04-90 Frederic Gabern, \`Angel Jorba

Generalizing the Restricted Three-Body Problem. The Bianular and Tricircular Coherent Problems. (1909K, Pdf) Mar 19, 04

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Abstract. In this paper we construct two models for the motion of a particle under the gravitational attraction of Sun, Jupiter, Saturn and Uranus, that can be seen as a generalization of the well known Restricted Three-Body Problem (RTBP). Both models are obtained by computing quasi-periodic solutions --with two basic frequencies-- of a suitable $N$-body problem. The first model is based on a quasi-periodic solution of the planar Sun-Jupiter-Saturn Three-Body problem, that tries to approach the real motion of Jupiter. The second model is based on a quasi-periodic solution of the Sun-Jupiter-Saturn-Uranus Four-Body problem. In both cases, we derive the equations of motion for a particle under the gravitational attraction of these bodies as a quasi-periodic time-dependent perturbation of the well-known RTBP.

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