Abstract
We present a method for solving Kepler's equation for elliptical orbits that represents a gain in efficiency and accuracy compared with those currently in use. The gain is obtained through a starter algorithm which uses Mikkola's ideas in a critical range, and less costly methods elsewhere. A higher-order Newton method is used thereafter. Our method requires two trigonometric evaluations.
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Nijenhuis, A. Solving Kepler's equation with high efficiency and accuracy. Celestial Mech Dyn Astr 51, 319–330 (1991). https://doi.org/10.1007/BF00052925
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DOI: https://doi.org/10.1007/BF00052925