On Solving Kepler's Equation

Details On Solving Kepler's Equation On Solving Kepler's Equation

Jun 1989

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1989cemda..46..163t&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 46, Issue 2, pp.163-176

Astronomy and Astrophysics

Astronomy

3

Scientific paper

Intrigued by the recent advances in research on solving Kepler's equation, we have attacked the problem too. Our contributions emphasize the unified derivation of all known bounds and several starting values, a proof of the optimality of these bounds, a very thorough numerical exploration of a large variety of starting values and solution techniques in both mean anomaly/eccentricity space and eccentric anomaly/eccentricity space, and finally the best and simplest starting value/solution algorithm: M + e and Wegstein's secant modification of the method of successive substitutions. The very close second is Broucke's bounds coupled with Newton's second-order scheme.

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