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An Integrable Model for Helene

Published online by Cambridge University Press:  07 August 2017

J.S. Bevilacqua  and
W. Sessin
J.S. Bevilacqua
Affiliation:
Instituto de Matemática e Estatística, Universidade de São Paulo, Brasil
W. Sessin
Affiliation:
Instituto Tecnológico de Aeronáutica, Centro Técnico Aeroespacial, Brasil

Abstract

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The goal of our work is to determine the influence of Enceladus in the motion of Helene. We constructed a model considering an oblated central body (Saturn) and three satellites (Enceladus, Dione and Helene) under the action of central forces. The development of the potential was made assuming small eccentricities, null inclinations and two resonances present in this system (2:1 between Enceladus and Dione and 1:1 between Dione and Helene). The mean Hamiltonian preserves terms derived of the oblateness of the central body and also terms of both resonant arguments. The auxiliary Hori's system generated by this Hamiltonian is completely integrable. In the solution for Helene we included the perturbative effects of Dione and Enceladus which extend the usual teatment.

Keywords

ResonanceOblatenessHori's auxiliary system
Type
Part IV - Planetary Satellites
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 227 - 230
Copyright
Copyright © Kluwer 1992 

References

Brouwer, D., Clemence, G.M.: 1961, Methods of Celestial Mechanics , (New York: Academic Press).Google Scholar
Hori, G-I.: 1966, Publ. Astron. Soc. Japan 18,287;Google Scholar
Salgado, T.V., Sessin, W.:1985 in Resonances in the Motion of Planets, Satellites and Asteroids , (São Paulo: Universidade de São Paulo), 93.Google Scholar
Sessin, W., Ferraz-Mello, S.:1984, Celestial Mechanics 32, 307.CrossRefGoogle Scholar