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
This commit is contained in:
@@ -0,0 +1,472 @@
|
||||
package basic
|
||||
|
||||
import (
|
||||
"math"
|
||||
|
||||
"b612.me/astro/planet"
|
||||
. "b612.me/astro/tools"
|
||||
)
|
||||
|
||||
const (
|
||||
MERCURY_S_PERIOD = 1 / ((1 / 87.9691) - (1 / 365.256363004))
|
||||
mercuryConjunctionDerivativeStepDay = 2e-5 * 36525.0
|
||||
mercuryLightTimeDaysPerAU = 0.0057755183
|
||||
)
|
||||
|
||||
type mercuryConjunctionLBR struct {
|
||||
lo float64
|
||||
bo float64
|
||||
r float64
|
||||
}
|
||||
|
||||
type mercuryConjunctionGeo struct {
|
||||
lo float64
|
||||
bo float64
|
||||
dist float64
|
||||
}
|
||||
|
||||
type mercuryConjunctionResult struct {
|
||||
diff float64
|
||||
sunLightDays float64
|
||||
geoLightDays float64
|
||||
}
|
||||
|
||||
func mercuryHelioN(planetIndex int, jd float64, n int) mercuryConjunctionLBR {
|
||||
return mercuryConjunctionLBR{
|
||||
lo: planet.WherePlanetN(planetIndex, 0, jd, n),
|
||||
bo: planet.WherePlanetN(planetIndex, 1, jd, n),
|
||||
r: planet.WherePlanetN(planetIndex, 2, jd, n),
|
||||
}
|
||||
}
|
||||
|
||||
func mercuryGeocentric(planetPos, earthPos mercuryConjunctionLBR) mercuryConjunctionGeo {
|
||||
x := planetPos.r*Cos(planetPos.bo)*Cos(planetPos.lo) - earthPos.r*Cos(earthPos.bo)*Cos(earthPos.lo)
|
||||
y := planetPos.r*Cos(planetPos.bo)*Sin(planetPos.lo) - earthPos.r*Cos(earthPos.bo)*Sin(earthPos.lo)
|
||||
z := planetPos.r*Sin(planetPos.bo) - earthPos.r*Sin(earthPos.bo)
|
||||
dist := math.Sqrt(x*x + y*y + z*z)
|
||||
return mercuryConjunctionGeo{
|
||||
lo: Limit360(math.Atan2(y, x) * 180 / math.Pi),
|
||||
bo: math.Atan2(z, math.Sqrt(x*x+y*y)) * 180 / math.Pi,
|
||||
dist: dist,
|
||||
}
|
||||
}
|
||||
|
||||
func mercuryConjunctionAngleDelta(diff float64) float64 {
|
||||
diff = Limit360(diff)
|
||||
if diff > 180 {
|
||||
diff -= 360
|
||||
}
|
||||
if diff < -180 {
|
||||
diff += 360
|
||||
}
|
||||
return diff
|
||||
}
|
||||
|
||||
func mercuryConjunctionHeliocentricDelta(jd, targetDeg float64, n int) float64 {
|
||||
planetLo := planet.WherePlanetN(1, 0, jd, n)
|
||||
earthLo := planet.WherePlanetN(-1, 0, jd, n)
|
||||
return mercuryConjunctionAngleDelta(planetLo - earthLo - targetDeg)
|
||||
}
|
||||
|
||||
func mercuryConjunctionDifference(jd float64, n int, targetDeg, sunLightDays, geoLightDays float64) mercuryConjunctionResult {
|
||||
earthForSun := mercuryHelioN(-1, jd-sunLightDays, n)
|
||||
sunLo := Limit360(earthForSun.lo + 180)
|
||||
earth := mercuryHelioN(-1, jd-geoLightDays, n)
|
||||
planetPos := mercuryHelioN(1, jd-geoLightDays, n)
|
||||
geo := mercuryGeocentric(planetPos, earth)
|
||||
return mercuryConjunctionResult{
|
||||
diff: mercuryConjunctionAngleDelta(geo.lo - sunLo - targetDeg),
|
||||
sunLightDays: earthForSun.r * mercuryLightTimeDaysPerAU,
|
||||
geoLightDays: geo.dist * mercuryLightTimeDaysPerAU,
|
||||
}
|
||||
}
|
||||
|
||||
func mercuryConjunctionExactDelta(jd float64) float64 {
|
||||
return mercuryConjunctionAngleDelta(MercuryApparentLo(jd) - HSunApparentLo(jd))
|
||||
}
|
||||
|
||||
