Saros — solar eclipses & the saros series (§15b.6, §9)
A live scan: every new moon in the chosen year, a solar eclipse if the Moon's ecliptic latitude |β| < 1.6° (the calibrated eclipse threshold). One year is fast; the full 5000-year enumeration that counts saros series members runs offline.
Why eclipses cluster at nodes: the Moon's path is inclined 5.1° to the ecliptic and crosses it only twice per month. A new moon within the |β|<1.6° window (green band) = solar eclipse; elsewhere = a normal new moon. The scan tests exactly this.
The saros-series count (§15b.6 — verified by calculation)
- The saros = 223 synodic months = 6585.32 d. Eclipses of one series are separated by ~6585.32 d; a chain = a saros series.
- Full enumeration (5000 years, all new moons, |β| < 1.6°): 152 complete series, lengths 54–87, median 72 — the empirical member count of a saros series.
Hebrew stellar-alphabet mnemonics for eclipse seasons
The Sefer Yetzirah does not predict eclipses, and the Sefer Raziel (p.144: “combine the signs and the wheel… compute the periods… compute in order to see the generations”) gives the letter-astronomy scaffold but no eclipse algorithm. The real engine is the Hebrew calendar, and its constants are the SY's constants:
| Astronomy | Stellar alphabet (SY) |
|---|---|
| Molad = 29d 12h 793p = 29.530594 d | ≈ synodic month 29.530589 d ⇒ a conjunction engine (eclipse = conjunction/opposition near a node) |
| Metonic cycle = 19 yr (12 common + 7 leap) | 19 = 7 doubles + 12 simples (the SY's own partition) |
| 7 leap years of the 19-yr cycle | = the 7 doubles (mnemonic) |
| 28 lunar mansions (node / Moon path) | 28 = T₇ — triangular number of the 7 doubles |
| Saros ≈ 19 eclipse years (Δ 0.46 d) | the SY's 19 structures the saros |
| Saros = 223 synodic = 242 draconic months | 242 − 223 = 19 — the SY number embedded in the saros |
Sources the Hebrew calendar actually uses (absent from the rest of this app): molad + tekufot (Shmuel/Ada), Baraita of Samuel (the one Jewish source with a nodal cycle), Maimonides Kiddush HaChodesh (mean lunar motion), Ibn Ezra Sefer ha-Olam (28 mansions, precession). Caveat: these mnemonics predict eclipse seasons (a window near a node), not individual eclipses or paths; the molad + 19-yr cycle is a real calculation engine, the stellar-alphabet constants are a mnemonic, not a physical model.