Periodic orbits close to that of the Moon
Abstract
A peculiar feature of the EarthMoonSun system is the existence of the Saros, a cycle of 6585^{d}.321 (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 MoonSun 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 3dimensional 3body problem of period equal to one Saros, with mean semimajor axis ‾a, eccentricity ‾e and inclination ‾i very close to those of the Moon. We have found numerically not just one, but a set of eight such periodic orbits, whose time evolutions of the osculating orbital elements are remarkably similar to those of the elements of the Moon. The significance of the existence of these periodic orbits for the dynamical evolution of the Moon is discussed. It is found that similar situations must have occurred also at other times in the past evolution of the lunar orbit and one example, relative to the probable lunar orbit of the late Precambrian, is given.
 Publication:

Astronomy and Astrophysics
 Pub Date:
 April 1993
 Bibcode:
 1993A&A...271..308V
 Keywords:

 celestial mechanics;
 eclipses;
 planets and satellites: moon