func mercuryConjunctionApproxTT(seed float64, inferior bool) float64 {
|
||||
heliocentricTarget := 180.0
|
||||
if inferior {
|
||||
heliocentricTarget = 0
|
||||
}
|
||||
jd := seed
|
||||
for i := 0; i < 6; i++ {
|
||||
jd -= mercuryConjunctionHeliocentricDelta(jd, heliocentricTarget, 8) / (360.0 / MERCURY_S_PERIOD)
|
||||
}
|
||||
|
||||
startSample := mercuryConjunctionDifference(jd, 8, 0, 0, 0)
|
||||
nextSample := mercuryConjunctionDifference(jd+mercuryConjunctionDerivativeStepDay, 8, 0, 0, 0)
|
||||
diffSlope := mercuryConjunctionAngleDelta(nextSample.diff-startSample.diff) / mercuryConjunctionDerivativeStepDay
|
||||
|
||||
refined := mercuryConjunctionDifference(jd, 40, 0, startSample.sunLightDays, startSample.geoLightDays)
|
||||
jd -= refined.diff / diffSlope
|
||||
final := mercuryConjunctionDifference(jd, -1, 0, refined.sunLightDays, refined.geoLightDays)
|
||||
jd -= final.diff / diffSlope
|
||||
return jd
|
||||
}
|
||||
|
||||
func mercuryConjunctionExactTT(seed float64, inferior bool) float64 {
|
||||
estimateJD := mercuryConjunctionApproxTT(seed, inferior)
|
||||
for {
|
||||
prevJD := estimateJD
|
||||
longitudeDelta := mercuryConjunctionExactDelta(prevJD)
|
||||
longitudeSlope := (mercuryConjunctionExactDelta(prevJD+0.000005) - mercuryConjunctionExactDelta(prevJD-0.000005)) / 0.00001
|
||||
estimateJD = prevJD - longitudeDelta/longitudeSlope
|
||||
if math.Abs(estimateJD-prevJD) <= 0.00001 {
|
||||
break
|
||||
}
|
||||
}
|
||||
return estimateJD
|
||||
}
|
||||
|
||||
func mercuryConjunctionLegacy(jde float64, next uint8) float64 {
|
||||
//0=last 1=next
|
||||
longitudeDeltaAt := func(jde float64) float64 {
|
||||
return mercuryConjunctionExactDelta(jde)
|
||||
}
|
||||
currentDelta := longitudeDeltaAt(jde)
|
||||
distanceTrend := math.Abs(longitudeDeltaAt(jde+1/86400.0)) - math.Abs(currentDelta)
|
||||
if distanceTrend >= 0 && next == 1 && currentDelta > 0 {
|
||||
jde += MERCURY_S_PERIOD/8.0 + 2
|
||||
}
|
||||
if distanceTrend >= 0 && next == 1 && currentDelta < 0 {
|
||||
jde += MERCURY_S_PERIOD/6.0 + 2
|
||||
}
|
||||
if distanceTrend <= 0 && next == 0 && currentDelta < 0 {
|
||||
jde -= MERCURY_S_PERIOD/8.0 + 2
|
||||
}
|
||||
if distanceTrend <= 0 && next == 0 && currentDelta > 0 {
|
||||
jde -= MERCURY_S_PERIOD/6.0 + 2
|
||||
}
|
||||
for {
|
||||
currentDelta := longitudeDeltaAt(jde)
|
||||
distanceTrend := math.Abs(longitudeDeltaAt(jde+1/86400.0)) - math.Abs(currentDelta)
|
||||
if math.Abs(currentDelta) > 12 || (distanceTrend > 0 && next == 1) || (distanceTrend < 0 && next == 0) {
|
||||
if next == 1 {
|
||||
jde += 2
|
||||
} else {
|
||||
jde -= 2
|
||||
}
|
||||
continue
|
||||
}
|
||||
break
|
||||
}
|
||||
estimateJD := jde
|
||||
for {
|
||||
prevJD := estimateJD
|
||||
longitudeDelta := longitudeDeltaAt(prevJD)
|
||||
longitudeSlope := (longitudeDeltaAt(prevJD+0.000005) - longitudeDeltaAt(prevJD-0.000005)) / 0.00001
|
||||
estimateJD = prevJD - longitudeDelta/longitudeSlope
|
||||
if math.Abs(estimateJD-prevJD) <= 0.00001 {
|
||||
break
|
||||
}
|
||||
}
|
||||
return TD2UT(estimateJD, false)
|
||||
}
|
||||
|
||||
func mercuryConjunction(jde float64, next uint8) float64 {
