  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.
