Highly Stable Evolution of Earthʼs Future Orbit despite Chaotic Behavior of the Solar System

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, for instance, based on numerical ensemble integrations of nearby orbits. Destabilization of the inner planets, including catastrophic encounters and/or collisions involving the Earth, has been suggested to be initiated through a large increase in Mercury’s eccentricity (e), 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 = 1600 with slightly different initial conditions) at unprecedented accuracy based on the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The standard symplectic algorithm used for long-term integrations 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 e values >0.93) for 80–100Myr before colliding with Venus or the Sun. Most importantly, none of the 1600 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 will be dynamically highly stable for billions of years in the future, despite the chaotic behavior of the solar system.