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F. Varadi, B. Runnegar, M. Ghil (UCLA)
Accurate long-term numerical simulations of the orbits of the nine major planets are carried out using several physical models of increasing complexity. The equations of motion are directly integrated by a Stormer-Cowell multi-step scheme which is optimized to reduce roundoff errors. The physical models include corrections due to general relativity, the finite size of the lunar orbit and the solar gravitational quadrupole moment. In one case, the Earth-Moon system is resolved as two separate bodies and the results are compared to those based on analytically averaging the lunar orbit. Through this comparison, a better averaged analytical model is obtained. The computed orbits are in good agreement with those of previous studies for the past five million years but not for earlier times. Chaos in the motion of the inner planets limits the validity of the computations beyond 50 million years. At this time we detect a transition between different dynamical regimes. We also observe a number of other transitions at earlier times. In particular, a regime transition around 65 million years before present is associated with clearly discernible, macroscopic changes in the evolution of Mercury's orbit. Such a dynamical transition could have been responsible for significant instabilities within the asteroid belt and corresponds, approximately and maybe fortuitously, to the Cretaceous-Tertiary boundary. We do not detect chaos in the motion of the Jovian planets. If it is present, its time scale has to be much longer than what has been reported in previous works based on simpler physical models.