starainrt
3ffdbe0034
- 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
126 lines
4.8 KiB
Go
126 lines
4.8 KiB
Go
package internal
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import (
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"math"
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. "b612.me/astro/tools"
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)
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type MoonState struct {
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Longitude float64
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Latitude float64
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DistanceEarthRadii float64
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RightAscension float64
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Declination float64
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}
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func MoonGeocentric(jd float64) MoonState {
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d := jd - 2451543.5
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node := Limit360(125.1228 - 0.0529538083*d)
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inclination := 5.1454
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perigee := Limit360(318.0634 + 0.1643573223*d)
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semiMajorAxis := 60.2666
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eccentricity := 0.054900
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meanAnomaly := Limit360(115.3654 + 13.0649929509*d)
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meanLongitude := Limit360(node + perigee + meanAnomaly)
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argumentLatitude := Limit360(meanLongitude - node)
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sunPerigee := Limit360(282.9404 + 0.0000470935*d)
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sunEccentricity := 0.016709 - 0.000000001151*d
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sunMeanAnomaly := Limit360(356.0470 + 0.9856002585*d)
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sunTrueLongitude, _ := orbitalLongitudeDistance(sunPerigee, sunEccentricity, 1, sunMeanAnomaly)
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longitude, latitude, distance := orbitalLongitudeLatitudeDistance(node, inclination, perigee, semiMajorAxis, eccentricity, meanAnomaly)
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elongation := Limit360(meanLongitude - sunTrueLongitude)
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longitude += -1.274 * Sin(meanAnomaly-2*elongation)
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longitude += 0.658 * Sin(2*elongation)
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longitude += -0.186 * Sin(sunMeanAnomaly)
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longitude += -0.059 * Sin(2*meanAnomaly-2*elongation)
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longitude += -0.057 * Sin(meanAnomaly-2*elongation+sunMeanAnomaly)
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longitude += 0.053 * Sin(meanAnomaly+2*elongation)
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longitude += 0.046 * Sin(2*elongation-sunMeanAnomaly)
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longitude += 0.041 * Sin(meanAnomaly-sunMeanAnomaly)
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longitude += -0.035 * Sin(elongation)
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longitude += -0.031 * Sin(meanAnomaly+sunMeanAnomaly)
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longitude += -0.015 * Sin(2*argumentLatitude-2*elongation)
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longitude += 0.011 * Sin(meanAnomaly-4*elongation)
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latitude += -0.173 * Sin(argumentLatitude-2*elongation)
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latitude += -0.055 * Sin(meanAnomaly-argumentLatitude-2*elongation)
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latitude += -0.046 * Sin(meanAnomaly+argumentLatitude-2*elongation)
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latitude += 0.033 * Sin(argumentLatitude+2*elongation)
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latitude += 0.017 * Sin(2*meanAnomaly+argumentLatitude)
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distance += -0.58 * Cos(meanAnomaly-2*elongation)
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distance += -0.46 * Cos(2*elongation)
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longitude = Limit360(longitude)
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ra, dec := EclipticToEquatorial(jd, longitude, latitude)
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return MoonState{
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Longitude: longitude,
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Latitude: latitude,
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DistanceEarthRadii: distance,
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RightAscension: ra,
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Declination: dec,
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}
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}
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func MoonTopocentric(jd, observerLon, observerLat, heightMeters float64) MoonState {
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geo := MoonGeocentric(jd)
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ra, dec := TopocentricRaDec(geo.RightAscension, geoDeclinationClamp(geo.Declination), observerLat, observerLon, jd, geo.DistanceEarthRadii, heightMeters)
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geo.RightAscension = ra
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geo.Declination = dec
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return geo
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}
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func orbitalLongitudeLatitudeDistance(node, inclination, perigee, axis, eccentricity, meanAnomaly float64) (float64, float64, float64) {
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meanAnomalyRad := meanAnomaly * math.Pi / 180.0
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eccentricAnomaly := meanAnomalyRad + eccentricity*math.Sin(meanAnomalyRad)*(1+eccentricity*math.Cos(meanAnomalyRad))
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for i := 0; i < 5; i++ {
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eccentricAnomaly -= (eccentricAnomaly - eccentricity*math.Sin(eccentricAnomaly) - meanAnomalyRad) / (1 - eccentricity*math.Cos(eccentricAnomaly))
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}
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xv := axis * (math.Cos(eccentricAnomaly) - eccentricity)
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yv := axis * math.Sqrt(1-eccentricity*eccentricity) * math.Sin(eccentricAnomaly)
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trueAnomaly := math.Atan2(yv, xv)
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radius := math.Hypot(xv, yv)
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nodeRad := node * math.Pi / 180.0
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inclinationRad := inclination * math.Pi / 180.0
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perigeeRad := perigee * math.Pi / 180.0
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xh := radius * (math.Cos(nodeRad)*math.Cos(trueAnomaly+perigeeRad) - math.Sin(nodeRad)*math.Sin(trueAnomaly+perigeeRad)*math.Cos(inclinationRad))
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yh := radius * (math.Sin(nodeRad)*math.Cos(trueAnomaly+perigeeRad) + math.Cos(nodeRad)*math.Sin(trueAnomaly+perigeeRad)*math.Cos(inclinationRad))
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zh := radius * math.Sin(trueAnomaly+perigeeRad) * math.Sin(inclinationRad)
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longitude := math.Atan2(yh, xh) * 180.0 / math.Pi
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latitude := math.Atan2(zh, math.Hypot(xh, yh)) * 180.0 / math.Pi
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return Limit360(longitude), latitude, radius
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}
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func orbitalLongitudeDistance(perigee, eccentricity, axis, meanAnomaly float64) (float64, float64) {
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meanAnomalyRad := meanAnomaly * math.Pi / 180.0
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eccentricAnomaly := meanAnomalyRad + eccentricity*math.Sin(meanAnomalyRad)*(1+eccentricity*math.Cos(meanAnomalyRad))
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for i := 0; i < 5; i++ {
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eccentricAnomaly -= (eccentricAnomaly - eccentricity*math.Sin(eccentricAnomaly) - meanAnomalyRad) / (1 - eccentricity*math.Cos(eccentricAnomaly))
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}
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xv := axis * (math.Cos(eccentricAnomaly) - eccentricity)
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yv := axis * math.Sqrt(1-eccentricity*eccentricity) * math.Sin(eccentricAnomaly)
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trueAnomaly := math.Atan2(yv, xv) * 180.0 / math.Pi
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radius := math.Hypot(xv, yv)
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return Limit360(trueAnomaly + perigee), radius
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}
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func geoDeclinationClamp(dec float64) float64 {
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if dec > 90 {
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return 90
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}
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if dec < -90 {
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return -90
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}
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return dec
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}
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