fix: 修正行星事件边界与留点计算

- 统一 UT 事件时刻与 TT 查询时刻的边界判断
- 将外行星留点搜索锚定到对应冲日周期
- 修正水星、金星合日、留、大距事件选择
- 统一七大行星视位置计算辅助逻辑
- 增加公开 Last/Next 边界和 JPL/NAOJ 基线回归测试

basic/planet_apparent.go

@@ -0,0 +1,84 @@
+package basic
+
+import (
+	"math"
+
+	"b612.me/astro/planet"
+	. "b612.me/astro/tools"
+)
+
+type planetGeocentricPosition struct {
+	x  float64
+	y  float64
+	z  float64
+	lo float64
+	bo float64
+}
+
+func planetHeliocentricXYZN(planetIndex int, jd float64, n int) (float64, float64, float64) {
+	l := planet.WherePlanetN(planetIndex, 0, jd, n)
+	b := planet.WherePlanetN(planetIndex, 1, jd, n)
+	r := planet.WherePlanetN(planetIndex, 2, jd, n)
+	return sphericalToRectangular(l, b, r)
+}
+
+func earthHeliocentricXYZN(jd float64, n int) (float64, float64, float64) {
+	l := planet.WherePlanetN(-1, 0, jd, n)
+	b := planet.WherePlanetN(-1, 1, jd, n)
+	r := planet.WherePlanetN(-1, 2, jd, n)
+	return sphericalToRectangular(l, b, r)
+}
+
+func sphericalToRectangular(lo, bo, radius float64) (float64, float64, float64) {
+	cosBo := math.Cos(bo * math.Pi / 180)
+	return radius * cosBo * math.Cos(lo*math.Pi/180),
+		radius * cosBo * math.Sin(lo*math.Pi/180),
+		radius * math.Sin(bo*math.Pi/180)
+}
+
+func geocentricPositionFromRectangular(x, y, z float64) planetGeocentricPosition {
+	lo := math.Atan2(y, x) * 180 / math.Pi
+	bo := math.Atan2(z, math.Sqrt(x*x+y*y)) * 180 / math.Pi
+	return planetGeocentricPosition{
+		x:  x,
+		y:  y,
+		z:  z,
+		lo: Limit360(lo),
+		bo: bo,
+	}
+}
+
+func planetGeocentricPositionN(planetIndex int, planetJD, earthJD float64, n int) planetGeocentricPosition {
+	px, py, pz := planetHeliocentricXYZN(planetIndex, planetJD, n)
+	ex, ey, ez := earthHeliocentricXYZN(earthJD, n)
+	return geocentricPositionFromRectangular(px-ex, py-ey, pz-ez)
+}
+
+func planetGeocentricPositionWithEarthN(planetIndex int, planetJD float64, ex, ey, ez float64, n int) planetGeocentricPosition {
+	px, py, pz := planetHeliocentricXYZN(planetIndex, planetJD, n)
+	return geocentricPositionFromRectangular(px-ex, py-ey, pz-ez)
+}
+
+func planetApparentGeocentricPositionN(planetIndex int, jd float64, n int) (planetGeocentricPosition, float64) {
+	ex, ey, ez := earthHeliocentricXYZN(jd, n)
+	geoNow := planetGeocentricPositionWithEarthN(planetIndex, jd, ex, ey, ez, n)
+	tau := 0.0057755183 * math.Sqrt(geoNow.x*geoNow.x+geoNow.y*geoNow.y+geoNow.z*geoNow.z)
+	geo := planetGeocentricPositionWithEarthN(planetIndex, jd-tau, ex, ey, ez, n)
+	baseLo := geo.lo
+	baseBo := geo.bo
+	geo.lo = Limit360(baseLo + GXCLo(baseLo, baseBo, jd)/3600.0 + Nutation2000Bi(jd))
+	geo.bo = baseBo + GXCBo(baseLo, baseBo, jd)/3600.0
+	return geo, tau
+}
+
+func planetTrueGeocentricPositionN(planetIndex int, jd float64, n int) (planetGeocentricPosition, float64) {
+	ex, ey, ez := earthHeliocentricXYZN(jd, n)
+	geoNow := planetGeocentricPositionWithEarthN(planetIndex, jd, ex, ey, ez, n)
+	tau := 0.0057755183 * math.Sqrt(geoNow.x*geoNow.x+geoNow.y*geoNow.y+geoNow.z*geoNow.z)
+	return planetGeocentricPositionWithEarthN(planetIndex, jd-tau, ex, ey, ez, n), tau
+}
+
+func planetEarthAwayExplicitN(planetIndex int, jd float64, n int) float64 {
+	geoNow := planetGeocentricPositionN(planetIndex, jd, jd, n)
+	return math.Sqrt(geoNow.x*geoNow.x + geoNow.y*geoNow.y + geoNow.z*geoNow.z)
+}