An Efficient Iterative Method for Solving the Elliptical Kepler’s Equation

Abstract

In this paper, a numerical technique, based on Banach’s fixed point theorem, is proposed to obtain an approximate solution of the elliptical Kepler equation which is often used to describe the motion of a planet orbiting its sun. The rapid convergence of the method results in qualitatively accurate solutions in relatively few iterations. In fact, the estimate of approximation error is given as a function of the number of steps of the method. Our results demonstrate that the presented method is very effective and reliable, the solution exists and is unique, provided that the nonlinear term is a contraction, therefore can be considered a very useful and valuable method.