Kepler Equation Solver

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Mar 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995cemda..63..101m&link_type=abstract

Celestial Mechanics & Dynamical Astronomy, Volume 63, Issue 1, pp.101-111

Astronomy and Astrophysics

Astronomy

6

Kepler'S Equation, Two-Body Problem, Elliptical Motion, Numerical Methods, Orbit Propagation

Scientific paper

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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