389 lines
11 KiB
Go
389 lines
11 KiB
Go
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package basic
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import "math"
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const (
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moonPlanetConjunctionEstimateN = 8
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moonPlanetConjunctionNearQueryDeltaDeg = 3.0
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moonPlanetConjunctionBracketStepDays = 0.5
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moonPlanetConjunctionNearQueryStepDays = 0.25
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moonPlanetConjunctionNearQueryHalfSpan = 1.5
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moonPlanetConjunctionBracketHalfSpan = 2.0
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moonPlanetConjunctionBracketGrowth = 2.0
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moonPlanetConjunctionBracketAttempts = 3
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moonPlanetConjunctionRefineStepDays = 0.5 / 86400.0
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moonPlanetConjunctionEventTolerance = 0.01
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moonPlanetConjunctionFallbackSpanScale = 1.5
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)
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type moonPlanetConjunctionLocalResult struct {
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lastUT float64
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nextUT float64
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}
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func emptyMoonPlanetConjunctionLocalResult() moonPlanetConjunctionLocalResult {
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return moonPlanetConjunctionLocalResult{
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lastUT: math.NaN(),
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nextUT: math.NaN(),
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}
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}
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// MoonPlanetConjunctionPlanet 月球合月目标行星 / target planet for Moon-planet conjunction events.
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type MoonPlanetConjunctionPlanet int
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const (
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MoonPlanetConjunctionMercury MoonPlanetConjunctionPlanet = iota + 1
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MoonPlanetConjunctionVenus
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MoonPlanetConjunctionMars
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MoonPlanetConjunctionJupiter
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MoonPlanetConjunctionSaturn
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MoonPlanetConjunctionUranus
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MoonPlanetConjunctionNeptune
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)
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func moonPlanetConjunctionWrappedDelta(diff float64) float64 {
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diff = math.Mod(diff+180, 360)
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if diff < 0 {
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diff += 360
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}
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return diff - 180
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}
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func moonPlanetConjunctionDeltaAt(jdTT float64, planet MoonPlanetConjunctionPlanet, n int) float64 {
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moonRA := HMoonGeocentricApparentRaN(jdTT, n)
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var planetRA float64
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switch planet {
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case MoonPlanetConjunctionMercury:
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planetRA = MercuryApparentRaN(jdTT, n)
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case MoonPlanetConjunctionVenus:
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planetRA = VenusApparentRaN(jdTT, n)
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case MoonPlanetConjunctionMars:
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planetRA = MarsApparentRaN(jdTT, n)
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case MoonPlanetConjunctionJupiter:
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planetRA = JupiterApparentRaN(jdTT, n)
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case MoonPlanetConjunctionSaturn:
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planetRA = SaturnApparentRaN(jdTT, n)
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case MoonPlanetConjunctionUranus:
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planetRA = UranusApparentRaN(jdTT, n)
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case MoonPlanetConjunctionNeptune:
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planetRA = NeptuneApparentRaN(jdTT, n)
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default:
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return math.NaN()
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}
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return moonPlanetConjunctionWrappedDelta(moonRA - planetRA)
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}
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func moonPlanetConjunctionPeriodDays(planet MoonPlanetConjunctionPlanet) float64 {
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switch planet {
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case MoonPlanetConjunctionMercury:
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return 28.1
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case MoonPlanetConjunctionVenus:
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return 28.4
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case MoonPlanetConjunctionMars:
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return 29.2
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case MoonPlanetConjunctionJupiter:
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return 28.0
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case MoonPlanetConjunctionSaturn:
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return 27.4
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case MoonPlanetConjunctionUranus:
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return 27.3
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case MoonPlanetConjunctionNeptune:
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return 27.3
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default:
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return math.NaN()
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}
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}
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func moonPlanetConjunctionInDirection(eventUT, queryTT float64, direction int) bool {
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switch direction {
