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T.A. Michtchenko (IAG-USP)
It is a well-known fact that the mean-motion near-resonances involve the orbits of Jupiter and Saturn which lie very close to the 2:5 commensurability, the orbits of Saturn and Uranus which lie close to the 1:3 commensurability, and the orbits of Uranus and Neptune to the 1:2 commensurability. In addition, the putative pair of planets around the pulsar PSR1257+12 is also close to the 2:3 resonance. A deeper understanding of the near-resonant behavior of the Jovian system should shed new light on the problem of stability of the Outer Solar System. The near-resonance problem is also of much relevance to the asteroidal motion. There is some evidence that the Great Inequality is responsible for the lack of asteroids in the 1:1 mean-motion resonance with Saturn and an enhancement of diffusion processes inside the 2:1 resonance. Finally, the problem of the near-resonant planetary configuration is connected with the hypothesis regarding a migration of the planets during the Solar System formation. It is likely that migration processes have guided the Jovian planets to the present nearly resonant configurations. Therefore an investigation of the planetary near-resonant behavior may help us to clarify some aspects of the migration hypothesis. In this work, we present the dynamical maps of the neighboring regions of the Jovian planets using a new numerical method for detecting the chaoticity of the planetary motion. We show that the regions around the planets are densely filled by three- and four-body mean-motion resonances as well as secular resonances, all these generating instabilities inside these regions. We show how close the actual positions of the planets are relative to the mean-motion resonances. The differential expansion of the planetary orbits during the late stages of the Solar System formation should force the passages of the planets through the regions of dynamical instability and affect the motion of the asteroids. We investigate the 3:2 resonance asteroidal motion under these conditions.
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