Secular terms in the theory of perturbations

Details Secular terms in the theory of perturbations Secular terms in the theory of perturbations

Dec 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..34..185i&link_type=abstract

(Bundesministerium für Wissenschaft und Forschung of Austria, Alexander von Humboldt Colloquium on Celestial Mechanics: The Stab

Mathematics

Orbit Perturbation, Perturbation Theory, Planetology, Secular Variations, Solar Orbits, Convergence, Resonance, Series (Mathematics), Solar System, Topology

Scientific paper

The convergence of the series which appear in the theory of planetary motions and contain secular terms is investigated analytically using a topological approach and applying the theorem of Bruns. The series are found to be divergent except in the rare case of an ensemble of the first category, a result contrary to that obtained by Gylden for the same case (where the ratio of mean motions is irrational). The fact that the series give reasonably accurate results in concrete calculations for the solar system is attributed to resonances and quasi-resonances arising from small irreversible perturbations over the long evolution of the system.

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