PERIODIC-ORBITS CLOSE TO THAT OF THE MOON

A peculiar feature of the Earth-Moon-Sun system is the existence of the Saros, a cycle of 6 585.d321 (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 aBAR, eccentricity eBAR and inclination iBAR 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.