Significant improvement in planetary system simulations from statistical averaging

TL;DR

This paper demonstrates that using statistical averaging over an ensemble of initial conditions in symplectic integrations reduces bias in planetary system simulations, leading to more accurate measurements of orbital properties.

Contribution

It introduces a statistical sampling approach to improve the accuracy of symplectic integrators in planetary system simulations.

Findings

Bias in semi-major axes is reduced through ensemble averaging.

Statistical sampling improves measurement of secular frequencies.

Traditional metrics fail to distinguish distribution differences.

Abstract

Symplectic integrators are widely used for the study of planetary dynamics and other $N$-body problems. In a study of the outer Solar system, we demonstrate that individual symplectic integrations can yield biased errors in the semi-major axes and possibly other orbital elements. The bias is resolved by studying an ensemble of initial conditions of the outer Solar system. Such statistical sampling could significantly improve measurement of planetary system properties like their secular frequencies. We also compared the distributions of action-like variables between high and low accuracy integrations; traditional statistical metrics are unable to distinguish the distribution functions.