An averaging method to study the motion of lunar artificial satellites I: Disturbing Function

Abstract

We describe a semi-analytical averaging method aimed at the computation of the motion of an artificial satellite of the Moon. In this paper, the first of the two part study, we expand the disturbing function with respect to the small parameters. In particular, a semi-analytic theory of the motion of the Moon around the Earth and the libration of the lunar equatorial plane using different reference frames are introduced. The second part of this article shows that the choice of the canonical Poincare variables lead to equations in closed form without singularities in e = 0 or I = 0. We introduce new expressions that are sufficiently compact to be used for the study of any artificial satellite.