Computer Science
Scientific paper
Jan 1988
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1988ltdb.conf...73m&link_type=abstract
NATO Advanced Study Institute on Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems, p. 73 - 108
Computer Science
4
Planets: Orbital Elements, Planetary System: Perturbation Theory, Planetary System: Resonances
Scientific paper
The long term changes of the orbital elements of the planets are described by secular perturbation theories. After a short historical discussion, the secular perturbation equations are derived by means of the formalism of the Lie series transformations. To solve the classical problem of the long term changes in the major semiaxes second order effects have to be computed. As for the long term changes in the eccentricities and inclinations, they can be computed by means of higher degree theories. However the time span over which the latter apply cannot be increased at will. This because of the divergence of the perturbative series, a fundamental property of a non-integrable system such as the N-body problem. Numerical integrations are therefore an essential tool both to assess the reliability of any analytic theory and to provide data on the fundamental frequencies of the secular system and on the occurrence of secular resonances. Examples are taken from the LONGSTOP integrations of the outer planets for 100 million years.
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