Abstract
An efficient algorithm is presented for the solution of Kepler's equationf(E)=E−M−e sinE=0, wheree is the eccentricity,M the mean anomaly andE the eccentric anomaly. This algorithm is based on simple initial approximations that are cubics inM, and an iterative scheme that is a slight generalization of the Newton-Raphson method. Extensive testing of this algorithm has been performed on the UNIVAC 1108 computer. Solutions for 20 000 pairs of values ofe andM show that for single precision (∼10−8) 42.0% of the cases require one iteration, 57.8% two and 0.2% three. For double precision (∼10−18) one additional iteration is required. Single- and double-precision FORTRAN subroutines are available from the author.
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Ng, E.W. A general algorithm for the solution of Kepler's equation for elliptic orbits. Celestial Mechanics 20, 243–249 (1979). https://doi.org/10.1007/BF01371365
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DOI: https://doi.org/10.1007/BF01371365