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
  • Physics
  • 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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