Trajectory control around non-spherical bodies modelled by parallelepipeds

This work is a study of the dynamics around bodies with non-spherical shapes. The gravitational field of a body with non-uniform mass distribution is not central, resulting on orbits around this body that behave different from a keplerian orbit, generating a perturbation on the gravitational field. Irregular objects can be modelled by combining several geometric figures like parallelepipeds. This model can be applied to asteroids, which are objects with non-spherical shapes. The disturbing force generated by these bodies can then be obtained as the sum of the force on each cube. The present paper makes a first study in this problem by showing the evolution of the keplerian elements of orbits around a cube. It also considers a closed loop control system for the trajectory, required to compensate the perturbations due to the irregular shape of the body with the use of a low thrust engine. The main goal is to show that it is possible to use this type of control to keep the orbit keplerian all the time and the details on how to do that.