astro/basic/saturn_events.go

package basic

import (
	"math"

	. "b612.me/astro/tools"
)

// Pos

const (
	SATURN_S_PERIOD            = 1 / ((1 / 365.256363004) - (1 / 10759.0))
	saturnEventSearchN         = 16
	saturnPhaseCoarseTolerance = 30.0 / 86400.0
)

func saturnSunLongitudeDelta(jde, degree float64, filter bool) float64 {
	sub := Limit360(Limit360(SaturnApparentLo(jde)-HSunApparentLo(jde)) - degree)
	if filter {
		if sub > 180 {
			sub -= 360
		}
		if sub < -180 {
			sub += 360
		}
	}
	return sub
}

func saturnSunLongitudeDeltaN(jde, degree float64, filter bool, n int) float64 {
	sub := Limit360(Limit360(SaturnApparentLoN(jde, n)-HSunApparentLoN(jde, n)) - degree)
	if filter {
		if sub > 180 {
			sub -= 360
		}
		if sub < -180 {
			sub += 360
		}
	}
	return sub
}

func saturnConjunctionFull(jde, degree float64, next uint8) float64 {
	//0=last 1=next
	daysPerDegree := SATURN_S_PERIOD / 360
	currentDelta := saturnSunLongitudeDelta(jde, degree, false)
	if next == 0 {
		jde -= (360 - currentDelta) * daysPerDegree
	} else {
		jde += daysPerDegree * currentDelta
	}
	estimateJD := jde
	for {
		prevJD := estimateJD
		longitudeDelta := saturnSunLongitudeDelta(prevJD, degree, true)
		longitudeSlope := (saturnSunLongitudeDelta(prevJD+0.000005, degree, true) - saturnSunLongitudeDelta(prevJD-0.000005, degree, true)) / 0.00001
		estimateJD = prevJD - longitudeDelta/longitudeSlope
		if math.Abs(estimateJD-prevJD) <= 0.00001 {
			break
		}
	}
	return TD2UT(estimateJD, false)
}

func saturnConjunction(jde, degree float64, next uint8) float64 {
	//0=last 1=next
	daysPerDegree := SATURN_S_PERIOD / 360
	currentDelta := saturnSunLongitudeDelta(jde, degree, false)
	if next == 0 {
		jde -= (360 - currentDelta) * daysPerDegree
	} else {
		jde += daysPerDegree * currentDelta
	}
	estimateJD := jde
	for {
		prevJD := estimateJD
		longitudeDelta := saturnSunLongitudeDeltaN(prevJD, degree, true, saturnEventSearchN)
		longitudeSlope := (saturnSunLongitudeDeltaN(prevJD+0.000005, degree, true, saturnEventSearchN) - saturnSunLongitudeDeltaN(prevJD-0.000005, degree, true, saturnEventSearchN)) / 0.00001
		estimateJD = prevJD - longitudeDelta/longitudeSlope
		if math.Abs(estimateJD-prevJD) <= saturnPhaseCoarseTolerance {
			break
		}
	}
	for {
		prevJD := estimateJD
		longitudeDelta := saturnSunLongitudeDelta(prevJD, degree, true)
		longitudeSlope := (saturnSunLongitudeDelta(prevJD+0.000005, degree, true) - saturnSunLongitudeDelta(prevJD-0.000005, degree, true)) / 0.00001
		estimateJD = prevJD - longitudeDelta/longitudeSlope
		if math.Abs(estimateJD-prevJD) <= 0.00001 {
			break
		}
	}
	return TD2UT(estimateJD, false)
}

func LastSaturnConjunction(jde float64) float64 {
	return saturnConjunction(jde, 0, 0)
}

func NextSaturnConjunction(jde float64) float64 {
	return saturnConjunction(jde, 0, 1)
}

func LastSaturnOpposition(jde float64) float64 {
	return saturnConjunction(jde, 180, 0)
}

func NextSaturnOpposition(jde float64) float64 {
	return saturnConjunction(jde, 180, 1)
}

func NextSaturnEasternQuadrature(jde float64) float64 {
	return saturnConjunction(jde, 90, 1)
}

func LastSaturnEasternQuadrature(jde float64) float64 {
	return saturnConjunction(jde, 90, 0)
}

func NextSaturnWesternQuadrature(jde float64) float64 {
	return saturnConjunction(jde, 270, 1)
}

func LastSaturnWesternQuadrature(jde float64) float64 {
	return saturnConjunction(jde, 270, 0)
}

func saturnRetrograde(jde float64, searchBeforeOpposition bool) float64 {
	//0=last 1=next
	raRate := func(jde float64, delta float64) float64 {
		sub := SaturnApparentRa(jde+delta) - SaturnApparentRa(jde-delta)
		if sub > 180 {
			sub -= 360
		}
		if sub < -180 {
			sub += 360
		}
		return sub / (2 * delta)
	}
	jde = saturnConjunctionFull(jde, 180, 1)
	if searchBeforeOpposition {
		jde -= 60
	} else {
		jde += 60
	}
	for {
		currentRate := raRate(jde, 1.0/86400.0)
		if math.Abs(currentRate) > 0.55 {
			jde += 2
			continue
		}
		break
	}
	estimateJD := jde
	for {
		prevJD := estimateJD
		rateValue := raRate(prevJD, 2.0/86400.0)
		rateSlope := (raRate(prevJD+15.0/86400.0, 2.0/86400.0) - raRate(prevJD-15.0/86400.0, 2.0/86400.0)) / (30.0 / 86400.0)
		estimateJD = prevJD - rateValue/rateSlope
		if math.Abs(estimateJD-prevJD) <= 30.0/86400.0 {
			break
		}
	}
	bestJD := eventZeroRefine(estimateJD, 15.0/86400.0, 0.5/86400.0, func(jd float64) float64 {
		return raRate(jd, 0.5/86400.0)
	})
	return TD2UT(bestJD, false)
}

func NextSaturnRetrogradeToPrograde(jde float64) float64 {
	date := saturnRetrograde(jde, false)
	if date < jde {
		oppositionJD := saturnConjunctionFull(jde, 180, 1)
		return saturnRetrograde(oppositionJD+10, false)
	}
	return date
}

func LastSaturnRetrogradeToPrograde(jde float64) float64 {
	jde = saturnConjunctionFull(jde, 180, 0) - 10
	date := saturnRetrograde(jde, false)
	if date > jde {
		oppositionJD := saturnConjunctionFull(jde, 180, 0)
		return saturnRetrograde(oppositionJD-10, false)
	}
	return date
}

func NextSaturnProgradeToRetrograde(jde float64) float64 {
	date := saturnRetrograde(jde, true)
	if date < jde {
		oppositionJD := saturnConjunctionFull(jde, 180, 1)
		return saturnRetrograde(oppositionJD+10, true)
	}
	return date
}

func LastSaturnProgradeToRetrograde(jde float64) float64 {
	jde = saturnConjunctionFull(jde, 180, 0) - 10
	date := saturnRetrograde(jde, true)
	if date > jde {
		oppositionJD := saturnConjunctionFull(jde, 180, 0)
		return saturnRetrograde(oppositionJD-10, true)
	}
	return date
}