An empirical initial estimate for the solution of Kepler's equation.
Abstract
In this paper an empirical formula is presented for an efficient initial estimate for the iterative solution of Kepler's equation. This formula is essentially a polynomial in eccentricity and mean anomaly whose coefficients have been obtained by minimizing the sum of the squared differences of the actual and calculated eccentric anomaly corresponding to a wide range of points in the Me plane. The efficiency in terms of the number of iterations for convergence is discussed along with comparisons with those of other starting formulas.
 Publication:

Journal of the Astronautical Sciences
 Pub Date:
 December 1982
 Bibcode:
 1982JAnSc..30..415S
 Keywords:

 Elliptical Orbits;
 Error Functions;
 Iterative Solution;
 Kepler Laws;
 Orbit Calculation;
 Polynomials;
 Approximation;
 Convergence;
 Eccentricity;
 Orbital Mechanics;
 Astrodynamics;
 Celestial Mechanics