|
||||
//0=last 1=next
|
||||
currentDelta := mercuryConjunctionExactDelta(jde)
|
||||
// pos 大于0:远离太阳 小于0:靠近太阳
|
||||
distanceTrend := math.Abs(mercuryConjunctionExactDelta(jde+1/86400.0)) - math.Abs(currentDelta)
|
||||
if distanceTrend >= 0 && next == 1 && currentDelta > 0 {
|
||||
jde += MERCURY_S_PERIOD/8.0 + 2
|
||||
}
|
||||
if distanceTrend >= 0 && next == 1 && currentDelta < 0 {
|
||||
jde += MERCURY_S_PERIOD/6.0 + 2
|
||||
}
|
||||
if distanceTrend <= 0 && next == 0 && currentDelta < 0 {
|
||||
jde -= MERCURY_S_PERIOD/8.0 + 2
|
||||
}
|
||||
if distanceTrend <= 0 && next == 0 && currentDelta > 0 {
|
||||
jde -= MERCURY_S_PERIOD/6.0 + 2
|
||||
}
|
||||
for {
|
||||
currentDelta := mercuryConjunctionExactDelta(jde)
|
||||
distanceTrend := math.Abs(mercuryConjunctionExactDelta(jde+1/86400.0)) - math.Abs(currentDelta)
|
||||
if math.Abs(currentDelta) > 12 || (distanceTrend > 0 && next == 1) || (distanceTrend < 0 && next == 0) {
|
||||
if next == 1 {
|
||||
jde += 2
|
||||
} else {
|
||||
jde -= 2
|
||||
}
|
||||
continue
|
||||
}
|
||||
break
|
||||
}
|
||||
|
||||
inferior := mercuryConjunctionExactTT(jde, true)
|
||||
superior := mercuryConjunctionExactTT(jde, false)
|
||||
best := inferior
|
||||
if math.Abs(superior-jde) < math.Abs(inferior-jde) {
|
||||
best = superior
|
||||
}
|
||||
return TD2UT(best, false)
|
||||
}
|
||||
|
||||
func LastMercuryConjunction(jde float64) float64 {
|
||||
return mercuryConjunction(jde, 0)
|
||||
}
|
||||
|
||||
func NextMercuryConjunction(jde float64) float64 {
|
||||
return mercuryConjunction(jde, 1)
|
||||
}
|
||||
|
||||
func NextMercuryInferiorConjunction(jde float64) float64 {
|
||||
date := NextMercuryConjunction(jde)
|
||||
if EarthMercuryAway(date) > EarthAway(date) {
|
||||
return NextMercuryConjunction(date + 2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func NextMercurySuperiorConjunction(jde float64) float64 {
|
||||
date := NextMercuryConjunction(jde)
|
||||
if EarthMercuryAway(date) < EarthAway(date) {
|
||||
return NextMercuryConjunction(date + 2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func LastMercuryInferiorConjunction(jde float64) float64 {
|
||||
date := LastMercuryConjunction(jde)
|
||||
if EarthMercuryAway(date) > EarthAway(date) {
|
||||
return LastMercuryConjunction(date - 2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func LastMercurySuperiorConjunction(jde float64) float64 {
|
||||
date := LastMercuryConjunction(jde)
|
||||
if EarthMercuryAway(date) < EarthAway(date) {
|
||||
return LastMercuryConjunction(date - 2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func mercuryRetrograde(jde float64) float64 {
|
||||
//0=last 1=next
|
||||
solarRADelta := func(jde float64) float64 {
|
||||
sub := Limit360(MercuryApparentRa(jde) - SunApparentRa(jde))
|
||||
if sub > 180 {
|
||||
sub -= 360
|
||||
}
|
||||
if sub < -180 {
|
||||
sub += 360
|
||||
}
|
||||
return sub
|
||||
}
|
||||
raRate := func(jde float64, delta float64) float64 {
|
||||
sub := MercuryApparentRa(jde+delta) - MercuryApparentRa(jde-delta)
|
||||
if sub > 180 {
|
||||
sub -= 360
|
||||
}
|
||||
if sub < -180 {
