The Mathematics of Solar Eclipses – Saros Cycle

The Saros cycle (18 years, 11 days, 8 hours) predicts eclipses. It is the period after which the Sun, Moon, and Earth return to nearly the same geometry. It corresponds to 223 synodic months (lunar phases) ≈ 242 draconic months (node crossings) ≈ 239 anomalistic months (perigee). The 8 hours shift longitude by 120°, so eclipses repeat at different locations. The Babylonians knew the Saros cycle around 500 BC. Modern eclipse prediction uses the same cycle plus corrections for the Moon’s orbit perturbations. Mathematics turns celestial mechanics into a timetable.