Dynamic stability of the Solar System: Statistically inconclusive results from ensemble integrations

TL;DR

This study uses ensemble numerical integrations to assess the long-term stability of the Solar System, revealing that results depend heavily on numerical methods and coordinate choices, thus challenging the reliability of previous stability estimates.

Contribution

It demonstrates that different numerical algorithms and coordinate systems produce statistically different stability outcomes, highlighting uncertainties in long-term Solar System stability predictions.

Findings

Different algorithms yield varying Mercury eccentricity evolution.

Heliocentric coordinates tend to underestimate destabilization probabilities.

Results depend strongly on initial conditions and numerical methods.

Abstract

Due to the chaotic nature of the Solar System, the question of its 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, leading to close encounters and/or collisions can be initiated through a large increase in Mercury's eccentricity, with a currently assumed likelihood of ~1%. However, little is known at present about the robustness of this number. Here I report ensemble integrations of the full equations of motion of the eight planets and Pluto over 5 Gyr, including contributions from general relativity. The results show that different numerical algorithms lead to statistically different results for the evolution of Mercury's eccentricity (eM). For instance, starting at present initial conditions (eM ~= 0.21), Mercury's maximum eccentricity achieved over 5 Gyr is on average significantly higher in symplectic ensemble integrations using heliocentricthan Jacobi coordinates and stricter error control. In contrast, starting at a possible future configuration (eM ~= 0.53), Mercury's maximum eccentricity achieved over the subsequent 500 Myr is on average significantly lower using heliocentric than Jacobi coordinates. For example, the probability for eM to increase beyond 0.53 over 500 Myr is >90% (Jacobi) vs. only 40-55% (heliocentric). This poses a dilemma as the physical evolution of the real system - and its probabilistic behavior - cannot depend on the coordinate system or numerical algorithm chosen to describe it. Some tests of the numerical algorithms suggest that symplectic integrators using heliocentric coordinates underestimate the odds for destabilization of Mercury's orbit at high initial eM.