Cumulative Perturbations Affecting a Spacecraft on a Mars Equatorial Orbit from the Waxing and Waning of the Polar Caps of the Planet - Open Access Library Journal

OALibJ > Vol.2 No.12, December 2015

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

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DOI: 10.4236/oalib.1102272 702 Downloads 1,517 Views

Author(s)

Jean-Pierre Barriot

Affiliation(s)

Geodesy Observatory of Tahiti, University of French Polynesia, Faa’a, Tahiti.

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.

KEYWORDS

Mars’ Length-of-Day, Orbit Perturbations, Floquet’s Theorem

Share and Cite:

Barriot, J. (2015) Cumulative Perturbations Affecting a Spacecraft on a Mars Equatorial Orbit from the Waxing and Waning of the Polar Caps of the Planet. Open Access Library Journal, 2, 1-9. doi: 10.4236/oalib.1102272.

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