|
||||
sub += 360
|
||||
}
|
||||
return sub / (2 * delta)
|
||||
}
|
||||
lastConjunction := mercuryConjunctionLegacy(jde, 0)
|
||||
nextConjunction := mercuryConjunctionLegacy(jde, 1)
|
||||
currentRADelta := solarRADelta(jde)
|
||||
if currentRADelta > 0 {
|
||||
jde = lastConjunction + ((nextConjunction - lastConjunction) / 5.0 * 3.5)
|
||||
} else {
|
||||
jde = lastConjunction + ((nextConjunction - lastConjunction) / 5.5)
|
||||
}
|
||||
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)
|
||||
})
|
||||
//fmt.Println((bestJD - lastConjunction) / (nextConjunction - lastConjunction))
|
||||
return TD2UT(bestJD, false)
|
||||
}
|
||||
|
||||
func NextMercuryRetrograde(jde float64) float64 {
|
||||
date := mercuryRetrograde(jde)
|
||||
if date < jde {
|
||||
nextConjunction := mercuryConjunctionLegacy(jde, 1)
|
||||
return mercuryRetrograde(nextConjunction + 2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func LastMercuryRetrograde(jde float64) float64 {
|
||||
lastConjunction := mercuryConjunctionLegacy(jde, 0)
|
||||
date := mercuryRetrograde(lastConjunction + 2)
|
||||
if date > jde {
|
||||
previousConjunction := mercuryConjunctionLegacy(lastConjunction-2, 0)
|
||||
return mercuryRetrograde(previousConjunction + 2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func NextMercuryProgradeToRetrograde(jde float64) float64 {
|
||||
date := NextMercuryRetrograde(jde)
|
||||
sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date))
|
||||
if sub > 180 {
|
||||
return NextMercuryRetrograde(date + MERCURY_S_PERIOD/2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func NextMercuryRetrogradeToPrograde(jde float64) float64 {
|
||||
date := NextMercuryRetrograde(jde)
|
||||
sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date))
|
||||
if sub < 180 {
|
||||
return NextMercuryRetrograde(date + 12)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func LastMercuryProgradeToRetrograde(jde float64) float64 {
|
||||
date := LastMercuryRetrograde(jde)
|
||||
sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date))
|
||||
if sub > 180 {
|
||||
return LastMercuryRetrograde(date - 12)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func LastMercuryRetrogradeToPrograde(jde float64) float64 {
|
||||
date := LastMercuryRetrograde(jde)
|
||||
sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date))
|
||||
if sub < 180 {
|
||||
return LastMercuryRetrograde(date - MERCURY_S_PERIOD/2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func MercurySunElongation(jde float64) float64 {
|
||||
lo1, bo1 := MercuryApparentLoBo(jde)
|
||||
lo2 := SunApparentLo(jde)
|
||||
bo2 := HSunTrueBo(jde)
|
||||
return StarAngularSeparation(lo1, bo1, lo2, bo2)
|
||||
}
|
||||
|
||||
func mercuryGreatestElongation(jde float64) float64 {
|
||||
solarRADelta := func(jde float64) float64 {
|
||||
sub := Limit360(MercuryApparentRa(jde) - SunApparentRa(jde))
|
||||
if sub > 180 {
|
||||
sub -= 360
|
||||
}
|
||||
if sub < -180 {
|
||||
sub += 360
|
||||
}
|
||||
return sub
|
||||
}
|
||||
elongationRate := func(jde float64, delta float64) float64 {
|
||||
