Quasi-critical orbits for artificial lunar satellites

We study the problem of critical inclination orbits for artificial lunar satellites, when in the lunar potential we include, besides the Keplerian term, the J ₂ and C ₂₂ terms and lunar rotation. We show that, at the fixed points of the 1-D averaged Hamiltonian, the inclination and the argument of pericenter do not remain both constant at the same time, as is the case when only the J ₂ 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 J ₂, C ₂₂ 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 J ₂, C ₂₂ and rotation rate.