Long-term effects on lunar orbiter

Abstract

The motion of lunar satellites has been intensively studied in the past by interesting semi-analytical methods. However, the poor knowledge of the Moon's gravity field makes those results incomplete. Subsequent lunar missions have allowed a more precise determination of the lunar gravity coefficients. Moreover, renewed scientific interest in the Moon has generated several more accurate models for the motion of a lunar orbiter. It is known that many zonal harmonic coefficients of the Moon have the same order of J 2 and must be included in a first-order perturbative theory. Despite of this, some success has been achieved in the study of long-term evolution of a lunar orbiter. In particular, “frozen” orbits have been found, that is orbits whose parameters have almost vanishing long period evolution. That is, these orbits can be regarded as equilibrium configurations of the orbital dynamics, and they are of interest for the general understanding of the free motion of an orbiter as well as reference orbits, taken in order to minimize the costs of a controlled spacecraft. However, stability of these equilibria has also to be checked with respect to other perturbations of the same order, such as the effects due to the Earth and, to a lesser degree, due to the Sun. We show that these perturbations, together with the effects induced by the lunar orbital plane motion, are rather relevant. We develop a picture analogous to the geometric approach to the motion of an Earth satellite under the influence of three poles ( J 2, Moon and Sun). The presence of more poles of perturbations (due to the other harmonics) makes the picture more complex but similar. Interesting effects on the frozen orbits as well as on the general motion of the pole and eccentricity of a lunar orbiter are found.