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
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package basic
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import (
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"math"
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"sort"
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"time"
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)
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const (
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earthApsisBaseTTJDE = 2451547.507
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earthApsisMeanYearDays = 365.2596358
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earthApsisQuadraticTerm = 0.0000000156
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earthApsisBaseYear = 2000.01
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earthApsisSeedScale = 0.99997
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earthApsisBracketHalfWidth = 5.0
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earthApsisSampleStep = 0.25
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earthApsisDerivativeStep = 1e-3
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earthApsisToleranceDays = 1e-8
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earthApsisMaxIterations = 24
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moonApsisBaseTTJDE = 2451534.6698
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moonApsisMeanMonthDays = 27.55454989
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moonApsisBaseCycle = 1325.55
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moonApsisQuadraticTerm = -0.0006691
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moonApsisCubicTerm = -0.000001098
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moonApsisQuarticTerm = 0.0000000052
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moonApsisBracketHalfWidth = 2.0
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moonApsisSampleStep = 0.125
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moonApsisDerivativeStep = 1e-4
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moonApsisToleranceDays = 1e-8
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moonApsisMaxIterations = 24
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)
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// ApsisEvent 轨道极值事件 / orbital distance extremum event.
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type ApsisEvent struct {
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// JDE 是事件发生时刻对应的世界时儒略日 / event time as UTC-based Julian day.
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JDE float64
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// Distance 是极值距离；地球相关事件单位 AU，月球相关事件单位 km / extremum distance.
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Distance float64
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}
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type apsisSearchConfig struct {
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bracketHalfWidth float64
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sampleStep float64
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derivativeStep float64
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toleranceDays float64
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maxIterations int
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maximize bool
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}
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// EarthPerihelion 地球指定年份的近日点 / Earth perihelion in the given year.
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func EarthPerihelion(year int) ApsisEvent {
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return earthApsis(year, false)
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}
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// EarthAphelion 地球指定年份的远日点 / Earth aphelion in the given year.
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func EarthAphelion(year int) ApsisEvent {
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return earthApsis(year, true)
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}
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// MoonPerigees 指定年月内的所有月球近地点 / all lunar perigees in the given Gregorian month.
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func MoonPerigees(year int, month time.Month) []ApsisEvent {
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return moonApsisInMonth(year, month, false)
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}
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// MoonApogees 指定年月内的所有月球远地点 / all lunar apogees in the given Gregorian month.
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func MoonApogees(year int, month time.Month) []ApsisEvent {
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return moonApsisInMonth(year, month, true)
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}
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func earthApsis(year int, aphelion bool) ApsisEvent {
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seedTT := earthApsisSeedTT(year, aphelion)
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cfg := apsisSearchConfig{
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bracketHalfWidth: earthApsisBracketHalfWidth,
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sampleStep: earthApsisSampleStep,
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derivativeStep: earthApsisDerivativeStep,
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toleranceDays: earthApsisToleranceDays,
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maxIterations: earthApsisMaxIterations,
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maximize: aphelion,
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}
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eventTT, distanceAU := refineDistanceExtremum(seedTT, cfg, EarthAway)
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return ApsisEvent{
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JDE: TD2UT(eventTT, false),
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Distance: distanceAU,
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}
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}
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func moonApsisInMonth(year int, month time.Month, apogee bool) []ApsisEvent {
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startUTC := time.Date(year, month, 1, 0, 0, 0, 0, time.UTC)
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endUTC := startUTC.AddDate(0, 1, 0)
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startTT := TD2UT(Date2JDE(startUTC), true)
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endTT := TD2UT(Date2JDE(endUTC), true)
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kStart := int(math.Floor((startTT-moonApsisBaseTTJDE)/moonApsisMeanMonthDays)) - 1
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kEnd := int(math.Ceil((endTT-moonApsisBaseTTJDE)/moonApsisMeanMonthDays)) + 1
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phase := 0.0
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if apogee {
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phase = 0.5
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}
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cfg := apsisSearchConfig{
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bracketHalfWidth: moonApsisBracketHalfWidth,
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sampleStep: moonApsisSampleStep,
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derivativeStep: moonApsisDerivativeStep,
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toleranceDays: moonApsisToleranceDays,
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maxIterations: moonApsisMaxIterations,
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maximize: apogee,
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}
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events := make([]ApsisEvent, 0, 2)
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for k := kStart; k <= kEnd; k++ {
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seedTT := moonApsisSeedTT(float64(k) + phase)
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eventTT, distanceKM := refineDistanceExtremum(seedTT, cfg, HMoonAway)
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eventUT := TD2UT(eventTT, false)
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eventTimeUTC := JDE2DateByZone(eventUT, time.UTC, false)
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if eventTimeUTC.Before(startUTC) || !eventTimeUTC.Before(endUTC) {
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continue
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}
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events = append(events, ApsisEvent{
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JDE: eventUT,
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Distance: distanceKM,
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})
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}
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sort.Slice(events, func(i, j int) bool {
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return events[i].JDE < events[j].JDE
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})
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return events
