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Long-term instability of the inner Solar system: numerical experiments

Abstract : 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 time-scale 1000 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 103-105 numerical integrations spanning 5-100 Gyr, we find that the Hamiltonian truncated at degree 4 practically does not allow any instability over 5 Gyr. The destabilization 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 time-scale of thermalization, which Fermi unsuccessfully looked for.
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Submitted on : Sunday, July 10, 2022 - 11:23:04 AM
Last modification on : Tuesday, August 2, 2022 - 4:02:36 AM

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Nam H. Hoang, Federico Mogavero, Jacques Laskar. Long-term instability of the inner Solar system: numerical experiments. Monthly Notices of the Royal Astronomical Society, 2022, 514, pp.1342-1350. ⟨10.1093/mnras/stac1299⟩. ⟨insu-03718974⟩

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