sub := MercurySunElongation(jde+delta) - MercurySunElongation(jde-delta)
|
||||
if sub > 180 {
|
||||
sub -= 360
|
||||
}
|
||||
if sub < -180 {
|
||||
sub += 360
|
||||
}
|
||||
return sub / (2 * delta)
|
||||
}
|
||||
lastConjunction := mercuryConjunctionLegacy(jde, 0)
|
||||
nextConjunction := mercuryConjunctionLegacy(jde, 1)
|
||||
currentRADelta := solarRADelta(jde)
|
||||
if currentRADelta > 0 {
|
||||
jde = lastConjunction + ((nextConjunction - lastConjunction) / 5.0 * 2.0)
|
||||
} else {
|
||||
jde = lastConjunction + ((nextConjunction - lastConjunction) / 6.0)
|
||||
}
|
||||
for {
|
||||
currentRate := elongationRate(jde, 1.0/86400.0)
|
||||
if math.Abs(currentRate) > 0.4 {
|
||||
jde += 2
|
||||
continue
|
||||
}
|
||||
break
|
||||
}
|
||||
estimateJD := jde
|
||||
for {
|
||||
prevJD := estimateJD
|
||||
rateValue := elongationRate(prevJD, 2.0/86400.0)
|
||||
rateSlope := (elongationRate(prevJD+15.0/86400.0, 2.0/86400.0) - elongationRate(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 elongationRate(jd, 0.5/86400.0)
|
||||
})
|
||||
//fmt.Println((bestJD - lastConjunction) / (nextConjunction - lastConjunction))
|
||||
return TD2UT(bestJD, false)
|
||||
}
|
||||
|
||||
func NextMercuryGreatestElongation(jde float64) float64 {
|
||||
date := mercuryGreatestElongation(jde)
|
||||
if date < jde {
|
||||
nextConjunction := mercuryConjunctionLegacy(jde, 1)
|
||||
return mercuryGreatestElongation(nextConjunction + 2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func LastMercuryGreatestElongation(jde float64) float64 {
|
||||
lastConjunction := mercuryConjunctionLegacy(jde, 0)
|
||||
date := mercuryGreatestElongation(lastConjunction + 2)
|
||||
if date > jde {
|
||||
previousConjunction := mercuryConjunctionLegacy(lastConjunction-2, 0)
|
||||
return mercuryGreatestElongation(previousConjunction + 2)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func NextMercuryGreatestElongationEast(jde float64) float64 {
|
||||
date := NextMercuryGreatestElongation(jde)
|
||||
sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date))
|
||||
if sub > 180 {
|
||||
return NextMercuryGreatestElongation(date + 1)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func NextMercuryGreatestElongationWest(jde float64) float64 {
|
||||
date := NextMercuryGreatestElongation(jde)
|
||||
sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date))
|
||||
if sub < 180 {
|
||||
return NextMercuryGreatestElongation(date + 1)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func LastMercuryGreatestElongationEast(jde float64) float64 {
|
||||
date := LastMercuryGreatestElongation(jde)
|
||||
sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date))
|
||||
if sub > 180 {
|
||||
return LastMercuryGreatestElongation(date - 1)
|
||||
}
|
||||
return date
|
||||
}
|
||||
|
||||
func LastMercuryGreatestElongationWest(jde float64) float64 {
|
||||
date := LastMercuryGreatestElongation(jde)
|
||||
sub := Limit360(MercuryApparentRa(date) - SunApparentRa(date))
|
||||
if sub < 180 {
|
||||
return LastMercuryGreatestElongation(date - 1)
|
||||
}
|
||||
return date
|
||||
}
|
||||
Reference in New Issue
Block a user