Synopsis In this work we solve the Kepler problem in the context of two theories: a) the Special Theory of Relativity and b) the Newtonian Mechanics. We simulate the motion of a particle according to the predictions of each model, for the same initial conditions. We observe and calculate the precession of the perihelion of the orbit for the case of the relativistic model and the closed-elliptic path in the Newtonian model. We check our calculations in the virtual measurements of the simulation.