310 lines
7.7 KiB
Go
310 lines
7.7 KiB
Go
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package basic
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import "math"
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// Precess 函数实现了基于 Explanatory Supplement 2nd ed. table 3.211.1 的岁差计算
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// ra0, dec0: 初始赤经和赤纬（弧度）
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// JD0: 初始儒略日
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// JD: 目标儒略日
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// 返回: 目标历元的赤经和赤纬（弧度）
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func PrecessIAU1976(ra0, dec0, JD0, JD float64) (float64, float64) {
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// 定义常量
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ra0 *= rad
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dec0 *= rad
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t := (JD - JD0) / 36525.0
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T := (JD0 - 2451545.0) / 36525.0
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// Explanatory Supplement 2nd ed. table 3.211.1
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zeta := ((2306.2181+1.39656*T-0.000139*T*T)*t +
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(0.30188-0.000344*T)*t*t + 0.017998*t*t*t) / 3600.0 * rad
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z := ((2306.2181+1.39656*T-0.000139*T*T)*t +
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(1.09468+0.000066*T)*t*t + 0.018203*t*t*t) / 3600.0 * rad
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theta := ((2004.3109-0.85330*T-0.000217*T*T)*t -
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(0.42665+0.000217*T)*t*t - 0.041833*t*t*t) / 3600.0 * rad
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A := math.Cos(dec0) * math.Sin(ra0+z)
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B := math.Cos(theta)*math.Cos(dec0)*math.Cos(ra0+z) - math.Sin(theta)*math.Sin(dec0)
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C := math.Sin(theta)*math.Cos(dec0)*math.Cos(ra0+z) + math.Cos(theta)*math.Sin(dec0)
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raMinZ := math.Atan2(A, B)
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dec := math.Asin(C)
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ra := raMinZ + zeta
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return ra / rad, dec / rad
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}
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// 常量定义
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const (
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AS2R = 4.848136811095359935899141e-6 // 角秒到弧度的转换因子
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D2PI = 6.283185307179586476925287 // 2π
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EPS0 = 84381.406 * AS2R // J2000.0历元的黄赤交角(弧度)
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)
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// 赤道坐标结构体
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type Equatorial struct {
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RA float64 // 赤经(度)
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Dec float64 // 赤纬(度)
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}
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// 三维向量
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type Vector3 [3]float64
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// 三维矩阵
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type Matrix3 [3][3]float64
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// 计算长期岁差的黄极向量
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func ltpPECL(epj float64) Vector3 {
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// 多项式系数
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pqPol := [2][4]float64{
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{+5851.607687, -0.1189000, -0.00028913, +0.000000101},
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{-1600.886300, +1.1689818, -0.00000020, -0.000000437},
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}
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// 周期项系数
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pqPer := [8][5]float64{
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{708.15, -5486.751211, -684.661560, 667.666730, -5523.863691},
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{2309.00, -17.127623, 2446.283880, -2354.886252, -549.747450},
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{1620.00, -617.517403, 399.671049, -428.152441, -310.998056},
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{492.20, 413.442940, -356.652376, 376.202861, 421.535876},
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{1183.00, 78.614193, -186.387003, 184.778874, -36.776172},
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{622.00, -180.732815, -316.800070, 335.321713, -145.278396},
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{882.00, -87.676083, 198.296071, -185.138669, -34.744450},
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{547.00, 46.140315, 101.135679, -120.972830, 22.885731},
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}
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// 计算从J2000.0起算的儒略世纪数
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t := (epj - 2000.0) / 100.0
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// 初始化P和Q累加器
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p, q := 0.0, 0.0
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// 周期项
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for i := 0; i < 8; i++ {
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w := D2PI * t
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a := w / pqPer[i][0]
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s := math.Sin(a)
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c := math.Cos(a)
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p += c*pqPer[i][1] + s*pqPer[i][3]
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q += c*pqPer[i][2] + s*pqPer[i][4]
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}
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// 多项式项
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w := 1.0
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for i := 0; i < 4; i++ {
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p += pqPol[0][i] * w
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q += pqPol[1][i] * w
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w *= t
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}
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// 转换为弧度
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p *= AS2R
