Chaotic diffusion in the Solar System

TL;DR

This study analyzes the long-term chaotic diffusion of Mercury's orbit in the Solar System, highlighting the role of secular resonances and general relativity in orbital stability over billions of years.

Contribution

It provides a comprehensive statistical analysis of Mercury's eccentricity evolution, comparing secular and direct integrations, and emphasizes the impact of general relativity on orbital chaos.

Findings

Probability of Mercury reaching eccentricity 0.6 in 5 Gyr is 1-2%.

Secular resonance without general relativity leads to higher eccentricities.

Direct integrations show potential for Mercury's orbit to become highly unstable.

Abstract

A statistical analysis is performed over more than 1001 different integrations of the secular equations of the Solar system over 5 Gyr. With this secular system, the probability of the eccentricity of Mercury to reach 0.6 in 5 Gyr is about 1 to 2 %. In order to compare with (Ito and Tanikawa, 2002), we have performed the same analysis without general relativity, and obtained even more orbits of large eccentricity for Mercury. We have performed as well a direct integration of the planetary orbits, without averaging, for a dynamical model that do not include the Moon or general relativity with 10 very close initial conditions over 3 Gyr. The statistics obtained with this reduced set are comparable to the statistics of the secular equations, and in particular we obtain two trajectories for which the eccentricity of Mercury increases beyond 0.8 in less than 1.3 Gyr and 2.8 Gyr respectively. These strong instabilities in the orbital motion of Mecury results from secular resonance beween the perihelion of Jupiter and Mercury that are facilitated by the absence of general relativity. The statistical analysis of the 1001 orbits of the secular equations also provides probability density functions (PDF) for the eccentricity and inclination of the terrestrial planets.