Abstract
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. Such a computation is feasible within a modern formalism and succeeds in matching the data from the numerical integrations over time spans of a few million years. 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 and not only a technical difficulty. 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 occurence of secular resonances. Examples of this use are taken from the LONGSTOP integrations of the outer planets for 100 million years.
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Milani, A. (1988). Secular Perturbations of Planetary Orbits and their Representation as Series. In: Roy, A.E. (eds) Long-Term Dynamical Behaviour of Natural and Artificial N-Body Systems. NATO ASI Series, vol 246. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-3053-7_6
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DOI: https://doi.org/10.1007/978-94-009-3053-7_6
Publisher Name: Springer, Dordrecht
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