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Kepler Equation solver

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Abstract

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 1018, exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are addressed, and procedures to avoid them are developed.

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Authors and Affiliations

  1. Guidance and Control Branch, Code 712, NASA Goddard Space Flight Center, 20771, Greenbelt, MD, USA

    F. Landis Markley

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  1. F. Landis Markley
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Markley, F.L. Kepler Equation solver. Celestial Mech Dyn Astr 63, 101–111 (1995). https://doi.org/10.1007/BF00691917

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  • DOI: https://doi.org/10.1007/BF00691917

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