Perihelion precession in binary systems: higher order corrections

TL;DR

This paper derives higher order corrections to perihelion precession in binary systems using complex integration and Schwarzschild metric, comparing with existing expansions and simulating relativistic orbital shapes.

Contribution

It provides new higher order correction formulas for perihelion precession in binary systems, extending previous second and third order results.

Findings

Derived n-th order corrections for perihelion precession.

Compared new corrections with existing literature.

Simulated relativistic orbital shapes for various binary masses.

Abstract

Higher order corrections (up to n-th order) are obtained for the perihelion precession in binary systems like OJ287 using the Schwarzschild metric and complex integration. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $r_s/\left(a(1-e^2)\right)$.}The results are compared with other expansions that appear in the literature giving corrections to second and third order. Finally, we simulate the shape of relativistic orbits for binary systems with different masses.