Spin contribution to the perihelion precession in binary systems like OJ287: higher order corrections

Higher order corrections are obtained for the perihelion precession in binary systems like OJ287, Sagittarius A*-S2 and H1821+643 using both the Schwarzschild metric and the Kerr metric to take into account the spin effect. The corrections are performed considering the third root of the motion equation and developing the expansion in terms of $\epsilon \equiv r_s/\left(a(1-e^2)\right)$ and $\epsilon^{*} \equiv \left(1- \frac{2 \alpha E'}{cJ}\right) \epsilon$.The results are compared with those obtained in a previous paper.