TITLE:
Cumulative Perturbations Affecting a Spacecraft on a Mars Equatorial Orbit from the Waxing and Waning of the Polar Caps of the Planet
AUTHORS:
Jean-Pierre Barriot
KEYWORDS:
Mars’ Length-of-Day, Orbit Perturbations, Floquet’s Theorem
JOURNAL NAME:
Open Access Library Journal,
Vol.2 No.12,
December
23,
2015
ABSTRACT: 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.