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case -1:
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return eventUTQueryBeforeOrEqual(eventUT, queryTT)
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case 1:
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return eventUTQueryAfterOrEqual(eventUT, queryTT)
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default:
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return true
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}
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}
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func moonPlanetConjunctionFindBracket(centerTT, halfSpan, step float64, planet MoonPlanetConjunctionPlanet) (float64, float64, bool) {
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if math.IsNaN(centerTT) || math.IsNaN(halfSpan) || math.IsNaN(step) || halfSpan <= 0 || step <= 0 {
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return 0, 0, false
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}
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start := centerTT - halfSpan
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end := centerTT + halfSpan
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samples := int(math.Ceil((end-start)/step)) + 1
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prevTT := start
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prevVal := moonPlanetConjunctionDeltaAt(prevTT, planet, -1)
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if math.IsNaN(prevVal) {
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return 0, 0, false
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}
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if prevVal == 0 {
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return prevTT, prevTT, true
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}
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bestLeft := 0.0
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bestRight := 0.0
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bestDistance := math.Inf(1)
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for i := 1; i <= samples; i++ {
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tt := start + float64(i)*step
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if tt > end {
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tt = end
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}
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val := moonPlanetConjunctionDeltaAt(tt, planet, -1)
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if math.IsNaN(val) {
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return 0, 0, false
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}
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if val == 0 {
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return tt, tt, true
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}
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if prevVal*val < 0 {
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mid := (prevTT + tt) / 2.0
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distance := math.Abs(mid - centerTT)
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if distance < bestDistance {
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bestLeft = prevTT
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bestRight = tt
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bestDistance = distance
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}
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}
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if tt == end {
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break
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}
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prevTT = tt
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prevVal = val
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}
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if math.IsInf(bestDistance, 1) {
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return 0, 0, false
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}
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return bestLeft, bestRight, true
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}
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func moonPlanetConjunctionRefineBracket(leftTT, rightTT float64, planet MoonPlanetConjunctionPlanet) float64 {
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if leftTT > rightTT {
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leftTT, rightTT = rightTT, leftTT
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}
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if leftTT == rightTT {
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return leftTT
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}
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center := (leftTT + rightTT) / 2.0
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halfWindow := (rightTT - leftTT) / 2.0
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return eventZeroRefine(center, halfWindow, moonPlanetConjunctionRefineStepDays, func(sampleTT float64) float64 {
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return moonPlanetConjunctionDeltaAt(sampleTT, planet, -1)
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})
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}
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func moonPlanetConjunctionEventUT(leftTT, rightTT float64, planet MoonPlanetConjunctionPlanet) float64 {
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eventTT := moonPlanetConjunctionRefineBracket(leftTT, rightTT, planet)
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if math.Abs(moonPlanetConjunctionDeltaAt(eventTT, planet, -1)) > moonPlanetConjunctionEventTolerance {
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return math.NaN()
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}
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return TD2UT(eventTT, false)
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}
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func moonPlanetConjunctionCollectLocalEvent(result *moonPlanetConjunctionLocalResult, queryTT, eventUT float64) {
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if math.IsNaN(eventUT) {
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return
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}
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if eventUTQueryBeforeOrEqual(eventUT, queryTT) {
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if math.IsNaN(result.lastUT) || math.Abs(eventUTQueryTTDelta(eventUT, queryTT)) < math.Abs(eventUTQueryTTDelta(result.lastUT, queryTT)) {
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result.lastUT = eventUT
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}
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}
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if eventUTQueryAfterOrEqual(eventUT, queryTT) {
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if math.IsNaN(result.nextUT) || math.Abs(eventUTQueryTTDelta(eventUT, queryTT)) < math.Abs(eventUTQueryTTDelta(result.nextUT, queryTT)) {
