Modified Kepler's Law, Escape Speed and Two-body Problem in MOND-like Theories

TL;DR

This paper derives a simple analytical expression for two-body forces in MOND-like theories, predicting orbital dynamics modifications and testing their consistency with satellite and galaxy orbits, including the Milky Way and Bullet Clusters.

Contribution

It introduces a new analytical formula for two-body forces in MOND-like theories and applies it to various astrophysical systems for the first time.

Findings

MOND can be consistent with satellite orbits within tight margins

Modified Kepler's law predicts changes in orbital period, shape, and precession

Results extend to three-body and many-body systems

Abstract

We derive a simple analytical expression for the two-body force in a sub-class of MOND-like theories and make testable predictions in the modification to the two-body orbital period, shape, and precession rate, and escape speed etc. We demonstrate the applications of the modified Kepler's law in the timing of satellite orbits around the Milky Way, and checking the feasibility of MOND in the orbit of Large Magellanic Cloud, the M31 galaxy, and the merging Bullet Clusters. MOND appears to be consistent with satellite orbits although with a tight margin. Our results on two-bodies are also generalized to restricted three-body, many-body problems, rings and shells.