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
2026-05-01 22:38:44 +08:00
parent 98ff574495
commit 3ffdbe0034
365 changed files with 63589 additions and 17508 deletions
@@ -0,0 +1,147 @@
+package internal
+
+import (
+	"errors"
+	"math"
+
+	. "b612.me/astro/tools"
+)
+
+const (
+	SynodicMonthDays = 29.530588853
+)
+
+var (
+	ErrNeverRise     = errors.New("rise event does not occur on this date")
+	ErrNeverSet      = errors.New("set event does not occur on this date")
+	ErrNotOnThisDate = errors.New("rise/set event occurs on adjacent date")
+)
+
+func MeanObliquity(jd float64) float64 {
+	t := (jd - 2451545.0) / 36525.0
+	return 23.4392911111 - (46.8150*t+0.00059*t*t-0.001813*t*t*t)/3600.0
+}
+
+func MeanSiderealTime(jd float64) float64 {
+	t := (jd - 2451545.0) / 36525.0
+	return Limit360(280.46061837 + 360.98564736629*(jd-2451545.0) + 0.000387933*t*t - t*t*t/38710000.0)
+}
+
+func EclipticToEquatorial(jd, lo, bo float64) (float64, float64) {
+	eps := MeanObliquity(jd)
+	ra := math.Atan2(Sin(lo)*Cos(eps)-Tan(bo)*Sin(eps), Cos(lo)) * 180.0 / math.Pi
+	if ra < 0 {
+		ra += 360
+	}
+	dec := ArcSin(Sin(bo)*Cos(eps) + Cos(bo)*Sin(eps)*Sin(lo))
+	return ra, dec
+}
+
+func HorizontalCoordinates(ra, dec, jd, lon, lat float64) (float64, float64, float64) {
+	lst := Limit360(MeanSiderealTime(jd) + lon)
+	hourAngle := Limit360(lst - ra)
+	altitude := ArcSin(clampUnit(Sin(lat)*Sin(dec) + Cos(lat)*Cos(dec)*Cos(hourAngle)))
+
+	y := Sin(hourAngle)
+	x := Cos(hourAngle)*Sin(lat) - Tan(dec)*Cos(lat)
+	azimuth := math.Atan2(y, x) * 180.0 / math.Pi
+	if azimuth < 0 {
+		if hourAngle < 180 {
+			azimuth += 360
+		} else {
+			azimuth += 180
+		}
+	} else if hourAngle < 180 {
+		azimuth += 180
+	}
+	return altitude, Limit360(azimuth), hourAngle
+}
+
+func TopocentricRaDec(ra, dec, observerLat, observerLon, jd, distanceEarthRadii, heightMeters float64) (float64, float64) {
+	u := math.Atan(0.99664719 * Tan(observerLat))
+	rhoSin := 0.99664719*math.Sin(u) + heightMeters/6378140.0*Sin(observerLat)
+	rhoCos := math.Cos(u) + heightMeters/6378140.0*Cos(observerLat)
+	parallax := math.Asin(1.0 / distanceEarthRadii)
+
+	hourAngle := (Limit360(MeanSiderealTime(jd) + observerLon - ra)) * math.Pi / 180.0
+	decRad := dec * math.Pi / 180.0
+
+	numerator := -rhoCos * math.Sin(parallax) * math.Sin(hourAngle)
+	denominator := math.Cos(decRad) - rhoCos*math.Sin(parallax)*math.Cos(hourAngle)
+	deltaRA := math.Atan2(numerator, denominator)
+
+	topRA := Limit360(ra + deltaRA*180.0/math.Pi)
+	topDec := math.Atan2((math.Sin(decRad)-rhoSin*math.Sin(parallax))*math.Cos(deltaRA), denominator) * 180.0 / math.Pi
+	return topRA, topDec
+}
+
+func SearchRiseSet(startJD, targetAltitude, stepMinutes float64, isRise bool, altitudeFn func(float64) float64) (float64, error) {
+	step := stepMinutes / 1440.0
+	prevJD := startJD
+	prevAlt := altitudeFn(prevJD) - targetAltitude
+	minAlt := prevAlt
+	maxAlt := prevAlt
+
+	for i := 1; i <= int(math.Round(1440.0/stepMinutes)); i++ {
+		currentJD := startJD + float64(i)*step
+		currentAlt := altitudeFn(currentJD) - targetAltitude
+		if currentAlt < minAlt {
+			minAlt = currentAlt
+		}
+		if currentAlt > maxAlt {
+			maxAlt = currentAlt
+		}
+		if crosses(prevAlt, currentAlt, isRise) {
+			return bisectEvent(prevJD, currentJD, targetAltitude, altitudeFn), nil
+		}
+		prevJD = currentJD
+		prevAlt = currentAlt
+	}
+
+	if maxAlt < 0 {
+		return 0, ErrNeverRise
+	}
+	if minAlt > 0 {
+		return 0, ErrNeverSet
+	}
+	return 0, ErrNotOnThisDate
+}
+
+func crosses(prevAlt, currentAlt float64, isRise bool) bool {
+	if isRise {
