A cubic approximation for Kepler's equation

@article{Mikkola1987ACA,
  title={A cubic approximation for Kepler's equation},
  author={Seppo Mikkola},
  journal={Celestial mechanics},
  year={1987},
  volume={40},
  pages={329-334}
}
  • S. Mikkola
  • Published 1 September 1987
  • Mathematics
  • Celestial mechanics
We derive a new method to obtain an approximate solution for Kepler's equation. By means of an auxiliary variable it is possible to obtain a starting approximation correct to about three figures. A high order iteration formula then corrects the solution to high precision at once. The method can be used for all orbit types, including hyperbolic. To obtain this solution the trigonometric or hyperbolic functions must be evaluated only once. 
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