feat: 完善日月食与月掩几何链路并扩展历法接口

- 新增日月食中心带、偏食带、阴影足迹、等时线、食分线及升落边界计算，支持极区与混合食拓扑
- 新增日食单时刻阴影求解器、站心状态查询、批量采样和 ΔT 覆盖接口
- 重构恒星与行星月掩路径，补充有限盘面接触、站心修正、掩带宽度、极区投影及升落边界
- 扩展 SVG 与 GeoJSON 输出，支持详细面板、全球/极区/地球投影、边界闭合、时间标记和拓扑签名
- 扩展日月食候选搜索、局地搜索、沙罗序列预计算与范围外推，补充系列锚点和成员一致性校验
- 补齐古历纪年、儒略历独有闰日、多公历候选、历法改革跨日及精确日期运算接口
- 优化 ΔT、章动、恒星时、月球地平线、事件根搜索和本地星历缓存，降低重复计算开销并提升边界稳定

basic/coordinate.go

@@ -10,7 +10,8 @@ import (
  * 坐标变换，黄道转赤道
  */
 func LoToRa(jde, lo, bo float64) float64 {
-	ra := math.Atan2(Sin(lo)*Cos(TrueObliquity(jde))-Tan(bo)*Sin(TrueObliquity(jde)), Cos(lo))
+	eps := TrueObliquity(jde)
+	ra := math.Atan2(Sin(lo)*Cos(eps)-Tan(bo)*Sin(eps), Cos(lo))
 	ra = ra * 180 / math.Pi
 	if ra < 0 {
 		ra += 360
@@ -19,13 +20,17 @@ func LoToRa(jde, lo, bo float64) float64 {
 }
 
 func BoToDec(jde, lo, bo float64) float64 {
-	dec := ArcSin(Sin(bo)*Cos(TrueObliquity(jde)) + Cos(bo)*Sin(TrueObliquity(jde))*Sin(lo))
+	eps := TrueObliquity(jde)
+	dec := ArcSin(Sin(bo)*Cos(eps) + Cos(bo)*Sin(eps)*Sin(lo))
 	return dec
 }
 
 func LoBoToRaDec(jde, lo, bo float64) (float64, float64) {
-	dec := ArcSin(Sin(bo)*Cos(TrueObliquity(jde)) + Cos(bo)*Sin(TrueObliquity(jde))*Sin(lo))
-	ra := math.Atan2(Sin(lo)*Cos(TrueObliquity(jde))-Tan(bo)*Sin(TrueObliquity(jde)), Cos(lo))
+	eps := TrueObliquity(jde)
+	sinEps := Sin(eps)
+	cosEps := Cos(eps)
+	dec := ArcSin(Sin(bo)*cosEps + Cos(bo)*sinEps*Sin(lo))
+	ra := math.Atan2(Sin(lo)*cosEps-Tan(bo)*sinEps, Cos(lo))
 	ra = ra * 180 / math.Pi
 	if ra < 0 {
 		ra += 360
@@ -81,10 +86,14 @@ func psini(lat, h float64) float64 {
 }
 
 func TopocentricRaDec(ra, dec, lat, lon, jd, au, h float64) (float64, float64) {
+	return topocentricRaDecWithSidereal(ra, dec, lat, lon, ApparentSiderealTime(jd)*15, au, h)
+}
+
+func topocentricRaDecWithSidereal(ra, dec, lat, lon, siderealDegrees, au, h float64) (float64, float64) {
 	sinpi := Sin(0.0024427777777) / au
 	pcosi := pcosi(lat, h)
 	psini := psini(lat, h)
-	tH := Limit360(ApparentSiderealTime(jd)*15 + lon - ra)
+	tH := Limit360(siderealDegrees + lon - ra)
 	nra := math.Atan2(-pcosi*sinpi*Sin(tH), (Cos(dec)-pcosi*sinpi*Cos(tH))) * 180 / math.Pi
 
 	ndec := math.Atan2((Sin(dec)-psini*sinpi)*Cos(nra), (Cos(dec)-pcosi*sinpi*Cos(tH))) * 180 / math.Pi