Highly stable evolution of Earth's future orbit despite chaotic behavior of the Solar System

Abstract: Due to the chaotic nature of the Solar System, the question of its dynamic long-term stability can only be answered in a statistical sense, e.g. based on numerical ensemble integrations of nearby orbits. Destabilization, including catastrophic encounters and/or collisions involving the Earth, has been suggested to be initiated through a large increase in Mercury's eccentricity (eM), with an estimated probability of ~1%. However, it has recently been shown that the statistics of numerical Solar System integrations are sensitive to the accuracy and type of numerical algorithm. Here I report results from computationally demanding ensemble integrations (N=1,600 with slightly different initial conditions) at unprecedented accuracy based on the full equations of motion of the eight planets and Pluto over 5Gyr, including contributions from general relativity. The standard symplectic algorithm produced spurious results for highly eccentric orbits and during close encounters, which were hence integrated with a suitable Bulirsch-Stoer algorithm, specifically designed for these situations. The present study yields odds for a large increase in Mercury's eccentricity that are less than previous estimates. Strikingly, in two solutions Mercury continued on highly eccentric orbits (after reaching eM values >0.93) for 80-100Myr before colliding with Venus or the Sun. Most importantly, none of the 1,600 solutions led to a close encounter involving the Earth or a destabilization of Earth's orbit in the future. I conclude that Earth's orbit is dynamically highly stable for billions of years, despite the chaotic behavior of the Solar System.