 0490 Frederic Gabern, \`Angel Jorba
 Generalizing the Restricted ThreeBody Problem.
The Bianular and Tricircular Coherent Problems.
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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 ThreeBody Problem (RTBP). Both models are obtained by
computing quasiperiodic solutions with two basic frequencies of a
suitable $N$body problem.
The first model is based on a quasiperiodic solution of the planar
SunJupiterSaturn ThreeBody problem, that tries to approach the real
motion of Jupiter. The second model is based on a quasiperiodic
solution of the SunJupiterSaturnUranus FourBody problem. In both
cases, we derive the equations of motion for a particle under the
gravitational attraction of these bodies as a quasiperiodic
timedependent perturbation of the wellknown RTBP.
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