feat: 扩展天文计算能力
- 新增日食、月食、本地可见性、中心线、半影区域、SVG 图示与沙罗周期信息 - 新增行星冲合、留、方照、物理星历、视直径、相位、亮肢角、轨道节点等计算 - 新增木星伽利略卫星位置、现象与接触事件计算 - 新增恒星星表、星座判定、自行修正与观测辅助能力 - 新增 coord、formula、orbit、sundial、lite/sun、lite/moon 等扩展包 - 完善农历年号、月相英文别名、视差角、大气质量、折射、日晷与双星计算 - 增加 NASA、JPL Horizons、IMCCE 等回归测试数据与基线测试 - 重构基础算法文件组织，补充大量公开 API 注释和语义回归测试 - 更新中文和英文 README，补充示例、精度说明、SVG 配图
This commit is contained in:
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package coord
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import "b612.me/astro/formula"
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// AirmassPlaneParallelFromTrueAltitude 平行平板大气质量 / plane-parallel airmass from true altitude.
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//
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// 输入为真高度角，单位度。适合中高空几何近似，接近地平线时会发散。
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func AirmassPlaneParallelFromTrueAltitude(trueAltitude float64) float64 {
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return formula.AirmassPlaneParallel(trueAltitude)
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}
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// AirmassKastenYoungFromApparentAltitude Kasten-Young 大气质量 / Kasten-Young airmass from apparent altitude.
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//
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// 输入为视高度角，单位度。
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func AirmassKastenYoungFromApparentAltitude(apparentAltitude float64) float64 {
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return formula.AirmassKastenYoung(apparentAltitude)
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}
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// AirmassPickeringFromApparentAltitude Pickering 大气质量 / Pickering airmass from apparent altitude.
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//
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// 输入为视高度角，单位度。
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func AirmassPickeringFromApparentAltitude(apparentAltitude float64) float64 {
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return formula.AirmassPickering(apparentAltitude)
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}
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// AirmassKastenYoungFromTrueAltitude Kasten-Young 大气质量 / Kasten-Young airmass from true altitude.
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//
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// 先用 pressureHPa / temperatureC 估算大气折射，将真高度角换算为视高度角，再代入经验公式。
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func AirmassKastenYoungFromTrueAltitude(trueAltitude, pressureHPa, temperatureC float64) float64 {
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return formula.AirmassKastenYoung(ApparentAltitude(trueAltitude, pressureHPa, temperatureC))
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}
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// AirmassPickeringFromTrueAltitude Pickering 大气质量 / Pickering airmass from true altitude.
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//
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// 先用 pressureHPa / temperatureC 估算大气折射，将真高度角换算为视高度角，再代入经验公式。
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func AirmassPickeringFromTrueAltitude(trueAltitude, pressureHPa, temperatureC float64) float64 {
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return formula.AirmassPickering(ApparentAltitude(trueAltitude, pressureHPa, temperatureC))
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}
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@@ -0,0 +1,33 @@
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package coord
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import (
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"math"
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"testing"
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"b612.me/astro/formula"
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)
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func TestAirmassWrappers(t *testing.T) {
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assertClose(t, "plane-parallel wrapper", AirmassPlaneParallelFromTrueAltitude(30), formula.AirmassPlaneParallel(30), 1e-15)
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assertClose(t, "kasten-young apparent wrapper", AirmassKastenYoungFromApparentAltitude(30), formula.AirmassKastenYoung(30), 1e-15)
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assertClose(t, "pickering apparent wrapper", AirmassPickeringFromApparentAltitude(30), formula.AirmassPickering(30), 1e-15)
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}
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func TestAirmassTrueAltitudeWrappers(t *testing.T) {
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trueAltitude := 5.0
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pressureHPa := 1013.25
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temperatureC := 10.0
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apparentAltitude := ApparentAltitude(trueAltitude, pressureHPa, temperatureC)
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gotKastenYoung := AirmassKastenYoungFromTrueAltitude(trueAltitude, pressureHPa, temperatureC)
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wantKastenYoung := formula.AirmassKastenYoung(apparentAltitude)
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assertClose(t, "kasten-young true-alt wrapper", gotKastenYoung, wantKastenYoung, 1e-12)
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gotPickering := AirmassPickeringFromTrueAltitude(trueAltitude, pressureHPa, temperatureC)
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wantPickering := formula.AirmassPickering(apparentAltitude)
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assertClose(t, "pickering true-alt wrapper", gotPickering, wantPickering, 1e-12)
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if math.IsNaN(gotKastenYoung) || math.IsNaN(gotPickering) {
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t.Fatal("expected finite airmass values for low but above-horizon altitude")
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}
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}
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+129
@@ -0,0 +1,129 @@
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// Package coord 坐标工具包 / coordinate utility package.
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//
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// 本包面向用户提供常用坐标变换、恒星时、岁差、站心和地平坐标封装。
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// 所有角度输入和输出默认使用度；恒星时输出使用小时。
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// date 按绝对时刻使用，内部会转换为 UTC 后计算。
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package coord
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import (
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"time"
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"b612.me/astro/basic"
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)
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// Ecliptic 黄道坐标 / ecliptic coordinates.
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type Ecliptic struct {
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Lon float64 // 黄经，单位度 / ecliptic longitude in degrees.
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Lat float64 // 黄纬，单位度 / ecliptic latitude in degrees.
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}
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// Equatorial 赤道坐标 / equatorial coordinates.
