Trajectories of close satellites of the moon

V. Summary

This paper deals with close satellites of the moon moving in orbits inclined to the lunar equator. Choosing the unperturbed orbit of the satellite as a Keplerian ellipse, the effect caused by the departure of the shape of the moon from a perfect sphere has been studied in detail. The equations of motion are solved for (u) the reciprocal of the radial distance of the satellite from the centre of mass of the moon, the angular momentum (M) of the satellite, the longitude (Ω) of the ascending node, the inclination (α) of the instantaneous orbital plane to lunar equator and the longitude (β) of the perigee of the satellite’s orbit, correct to terms of first order in (B-A), (C-A). It is shown that the orbital plane remains fixed in space, if it coincides with one of the three principal planes of the moon and that the angular momentum of the satellite remains constant throughout the motion of the satellite, if the satellite is launched at the latitudeα=sin⁻¹ {(B-A/C-A)^1/2} andΩ=π/2. The conditions for the vanishing of the rotation of the perigee of the orbit are also discussed.