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

eclipse/saros_lunar_count_test.go

@@ -0,0 +1,71 @@
+package eclipse
+
+import (
+	"testing"
+	"time"
+)
+
+// 把某个时间窗内落入指定沙罗系列的月食枚举出来。
+func lunarSarosMembersInWindow(t *testing.T, series int, start, end time.Time) []time.Time {
+	t.Helper()
+	seen := map[int64]bool{}
+	members := make([]time.Time, 0, 4)
+	for cursor := start; cursor.Before(end); cursor = cursor.AddDate(0, 1, 0) {
+		info := ClosestLunarEclipse(cursor)
+		if info.Maximum.IsZero() || info.Saros.Series != series {
+			continue
+		}
+		key := info.Maximum.UTC().Unix()
+		if seen[key] {
+			continue
+		}
+		seen[key] = true
+		members = append(members, info.Maximum)
+	}
+	return members
+}
+
+// 月食沙罗系列的总成员数与成员序号必须与 NASA 目录一致。
+// 123 号 72 次（NASA LEsaros123：24N 6P 25T 8P 9N = 72），157 号 73 次；
+// 2025-03-14 是 123 号的第 53 个成员。
+func TestLunarSarosSeriesMemberCounts(t *testing.T) {
+	for _, test := range []struct {
+		name   string
+		probe  time.Time
+		series int
+		member int
+		count  int
+	}{
+		{name: "123-2025", probe: time.Date(2025, time.March, 14, 0, 0, 0, 0, time.UTC), series: 123, member: 53, count: 72},
+		{name: "157-2360", probe: time.Date(2360, time.April, 2, 0, 0, 0, 0, time.UTC), series: 157, member: 4, count: 73},
+	} {
+		info := ClosestLunarEclipse(test.probe)
+		if info.Saros.Series != test.series || info.Saros.Member != test.member || info.Saros.Count != test.count {
+			t.Fatalf("%s: series %d member %d/%d, want %d member %d/%d",
+				test.name, info.Saros.Series, info.Saros.Member, info.Saros.Count,
+				test.series, test.member, test.count)
+		}
+	}
+}
+
+// 123 号系列的边界必须与 NASA 目录一致：首 1087-08-16、末 2367-10-08，两端之外再无成员。
+func TestLunarSarosSeries123Boundaries(t *testing.T) {
+	// 系列开始前的三年窗口里不应有任何 123 号成员。
+	if members := lunarSarosMembersInWindow(t, 123,
+		time.Date(1084, time.January, 1, 0, 0, 0, 0, time.UTC),
+		time.Date(1087, time.January, 1, 0, 0, 0, 0, time.UTC)); len(members) != 0 {
+		t.Fatalf("series 123 starts before 1087: %v", members)
+	}
+	if members := lunarSarosMembersInWindow(t, 123,
+		time.Date(1087, time.January, 1, 0, 0, 0, 0, time.UTC),
+		time.Date(1090, time.January, 1, 0, 0, 0, 0, time.UTC)); len(members) != 1 ||
+		members[0].UTC().Format("2006-01-02") != "1087-08-16" {
+		t.Fatalf("series 123 first members = %v, want one on 1087-08-16", members)
+	}
+	if members := lunarSarosMembersInWindow(t, 123,
+		time.Date(2367, time.January, 1, 0, 0, 0, 0, time.UTC),
+		time.Date(2371, time.January, 1, 0, 0, 0, 0, time.UTC)); len(members) != 1 ||
+		members[0].UTC().Format("2006-01-02") != "2367-10-08" {
+		t.Fatalf("series 123 last members = %v, want one on 2367-10-08", members)
+	}
+}