  We propose a new approach in studying the planetary orbits and the perihelion
precession in General Relativity by means of the Homotopy Perturbation Method
(HPM).For this purpose, we give a brief review of the nonlinear geodesic
equations in the spherical symmetry spacetime which are to be studied in our
work. On the basis of the main idea of HPM, we construct the appropriate
homotopy what leads to the problem of solving the set of linear equations.
First of all, we consider the simple example of the Schwarzschild metric for
which the approximate geodesics solutions are known, in order to compare the
HPM solution for orbits with those obtained earlier. Moreover, we obtain an
approximate HPM solution for the Reissner-Nordstorm spacetime of a charged
star.
