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Astron. Astrophys. 327, 416-427 (1997)

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A second order Laplace-Lagrange theory applied to the uranian satellite system

Apostolos A. Christou and Carl D. Murray

Astronomy Unit, Queen Mary and Westfield College, Mile End Road, London E1 4NS, UK (A.Christou@qmw.ac.uk, C.D.Murray@qmw.ac.uk)

Received 18 December 1996 / Accepted 11 June 1997

Abstract

Computer algebra is used to derive analytical expressions for the elements of a secular perturbation theory of the second order in the masses. The linear part of this theory is incorporated into the standard Laplace-Lagrange solution which is then applied to the motion of the uranian satellites. This enables the effects of mean motion near-resonances in this system to be modelled. The results are in very good agreement with the filtered output of a numerical integration by Malhotra et al (1989). The additional complexities of studying the outer solar system using a similar approach are discussed.

Key words: celestial mechanics – satellites: satellites of Uranus – methods: analytical

Send offprint requests to: Carl D. Murray

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© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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