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result.nextUT = eventUT
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}
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}
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}
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func moonPlanetConjunctionShouldCheckLocal(queryTT float64, planet MoonPlanetConjunctionPlanet) bool {
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delta := moonPlanetConjunctionDeltaAt(queryTT, planet, moonPlanetConjunctionEstimateN)
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if math.IsNaN(delta) {
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return false
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}
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return math.Abs(delta) <= moonPlanetConjunctionNearQueryDeltaDeg
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}
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func moonPlanetConjunctionLocalEvents(queryTT float64, planet MoonPlanetConjunctionPlanet) moonPlanetConjunctionLocalResult {
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result := emptyMoonPlanetConjunctionLocalResult()
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start := queryTT - moonPlanetConjunctionNearQueryHalfSpan
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end := queryTT + moonPlanetConjunctionNearQueryHalfSpan
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step := moonPlanetConjunctionNearQueryStepDays
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prevTT := start
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prevVal := moonPlanetConjunctionDeltaAt(prevTT, planet, -1)
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if math.IsNaN(prevVal) {
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return result
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}
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samples := int(math.Ceil((end-start)/step)) + 1
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for i := 1; i <= samples; i++ {
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tt := start + float64(i)*step
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if tt > end {
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tt = end
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}
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val := moonPlanetConjunctionDeltaAt(tt, planet, -1)
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if math.IsNaN(val) {
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return emptyMoonPlanetConjunctionLocalResult()
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}
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if prevVal == 0 || val == 0 || prevVal*val < 0 {
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moonPlanetConjunctionCollectLocalEvent(&result, queryTT, moonPlanetConjunctionEventUT(prevTT, tt, planet))
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}
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if tt == end {
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break
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}
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prevTT = tt
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prevVal = val
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}
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return result
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}
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func moonPlanetConjunctionMaybeLocalEvents(queryTT float64, planet MoonPlanetConjunctionPlanet) moonPlanetConjunctionLocalResult {
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if !moonPlanetConjunctionShouldCheckLocal(queryTT, planet) {
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return emptyMoonPlanetConjunctionLocalResult()
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}
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return moonPlanetConjunctionLocalEvents(queryTT, planet)
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}
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func moonPlanetConjunctionGuessTT(queryTT float64, planet MoonPlanetConjunctionPlanet, direction int) float64 {
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delta := moonPlanetConjunctionDeltaAt(queryTT, planet, moonPlanetConjunctionEstimateN)
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if math.IsNaN(delta) {
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return math.NaN()
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}
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period := moonPlanetConjunctionPeriodDays(planet)
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if math.IsNaN(period) {
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return math.NaN()
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}
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switch direction {
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case -1:
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return queryTT - innerLastCycleOffset(delta, period)
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case 1:
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return queryTT + innerNextCycleOffset(delta, period)
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default:
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return math.NaN()
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}
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}
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func moonPlanetConjunctionDirectionalFallback(queryTT float64, planet MoonPlanetConjunctionPlanet, direction int) float64 {
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period := moonPlanetConjunctionPeriodDays(planet)
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if math.IsNaN(period) {
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return math.NaN()
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}
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span := period * moonPlanetConjunctionFallbackSpanScale
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if span <= 0 {
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return math.NaN()
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}
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step := moonPlanetConjunctionNearQueryStepDays
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start := queryTT
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end := queryTT
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switch direction {
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case -1:
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start -= span
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case 1:
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end += span
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default:
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return math.NaN()
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}
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prevTT := start
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prevVal := moonPlanetConjunctionDeltaAt(prevTT, planet, -1)
