astro/internal/ltp/ltp.go

// Package ltp 长期岁差的黄极与赤道极向量（J2000 平赤道坐标，±20 万年有效）。
package ltp

import "math"

const (
	as2r = 4.848136811095359935899141e-6
	d2pi = 6.283185307179586476925287
	eps0 = 84381.406 * as2r
)

// Vector3 三维向量 / a 3-vector.
type Vector3 [3]float64

// EclipticPole 历元平黄道极 / mean ecliptic pole of epoch, epj in Julian years.
func EclipticPole(epj float64) Vector3 {
	pqPol := [2][4]float64{
		{+5851.607687, -0.1189000, -0.00028913, +0.000000101},
		{-1600.886300, +1.1689818, -0.00000020, -0.000000437},
	}
	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},
	}
	t := (epj - 2000.0) / 100.0
	p, q := 0.0, 0.0
	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]
	}
	w := 1.0
	for i := 0; i < 4; i++ {
		p += pqPol[0][i] * w
		q += pqPol[1][i] * w
		w *= t
	}
	p *= as2r
	q *= as2r
	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}
}

// EquatorPole 历元平赤道极 / mean equator pole of epoch, epj in Julian years.
func EquatorPole(epj float64) Vector3 {
	xyPol := [2][4]float64{
		{+5453.282155, +0.4252841, -0.00037173, -0.000000152},
		{-73750.930350, -0.7675452, -0.00018725, +0.000000231},
	}
	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},
	}
	t := (epj - 2000.0) / 100.0
	x, y := 0.0, 0.0
	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]
	}
	w := 1.0
	for i := 0; i < 4; i++ {
		x += xyPol[0][i] * w
		y += xyPol[1][i] * w
		w *= t
	}
	x *= as2r
	y *= as2r
	w = x*x + y*y
	z := 0.0
	if w < 1.0 {
		z = math.Sqrt(1.0 - w)
	}
	return Vector3{x, y, z}
}

// Cross 叉乘 / cross product.
func Cross(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],
	}
}

// Normalize 单位向量与原模长，零向量返回零 / unit vector and norm; zero stays zero.
func Normalize(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
}