧链在数学上等价，只差 EMB 的二阶外推项（< 0.01 mas）。
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// 旧链自身带有 jd−τ 的舍入（~1e-10 日）乘地月质心速度（2.6e6 km/日）的误差，最大约 0.35 mas，
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// 因此容差取 0.5 mas；两者差值反映的是旧链误差，不是新链误差。
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func TestApparentMoonMatchesHeliocentricChain(t *testing.T) {
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for _, jd := range []float64{2451545.0, 2460409.25, 2433282.5, 2810139.6097, 2086000.5} {
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got, gd, gt, err := Apparent(ephem.Moon, jd)
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if err != nil {
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t.Fatal(err)
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}
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o, err := observerAt(jd)
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if err != nil {
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t.Fatal(err)
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}
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tau := gt
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r, err := targetHelio(ephem.Moon, jd-tau, false)
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if err != nil {
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t.Fatal(err)
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}
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var g [3]float64
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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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want := toICRF(aberrate(vscale(g, 1/vlen(g)), o.v))
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cx := got[1]*want[2] - got[2]*want[1]
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cy := got[2]*want[0] - got[0]*want[2]
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cz := got[0]*want[1] - got[1]*want[0]
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c := got[0]*want[0] + got[1]*want[1] + got[2]*want[2]
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mas := math.Atan2(math.Sqrt(cx*cx+cy*cy+cz*cz), c) * 206264806.2
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if mas > 0.5 {
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t.Errorf("jd %.1f: geocentric chain differs by %.4f mas", jd, mas)
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}
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now, err := targetHelio(ephem.Moon, jd, true)
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if err != nil {
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t.Fatal(err)
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}
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if wd := vlen(vsub(now, o.p)); math.Abs(gd-wd) > 1 {
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t.Errorf("jd %.1f: geometric distance %.3f km, heliocentric chain %.3f km", jd, gd, wd)
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}
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}
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}
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