Periodic orbits close to that of the Moon

Abstract

A peculiar feature of the Earth-Moon-Sun system is the existence of the Saros, a cycle of 6585 d ,21 (about 18 years), widely used for eclipse prediction since the time of the ancient Chaldeans who discovered it. After one Saros the type of eclipse repeats itself, implying that the geometry of the Earth-Moon-Sun system also repeats. It has recently been shown that this repetition after one Saros occurs not only at eclipses but also at any phase of the cycle, indicating that the Moon moves in a nearly periodic orbit. This has led us to investigate the possible existence of a periodic orbit in the restricted circular 3-dimensional 3-body problem of period equal to one Saros, with mean semimajor axis a, eccentricity e and inclination i very close to those of the Moon