Long-term dynamics of the solar system inner planets

Abstract

Although the discovery of the chaotic motion of the inner planets in the solar system dates back to more than thirty years ago, the secular chaos of their orbits still dares more analytical analyses. Apart from the high-dimensional structure of the motion, this is probably related to the lack of an adequately simple dynamical model. Here, we consider a new secular dynamics for the inner planets, with the aim of retaining a fundamental set of interactions responsible for their chaotic behaviour, while being consistent with the predictions of the most precise orbital solutions currently available. We exploit the regularity in the secular motion of the outer planets, 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. On top of that, the smallness of the inner planet masses and the absence of strong mean-motion resonances permits 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 for analytical inspection of planet interactions, once the Hamiltonian is truncated at a given total degree in eccentricities and inclinations. The new model matches very satisfactorily reference orbital solutions of the solar system over timescales shorter than or comparable to the Lyapunov time. 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 $g_1-g_5$ 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.

arXiv comment25 pages, 10 figures. Accepted for publication in Astronomy & Astrophysics

References in corpus (14)

• La2010: A new orbital solution for the long term motion of the Earth
• High order symplectic integrators for perturbed Hamiltonian systems
• Distant future of the Sun and Earth revisited
• Chaotic diffusion in the Solar System
• Use of MESSENGER radioscience data to improve planetary ephemeris and to test general relativity
• Explicit expansion of the three-body disturbing function for arbitrary eccentricities and inclinations
• Theory of Secular Chaos and Mercury's Orbit
• Gauss's method for secular dynamics, softened
• On the Dynamical Stability of the Solar System
• Chaotic Disintegration of the Inner Solar System
• A simple model of the chaotic eccentricity of Mercury
• Instantons for the destabilization of the inner Solar System
• JANUS: A bit-wise reversible integrator for N-body dynamics
• Addressing the statistical mechanics of planet orbits in the solar system

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