The problem of small divisors in planetary motion

Details The problem of small divisors in planetary motion The problem of small divisors in planetary motion

Dec 1984

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1984cemec..34..395w&link_type=abstract

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

Physics

4

Celestial Mechanics, Orbit Calculation, Planetology, Solar Orbits, Solar System, Gas Giant Planets, Gravitational Effects, Kolmogoroff Theory, Resonance

Scientific paper

The problem of small divisors in planetary theories is examined with reference to results of analytical and numerical studies. Solutions at both deep and shallow resonance are considered, and it is noted that, with the exception of the deep resonance between Neptune and Pluto, small divisors can be removed at the expense of introducing secular and mixed secular terms, limiting the domain in which the solution is valid. Kolmogorov's theorem and a set of related results by Kolmogorov, Arnold, and Moser (KAM theory) are reviewed.

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