An Improved Algorithm For The Solution of Kepler‘s Equation For An Elliptical Orbit

Abstract

In this paper, a root finding method due to iterative method is used first to thesolution of Kepler's equation for an elliptical orbit. Then the extrapolationtechnique in the form of Aitken D2 - acceleration is applied to improve theconvergence of the iterative method.In addition, by making use a new improvement to Aitken's method enables oneto obtain efficiently the numerical solution of the Kepler's equation. The speed ofthe proposed algorithms is compared using different values of eccentricity( e ) inthe range eÎ( 0,1 ) and for given mean anomaly (M).