Long-term instability of the inner Solar System: numerical experiments
| Title: | Long-term instability of the inner Solar System: numerical experiments |
|---|---|
| Authors: | Hoang, Nam H., Mogavero, Federico, Laskar, Jacques |
| Publication Year: | 2022 |
| Collection: | Astrophysics Nonlinear Sciences Physics (Other) |
| Subject Terms: | Astrophysics - Earth and Planetary Astrophysics, Nonlinear Sciences - Chaotic Dynamics, Physics - Classical Physics, Physics - Computational Physics |
| More Details: | Apart from being chaotic, the inner planets in the Solar System constitute an open system, as they are forced by the regular long-term motion of the outer ones. No integrals of motion can bound a priori the stochastic wanderings in their high-dimensional phase space. Still, the probability of a dynamical instability is remarkably low over the next 5 billion years, a timescale thousand times longer than the Lyapunov time. The dynamical half-life of Mercury has indeed been estimated recently at 40 billion years. By means of the computer algebra system TRIP, we consider a set of dynamical models resulting from truncation of the forced secular dynamics recently proposed for the inner planets at different degrees in eccentricities and inclinations. Through ensembles of $10^3$ to $10^5$ numerical integrations spanning 5 to 100 Gyr, we find that the Hamiltonian truncated at degree 4 practically does not allow any instability over 5 Gyr. The destabilisation is mainly due to terms of degree 6. This surprising result suggests an analogy to the Fermi-Pasta-Ulam-Tsingou problem, in which tangency to Toda Hamiltonian explains the very long timescale of thermalisation, which Fermi unsuccessfully looked for. Comment: Accepted for publication in MNRAS. 9 pages, 7 figures |
| Document Type: | Working Paper |
| DOI: | 10.1093/mnras/stac1299 |
| Access URL: | http://arxiv.org/abs/2205.04170 |
| Accession Number: | edsarx.2205.04170 |
| Database: | arXiv |
| DOI: | 10.1093/mnras/stac1299 |
|---|