Gravity-gradient effects on the rotational mechanics of a satellite in near-rectilinear halo orbits

Since the announcement of the NASA Artemis program 'Lunar Gateway', considerable attention has been dedicated to the near-rectilinear halo orbits (NRHOs) about the Earth–Moon L2 point. This paper aims at studying the dynamical phenomena related to the rotational dynamics of an axysimmetric satellite along the NRHOs. We consider a model in which the gravity torque is expanded in Taylor series up to second order in the satellite’s distances from the primaries, and we prove that the gravity-gradient can be approximated as an instantaneous excitation acting at each periselene passage in a 'single attractor' model. Then, a semi-analytical recursive map is built, describing the attitude dynamics for repeated periselene passages. It is found that initial attitude states exist for which the angular velocity remains bounded, as well as other states for which the angular velocity grows unbounded. This investigation has both theoretical and practical importance for satellites orbiting in NRHOs, since it enhances our understanding of their attitude dynamics. Numerical experiments are presented for the case ofa sample NRHO having period of one week.