Abstract
Space exploration missions for heavenly bodies generally call a phase of orbital operations in close proximity to the body. Moons and asteroids have irregular shapes and may considerably disturb the periodic orbit of spacecraft. This paper aims at clarifying the relationships between the orbit stability and the irregular shapes of the body in a pure rotation. First, the general gravitational field is expanded in terms of spherical harmonics, whose 1st and 2nd coefficients are shown to correspond to the mass parameters of the body. Secondly, the analytic approximations for the equations of motion are derived for the planar motion using a proposed perturbation method. The true anomaly is chosen as an independent variable instead of time to utilize the periodicity of the motion. Finally, numerical simulations are given to validate the derived analytic approximations, where a dumbbell model is used as a representative gravitational model for an asteroid. The main results are : 1) in a direct orbit, when the orbital period is close to the rotation period, the perturbations become large and 2) in a retrograde orbit, the perturbations are always small.
