Martin T Brown

An improved cubic approximation for Kepler’s equation

  • Space and Planetary Science
  • Astronomy and Astrophysics

ABSTRACT A novel cubic Pade approximation of sin(e sin E) is used to solve Kepler’s equation and compute the eccentric anomaly with high accuracy without requiring iteration. It requires computation of sin, cos, atan, sqrt, and a cube root. A refinement of the higher order difference methods is described that is faster and gives improved numerical accuracy.

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