Non-equatorial equilibrium points around an asteroid with gravitational orbit-attitude coupling perturbation

A recently proposed orbital dynamics model in the close proximity of an asteroid, which is called “attitude-restricted orbital dynamics”, includes the perturbation caused by the spacecraft’s gravitational orbit–attitude coupling. This orbital model improves the precision of classical point-mass orbital model with only the non-spherical gravity. Equatorial equilibrium points have been investigated in the previous paper. In this paper, the in-plane non-equatorial equilibrium points, which are outside the asteroid’s equatorial plane but within its longitudinal principal plane, are further studied for a uniformly-rotating asteroid. These non-equatorial equilibrium points are more diverse than those in the classical point-mass orbital dynamics without gravitational orbit–attitude coupling perturbation (GOACP). Two families of them have been found. The equatorial equilibrium points studied before and the non-equatorial ones studied here give a complete map of equilibrium points in the asteroid’s principal planes. Compared with the classical point-mass orbital dynamics without GOACP, the equatorial equilibrium points have extended the longitude range of equilibrium points around an asteroid, while the non-equatorial ones studied here will extend the latitude range. These equatorial and non-equatorial equilibrium points provide natural hovering positions for the asteroid close-proximity operations.