An Improved Algorithm For The Solution of Kepler‘s

Abstract EN

In this paper, a root finding method due to iterative method is used first to the solution of Kepler's equation for an elliptical orbit.

Then the extrapolation technique in the form of Aitken2  acceleration is applied to improve the convergence of the iterative method In addition, by making use a new improvement to Aitken's method enables one to obtain efficiently the numerical solution of the Kepler's equation.

The speed of the proposed algorithms is compared using different values of eccentricity e ( e ) in the range eI ( 0,1 ) and for given mean anomaly (M).