feat: 引入可切换星历模型并扩展天象观测链路
- 新增半解析、旧模型、自定义与多源堆叠星历实例，提供 Context、Instance、SPK 读取及状态与视位置计算 - 统一太阳、月球和行星实例接口，扩展黄经穿越、留、相位、最近角距、偕日可见、任意高度升落、轨道节点及凌日等天象查询 - 完善日月食、月掩与凌日的月缘剖面、有限盘面接触、站心修正、局地可见性、全球路径和地图输出 - 新增 SVG、GeoJSON、KML 天象输出及凌日、月掩和月缘地形相关缓存与几何求解 - 新增恒星星表导入与查询，支持 CSV、Hipparcos、BSC5、Stellarium 等格式及名称、交叉标识、锥面检索和星等过滤 - 补充 IAU 2006、地球定向、折射消光、大气观测、轨道传播及半解析行星/月球数据支持 - 将默认未来民用时标切换为 TimeScaleLeapHour，更新 2027–2400 农历速查表、中文日期解析和时区边界处理 - 增加事件基线、跨模型回归、几何边界、月缘地形和输出契约测试，完善中英文手册、示例资源、NOTICE 与忽略规则
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package formula
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import "math"
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const arcsecToRadian = math.Pi / 180 / 3600
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// TIOLocatorArcsec 地球自转原点定位角 s′，单位角秒 / TIO locator s′ in arcseconds.
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//
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// jdeTT 为 TT 儒略日。采用 IERS 2010 的线性近似 s′ = −47 µas·t，t 为 J2000 起的儒略世纪数。
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// jdeTT is a TT Julian date. Uses the IERS 2010 linear model s′ = −47 µas·t,
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// with t in Julian centuries since J2000.
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func TIOLocatorArcsec(jdeTT float64) float64 {
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if !isFinitePhotometry(jdeTT) {
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return math.NaN()
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}
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return -47e-6 * (jdeTT - 2451545.0) / 36525
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}
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// PolarMotionMatrix 极移矩阵 W，把地球中间参考系 (TIRS) 矢量转到 ITRS / polar-motion matrix from TIRS to ITRS.
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//
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// xp、yp 为 IERS 公布的极坐标，sPrime 为 TIOLocatorArcsec 的结果，单位都是角秒。
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// 返回 W = R1(−yp)·R2(−xp)·R3(s′)，按 v_ITRS = W·v_TIRS 使用。
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// xp and yp are IERS pole coordinates and sPrime is the TIO locator, all in
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// arcseconds. Returns W = R1(−yp)·R2(−xp)·R3(s′) for v_ITRS = W·v_TIRS.
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func PolarMotionMatrix(xp, yp, sPrime float64) [3][3]float64 {
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if !isFinitePhotometry(xp) || !isFinitePhotometry(yp) || !isFinitePhotometry(sPrime) {
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return nanMatrix()
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}
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return multiplyMatrix(rotationX(-yp*arcsecToRadian),
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multiplyMatrix(rotationY(-xp*arcsecToRadian), rotationZ(sPrime*arcsecToRadian)))
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}
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// CelestialPoleOffsetMatrix 天球极偏差修正矩阵 / celestial pole offset correction matrix.
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//
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// dX、dY 为 IERS 公布的 CIP 坐标改正，单位毫角秒。返回一阶小角矩阵 Δ，
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// 左乘模型给出的 GCRS→CIRS（或 GCRS→真赤道）矩阵即得改正后的矩阵：C′ = Δ·C。
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// dX and dY are IERS CIP corrections in milliarcseconds. Returns the
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// first-order matrix Δ; left-multiply a model GCRS→CIRS (or GCRS→true-equator)
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// matrix to apply the offsets: C′ = Δ·C.
