Surfing on the Edge: Chaos vs. Near-Integrability in the System of Jovian Planets

TL;DR

This study investigates the long-term dynamical behavior of the Jovian planetary system, showing it can exhibit both chaotic and near-integrable motions over hundreds of millions of years, with implications for predictability.

Contribution

The paper demonstrates that the Jovian system can display chaos or near-integrability depending on initial conditions and integrator parameters, providing insights into its long-term stability and predictability.

Findings

The Jovian system can be chaotic or near-integrable over 200 million years.

Reliable chaos detection requires small timesteps in symplectic integrators.

The system's Lyapunov time suggests possible predictability over hundreds of millions of years.

Abstract

We demonstrate that the system of Jovian planets (Sun+Jupiter+Saturn+Uranus+Neptune), integrated for 200 million years as an isolated 5-body system using many sets of initial conditions all within the uncertainty bounds of their currently known positions, can display both chaos and near-integrability. The conclusion is consistent across four different integrators, including several comparisons against integrations utilizing quadruple precision. We demonstrate that the Wisdom-Holman symplectic map using simple symplectic correctors as implemented in Mercury 6.2 (Chambers 1999) gives a reliable characterization of the existence of chaos for a particular initial condition only with timesteps less than about 10 days, corresponding to about 400 steps per orbit. We also integrate the canonical DE405 initial condition out to 5 Gy, and show that it has a Lyapunov Time of 200--400 My, opening the remote possibility of accurate prediction of the Jovian planetary positions for 5 Gy.