Significant high number commensurabilities in the main lunar problem. I: the Saros as a near-periodicity of the moon's orbit

A description is given of certain historically known cycles associated with high-number near commensurabilities among the synodic, anomalistic and nodical lunar months and the anomalistic year. Using eclipse records, the JPL ephemeris and results from three-body numerical integrations, any dynamical configuration of the Earth-Moon-Sun system (within the framework of the main lunar problem) is shown to repeat itself closely after a period of time equal in length to the classical Saros cycle of 18 years and 10 or 11 days. The role played by mirror configurations in reversing solar perturbations on the lunar orbit is examined and it is shown that the Earth-Moon-Sun system moves in a nearly periodic orbit of period equivalent to the Saros. The Saros cycle is therefore the natural averaging period of time by which solar perturbations can be most effectively removed in any search into the long term evolution of the lunar orbit.