Celestial mechanics in Newtonian-like gravity with variable $G$

TL;DR

This paper explores a Newtonian-like gravity theory inspired by Brans-Dicke, showing it can explain Mercury's perihelion advance without affecting the Roche limit significantly, and constrains its free parameter using celestial mechanics.

Contribution

It demonstrates that a modified gravity theory with a variable G can replicate key celestial phenomena and constrains its parameters based on observational data.

Findings

The theory predicts a perihelion advance compatible with observations.

The Roche limit remains consistent with classical Newtonian predictions.

The free parameter ω is constrained by celestial mechanics data.

Abstract

A Newtonian-like theory inspired by the Brans-Dicke gravitational Lagrangian has been recently proposed in Ref. arXiv:2009.04434(v4). This work demonstrates that the modified gravitational force acting on a test particle is analogous to that derived from the Manev potential. Specifically, an additional term $\propto r^{-3}$ emerges alongside the conventional Newtonian component. We analyse the predicted expression for the pericenter advance and the Roche limit and use them to constraint the theory's single free parameter $\omega$ which is analogous to the Brans-Dicke parameter. At the same time this theory is able to solve the advance of Mercury's perihelion, we also show that there is no relevant impact on the Roche limit in comparison to the well known Newtonian results.