Approximations and modifications of celestial dynamics tested on the three-body system

TL;DR

This paper evaluates various approximations and modifications of celestial dynamics using three-body system simulations, revealing that some destabilize the system while others preserve stability.

Contribution

It provides a comparative analysis of particle-mesh, MOND, and MOGA modifications, highlighting their effects on the stability of celestial three-body systems.

Findings

PM approximation and MOND destabilize the three-body system.

MOGA modification stabilizes the three-body system.

PM and MOND violate momentum and angular momentum conservation.

Abstract

Large-scale simulations of celestial systems are based on approximations or modifications of classical dynamics. The approximations are with ``particle-mesh'' (PM) substitutions of the attractions from objects far away, or one modify the Newtonian accelerations (MOND) or the gravities (MOGA). The PM approximation and MOND modification of classical dynamics break the invariances of classical dynamics. The simple three-body system (TBS) is the simplest system to test the approximations and modifications of celestial dynamics, and it is easy to implement on a computer. Simulations of the TBS show that the PM approximation and MOND destabilize TBS. In contrast, the MOGA modification of gravity by replacing Newton's inverse square attraction with an inverse attraction for far-away interactions stabilizes the system. The PM approximation and the MOND modification of classical dynamics do not preserve the momentum and angular momentum of a conservative system exactly, and PM does not obey Newton's third law. Although the errors and shortcomings of these PM approximations and MOND modifications are small, they cause the instability of the regular dynamics.