Fifth John V. Breakwell memorial lecture: The restricted three-body problem revisited

Abstract

The circular and elliptic restricted three-body problems modelizes respectively 95% and 99.9% of the lunar motion perturbations. They are also usually the main orbital problem of natural and artificial satellites and space probes. A simple decomposition allows to separate the secular and long period effects from the short period effects. The perturbations remain small if the inclination is small, but they become very large if the initial orbit is polar or near polar. The lunar equatorial bulge is much smaller than the Earth's one, nevertheless it has a major interest for lunar polar orbits: it stabilizes them, at least when they are sufficiently low. We thus are in a paradoxical situation: lunar polar orbits with a large semi-major axis are more dangerous than those with a small one. This latter point is illustrated by a numerical computation. A lunar satellite has initially the following orbital elements: semi-major axis = 4 lunar radii; eccentricity = 0.2; inclination on ecliptic = 85 °. After only six months the eccentricity has increased up to 0.75 while the semi-major axis remains almost constant and the satellite falls on the Moon ! The four major satellites of Jupiter are in an even worse situtation: all their polar and near polar orbits are unstable and most of them lead to a fall on the Jupiter's satellite within a few months.