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type Equatorial struct {
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RA float64 // 赤经，单位度 / right ascension in degrees.
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Dec float64 // 赤纬，单位度 / declination in degrees.
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}
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// Horizontal 地平坐标 / horizontal coordinates.
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type Horizontal struct {
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Azimuth float64 // 方位角，正北为0，顺时针增加 / azimuth from north clockwise, degrees.
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Altitude float64 // 高度角，单位度 / altitude in degrees.
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Zenith float64 // 天顶距，单位度 / zenith distance in degrees.
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HourAngle float64 // 时角，单位度 / hour angle in degrees.
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}
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func jdeUTC(date time.Time) float64 {
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return basic.Date2JDE(date.UTC())
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}
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// EclipticToEquatorial 黄道坐标转赤道坐标 / converts ecliptic to equatorial coordinates.
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func EclipticToEquatorial(date time.Time, lon, lat float64) Equatorial {
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ra, dec := basic.LoBoToRaDec(jdeUTC(date), lon, lat)
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return Equatorial{RA: ra, Dec: dec}
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}
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// EquatorialToEcliptic 赤道坐标转黄道坐标 / converts equatorial to ecliptic coordinates.
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func EquatorialToEcliptic(date time.Time, ra, dec float64) Ecliptic {
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lon, lat := basic.RaDecToLoBo(jdeUTC(date), ra, dec)
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return Ecliptic{Lon: lon, Lat: lat}
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}
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// Precess 岁差修正 / precesses equatorial coordinates from one date to another.
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func Precess(from, to time.Time, ra, dec float64) Equatorial {
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nextRA, nextDec := basic.Precess(ra, dec, jdeUTC(from), jdeUTC(to))
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return Equatorial{RA: nextRA, Dec: nextDec}
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}
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// EclipticObliquity 黄赤交角 / ecliptic obliquity.
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func EclipticObliquity(date time.Time, nutation bool) float64 {
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return basic.EclipticObliquity(jdeUTC(date), nutation)
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}
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// Nutation2000B IAU 2000B 章动 / IAU 2000B nutation.
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func Nutation2000B(date time.Time) (longitude, obliquity float64) {
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return basic.Nutation2000B(jdeUTC(date))
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}
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// Nutation1980 IAU 1980 章动 / IAU 1980 nutation.
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func Nutation1980(date time.Time) (longitude, obliquity float64) {
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return basic.Nutation1980(jdeUTC(date))
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}
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// MeanSiderealTime 平恒星时，单位小时 / mean sidereal time in hours.
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func MeanSiderealTime(date time.Time) float64 {
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return basic.MeanSiderealTime(jdeUTC(date))
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}
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// ApparentSiderealTime 真恒星时，单位小时 / apparent sidereal time in hours.
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func ApparentSiderealTime(date time.Time) float64 {
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return basic.ApparentSiderealTime(jdeUTC(date))
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}
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// HourAngle 时角 / hour angle.
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//
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// ra 为瞬时赤经；observerLon 为观测者经度，东正西负。
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// ra is apparent right ascension; observerLon is east-positive longitude.
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func HourAngle(date time.Time, ra, observerLon float64) float64 {
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return basic.StarHourAngle(jdeUTC(date), ra, observerLon, 0)
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}
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// EquatorialToHorizontal 赤道坐标转地平坐标 / converts equatorial to horizontal coordinates.
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//
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// ra/dec 为瞬时赤经赤纬；observerLon/observerLat 为观测者经纬度，东正西负、北正南负。
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// ra/dec are apparent coordinates; observerLon/observerLat are east-positive and north-positive.
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func EquatorialToHorizontal(date time.Time, ra, dec, observerLon, observerLat float64) Horizontal {
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jde := jdeUTC(date)
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altitude := basic.StarHeight(jde, ra, dec, observerLon, observerLat, 0)
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return Horizontal{
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Azimuth: basic.StarAzimuth(jde, ra, dec, observerLon, observerLat, 0),
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Altitude: altitude,
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Zenith: 90 - altitude,
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HourAngle: basic.StarHourAngle(jde, ra, observerLon, 0),
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}
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}
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// TopocentricEquatorial 地心赤道坐标转站心赤道坐标 / converts geocentric to topocentric equatorial coordinates.
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//
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// distanceAU 为目标天体到地心距离，单位 AU；height 为观测者海拔，单位米。
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// distanceAU is geocentric distance in AU; height is observer elevation in meters.
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func TopocentricEquatorial(date time.Time, ra, dec, observerLon, observerLat, distanceAU, height float64) Equatorial {
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topRA, topDec := basic.TopocentricRaDec(ra, dec, observerLat, observerLon, jdeUTC(date), distanceAU, height)
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return Equatorial{RA: topRA, Dec: topDec}
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}
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// TopocentricEcliptic 地心黄道坐标转站心黄道坐标 / converts geocentric to topocentric ecliptic coordinates.
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//
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// distanceAU 为目标天体到地心距离，单位 AU；height 为观测者海拔，单位米。
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// distanceAU is geocentric distance in AU; height is observer elevation in meters.
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func TopocentricEcliptic(date time.Time, lon, lat, observerLon, observerLat, distanceAU, height float64) Ecliptic {
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topLon := basic.TopocentricLo(lon, lat, observerLat, observerLon, jdeUTC(date), distanceAU, height)
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topLat := basic.TopocentricBo(lon, lat, observerLat, observerLon, jdeUTC(date), distanceAU, height)
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return Ecliptic{Lon: topLon, Lat: topLat}
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}
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// AngularSeparation 角距离 / angular separation.
