The origin of chaos in the Solar System through computer algebra

TL;DR

This paper uses computer algebra to analyze the origin of chaos in the Solar System, identifying resonances and their role in planetary dynamics through systematic perturbation theory and numerical validation.

Contribution

It introduces a novel analytical approach using computer algebra to identify and verify the sources of chaos in the Solar System's inner planets.

Findings

Identification of secular resonances contributing to chaos

Prediction of new resonances confirmed by numerical simulations

Establishment of dynamical sources of chaos in an unbiased manner

Abstract

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.