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q *= AS2R
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// 形成黄极向量
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z := math.Sqrt(math.Max(1.0-p*p-q*q, 0.0))
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s := math.Sin(EPS0)
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c := math.Cos(EPS0)
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return Vector3{p, -q*c - z*s, -q*s + z*c}
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}
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// 计算长期岁差的赤道极向量
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func ltpPEQU(epj float64) Vector3 {
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// 多项式系数
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xyPol := [2][4]float64{
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{+5453.282155, +0.4252841, -0.00037173, -0.000000152},
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{-73750.930350, -0.7675452, -0.00018725, +0.000000231},
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}
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// 周期项系数
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xyPer := [14][5]float64{
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{256.75, -819.940624, 75004.344875, 81491.287984, 1558.515853},
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{708.15, -8444.676815, 624.033993, 787.163481, 7774.939698},
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{274.20, 2600.009459, 1251.136893, 1251.296102, -2219.534038},
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{241.45, 2755.175630, -1102.212834, -1257.950837, -2523.969396},
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{2309.00, -167.659835, -2660.664980, -2966.799730, 247.850422},
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{492.20, 871.855056, 699.291817, 639.744522, -846.485643},
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{396.10, 44.769698, 153.167220, 131.600209, -1393.124055},
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{288.90, -512.313065, -950.865637, -445.040117, 368.526116},
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{231.10, -819.415595, 499.754645, 584.522874, 749.045012},
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{1610.00, -538.071099, -145.188210, -89.756563, 444.704518},
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{620.00, -189.793622, 558.116553, 524.429630, 235.934465},
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{157.87, -402.922932, -23.923029, -13.549067, 374.049623},
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{220.30, 179.516345, -165.405086, -210.157124, -171.330180},
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{1200.00, -9.814756, 9.344131, -44.919798, -22.899655},
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}
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// 计算从J2000.0起算的儒略世纪数
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t := (epj - 2000.0) / 100.0
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// 初始化X和Y累加器
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x, y := 0.0, 0.0
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// 周期项
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for i := 0; i < 14; i++ {
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w := D2PI * t
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a := w / xyPer[i][0]
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s := math.Sin(a)
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c := math.Cos(a)
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x += c*xyPer[i][1] + s*xyPer[i][3]
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y += c*xyPer[i][2] + s*xyPer[i][4]
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}
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// 多项式项
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w := 1.0
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for i := 0; i < 4; i++ {
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x += xyPol[0][i] * w
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y += xyPol[1][i] * w
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w *= t
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}
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// 转换为弧度
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x *= AS2R
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y *= AS2R
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// 形成赤道极向量
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w = x*x + y*y
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z := 0.0
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if w < 1.0 {
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z = math.Sqrt(1.0 - w)
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}
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return Vector3{x, y, z}
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}
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// 向量叉乘
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func pxp(a, b Vector3) Vector3 {
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return Vector3{
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a[1]*b[2] - a[2]*b[1],
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a[2]*b[0] - a[0]*b[2],
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a[0]*b[1] - a[1]*b[0],
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}
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}
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// 向量归一化
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func pn(p Vector3) (Vector3, float64) {
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w := math.Sqrt(p[0]*p[0] + p[1]*p[1] + p[2]*p[2])
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if w == 0.0 {
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return Vector3{0, 0, 0}, 0
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}
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return Vector3{p[0] / w, p[1] / w, p[2] / w}, w
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}
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// 计算长期岁差矩阵
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func ltpPMAT(epj float64) Matrix3 {
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// 计算赤道极向量和黄极向量
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peqr := ltpPEQU(epj)
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pecl := ltpPECL(epj)
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// 计算春分点向量
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v := pxp(peqr, pecl)
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eqx, _ := pn(v)
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// 计算中间行向量
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v = pxp(peqr, eqx)
