The origin of chaos in the Solar System through computer algebra

The discovery of the chaotic motion of the planets in the Solar System dates back more than 30 years. Still, no analytical theory has satisfactorily addressed the origin of chaos so far. Implementing canonical perturbation theory in the computer algebra system TRIP, we systematically retrieve the secular resonances at work along the orbital solution of a forced long-term dynamics of the inner planets. We compare the time statistic of their half-widths to the ensemble distribution of the maximum Lyapunov exponent and establish dynamical sources of chaos in an unbiased way. New resonances are predicted by the theory and checked against direct integrations of the Solar System. The image of an entangled dynamics of the inner planets emerges.

Automated summary

This study uses computer algebra systems and canonical perturbation theory to explore the long-term dynamics of planets in the Solar System. It discovers dynamical resonances and chaos, and provides verifications and explanations for these phenomena.