Analysis of J ₂-perturbed motion using mean non-osculating orbital elements

Author: Gurfil, Pini¹

Source: Celestial Mechanics and Dynamical Astronomy, Volume 90, Numbers 3-4, November 2004 , pp. 289-306(18)

Publisher: Springer

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Abstract:

This paper investigates the long-period and secular dynamics of a satellite about an oblate primary while relieving the assumption that the perturbed orbit is instantaneously parameterized by osculating Keplerian orbits. The inherent freedom obtained by transforming the orbital dynamics from the Cartesian inertial space to the orbital elements space, termed gauge freedom, is utilized to nullify four planetary equations. It is shown that there exists an orbit representation in which the mean non-osculating perigee is stable under the oblateness perturbation and that nodal precession, apsidal rotation and epoch drift may be simultaneously nullified on the expense of secular eccentricity and inclination variations. These observations considerably expand the standard description of J ₂-perturbed motion using mean osculating orbital elements, which predicts secular variation nullification of semi-major axis, eccentricity and inclination only.

Keywords: oblateness; Lagrange’s equation; orbital perturbations; orbital elements; gauge invariance

Document Type: Research article

DOI: 10.1007/s10569-004-0890-x

Affiliations: 1: Faculty of Aerospace Engineering, 011011011011011011011011Technion – Israel Institute of Technology, Haifa, 01101101101101101101101101132000, 011011011011011011011011011Israel, Email: pgurfil@technion.ac.il

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