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//
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// 输入为两组赤道坐标，单位度；返回角距离，单位度。
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// Inputs are two equatorial coordinates in degrees; return value is in degrees.
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func AngularSeparation(ra1, dec1, ra2, dec2 float64) float64 {
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return basic.StarAngularSeparation(ra1, dec1, ra2, dec2)
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}
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@@ -0,0 +1,84 @@
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package coord
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import (
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"math"
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"testing"
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"time"
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"b612.me/astro/basic"
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)
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func assertClose(t *testing.T, name string, got, want, tolerance float64) {
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t.Helper()
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if math.Abs(got-want) > tolerance {
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t.Fatalf("%s mismatch: got %.15f want %.15f", name, got, want)
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}
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}
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func TestEclipticEquatorialWrappers(t *testing.T) {
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date := time.Date(2026, 4, 27, 10, 30, 45, 0, time.FixedZone("CST", 8*3600))
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jde := basic.Date2JDE(date.UTC())
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lon := 139.686111
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lat := 4.875278
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got := EclipticToEquatorial(date, lon, lat)
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wantRA, wantDec := basic.LoBoToRaDec(jde, lon, lat)
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assertClose(t, "ra", got.RA, wantRA, 1e-12)
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assertClose(t, "dec", got.Dec, wantDec, 1e-12)
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back := EquatorialToEcliptic(date, got.RA, got.Dec)
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assertClose(t, "lon", back.Lon, lon, 1e-10)
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assertClose(t, "lat", back.Lat, lat, 1e-10)
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}
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func TestTimeAndPrecessionWrappers(t *testing.T) {
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date := time.Date(2026, 4, 27, 2, 30, 45, 0, time.UTC)
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to := time.Date(2050, 1, 1, 0, 0, 0, 0, time.UTC)
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jde := basic.Date2JDE(date.UTC())
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assertClose(t, "mean sidereal time", MeanSiderealTime(date), basic.MeanSiderealTime(jde), 1e-12)
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assertClose(t, "apparent sidereal time", ApparentSiderealTime(date), basic.ApparentSiderealTime(jde), 1e-12)
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assertClose(t, "obliquity", EclipticObliquity(date, true), basic.EclipticObliquity(jde, true), 1e-12)
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gotLon, gotObl := Nutation2000B(date)
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wantLon, wantObl := basic.Nutation2000B(jde)
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assertClose(t, "nutation longitude", gotLon, wantLon, 1e-12)
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assertClose(t, "nutation obliquity", gotObl, wantObl, 1e-12)
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got := Precess(date, to, 101.28715533, -16.71611586)
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wantRA, wantDec := basic.Precess(101.28715533, -16.71611586, jde, basic.Date2JDE(to.UTC()))
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assertClose(t, "precess ra", got.RA, wantRA, 1e-12)
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assertClose(t, "precess dec", got.Dec, wantDec, 1e-12)
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}
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func TestHorizontalAndTopocentricWrappers(t *testing.T) {
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date := time.Date(2026, 4, 27, 2, 30, 45, 0, time.UTC)
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jde := basic.Date2JDE(date.UTC())
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ra := 101.28715533
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dec := -16.71611586
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observerLon := 115.0
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observerLat := 40.0
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hz := EquatorialToHorizontal(date, ra, dec, observerLon, observerLat)
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wantAltitude := basic.StarHeight(jde, ra, dec, observerLon, observerLat, 0)
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assertClose(t, "altitude", hz.Altitude, wantAltitude, 1e-12)
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assertClose(t, "zenith", hz.Zenith, 90-wantAltitude, 1e-12)
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assertClose(t, "azimuth", hz.Azimuth, basic.StarAzimuth(jde, ra, dec, observerLon, observerLat, 0), 1e-12)
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assertClose(t, "hour angle", hz.HourAngle, basic.StarHourAngle(jde, ra, observerLon, 0), 1e-12)
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assertClose(t, "hour angle func", HourAngle(date, ra, observerLon), hz.HourAngle, 1e-12)
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top := TopocentricEquatorial(date, ra, dec, observerLon, observerLat, 0.00257, 53)
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wantRA, wantDec := basic.TopocentricRaDec(ra, dec, observerLat, observerLon, jde, 0.00257, 53)
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assertClose(t, "topocentric ra", top.RA, wantRA, 1e-12)
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assertClose(t, "topocentric dec", top.Dec, wantDec, 1e-12)
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ecl := TopocentricEcliptic(date, 139.686111, 4.875278, observerLon, observerLat, 0.00257, 53)
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assertClose(t, "topocentric lon", ecl.Lon, basic.TopocentricLo(139.686111, 4.875278, observerLat, observerLon, jde, 0.00257, 53), 1e-12)
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assertClose(t, "topocentric lat", ecl.Lat, basic.TopocentricBo(139.686111, 4.875278, observerLat, observerLon, jde, 0.00257, 53), 1e-12)
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}
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func TestAngularSeparationWrapper(t *testing.T) {
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got := AngularSeparation(101.28715533, -16.71611586, 95.9879578, -52.6956611)
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want := basic.StarAngularSeparation(101.28715533, -16.71611586, 95.9879578, -52.6956611)
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assertClose(t, "angular separation", got, want, 1e-12)
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}
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@@ -0,0 +1,23 @@
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package coord
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import (
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"time"
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"b612.me/astro/basic"
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)
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// ParallacticAngleByHourAngle 由时角计算视差角（天顶方向角） / parallactic angle from hour angle.