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func CelestialPoleOffsetMatrix(dX, dY float64) [3][3]float64 {
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if !isFinitePhotometry(dX) || !isFinitePhotometry(dY) {
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return nanMatrix()
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}
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x := dX * arcsecToRadian / 1000
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y := dY * arcsecToRadian / 1000
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return [3][3]float64{
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{1, 0, -x},
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{0, 1, -y},
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{x, y, 1},
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}
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}
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// rotationX 等为被动旋转：把矢量所在坐标轴绕 x/y/z 轴转 angle 弧度。
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func rotationX(angle float64) [3][3]float64 {
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s, c := math.Sincos(angle)
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return [3][3]float64{{1, 0, 0}, {0, c, s}, {0, -s, c}}
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}
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func rotationY(angle float64) [3][3]float64 {
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s, c := math.Sincos(angle)
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return [3][3]float64{{c, 0, -s}, {0, 1, 0}, {s, 0, c}}
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}
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func rotationZ(angle float64) [3][3]float64 {
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s, c := math.Sincos(angle)
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return [3][3]float64{{c, s, 0}, {-s, c, 0}, {0, 0, 1}}
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}
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func multiplyMatrix(a, b [3][3]float64) [3][3]float64 {
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var out [3][3]float64
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for i := 0; i < 3; i++ {
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for j := 0; j < 3; j++ {
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out[i][j] = a[i][0]*b[0][j] + a[i][1]*b[1][j] + a[i][2]*b[2][j]
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}
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}
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return out
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}
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func nanMatrix() [3][3]float64 {
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n := math.NaN()
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return [3][3]float64{{n, n, n}, {n, n, n}, {n, n, n}}
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}
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package formula
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import (
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"math"
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"testing"
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)
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func TestTIOLocator(t *testing.T) {
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// 2002-09-29 0h TT（MJD 52541）：s′ = −6.216698469981019e-12 rad。
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got := TIOLocatorArcsec(2452541.5) * arcsecToRadian
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assertFormulaClose(t, "TIOLocator", got, -0.6216698469981019309e-11, 1e-24)
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if !math.IsNaN(TIOLocatorArcsec(math.NaN())) {
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t.Fatal("expected NaN")
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}
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}
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func TestPolarMotionMatrix(t *testing.T) {
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const r2as = 1 / arcsecToRadian
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w := PolarMotionMatrix(2.55060238e-7*r2as, 1.860359247e-6*r2as, -0.1367174580728891460e-10*r2as)
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want := [3][3]float64{
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{0.9999999999999674721, -0.1367174580728846989e-10, 0.2550602379999972345e-6},
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{0.1414624947957029801e-10, 0.9999999999982695317, -0.1860359246998866389e-5},
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{-0.2550602379741215021e-6, 0.1860359247002414021e-5, 0.9999999999982370039},
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}
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for i := range want {
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for j := range want[i] {
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assertFormulaClose(t, "PolarMotionMatrix", w[i][j], want[i][j], 1e-16)
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}
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}
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}
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func TestCelestialPoleOffsetMatrix(t *testing.T) {
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// 改正后的极方向必须被映射到 z 轴：Δ·(dX, dY, 1) ≈ (0, 0, 1)。
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d := CelestialPoleOffsetMatrix(0.3, -0.2)
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x, y := 0.3*arcsecToRadian/1000, -0.2*arcsecToRadian/1000
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p := [3]float64{x, y, 1}
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for i, want := range [3]float64{0, 0, 1} {
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got := d[i][0]*p[0] + d[i][1]*p[1] + d[i][2]*p[2]
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assertFormulaClose(t, "CelestialPoleOffsetMatrix", got, want, 1e-20)
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}
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if !math.IsNaN(CelestialPoleOffsetMatrix(math.Inf(1), 0)[0][0]) {
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t.Fatal("expected NaN matrix")
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}
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}
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package formula
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import "math"
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// ExtinctionComponents V 波段天顶消光系数分量，单位星等/大气质量 / V-band zenith extinction components in magnitudes per airmass.
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type ExtinctionComponents struct {
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Rayleigh float64 // 分子散射 / molecular scattering
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Aerosol float64 // 气溶胶 / aerosol
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Ozone float64 // 臭氧 / ozone
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Water float64 // 水汽 / water vapour
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Total float64 // 四项之和 / sum of the four terms
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}
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// ExtinctionSchaefer 按 Schaefer 经验模型由气象条件合成 V 波段天顶消光系数 / V-band zenith extinction from weather by Schaefer's empirical model.
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//
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// heightM 为测站海拔（米），temperatureC 为气温（°C），relativeHumidity 为相对湿度（百分比，
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// 须在 (0, 100) 内），latitude 为测站纬度（度），sunRA 为太阳赤经（度，用于季节项）。
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// Total 可直接作为 basic.HeliacalOptions.ExtinctionCoefficient；输入越界时各分量为 NaN。
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// heightM is site elevation in metres, temperatureC is air temperature,
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// relativeHumidity is a percentage in (0, 100), latitude is the site latitude,
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// and sunRA is the Sun's right ascension in degrees for the seasonal terms.
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// Total can be used as basic.HeliacalOptions.ExtinctionCoefficient. Out-of-range
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// inputs yield NaN components.