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if math.IsNaN(prevVal) {
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return math.NaN()
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}
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bestEventUT := math.NaN()
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for tt := start + step; ; tt += step {
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if tt > end {
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tt = end
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}
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val := moonPlanetConjunctionDeltaAt(tt, planet, -1)
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if math.IsNaN(val) {
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return math.NaN()
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}
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if prevVal == 0 || val == 0 || prevVal*val < 0 {
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eventUT := moonPlanetConjunctionEventUT(prevTT, tt, planet)
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if !math.IsNaN(eventUT) && moonPlanetConjunctionInDirection(eventUT, queryTT, direction) {
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if direction == 1 {
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return eventUT
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}
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bestEventUT = eventUT
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}
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}
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if tt == end {
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break
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}
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prevTT = tt
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prevVal = val
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}
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return bestEventUT
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}
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func moonPlanetConjunctionDirectionalEventWithLocal(queryTT float64, planet MoonPlanetConjunctionPlanet, direction int, local moonPlanetConjunctionLocalResult) float64 {
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switch direction {
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case -1:
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if !math.IsNaN(local.lastUT) {
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return local.lastUT
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}
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case 1:
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if !math.IsNaN(local.nextUT) {
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return local.nextUT
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}
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}
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guessTT := moonPlanetConjunctionGuessTT(queryTT, planet, direction)
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if math.IsNaN(guessTT) {
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return math.NaN()
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}
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halfSpan := moonPlanetConjunctionBracketHalfSpan
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for attempt := 0; attempt < moonPlanetConjunctionBracketAttempts; attempt++ {
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left, right, ok := moonPlanetConjunctionFindBracket(guessTT, halfSpan, moonPlanetConjunctionBracketStepDays, planet)
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if ok {
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eventUT := moonPlanetConjunctionEventUT(left, right, planet)
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if math.IsNaN(eventUT) {
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halfSpan *= moonPlanetConjunctionBracketGrowth
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continue
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}
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if moonPlanetConjunctionInDirection(eventUT, queryTT, direction) {
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return eventUT
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}
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}
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halfSpan *= moonPlanetConjunctionBracketGrowth
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}
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return moonPlanetConjunctionDirectionalFallback(queryTT, planet, direction)
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}
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func moonPlanetConjunctionDirectionalEvent(queryTT float64, planet MoonPlanetConjunctionPlanet, direction int) float64 {
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return moonPlanetConjunctionDirectionalEventWithLocal(queryTT, planet, direction, moonPlanetConjunctionMaybeLocalEvents(queryTT, planet))
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}
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// LastMoonPlanetConjunction 指定时刻之前最近一次行星合月（赤经合） / previous Moon-planet conjunction at or before jde.
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func LastMoonPlanetConjunction(jde float64, planet MoonPlanetConjunctionPlanet) float64 {
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return moonPlanetConjunctionDirectionalEvent(jde, planet, -1)
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}
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// NextMoonPlanetConjunction 指定时刻之后最近一次行星合月（赤经合） / next Moon-planet conjunction at or after jde.
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func NextMoonPlanetConjunction(jde float64, planet MoonPlanetConjunctionPlanet) float64 {
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return moonPlanetConjunctionDirectionalEvent(jde, planet, 1)
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}
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// ClosestMoonPlanetConjunction 离指定时刻最近一次行星合月（赤经合） / closest Moon-planet conjunction to jde.
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func ClosestMoonPlanetConjunction(jde float64, planet MoonPlanetConjunctionPlanet) float64 {
|
||
|
|
local := moonPlanetConjunctionMaybeLocalEvents(jde, planet)
|
||
|
|
if !math.IsNaN(local.lastUT) && !math.IsNaN(local.nextUT) {
|
||
|
|
if sameEventJD(local.lastUT, local.nextUT) {
|
||
|
|
return local.lastUT
|
||
|
|
}
|
||
|
|
return closestEventUTToQueryTT(jde, local.lastUT, local.nextUT)
|
||
|
|
}
|
||
|
|
if !math.IsNaN(local.lastUT) {
|
||
|
|
return local.lastUT
|
||
|
|
}
|
||
|
|
if !math.IsNaN(local.nextUT) {
|
||
|
|
return local.nextUT
|
||
|
|
}
|
||
|
|
last := moonPlanetConjunctionDirectionalEventWithLocal(jde, planet, -1, local)
|
||
|
|
next := moonPlanetConjunctionDirectionalEventWithLocal(jde, planet, 1, local)
|
||
|
|
if math.IsNaN(last) {
|
||
|
|
return next
|
||
|
|
}
|
||
|
|
if math.IsNaN(next) {
|
||
|
|
return last
|
||
|
|
}
|
||
|
|
return closestEventUTToQueryTT(jde, last, next)
|
||
|
|
}
|