Modeling the 5 : 2 mean-motion resonance in the Jupiter-Saturn planetary system

The motion of the Jupiter-Saturn planetary system near the 5 : 2 mean-motio n resonance is modeled analytically in the frame of the planar general thre e-body problem. The topology of the phase space in the resonance and near-r esonance domains is investigated in detail by means of surfaces of section and spectral map techniques. Various regimes of motion of the Jupiter-Satur n system are observed, and their domains are represented on the parameter p lane defined by the total energy of the system and the parameter of proximi ty to the 5 :2 resonance. The regions of transition between domains of diff erent regimes of motion are characterized by chaotic motion, We show that t here is a significant chaotic zone associated with the 5 :2 mean-motion res onance, but large-scale excursions of the planet eccentricities are not pos sible in the planar three-body model. (C) 2001 Academic Press.