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The origin of chaos in the Solar System through computer algebra

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arxiv 2205.03298 v1 pith:234PTJ6Y submitted 2022-05-06 astro-ph.EP nlin.CDphysics.class-phphysics.comp-ph

classification astro-ph.EPnlin.CDphysics.class-phphysics.comp-ph
keywords systemchaosplanetssolartheoryalgebracomputerdynamics
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The discovery of the chaotic motion of the planets in the Solar System dates back more than 30 years. Still, no analytical theory has satisfactorily addressed the origin of chaos so far. Implementing canonical perturbation theory in the computer algebra system TRIP, we systematically retrieve the secular resonances at work along the orbital solution of a forced long-term dynamics of the inner planets. We compare the time statistic of their half-widths to the ensemble distribution of the maximum Lyapunov exponent and establish dynamical sources of chaos in an unbiased way. New resonances are predicted by the theory and checked against direct integrations of the Solar System. The image of an entangled dynamics of the inner planets emerges.

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  1. Numerical approach to second-order canonical perturbation theory in the planetary 3-body problem: Application to exoplanets

    astro-ph.EP 2025-06 conditional novelty 7.0 of 10

    A FFT-based second-order secular perturbation method for planetary three-body systems reproduces n-body secular frequencies with sub-percent errors even near mean-motion resonances.

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