Long-term dynamics of the inner planets in the Solar System

Abstract

Although the discovery of the chaotic motion of the inner planets in the Solar System (Mercury to Mars) was made more than 30 years ago, the secular chaos of their orbits still demands more analytical analyses. In addition to the high-dimensional structure of the motion, this is probably related to the lack of an adequately simple dynamical model. We consider a new secular dynamics for the inner planets, with the aim of retaining a fundamental set of interactions that explains their chaotic behaviour and at the same time is consistent with the predictions of the most precise orbital solutions currently available. We exploit the regularity in the secular motion of the outer planets (Jupiter to Neptune) to predetermine a quasi-periodic solution for their orbits. This reduces the secular phase space to the degrees of freedom dominated by the inner planets. In addition, the low masses of the inner planets and the absence of strong mean-motion resonances permits us to restrict ourselves to first-order secular averaging. The resulting dynamics can be integrated numerically in a very efficient way through Gauss’s method, while computer algebra allows an analytical inspection of planet interactions when the Hamiltonian is truncated at a given total degree in eccentricities and inclinations. The new model matches reference orbital solutions of the Solar System over timescales shorter than or comparable to the Lyapunov time very satisfactorily. It correctly reproduces the maximum Lyapunov exponent of the inner system and the statistics of the high eccentricities of Mercury over the next five billion years. The destabilizing role of the g1 − g5 secular resonance also arises. A numerical experiment, consisting of a thousand orbital solutions over one hundred billion years, reveals the essential properties of the stochastic process driving the destabilization of the inner Solar System and clarifies its current metastable state.

Simple Physics and Integrators Accurately Reproduce Mercury Instability Statistics

“…The most likely identified route to solar system instability is Mercury's eccentricity being pumped up to a high enough value that it has a close encounter with Venus (Laskar 1994;Laskar & Gastineau 2009), either colliding with Venus or being scattered into the Sun (Zeebe 2015). Mercury instability events are ultimately due to resonances of the secular system's modes (Lithwick & Wu 2011, 2014Boué et al 2012;Batygin et al 2015;Mogavero & Laskar 2021.…”

The stability of galaxies in an expanding Universe obtained by Newtonian dynamics

“…number of rotations of the Earth. The stability of the Solar System is still to debate [43,44], and in the light of these facts the Universe must be characterized as a very young Universe. The dynamics and aging of the MD systems with gravitational matter shows, however, that the objects in the small MD systems are not in a stable steady state after only sixty rotations, so how can hundred of billion of stars and a substantial amount of baryonic gas then be it?…”

Tackling the Puzzle of Our Solar System’s Stability

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