Quasi-critical orbits for artificial lunar satellites

Abstract

We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include, besides the Keplerian term, the J2 and C22 terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the incli- nation and the argument of pericenter do not remain both constant at the same time, as is the case when only the J2 term is taken into account. Instead, there exist quasi-critical solutions, for which the argument of pericenter librates around a constant value. These solutions are represented by smooth curves in phase space, which determine the dependence of the quasi- critical inclination on the initial nodal phase. The amplitude of libration of both argument of pericenter and inclination would be quite large for a non-rotating Moon, but is reduced to <0 ◦ .1 for both quantities, when a uniform rotation of the Moon is taken into account. The values of J2, C22 and the rotation rate strongly affect the quasi-critical inclination and the libration amplitude of the argument of pericenter. Examples for other celestial bodies are given, showing the dependence of the results on J2, C22 and rotation rate.