On the 3/1 planar and circular resonant problem

Details On the 3/1 planar and circular resonant problem On the 3/1 planar and circular resonant problem

Jun 1986

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986cemec..39..117y&link_type=abstract

Celestial Mechanics (ISSN 0008-8714), vol. 39, no. 2, 1986, p. 117-132. Research supported by the Fundacao de Amparo a Pesquisa

Physics

2

Asteroids, Jupiter (Planet), Orbit Perturbation, Orbital Mechanics, Resonance, Solar Orbits, Degrees Of Freedom, Eccentric Orbits, Equations Of Motion, Hamiltonian Functions

Scientific paper

The simplest model of a resonant problem of second order is the planar and circular case. In this work, the authors test this model for the available asteroids, by applying Hori's perturbation method. Explicit solutions of the intermediate orbit are obtained. In the plane of two constants of the problem, all types of motion are described. By testing the model, it is shown that, in general, one can confirm results of numerical integrations indicating libration for a few number of asteroids and circulation for most of them. However, agreement in numerical values for amplitude and period of librations seems to be not possible mainly if Jupiter's eccentricity is neglected.

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