Precession of Pericenter: A More Accurate Approach
  In this paper we study the orbits of massive bodies moving in the spacetime generated by a spherically symmetric and non-rotating distribution of mass. More specifically, our treatment discusses the more accurate calculation of the precession of pericenter due to general-relativistic effects. Our result is accurate up to terms of second order, while the precession met in the bibliography is accurate only up to first-order terms. 
Andreas Stergiou