Significant high number commensurabilities in the main lunar problem II: The occurrence of Saros-like near periodicities

The effect of changes in the Moon's semimajor axis and the Earth's orbital eccentricity on the occurrence of Saros-like cycles is examined. The Earth-Moon-Sun dynamical system exhibits such cycles for only 25 to 30% of the time interval between –5×10⁷ to +5×10⁷ years. Not only has the present Saros the smallest period during this time, but it also has one of the longest durations and the period closest to an integral number of anomalistic years, thus making it one of the most efficient Saros-like cycles for reversing solar perturbations in the main lunar problem. During the lifetime of a Saros-like cycle, variations of the Earth's orbital eccentricity cause frequent disappearances and reappearances of the cycle.