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//
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// hourAngle/dec/observerLat 单位均为度，返回值通常落在 [-180, 180] 度。
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func ParallacticAngleByHourAngle(hourAngle, dec, observerLat float64) float64 {
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return basic.ParallacticAngleByHourAngle(hourAngle, dec, observerLat)
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}
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// ParallacticAngle 由赤经赤纬计算视差角（天顶方向角） / parallactic angle from right ascension and declination.
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//
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// ra/dec 为瞬时赤经赤纬；observerLon/observerLat 为观测者经纬度，东正西负、北正南负。
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// Returns the signed parallactic angle for the apparent equatorial coordinates
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// at the observing instant.
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func ParallacticAngle(date time.Time, ra, dec, observerLon, observerLat float64) float64 {
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return basic.StarParallacticAngle(jdeUTC(date), ra, dec, observerLon, observerLat, 0)
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}
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@@ -0,0 +1,27 @@
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package coord
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import (
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"math"
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"testing"
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"time"
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"b612.me/astro/basic"
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)
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func TestParallacticAngleWrappers(t *testing.T) {
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date := time.Date(2026, 4, 29, 13, 15, 0, 0, time.UTC)
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ra := 101.28715533
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dec := -16.71611586
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observerLon := 115.0
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observerLat := 40.0
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got := ParallacticAngle(date, ra, dec, observerLon, observerLat)
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want := basic.ParallacticAngleByHourAngle(HourAngle(date, ra, observerLon), dec, observerLat)
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if math.Abs(got-want) > 1e-12 {
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t.Fatalf("parallactic angle mismatch: got %.15f want %.15f", got, want)
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}
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if direct := ParallacticAngleByHourAngle(30, 0, 0); math.Abs(direct-90) > 1e-12 {
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t.Fatalf("direct formula mismatch: got %.15f want %.15f", direct, 90.0)
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}
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}
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@@ -0,0 +1,43 @@
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package coord
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import (
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"time"
|
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|
||||
"b612.me/astro/basic"
|
||||
)
|
||||
|
||||
// AtmosphericRefractionFromTrueAltitude 真高度角折射修正 / atmospheric refraction from true altitude.
|
||||
//
|
||||
// 输入真高度角，返回应加到真高度角上的大气折射修正量，单位度。
|
||||
func AtmosphericRefractionFromTrueAltitude(trueAltitude, pressureHPa, temperatureC float64) float64 {
|
||||
return basic.RefractionFromTrueAltitude(trueAltitude, pressureHPa, temperatureC)
|
||||
}
|
||||
|
||||
// AtmosphericRefractionFromApparentAltitude 视高度角折射修正 / atmospheric refraction from apparent altitude.
|
||||
//
|
||||
// 输入视高度角，返回对应的大气折射修正量，单位度。
|
||||
func AtmosphericRefractionFromApparentAltitude(apparentAltitude, pressureHPa, temperatureC float64) float64 {
|
||||
return basic.RefractionFromApparentAltitude(apparentAltitude, pressureHPa, temperatureC)
|
||||
}
|
||||
|
||||
// ApparentAltitude 真高度角转视高度角 / apparent altitude from true altitude.
|
||||
//
|
||||
// 输入真高度角，返回加入标准大气折射后的视高度角，单位度。
|
||||
func ApparentAltitude(trueAltitude, pressureHPa, temperatureC float64) float64 {
|
||||
return basic.ApparentAltitude(trueAltitude, pressureHPa, temperatureC)
|
||||
}
|
||||
|
||||
// TrueAltitude 视高度角转真高度角 / true altitude from apparent altitude.
|
||||
//
|
||||
// 输入视高度角，返回去除大气折射后的真高度角，单位度。
|
||||
func TrueAltitude(apparentAltitude, pressureHPa, temperatureC float64) float64 {
|
||||
return basic.TrueAltitude(apparentAltitude, pressureHPa, temperatureC)
|
||||
}
|
||||
|
||||
// EquatorialToApparentHorizontal 赤道坐标转视地平坐标 / converts equatorial coordinates to apparent horizontal coordinates.
