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