The Motion of a Satellite of the Moon

The motion of a satellite of the Moon depends on the potential field due to the Moon as well as the gravitational effects of the Earth and Sun. If one chooses a frame of reference attached to the Moon, it can be shown that the force field resulting from the Sun can be neglected when compared with the perturbing field of the Moon resulting from its oblateness. The effect of the Earth's field on the satellite is of the some order of magnitude as the Moon's perturbing field and must be included in an analysis of the motion of a satellite of the Moon. We will assume that the distance between Earth and Moon remains constant, and we will consider satellite orbits of small eccentricity. It will be shown that a nearly circular polar orbit will digress less than 1 deg from a polar orbit and that the change in eccentricity is less than a factor of e in one year.