+		return prevAlt < 0 && currentAlt >= 0
+	}
+	return prevAlt > 0 && currentAlt <= 0
+}
+
+func bisectEvent(lo, hi, targetAltitude float64, altitudeFn func(float64) float64) float64 {
+	loAlt := altitudeFn(lo) - targetAltitude
+	for i := 0; i < 40; i++ {
+		mid := (lo + hi) / 2.0
+		midAlt := altitudeFn(mid) - targetAltitude
+		if midAlt == 0 {
+			return mid
+		}
+		if sameSign(loAlt, midAlt) {
+			lo = mid
+			loAlt = midAlt
+		} else {
+			hi = mid
+		}
+	}
+	return (lo + hi) / 2.0
+}
+
+func sameSign(a, b float64) bool {
+	return (a >= 0 && b >= 0) || (a <= 0 && b <= 0)
+}
+
+func clampUnit(v float64) float64 {
+	if v > 1 {
+		return 1
+	}
+	if v < -1 {
+		return -1
+	}
+	return v
+}
@@ -0,0 +1,125 @@
+package internal
+
+import (
+	"math"
+
+	. "b612.me/astro/tools"
+)
+
+type MoonState struct {
+	Longitude          float64
+	Latitude           float64
+	DistanceEarthRadii float64
+	RightAscension     float64
+	Declination        float64
+}
+
+func MoonGeocentric(jd float64) MoonState {
+	d := jd - 2451543.5
+
+	node := Limit360(125.1228 - 0.0529538083*d)
+	inclination := 5.1454
+	perigee := Limit360(318.0634 + 0.1643573223*d)
+	semiMajorAxis := 60.2666
+	eccentricity := 0.054900
+	meanAnomaly := Limit360(115.3654 + 13.0649929509*d)
+	meanLongitude := Limit360(node + perigee + meanAnomaly)
+	argumentLatitude := Limit360(meanLongitude - node)
+
+	sunPerigee := Limit360(282.9404 + 0.0000470935*d)
+	sunEccentricity := 0.016709 - 0.000000001151*d
+	sunMeanAnomaly := Limit360(356.0470 + 0.9856002585*d)
+	sunTrueLongitude, _ := orbitalLongitudeDistance(sunPerigee, sunEccentricity, 1, sunMeanAnomaly)
+
+	longitude, latitude, distance := orbitalLongitudeLatitudeDistance(node, inclination, perigee, semiMajorAxis, eccentricity, meanAnomaly)
+	elongation := Limit360(meanLongitude - sunTrueLongitude)
+
+	longitude += -1.274 * Sin(meanAnomaly-2*elongation)
+	longitude += 0.658 * Sin(2*elongation)
+	longitude += -0.186 * Sin(sunMeanAnomaly)
+	longitude += -0.059 * Sin(2*meanAnomaly-2*elongation)
+	longitude += -0.057 * Sin(meanAnomaly-2*elongation+sunMeanAnomaly)
+	longitude += 0.053 * Sin(meanAnomaly+2*elongation)
+	longitude += 0.046 * Sin(2*elongation-sunMeanAnomaly)
+	longitude += 0.041 * Sin(meanAnomaly-sunMeanAnomaly)
+	longitude += -0.035 * Sin(elongation)
+	longitude += -0.031 * Sin(meanAnomaly+sunMeanAnomaly)
+	longitude += -0.015 * Sin(2*argumentLatitude-2*elongation)
+	longitude += 0.011 * Sin(meanAnomaly-4*elongation)
+
+	latitude += -0.173 * Sin(argumentLatitude-2*elongation)
+	latitude += -0.055 * Sin(meanAnomaly-argumentLatitude-2*elongation)
+	latitude += -0.046 * Sin(meanAnomaly+argumentLatitude-2*elongation)
+	latitude += 0.033 * Sin(argumentLatitude+2*elongation)
+	latitude += 0.017 * Sin(2*meanAnomaly+argumentLatitude)
+
+	distance += -0.58 * Cos(meanAnomaly-2*elongation)
+	distance += -0.46 * Cos(2*elongation)
+
+	longitude = Limit360(longitude)
+	ra, dec := EclipticToEquatorial(jd, longitude, latitude)
+	return MoonState{
+		Longitude:          longitude,
+		Latitude:           latitude,
+		DistanceEarthRadii: distance,
+		RightAscension:     ra,
+		Declination:        dec,
+	}
+}
+
+func MoonTopocentric(jd, observerLon, observerLat, heightMeters float64) MoonState {
+	geo := MoonGeocentric(jd)
+	ra, dec := TopocentricRaDec(geo.RightAscension, geoDeclinationClamp(geo.Declination), observerLat, observerLon, jd, geo.DistanceEarthRadii, heightMeters)
+	geo.RightAscension = ra
+	geo.Declination = dec
+	return geo
+}
+
+func orbitalLongitudeLatitudeDistance(node, inclination, perigee, axis, eccentricity, meanAnomaly float64) (float64, float64, float64) {
