## A second order Laplace-Lagrange theory applied to the uranian satellite system
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.
## Contents- 1. Introduction
- 2. Analytical model
- 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 |