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/lunar_eclipse_geometry_test.go

@@ -0,0 +1,53 @@
+package basic
+
+import (
+	"math"
+	"testing"
+	"time"
+)
+
+// Axis 与 Gamma 是同一个量的两种刻度：Gamma × 月球处的地球视差 = Axis。
+func TestLunarEclipseShadowGeometryAxisMatchesGamma(t *testing.T) {
+	for _, date := range []time.Time{
+		time.Date(2025, time.March, 14, 0, 0, 0, 0, time.UTC),
+		time.Date(2026, time.March, 3, 0, 0, 0, 0, time.UTC),
+		time.Date(2028, time.July, 6, 0, 0, 0, 0, time.UTC),
+	} {
+		result := LunarEclipse(TD2UT(Date2JDE(date), true))
+		geometry := LunarEclipseShadowGeometryAt(result.Maximum)
+		// 影几何内部用的是小角近似的地球视差（R⊕/月距），这里必须用同一形式，否则二级差会露出来。
+		earthParallaxDegrees := (1 / geometry.MoonDistanceEarthRadii) * 180 / math.Pi
+		if delta := geometry.Gamma*earthParallaxDegrees - geometry.AxisDegrees; math.Abs(delta) > 1e-9 {
+			t.Fatalf("%s: Gamma×parallax - Axis = %g", date.Format("2006-01-02"), delta)
+		}
+	}
+}
+
+// 食分公式反解出的月心到影轴距离必须等于 Axis：这条把影几何与食分求解器对起来。
+// 食分 = (影半径 + 月视半径 − Axis) / (2 × 月视半径)。
+func TestLunarEclipseMagnitudeInvertsToAxis(t *testing.T) {
+	for _, date := range []time.Time{
+		time.Date(2025, time.March, 14, 0, 0, 0, 0, time.UTC),
+		time.Date(2026, time.March, 3, 0, 0, 0, 0, time.UTC),
+		time.Date(2028, time.July, 6, 0, 0, 0, 0, time.UTC),
+		time.Date(2020, time.November, 30, 0, 0, 0, 0, time.UTC),
+	} {
+		result := LunarEclipse(TD2UT(Date2JDE(date), true))
+		geometry := LunarEclipseShadowGeometryAt(result.Maximum)
+		moonSemidiameter := MoonSemidiameter(result.Maximum) / 3600
+		fromUmbral := geometry.UmbralRadiusDegrees + moonSemidiameter -
+			2*moonSemidiameter*result.Magnitude
+		fromPenumbral := geometry.PenumbralRadiusDegrees + moonSemidiameter -
+			2*moonSemidiameter*result.PenumbralMagnitude
+		t.Logf("%s %s: Axis=%.4f 本影反推=%.4f 半影反推=%.4f",
+			date.Format("2006-01-02"), result.Type, geometry.AxisDegrees, fromUmbral, fromPenumbral)
+		if math.Abs(fromUmbral-geometry.AxisDegrees) > 0.002 {
+			t.Fatalf("%s: umbral magnitude implies axis %.4f, geometry gives %.4f",
+				date.Format("2006-01-02"), fromUmbral, geometry.AxisDegrees)
+		}
+		if math.Abs(fromPenumbral-geometry.AxisDegrees) > 0.002 {
+			t.Fatalf("%s: penumbral magnitude implies axis %.4f, geometry gives %.4f",
+				date.Format("2006-01-02"), fromPenumbral, geometry.AxisDegrees)
+		}
+	}
+}