The Saros cycle: obtaining eclipse periodicity from Newton's laws

O ciclo do Saros: como obter a periodicidade dos eclipses a partir das leis de Newton

Abstract

The Saros cycle has been known since antiquity and refers to the periodicity of eclipses. It is the least common multiple of three periods: the synodic, the draconic, and the anomalistic months. We show how to obtain these periods from Newton's laws with a precision greater than 0.02% using only the sidereal month and year as references.

Saros cycles; eclipses; Newton's laws; restricted 3-body problem