|
||||
func EquatorialToApparentHorizontal(date time.Time, ra, dec, observerLon, observerLat, pressureHPa, temperatureC float64) Horizontal {
|
||||
horizontal := EquatorialToHorizontal(date, ra, dec, observerLon, observerLat)
|
||||
horizontal.Altitude = basic.ApparentAltitude(horizontal.Altitude, pressureHPa, temperatureC)
|
||||
horizontal.Zenith = 90 - horizontal.Altitude
|
||||
return horizontal
|
||||
}
|
||||
@@ -0,0 +1,33 @@
|
||||
package coord
|
||||
|
||||
import (
|
||||
"testing"
|
||||
"time"
|
||||
|
||||
"b612.me/astro/basic"
|
||||
)
|
||||
|
||||
func TestRefractionWrappers(t *testing.T) {
|
||||
assertClose(t, "AtmosphericRefractionFromTrueAltitude", AtmosphericRefractionFromTrueAltitude(10, 1010, 10), basic.RefractionFromTrueAltitude(10, 1010, 10), 1e-12)
|
||||
assertClose(t, "AtmosphericRefractionFromApparentAltitude", AtmosphericRefractionFromApparentAltitude(10, 1010, 10), basic.RefractionFromApparentAltitude(10, 1010, 10), 1e-12)
|
||||
assertClose(t, "ApparentAltitude", ApparentAltitude(10, 1010, 10), basic.ApparentAltitude(10, 1010, 10), 1e-12)
|
||||
assertClose(t, "TrueAltitude", TrueAltitude(10, 1010, 10), basic.TrueAltitude(10, 1010, 10), 1e-12)
|
||||
}
|
||||
|
||||
func TestEquatorialToApparentHorizontal(t *testing.T) {
|
||||
date := time.Date(2026, 4, 27, 2, 30, 45, 0, time.UTC)
|
||||
ra := 101.28715533
|
||||
dec := -16.71611586
|
||||
observerLon := 115.0
|
||||
observerLat := 40.0
|
||||
pressureHPa := 1010.0
|
||||
temperatureC := 10.0
|
||||
|
||||
trueHorizontal := EquatorialToHorizontal(date, ra, dec, observerLon, observerLat)
|
||||
apparentHorizontal := EquatorialToApparentHorizontal(date, ra, dec, observerLon, observerLat, pressureHPa, temperatureC)
|
||||
|
||||
assertClose(t, "apparent altitude", apparentHorizontal.Altitude, basic.ApparentAltitude(trueHorizontal.Altitude, pressureHPa, temperatureC), 1e-12)
|
||||
assertClose(t, "apparent zenith", apparentHorizontal.Zenith, 90-apparentHorizontal.Altitude, 1e-12)
|
||||
assertClose(t, "apparent azimuth unchanged", apparentHorizontal.Azimuth, trueHorizontal.Azimuth, 1e-12)
|
||||
assertClose(t, "apparent hour angle unchanged", apparentHorizontal.HourAngle, trueHorizontal.HourAngle, 1e-12)
|
||||
}
|
||||
@@ -0,0 +1,220 @@
|
||||
package coord
|
||||
|
||||
import "math"
|
||||
|
||||
// Galactic 银道坐标 / galactic coordinates.
|
||||
type Galactic struct {
|
||||
Lon float64 // 银经，单位度 / galactic longitude in degrees.
|
||||
Lat float64 // 银纬，单位度 / galactic latitude in degrees.
|
||||
}
|
||||
|
||||
// SOFA ICRS2G/G2ICRS fixed rotation matrix.
|
||||
// Source: IAU SOFA 2023-10-11, iauIcrs2g/iauG2icrs.
|
||||
var icrsToGalacticMatrix = [3][3]float64{
|
||||
{-0.054875560416215368492398900454, -0.873437090234885048760383168409, -0.483835015548713226831774175116},
|
||||
{+0.494109427875583673525222371358, -0.444829629960011178146614061616, +0.746982244497218890527388004556},
|
||||
{-0.867666149019004701181616534570, -0.198076373431201528180486091412, +0.455983776175066922272100478348},
|
||||
}
|
||||
|
||||
// EclipticToEquatorialByObliquity 黄道转赤道坐标（指定黄赤交角） / ecliptic to equatorial by obliquity.
|
||||
//
|
||||
// lon: 黄经，单位度
|
||||
// lat: 黄纬，单位度
|
||||
// obliquity: 黄赤交角，单位度
|
||||
//
|
||||
// 返回：
|
||||
//
|
||||
// 赤经 RA，单位度；赤纬 Dec，单位度
|
||||
func EclipticToEquatorialByObliquity(lon, lat, obliquity float64) Equatorial {
|
||||
sinLon, cosLon := sinCosDeg(lon)
|
||||
sinLat, cosLat := sinCosDeg(lat)
|
||||
sinObliquity, cosObliquity := sinCosDeg(obliquity)
|
||||
|
||||
ra := normalize360(math.Atan2(sinLon*cosObliquity-math.Tan(lat*math.Pi/180)*sinObliquity, cosLon) * 180 / math.Pi)
|
||||
dec := math.Asin(clampUnit(sinLat*cosObliquity+cosLat*sinObliquity*sinLon)) * 180 / math.Pi
|
||||
return Equatorial{RA: ra, Dec: dec}
|
||||
}
|
||||
|
||||
// EquatorialToEclipticByObliquity 赤道转黄道坐标（指定黄赤交角） / equatorial to ecliptic by obliquity.
|
||||
//
|
||||
// ra: 赤经，单位度
|
||||
// dec: 赤纬，单位度
|
||||
// obliquity: 黄赤交角，单位度
|
||||
//
|
||||
// 返回：
|
||||
//
|
||||
// 黄经 Lon，单位度；黄纬 Lat，单位度
|
||||
func EquatorialToEclipticByObliquity(ra, dec, obliquity float64) Ecliptic {
|
||||
sinRA, cosRA := sinCosDeg(ra)
|
||||
sinDec, cosDec := sinCosDeg(dec)
|
||||
sinObliquity, cosObliquity := sinCosDeg(obliquity)
|
||||
|
||||
lon := normalize360(math.Atan2(sinRA*cosObliquity+math.Tan(dec*math.Pi/180)*sinObliquity, cosRA) * 180 / math.Pi)
|
||||
lat := math.Asin(clampUnit(sinDec*cosObliquity-cosDec*sinObliquity*sinRA)) * 180 / math.Pi
|
||||
return Ecliptic{Lon: lon, Lat: lat}
|
||||
}
|
||||
|
||||
// HourAngleDeclinationToHorizontal 时角赤纬转地平坐标 / horizontal coordinates from hour angle and declination.
