Higher-order corrections to the relativistic perihelion advance and the mass of binary pulsars

TL;DR

This paper derives higher-order relativistic corrections to planetary perihelion advance using perturbation methods, improving mass estimates of binary pulsars like J0737-3039.

Contribution

It introduces a novel perturbation approach with d'Alembert's method to approximate orbital equations and perihelion advance in general relativity.

Findings

Derived higher-order perihelion advance expressions

Applied results to refine binary pulsar mass estimates

Provided more accurate orbital models for relativistic systems

Abstract

We study the general relativistic orbital equation and using a straightforward perturbation method and a mathematical device first introduced by d'Alembert, we work out approximate expressions of a bound planetary orbit in the form of trigonometrical polynomials and the first three terms of the power series development of the perihelion advance. The results are applied to a more precise determination of the total mass of the double pulsar J0737-3039.