Kepler Equation solver
Abstract
Kepler's Equation is solved over the entire range of elliptic motion by a fifthorder 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 10(exp 18), exceeding the capability of doubleprecision computer arithmetic. Roundoff errors in doubleprecision implementation of the algorithm are addressed, and procedures to avoid them are developed.
 Publication:

Flight Mechanics/Estimation Theory Symposium 1995
 Pub Date:
 May 1995
 Bibcode:
 1995fmet.symp...47M
 Keywords:

 Algorithms;
 Anomalies;
 Computer Programs;
 Cubic Equations;
 Elliptical Orbits;
 Kepler Laws;
 Orbital Mechanics;
 Transcendental Functions;
 Trigonometric Functions;
 Two Body Problem;
 Approximation;
 Computational Grids;
 Eccentricity;
 Errors;
 Iterative Solution;
 Refining;
 Astrodynamics