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

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.