Evaluation the Initial Values for Eccentric Anomaly for an Ellipse Orbit: Article Review

The equation of Kepler is used to solve different problems associated with celestial mechanics and the dynamics of the orbit. It is an exact explanation for the movement of any two bodies in space under the effect of gravity. This equation represents the body in space in terms of polar coordinates; thus, it can also specify the time required for the body to complete its period along the orbit around another body. This paper is an article review for previous published papers that related to solve Kepler’s equation and finding a value for eccentric anomaly, it aims to collect and assess changed iterative initial values for eccentric anomaly for forty previous years. Those initial values are tested in order to select the finest one based on the number of iterations as well as the run time for each starting initial value that is required for completing the solution. The method of Newton-Raphson is employed to acquire a final value for an eccentric anomaly; this method considers a typical method for a solution with less divergence as compared with an ideal solution, and the best initial value is chosen. The applicable selection of the initial value of the eccentric anomaly will decrease the calculation time and confirm the convergence of the curves of the eccentric anomaly with ideal curves.