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}
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func earthApsisSeedTT(year int, aphelion bool) float64 {
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k := math.Round(earthApsisSeedScale * (float64(year) - earthApsisBaseYear))
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if aphelion {
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k += 0.5
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}
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return earthApsisBaseTTJDE + earthApsisMeanYearDays*k + earthApsisQuadraticTerm*k*k
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}
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func moonApsisSeedTT(k float64) float64 {
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t := k / moonApsisBaseCycle
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return moonApsisBaseTTJDE +
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moonApsisMeanMonthDays*k +
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moonApsisQuadraticTerm*t*t +
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moonApsisCubicTerm*t*t*t +
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moonApsisQuarticTerm*t*t*t*t
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}
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func refineDistanceExtremum(seed float64, cfg apsisSearchConfig, distanceFn func(float64) float64) (float64, float64) {
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best := seed
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bestDistance := distanceFn(seed)
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for sample := seed - cfg.bracketHalfWidth; sample <= seed+cfg.bracketHalfWidth+1e-12; sample += cfg.sampleStep {
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dist := distanceFn(sample)
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if distanceBetter(dist, bestDistance, cfg.maximize) {
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best = sample
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bestDistance = dist
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}
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}
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left, right, ok := apsisDerivativeBracket(best, seed, cfg, distanceFn)
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if !ok {
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return best, bestDistance
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}
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leftDeriv := apsisDistanceDerivative(distanceFn, left, cfg.derivativeStep)
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rightDeriv := apsisDistanceDerivative(distanceFn, right, cfg.derivativeStep)
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current := best
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for i := 0; i < cfg.maxIterations; i++ {
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first, second := apsisDistanceDerivatives(distanceFn, current, cfg.derivativeStep)
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next := current
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if math.Abs(second) > 0 {
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next = current - first/second
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}
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if !(next > left && next < right) || math.IsNaN(next) || math.IsInf(next, 0) {
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next = (left + right) / 2
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}
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nextDeriv := apsisDistanceDerivative(distanceFn, next, cfg.derivativeStep)
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if leftDeriv == 0 {
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right = next
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rightDeriv = nextDeriv
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} else if leftDeriv*nextDeriv <= 0 {
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right = next
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rightDeriv = nextDeriv
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} else {
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left = next
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leftDeriv = nextDeriv
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}
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if math.Abs(next-current) <= cfg.toleranceDays || math.Abs(right-left) <= cfg.toleranceDays {
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current = next
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break
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}
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current = next
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_ = rightDeriv
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}
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return current, distanceFn(current)
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}
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func apsisDerivativeBracket(best, seed float64, cfg apsisSearchConfig, distanceFn func(float64) float64) (float64, float64, bool) {
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leftBound := seed - cfg.bracketHalfWidth
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rightBound := seed + cfg.bracketHalfWidth
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left := best - cfg.sampleStep
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right := best + cfg.sampleStep
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if left < leftBound {
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left = leftBound
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}
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if right > rightBound {
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right = rightBound
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}
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leftDeriv := apsisDistanceDerivative(distanceFn, left, cfg.derivativeStep)
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rightDeriv := apsisDistanceDerivative(distanceFn, right, cfg.derivativeStep)
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for i := 0; i < cfg.maxIterations; i++ {
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if leftDeriv == 0 || rightDeriv == 0 || leftDeriv*rightDeriv < 0 {
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return left, right, true
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}
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if left > leftBound {
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left -= cfg.sampleStep
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if left < leftBound {
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left = leftBound
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}
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leftDeriv = apsisDistanceDerivative(distanceFn, left, cfg.derivativeStep)
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}
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if right < rightBound {
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right += cfg.sampleStep
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if right > rightBound {
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right = rightBound
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}
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rightDeriv = apsisDistanceDerivative(distanceFn, right, cfg.derivativeStep)
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}
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}
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return 0, 0, false
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}
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func apsisDistanceDerivative(distanceFn func(float64) float64, jd, h float64) float64 {
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return (distanceFn(jd+h) - distanceFn(jd-h)) / (2 * h)
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}
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func apsisDistanceDerivatives(distanceFn func(float64) float64, jd, h float64) (float64, float64) {
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prev := distanceFn(jd - h)
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curr := distanceFn(jd)
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next := distanceFn(jd + h)
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first := (next - prev) / (2 * h)
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second := (next - 2*curr + prev) / (h * h)
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return first, second
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}
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func distanceBetter(candidate, current float64, maximize bool) bool {
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if maximize {
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return candidate > current
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}
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return candidate < current
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}
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