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func ExtinctionSchaefer(heightM, temperatureC, relativeHumidity, latitude, sunRA float64) ExtinctionComponents {
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if !isFinitePhotometry(heightM) || !isFinitePhotometry(temperatureC) || !isFinitePhotometry(relativeHumidity) ||
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!isFinitePhotometry(latitude) || !isFinitePhotometry(sunRA) ||
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relativeHumidity <= 0 || relativeHumidity >= 100 || latitude < -90 || latitude > 90 {
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n := math.NaN()
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return ExtinctionComponents{n, n, n, n, n}
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}
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lat := latitude * math.Pi / 180
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ra := sunRA * math.Pi / 180
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hemisphere := 1.0
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if latitude < 0 {
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hemisphere = -1
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}
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// 标高：分子与水汽 8200 m，气溶胶 1500 m；臭氧层在高空，不随测站海拔变化。
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components := ExtinctionComponents{
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Rayleigh: 0.1066 * math.Exp(-heightM/8200),
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Aerosol: 0.1 * math.Exp(-heightM/1500) * math.Pow(1-0.32/math.Log(relativeHumidity/100), 1.33) *
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(1 + 0.33*hemisphere*math.Sin(ra)),
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Ozone: 0.031 * (3 + 0.4*(lat*math.Cos(ra)-math.Cos(3*lat))) / 3,
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Water: 0.031 * 0.94 * (relativeHumidity / 100) * math.Exp(temperatureC/15) * math.Exp(-heightM/8200),
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}
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components.Total = components.Rayleigh + components.Aerosol + components.Ozone + components.Water
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return components
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}
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package formula
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import (
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"math"
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"testing"
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)
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func TestExtinctionSchaefer(t *testing.T) {
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// 海平面、20 °C、湿度 50%、北纬 30°、春分点：逐项手算。
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got := ExtinctionSchaefer(0, 20, 50, 30, 0)
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aerosol := 0.1 * math.Pow(1-0.32/math.Log(0.5), 1.33)
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lat := math.Pi / 6
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ozone := 0.031 * (3 + 0.4*(lat-math.Cos(3*lat))) / 3
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water := 0.031 * 0.94 * 0.5 * math.Exp(20.0/15)
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assertFormulaClose(t, "Rayleigh", got.Rayleigh, 0.1066, 1e-15)
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assertFormulaClose(t, "Aerosol", got.Aerosol, aerosol, 1e-15)
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assertFormulaClose(t, "Ozone", got.Ozone, ozone, 1e-15)
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assertFormulaClose(t, "Water", got.Water, water, 1e-15)
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assertFormulaClose(t, "Total", got.Total, 0.1066+aerosol+ozone+water, 1e-15)
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if got.Total < 0.2 || got.Total > 0.5 {
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t.Fatalf("sea-level humid extinction out of typical range: %.3f", got.Total)
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}
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// 高山干燥站点消光明显更小。
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high := ExtinctionSchaefer(2500, 0, 20, 30, 0)
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if high.Total >= got.Total*0.6 {
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t.Fatalf("high dry site %.3f should be well below sea level %.3f", high.Total, got.Total)
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}
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for _, rh := range []float64{0, 100, -1, math.NaN()} {
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if !math.IsNaN(ExtinctionSchaefer(0, 20, rh, 30, 0).Total) {
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t.Fatalf("humidity %v should be rejected", rh)
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}
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}
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if !math.IsNaN(ExtinctionSchaefer(0, 20, 50, 91, 0).Total) {
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t.Fatal("latitude out of range should be rejected")
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}
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}
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package formula
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import "b612.me/astro/internal/refraction"
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// RefractionStandardPressureHPa 与 RefractionStandardTemperatureC 是折射公式的标准气压与气温 / standard pressure and temperature of the refraction formula.
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const (
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RefractionStandardPressureHPa = refraction.StandardPressureHPa
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RefractionStandardTemperatureC = refraction.StandardTemperatureC
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)
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// RefractionFromApparentAltitude 由视高度角求折射量（度，视高度减去它得真高度），无逆解时为 NaN / refraction from apparent altitude.
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func RefractionFromApparentAltitude(apparentAltitude, pressureHPa, temperatureC float64) float64 {
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return refraction.RefractionFromApparentAltitude(apparentAltitude, pressureHPa, temperatureC)
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}
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// TrueAltitude 视高度角转真高度角（度），无逆解时为 NaN / true altitude from apparent altitude.
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func TrueAltitude(apparentAltitude, pressureHPa, temperatureC float64) float64 {
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return refraction.TrueAltitude(apparentAltitude, pressureHPa, temperatureC)
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}
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// ApparentAltitude 真高度角转视高度角（度） / apparent altitude from true altitude.
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func ApparentAltitude(trueAltitude, pressureHPa, temperatureC float64) float64 {
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return refraction.ApparentAltitude(trueAltitude, pressureHPa, temperatureC)
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}
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// RefractionFromTrueAltitude 由真高度角求折射量（度，加到真高度上得视高度） / refraction from true altitude.
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func RefractionFromTrueAltitude(trueAltitude, pressureHPa, temperatureC float64) float64 {
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return refraction.RefractionFromTrueAltitude(trueAltitude, pressureHPa, temperatureC)
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}
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@@ -0,0 +1,21 @@
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package formula
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import (
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"math"
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"testing"
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)
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func TestRefractionRoundTrip(t *testing.T) {
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for _, alt := range []float64{-1, 0, 0.5, 5, 30, 80} {
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apparent := ApparentAltitude(alt, RefractionStandardPressureHPa, RefractionStandardTemperatureC)
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if back := TrueAltitude(apparent, RefractionStandardPressureHPa, RefractionStandardTemperatureC); math.Abs(back-alt) > 1e-9 {
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t.Errorf("alt %v: round trip %v", alt, back)
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}
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}
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if r := RefractionFromTrueAltitude(0, 1010, 10) * 60; r < 28 || r > 36 {
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t.Errorf("horizon refraction %.2f arcmin", r)
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}
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if !math.IsNaN(RefractionFromTrueAltitude(0, 0, 10)) {
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t.Error("zero pressure must be NaN")
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}
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}
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