|
||||
//
|
||||
// hourAngle: 时角，单位度
|
||||
// declination: 赤纬，单位度
|
||||
// latitude: 观测者地理纬度，单位度，北正南负
|
||||
//
|
||||
// 返回：
|
||||
//
|
||||
// 方位角 Azimuth（正北为0，顺时针增加）、高度角 Altitude、天顶距 Zenith，均为度
|
||||
func HourAngleDeclinationToHorizontal(hourAngle, declination, latitude float64) Horizontal {
|
||||
sinLatitude, cosLatitude := sinCosDeg(latitude)
|
||||
sinDeclination, cosDeclination := sinCosDeg(declination)
|
||||
sinHourAngle, cosHourAngle := sinCosDeg(hourAngle)
|
||||
|
||||
altitude := math.Asin(clampUnit(sinLatitude*sinDeclination+cosLatitude*cosDeclination*cosHourAngle)) * 180 / math.Pi
|
||||
azimuth := normalize360(math.Atan2(-cosDeclination*sinHourAngle, cosLatitude*sinDeclination-sinLatitude*cosDeclination*cosHourAngle) * 180 / math.Pi)
|
||||
return Horizontal{
|
||||
Azimuth: azimuth,
|
||||
Altitude: altitude,
|
||||
Zenith: 90 - altitude,
|
||||
HourAngle: normalize360(hourAngle),
|
||||
}
|
||||
}
|
||||
|
||||
// HorizontalToHourAngleDeclination 地平坐标转时角赤纬 / hour angle and declination from horizontal coordinates.
|
||||
//
|
||||
// azimuth: 方位角，单位度，正北为0，顺时针增加
|
||||
// altitude: 高度角，单位度
|
||||
// latitude: 观测者地理纬度，单位度，北正南负
|
||||
//
|
||||
// 返回：
|
||||
//
|
||||
// 时角 HourAngle，单位度；赤纬 Declination，单位度
|
||||
func HorizontalToHourAngleDeclination(azimuth, altitude, latitude float64) (hourAngle, declination float64) {
|
||||
sinLatitude, cosLatitude := sinCosDeg(latitude)
|
||||
sinAltitude, cosAltitude := sinCosDeg(altitude)
|
||||
sinAzimuth, cosAzimuth := sinCosDeg(azimuth)
|
||||
|
||||
declination = math.Asin(clampUnit(sinLatitude*sinAltitude+cosLatitude*cosAltitude*cosAzimuth)) * 180 / math.Pi
|
||||
sinHourAngle := -cosAltitude * sinAzimuth
|
||||
cosHourAngle := sinAltitude*cosLatitude - cosAltitude*sinLatitude*cosAzimuth
|
||||
hourAngle = normalize360(math.Atan2(sinHourAngle, cosHourAngle) * 180 / math.Pi)
|
||||
return hourAngle, declination
|
||||
}
|
||||
|
||||
// EquatorialToHorizontalByLocalSiderealTime 赤道转地平坐标（指定地方恒星时） / equatorial to horizontal by local sidereal time.
|
||||
//
|
||||
// localSiderealTimeHours: 站点本地恒星时，单位小时
|
||||
// ra: 赤经，单位度
|
||||
// dec: 赤纬，单位度
|
||||
// latitude: 观测者地理纬度，单位度，北正南负
|
||||
//
|
||||
// 返回：
|
||||
//
|
||||
// 方位角 Azimuth（正北为0，顺时针增加）、高度角 Altitude、天顶距 Zenith，均为度；
|
||||
// 附带返回对应的时角 HourAngle，单位度
|
||||
//
|
||||
// 例：
|
||||
//
|
||||
// hz := coord.EquatorialToHorizontalByLocalSiderealTime(10.5, 83.6331, 22.0145, 31.2)
|
||||
func EquatorialToHorizontalByLocalSiderealTime(localSiderealTimeHours, ra, dec, latitude float64) Horizontal {
|
||||
hourAngle := normalize360(localSiderealTimeHours*15 - ra)
|
||||
return HourAngleDeclinationToHorizontal(hourAngle, dec, latitude)
|
||||
}
|
||||
|
||||
// HorizontalToEquatorialByLocalSiderealTime 地平转赤道坐标（指定地方恒星时） / horizontal to equatorial by local sidereal time.
|
||||
//
|
||||
// localSiderealTimeHours: 站点本地恒星时，单位小时
|
||||
// azimuth: 方位角，单位度，正北为0，顺时针增加
|
||||
// altitude: 高度角，单位度
|
||||
// latitude: 观测者地理纬度，单位度，北正南负
|
||||
//
|
||||
// 返回：
|
||||
//
|
||||
// 赤经 RA，单位度；赤纬 Dec，单位度
|
||||
//
|
||||
// 例：
|
||||
//
|
||||
// eq := coord.HorizontalToEquatorialByLocalSiderealTime(10.5, 128.2, 37.6, 31.2)
|
||||
func HorizontalToEquatorialByLocalSiderealTime(localSiderealTimeHours, azimuth, altitude, latitude float64) Equatorial {
|
||||
hourAngle, declination := HorizontalToHourAngleDeclination(azimuth, altitude, latitude)
|
||||
ra := normalize360(localSiderealTimeHours*15 - hourAngle)
|
||||
return Equatorial{RA: ra, Dec: declination}
|
||||
}
|
||||
|
||||
// EquatorialToGalactic 赤道转银道坐标 / equatorial to galactic coordinates.
