Problems in Solar System Dynamics
Tuesday, October 30, 2001 - 3:30pm - 4:30pm
Ferenc Varadi (University of California, Los Angeles)
Several related topics are discussed, from large-scale perturbation computations to periodic orbits and chaos. Secular perturbation theory and its implementation for large-scale computations are demonstrated for the case of the Jovian planets. The theory ultimately fails due to the 2:5 orbital near-resonance between Jupiter and Saturn, which is elucidated through numerical simulations. Next another resonance, the well-known and somewhat misunderstood 3:1 case, is discussed, from the point of view classical Hamiltonian chaos and periodic orbits. The properties of periodic orbits and their continuation is also illustrated for 2:3 case. Finally, the latest results of solar system simulations are presented, showing chaotic jumps between different dynamical regimes in the motion of the major planets. The dynamics of asteroid orbits exhibits a surprisingly large variety of behaviors, ranging from the very regular to the chaotic, accompanied with intermittent capture into resonances and drift in phase space.