+	meanAnomalyRad := meanAnomaly * math.Pi / 180.0
+	eccentricAnomaly := meanAnomalyRad + eccentricity*math.Sin(meanAnomalyRad)*(1+eccentricity*math.Cos(meanAnomalyRad))
+	for i := 0; i < 5; i++ {
+		eccentricAnomaly -= (eccentricAnomaly - eccentricity*math.Sin(eccentricAnomaly) - meanAnomalyRad) / (1 - eccentricity*math.Cos(eccentricAnomaly))
+	}
+
+	xv := axis * (math.Cos(eccentricAnomaly) - eccentricity)
+	yv := axis * math.Sqrt(1-eccentricity*eccentricity) * math.Sin(eccentricAnomaly)
+	trueAnomaly := math.Atan2(yv, xv)
+	radius := math.Hypot(xv, yv)
+
+	nodeRad := node * math.Pi / 180.0
+	inclinationRad := inclination * math.Pi / 180.0
+	perigeeRad := perigee * math.Pi / 180.0
+
+	xh := radius * (math.Cos(nodeRad)*math.Cos(trueAnomaly+perigeeRad) - math.Sin(nodeRad)*math.Sin(trueAnomaly+perigeeRad)*math.Cos(inclinationRad))
+	yh := radius * (math.Sin(nodeRad)*math.Cos(trueAnomaly+perigeeRad) + math.Cos(nodeRad)*math.Sin(trueAnomaly+perigeeRad)*math.Cos(inclinationRad))
+	zh := radius * math.Sin(trueAnomaly+perigeeRad) * math.Sin(inclinationRad)
+
+	longitude := math.Atan2(yh, xh) * 180.0 / math.Pi
+	latitude := math.Atan2(zh, math.Hypot(xh, yh)) * 180.0 / math.Pi
+	return Limit360(longitude), latitude, radius
+}
+
+func orbitalLongitudeDistance(perigee, eccentricity, axis, meanAnomaly float64) (float64, float64) {
+	meanAnomalyRad := meanAnomaly * math.Pi / 180.0
+	eccentricAnomaly := meanAnomalyRad + eccentricity*math.Sin(meanAnomalyRad)*(1+eccentricity*math.Cos(meanAnomalyRad))
+	for i := 0; i < 5; i++ {
+		eccentricAnomaly -= (eccentricAnomaly - eccentricity*math.Sin(eccentricAnomaly) - meanAnomalyRad) / (1 - eccentricity*math.Cos(eccentricAnomaly))
+	}
+
+	xv := axis * (math.Cos(eccentricAnomaly) - eccentricity)
+	yv := axis * math.Sqrt(1-eccentricity*eccentricity) * math.Sin(eccentricAnomaly)
+	trueAnomaly := math.Atan2(yv, xv) * 180.0 / math.Pi
+	radius := math.Hypot(xv, yv)
+	return Limit360(trueAnomaly + perigee), radius
+}
+
+func geoDeclinationClamp(dec float64) float64 {
+	if dec > 90 {
+		return 90
+	}
+	if dec < -90 {
+		return -90
+	}
+	return dec
+}
@@ -0,0 +1,48 @@
+package internal
+
+import . "b612.me/astro/tools"
+
+func SunLo(jd float64) float64 {
+	t := (jd - 2451545.0) / 365250.0
+	return Limit360(280.4664567 + 360007.6982779*t + 0.03032028*t*t + t*t*t/49931.0 - t*t*t*t/15299.0 - t*t*t*t*t/1988000.0)
+}
+
+func SunMeanAnomaly(jd float64) float64 {
+	t := (jd - 2451545.0) / 36525.0
+	return Limit360(357.5291092 + 35999.0502909*t - 0.0001559*t*t - 0.00000048*t*t*t)
+}
+
+func EarthEccentricity(jd float64) float64 {
+	t := (jd - 2451545.0) / 36525.0
+	return 0.016708617 - 0.000042037*t - 0.0000001236*t*t
+}
+
+func SunCenter(jd float64) float64 {
+	t := (jd - 2451545.0) / 36525.0
+	m := SunMeanAnomaly(jd)
+	return (1.9146-0.004817*t-0.000014*t*t)*Sin(m) + (0.019993-0.000101*t)*Sin(2*m) + 0.00029*Sin(3*m)
+}
+
+func SunTrueLo(jd float64) float64 {
+	return Limit360(SunLo(jd) + SunCenter(jd))
+}
+
+func SunApparentLo(jd float64) float64 {
+	t := (jd - 2451545.0) / 36525.0
+	return Limit360(SunTrueLo(jd) - 0.00569 - 0.00478*Sin(125.04-1934.136*t))
+}
+
+func SunDistanceAU(jd float64) float64 {
+	c := SunCenter(jd)
+	m := SunMeanAnomaly(jd)
+	e := EarthEccentricity(jd)
+	return 1.000001018 * (1 - e*e) / (1 + e*Cos(m+c))
+}
+
+func SunTrueRaDec(jd float64) (float64, float64) {
+	return EclipticToEquatorial(jd, SunTrueLo(jd), 0)
+}
+
+func SunApparentRaDec(jd float64) (float64, float64) {
+	return EclipticToEquatorial(jd, SunApparentLo(jd), 0)
+}