|
||||
//
|
||||
// ra: ICRS 赤经，单位度
|
||||
// dec: ICRS 赤纬，单位度
|
||||
//
|
||||
// 返回：
|
||||
//
|
||||
// 银经 Lon，单位度；银纬 Lat，单位度
|
||||
func EquatorialToGalactic(ra, dec float64) Galactic {
|
||||
vector := sphericalToVector(ra, dec)
|
||||
rotated := matrixVectorMul(icrsToGalacticMatrix, vector)
|
||||
lon, lat := vectorToSpherical(rotated)
|
||||
return Galactic{Lon: lon, Lat: lat}
|
||||
}
|
||||
|
||||
// GalacticToEquatorial 银道转赤道坐标 / galactic to equatorial coordinates.
|
||||
//
|
||||
// lon: 银经，单位度
|
||||
// lat: 银纬，单位度
|
||||
//
|
||||
// 返回：
|
||||
//
|
||||
// ICRS 赤经 RA，单位度；ICRS 赤纬 Dec，单位度
|
||||
func GalacticToEquatorial(lon, lat float64) Equatorial {
|
||||
vector := sphericalToVector(lon, lat)
|
||||
rotated := matrixTransposeVectorMul(icrsToGalacticMatrix, vector)
|
||||
ra, dec := vectorToSpherical(rotated)
|
||||
return Equatorial{RA: ra, Dec: dec}
|
||||
}
|
||||
|
||||
func sinCosDeg(angle float64) (sinValue, cosValue float64) {
|
||||
return math.Sincos(angle * math.Pi / 180)
|
||||
}
|
||||
|
||||
func normalize360(angle float64) float64 {
|
||||
angle = math.Mod(angle, 360)
|
||||
if angle < 0 {
|
||||
angle += 360
|
||||
}
|
||||
return angle
|
||||
}
|
||||
|
||||
func clampUnit(value float64) float64 {
|
||||
if value > 1 {
|
||||
return 1
|
||||
}
|
||||
if value < -1 {
|
||||
return -1
|
||||
}
|
||||
return value
|
||||
}
|
||||
|
||||
func sphericalToVector(lon, lat float64) [3]float64 {
|
||||
sinLon, cosLon := sinCosDeg(lon)
|
||||
sinLat, cosLat := sinCosDeg(lat)
|
||||
return [3]float64{cosLat * cosLon, cosLat * sinLon, sinLat}
|
||||
}
|
||||
|
||||
func vectorToSpherical(vector [3]float64) (lon, lat float64) {
|
||||
lon = normalize360(math.Atan2(vector[1], vector[0]) * 180 / math.Pi)
|
||||
lat = math.Asin(clampUnit(vector[2])) * 180 / math.Pi
|
||||
return lon, lat
|
||||
}
|
||||
|
||||
func matrixVectorMul(matrix [3][3]float64, vector [3]float64) [3]float64 {
|
||||
return [3]float64{
|
||||
matrix[0][0]*vector[0] + matrix[0][1]*vector[1] + matrix[0][2]*vector[2],
|
||||
matrix[1][0]*vector[0] + matrix[1][1]*vector[1] + matrix[1][2]*vector[2],
|
||||
matrix[2][0]*vector[0] + matrix[2][1]*vector[1] + matrix[2][2]*vector[2],
|
||||
}
|
||||
}
|
||||
|
||||
func matrixTransposeVectorMul(matrix [3][3]float64, vector [3]float64) [3]float64 {
|
||||
return [3]float64{
|
||||
matrix[0][0]*vector[0] + matrix[1][0]*vector[1] + matrix[2][0]*vector[2],
|
||||
matrix[0][1]*vector[0] + matrix[1][1]*vector[1] + matrix[2][1]*vector[2],
|
||||
matrix[0][2]*vector[0] + matrix[1][2]*vector[1] + matrix[2][2]*vector[2],
|
||||
}
|
||||
}
|
||||
@@ -0,0 +1,105 @@
|
||||
package coord
|
||||
|
||||
import (
|
||||
"math"
|
||||
"testing"
|
||||
"time"
|
||||
)
|
||||
|
||||
func TestObliquityDrivenCoordinateConversions(t *testing.T) {
|
||||
date := time.Date(2026, 4, 27, 10, 30, 45, 0, time.FixedZone("CST", 8*3600))
|
||||
lon := 139.686111
|
||||
lat := 4.875278
|
||||
obliquity := EclipticObliquity(date, true)
|
||||
|
||||
got := EclipticToEquatorialByObliquity(lon, lat, obliquity)
|
||||
want := EclipticToEquatorial(date, lon, lat)
|
||||
assertClose(t, "manual obliquity ra", got.RA, want.RA, 1e-12)
|
||||
assertClose(t, "manual obliquity dec", got.Dec, want.Dec, 1e-12)
|
||||
|
||||
back := EquatorialToEclipticByObliquity(got.RA, got.Dec, obliquity)
|
||||
assertClose(t, "manual obliquity lon", back.Lon, lon, 1e-10)
|
||||
assertClose(t, "manual obliquity lat", back.Lat, lat, 1e-10)
|
||||
}
|
||||
|
||||
func TestHourAngleDrivenHorizontalConversions(t *testing.T) {
|
||||
date := time.Date(2026, 4, 27, 2, 30, 45, 0, time.UTC)
|
||||
ra := 101.28715533
|
||||
dec := -16.71611586
|
||||
observerLon := 115.0
|
||||
observerLat := 40.0
|
||||
hourAngle := HourAngle(date, ra, observerLon)
