Perihelion precession in binary systems: higher order corrections

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 $r_{s}/ (a(1-e^{2}) )$ .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.