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// 形成旋转矩阵
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return Matrix3{
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{eqx[0], eqx[1], eqx[2]},
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{v[0], v[1], v[2]},
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{peqr[0], peqr[1], peqr[2]},
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}
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}
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// 计算包含GCRS框架偏差的长期岁差矩阵
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func ltpPBMAT(epj float64) Matrix3 {
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// 框架偏差 (IERS Conventions 2010, Eqs. 5.21 and 5.33)
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dx := -0.016617 * AS2R
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de := -0.0068192 * AS2R
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dr := -0.0146 * AS2R
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// 计算基本岁差矩阵
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rp := ltpPMAT(epj)
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// 应用偏差
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return Matrix3{
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{
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rp[0][0] - rp[0][1]*dr + rp[0][2]*dx,
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rp[0][0]*dr + rp[0][1] + rp[0][2]*de,
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-rp[0][0]*dx - rp[0][1]*de + rp[0][2],
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},
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{
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rp[1][0] - rp[1][1]*dr + rp[1][2]*dx,
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rp[1][0]*dr + rp[1][1] + rp[1][2]*de,
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-rp[1][0]*dx - rp[1][1]*de + rp[1][2],
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},
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{
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rp[2][0] - rp[2][1]*dr + rp[2][2]*dx,
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rp[2][0]*dr + rp[2][1] + rp[2][2]*de,
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-rp[2][0]*dx - rp[2][1]*de + rp[2][2],
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},
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}
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}
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// 将赤道坐标转换为直角坐标向量
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func raDecToVector(ra, dec float64) Vector3 {
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raRad := ra * math.Pi / 180
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decRad := dec * math.Pi / 180
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cosDec := math.Cos(decRad)
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return Vector3{
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math.Cos(raRad) * cosDec,
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math.Sin(raRad) * cosDec,
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math.Sin(decRad),
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}
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}
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// 将直角坐标向量转换为赤道坐标
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func vectorToRaDec(v Vector3) (float64, float64) {
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dec := math.Asin(v[2]) * 180 / math.Pi
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ra := math.Atan2(v[1], v[0]) * 180 / math.Pi
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if ra < 0 {
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ra += 360
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}
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return ra, dec
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}
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// 应用长期岁差转换
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func Precess(ra, dec, jdFrom, jdTo float64) (float64, float64) {
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// 将儒略日转换为儒略纪元
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epjFrom := 2000.0 + (jdFrom-2451545.0)/365.25
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epjTo := 2000.0 + (jdTo-2451545.0)/365.25
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// 计算从起始历元到J2000.0的逆矩阵
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rpFrom := ltpPMAT(epjFrom)
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rpFromInv := Matrix3{
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{rpFrom[0][0], rpFrom[1][0], rpFrom[2][0]},
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{rpFrom[0][1], rpFrom[1][1], rpFrom[2][1]},
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{rpFrom[0][2], rpFrom[1][2], rpFrom[2][2]},
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}
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// 计算从J2000.0到目标历元的矩阵
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rpTo := ltpPMAT(epjTo)
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// 计算复合旋转矩阵
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var rpFinal Matrix3
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for i := 0; i < 3; i++ {
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for j := 0; j < 3; j++ {
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for k := 0; k < 3; k++ {
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rpFinal[i][j] += rpTo[i][k] * rpFromInv[k][j]
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}
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}
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}
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// 将赤道坐标转换为直角坐标向量
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vector := raDecToVector(ra, dec)
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// 应用旋转矩阵
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rotatedVector := Vector3{
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rpFinal[0][0]*vector[0] + rpFinal[0][1]*vector[1] + rpFinal[0][2]*vector[2],
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rpFinal[1][0]*vector[0] + rpFinal[1][1]*vector[1] + rpFinal[1][2]*vector[2],
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rpFinal[2][0]*vector[0] + rpFinal[2][1]*vector[1] + rpFinal[2][2]*vector[2],
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}
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// 将直角坐标向量转换回赤道坐标
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return vectorToRaDec(rotatedVector)
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}
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