Significant High Number Commensurabilities in the Main Lunar Problem: A Postscript to a Discovery of the Ancient Chaldeans
Since ancient times the knowledge of several "lunar cycles" helped mankind to predict lunar phases and eclipses. These cycles owe their existence to high-number commensurabilities between the mean motions of the Sun and the Moon and the lunar nodical (or draconitic) and anomalistic months (Deslambre, 1817); some of them are reported in Table 1. The Metonic cycle ensures that, if a full Moon or new Moon occurs on a particular date, a full Moon or new Moon will occur on the same date 19 years later, allowing easy calibration of the lunar phase to the solar calendar. The Saros period of slightly more than 18 years gives the basic time span for eclipse prediction. Hipparcus (circa 140 B.C.) introduced three additional cycles, the shortest of which is reported in Table 1, involving the synodic, anomalistic and nodical months of the Moon, in an attempt to improve the predictability of events in the Earth-Moon-Sun system.
KeywordsPeriodic Orbit Orbital Element Semimajor Axis Lunar Cycle Mirror Theorem
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