Cumulative Perturbations Affecting a Spacecraft on a Mars Equatorial Orbit from the Waxing and Waning of the Polar Caps of the Planet

We demonstrate in this paper that periodic variations of the J₂ gravity coefficient of a planet induce small cumulative perturbations on a given family of circular equatorial orbits, and that these perturbations could be measurable with current radiosciences technology. For this purpose, we first consider a Poincaré expansion of the Newtonian equations of motion. Then, by using Floquet’s theory, we demonstrate that, unlike the excitation mechanism, the perturbations are non- periodic, and that the orbit is not “stable” in the long-term, with perturbations growing exponentially. We give the full theory and an application to the case of planet Mars.