A general algorithm for the solution of Kepler's equation for elliptic orbits

@article{Ng1979AGA,
  title={A general algorithm for the solution of Kepler's equation for elliptic orbits},
  author={Edward W. Ng},
  journal={Celestial mechanics},
  year={1979},
  volume={20},
  pages={243-249}
}
  • E. W. Ng
  • Published 1 October 1979
  • Physics
  • Celestial mechanics
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… 
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