Bound States of Central Force System in Special Relativity

TL;DR

This paper extends the classical central force problem into special relativity, deriving a relativistic Binet equation, analyzing planetary orbits with modified potentials, and comparing orbital precession with general relativity predictions.

Contribution

It introduces a relativistic version of the Binet equation and explores orbital dynamics with a modified potential, providing new insights into relativistic orbital precession.

Findings

Derived the special relativistic Binet equation.

Obtained explicit orbital functions using perturbation.

Discussed orbital precession in relation to general relativity.

Abstract

In this paper we consider the central force problem in the special theory of relativity. We derive the special relativistic version of the Binet equation describing the orbit of a body. Then, the motion of a planet in a solar-like system where the gravitational potential is modified by adding a term that is proportional to the inverse of the square of the radial coordinate is discussed. Using perturbative method, we obtain the explicit orbital function. At the end, the orbital precession of the planet and its relation to the result from general relativity are also discussed.