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

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

Contents

• 1. Introduction
• 2. Analytical model
  • 2.1. The general formulation
  • 2.2. Extension to second order in the masses
• 3. An example
• 4. General results for the uranian system
• 5. Conclusions and discussion
• Acknowledgements
• Appendix A
  • Appendix A: auxiliary quantities for the computation of Laplace-Lagrange matrix elements
  • Appendix B: expressions for the dominant terms in the nonzero elements of the second order correction matrix for first order MMNRs of the general form
  • Appendix C: coefficients for first order arguments that contribute to the second order part of the system for specific near-resonances
• References

© European Southern Observatory (ESO) 1997

Online publication: April 8, 1998
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