On the Stability of the Orbital Motion around an Irregular Shaped Body

Abstract

Preliminary analysis is performed on the stability of a periodic orbit around an irregular shaped body. The latus rectum (the amount of the angular momentum) and the semi-major axis (the amount of the total energy) of the orbital motion are chosen as indices of the orbit stability. Analytical approximations for the two indices are derived for orbits of an arbitrary inclination angle with a small eccentricity using a proposed perturbation method and are validated by numerical simulations of a dumbbell model. The relationships between the orbit stability and the inclination angle as well as the ratio of the rotation period of the body to the orbital period of the spacecraft are clarified through the analysis. An example of designing the orbit injection based on the derived analytical approximations is also given.