|
||||
|
||||
got := HourAngleDeclinationToHorizontal(hourAngle, dec, observerLat)
|
||||
want := EquatorialToHorizontal(date, ra, dec, observerLon, observerLat)
|
||||
assertClose(t, "manual hour angle azimuth", got.Azimuth, want.Azimuth, 1e-12)
|
||||
assertClose(t, "manual hour angle altitude", got.Altitude, want.Altitude, 1e-12)
|
||||
assertClose(t, "manual hour angle zenith", got.Zenith, want.Zenith, 1e-12)
|
||||
assertClose(t, "manual hour angle value", got.HourAngle, want.HourAngle, 1e-12)
|
||||
|
||||
roundTripHourAngle, roundTripDeclination := HorizontalToHourAngleDeclination(got.Azimuth, got.Altitude, observerLat)
|
||||
assertClose(t, "round trip hour angle", roundTripHourAngle, normalize360(hourAngle), 1e-10)
|
||||
assertClose(t, "round trip declination", roundTripDeclination, dec, 1e-10)
|
||||
}
|
||||
|
||||
func TestLocalSiderealTimeDrivenHorizontalConversions(t *testing.T) {
|
||||
date := time.Date(2026, 4, 27, 2, 30, 45, 0, time.UTC)
|
||||
ra := 101.28715533
|
||||
dec := -16.71611586
|
||||
observerLon := 115.0
|
||||
observerLat := 40.0
|
||||
localSiderealTimeHours := math.Mod(ApparentSiderealTime(date)+observerLon/15, 24)
|
||||
if localSiderealTimeHours < 0 {
|
||||
localSiderealTimeHours += 24
|
||||
}
|
||||
|
||||
got := EquatorialToHorizontalByLocalSiderealTime(localSiderealTimeHours, ra, dec, observerLat)
|
||||
want := EquatorialToHorizontal(date, ra, dec, observerLon, observerLat)
|
||||
assertClose(t, "LST azimuth", got.Azimuth, want.Azimuth, 1e-12)
|
||||
assertClose(t, "LST altitude", got.Altitude, want.Altitude, 1e-12)
|
||||
assertClose(t, "LST zenith", got.Zenith, want.Zenith, 1e-12)
|
||||
assertClose(t, "LST hour angle", got.HourAngle, want.HourAngle, 1e-12)
|
||||
|
||||
back := HorizontalToEquatorialByLocalSiderealTime(localSiderealTimeHours, got.Azimuth, got.Altitude, observerLat)
|
||||
assertClose(t, "LST round trip ra", back.RA, ra, 1e-10)
|
||||
assertClose(t, "LST round trip dec", back.Dec, dec, 1e-10)
|
||||
}
|
||||
|
||||
func TestGalacticCoordinateConversions(t *testing.T) {
|
||||
galacticCenter := EquatorialToGalactic(266.4051, -28.936175)
|
||||
assertClose(t, "galactic center lon", galacticCenter.Lon, 0, 5e-4)
|
||||
assertClose(t, "galactic center lat", galacticCenter.Lat, 0, 5e-4)
|
||||
|
||||
pole := GalacticToEquatorial(0, 90)
|
||||
assertClose(t, "north galactic pole ra", pole.RA, 192.85948, 1e-5)
|
||||
assertClose(t, "north galactic pole dec", pole.Dec, 27.12825, 1e-5)
|
||||
|
||||
sample := EquatorialToGalactic(83.6331, 22.0145)
|
||||
back := GalacticToEquatorial(sample.Lon, sample.Lat)
|
||||
assertClose(t, "galactic round trip ra", back.RA, 83.6331, 1e-10)
|
||||
assertClose(t, "galactic round trip dec", back.Dec, 22.0145, 1e-10)
|
||||
}
|
||||
|
||||
func TestHorizontalRoundTripAcrossQuadrants(t *testing.T) {
|
||||
samples := []struct {
|
||||
hourAngle float64
|
||||
declination float64
|
||||
latitude float64
|
||||
}{
|
||||
{15, 20, 35},
|
||||
{95, -10, 52},
|
||||
{210, 45, -20},
|
||||
{315, -35, 10},
|
||||
}
|
||||
|
||||
for _, sample := range samples {
|
||||
hz := HourAngleDeclinationToHorizontal(sample.hourAngle, sample.declination, sample.latitude)
|
||||
hourAngle, declination := HorizontalToHourAngleDeclination(hz.Azimuth, hz.Altitude, sample.latitude)
|
||||
if math.Abs(hourAngle-normalize360(sample.hourAngle)) > 1e-10 {
|
||||
t.Fatalf("hour angle round trip mismatch: got %.15f want %.15f", hourAngle, normalize360(sample.hourAngle))
|
||||
}
|
||||
if math.Abs(declination-sample.declination) > 1e-10 {
|
||||
t.Fatalf("declination round trip mismatch: got %.15f want %.15f", declination, sample.declination)
|
||||
}
|
||||
}
|
||||
}
|
||||
Reference in New Issue
Block a user