Astronomy and Astrophysics – Astrophysics
Scientific paper
Dec 1987
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987ap%26ss.139..353z&link_type=abstract
Astrophysics and Space Science (ISSN 0004-640X), vol. 139, no. 2, Dec. 1987, p. 353-364.
Astronomy and Astrophysics
Astrophysics
2
Orbital Elements, Perturbation Theory, Planetary Orbits, Spherical Harmonics, Hansen Lunar Theory, Lagrange Coordinates, Periodic Variations, Planetary Rings, Secular Variations
Scientific paper
This investigation presents the orbital elements of a satellite moving in a circular ring potential. The ring is considered to be of infinitesimal thickness and of unit radius. The components of the perturbing accelerations due to the ring potential have been substituted into the Gauss form of Lagrange's planetary equations to yield the first-order approximations. The elements of the orbit have been expressed by means of Hansen coefficients. The results include the effects produced by the 2nd, 4th, 6th, and 8th spherical harmonics. Due to their importance the secular terms are presented separately from the periodic ones. The general expressions for the orbital elements can be easily extended to include the effects produced by any other higher harmonic.
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