Analysis of the Yukawa gravitational potential in $f(R)$ gravity II: relativistic periastron advance

TL;DR

This paper investigates how $f(R)$ gravity models with Yukawa-like modifications affect relativistic orbital precession, providing analytical and numerical tools to test these theories against astrophysical data.

Contribution

It offers a combined analytical and numerical analysis of Yukawa modifications in $f(R)$ gravity on orbital precession, extending previous work to binary systems.

Findings

Derived an analytic expression for periastron advance in Yukawa-modified gravity.

Numerically demonstrated orbital precession effects due to Yukawa potential.

Provided a framework to constrain $f(R)$ models with observational data.

Abstract

Alternative theories of gravity may serve to overcame several shortcomings of the standard cosmological model but, in their weak field limit, General Relativity must be recovered so as to match the tight constraints at the Solar System scale. Therefore, testing such alternative models at scales of stellar systems could give a unique opportunity to confirm or rule them out. One of the most straightforward modifications is represented by analytical $f(R)$-gravity models that introduce a Yukawa-like modification to the Newtonian potential thus modifying the dynamics of particles. Using the geodesics equations, we have illustrated the amplitude of these modifications. First, we have integrated numerically the equations of motion showing the orbital precession of a particle around a massive object. Second, we have computed an analytic expression for the periastron advance of systems having their semi-major axis much shorter than the Yukawa-scale length. Finally, we have extended our results to the case of a binary system composed of two massive objects. Our analysis provides a powerful tool to obtain constraints on the underlying theory of gravity using current and forthcoming datasets.