Kepler Equation Solver
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.
- Publication:
-
Celestial Mechanics and Dynamical Astronomy
- Pub Date:
- March 1995
- DOI:
- 10.1007/BF00691917
- Bibcode:
- 1995CeMDA..63..101M
- Keywords:
-
- Kepler's Equation;
- two-body problem;
- elliptical motion;
- numerical methods;
- orbit propagation