Solving Kepler's equation with high efficiency and accuracy

@article{Nijenhuis1991SolvingKE,
title={Solving Kepler's equation with high efficiency and accuracy},
author={Albert Nijenhuis},
journal={Celestial Mechanics and Dynamical Astronomy},
year={1991},
volume={51},
pages={319-330}
}
• A. Nijenhuis
• Published 1 December 1991
• Mathematics
• Celestial Mechanics and Dynamical Astronomy
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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