Abstract
We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series expansion. A combination of these was applied to solving Kepler's equation for the elliptic case. The resulting method requires no evaluation of transcendental functions. Numerical measurements showed that, in the case of Intel Pentium processor, the new method is three times as fast as the original Newton-Raphson method. Also it is more than 2.5 times as fast as Halley's method, Nijenhuis's method, and others.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Danby, J. M. A.: 1988, Fundamentals of Celestial Mechanics, 2nd ed., MacMillan, New York, NY
Markley, F. L.: 1996, Kepler Equation Solver, Celest. Mech. and Dynam. Astronomy 63, 101–111.
Nijenhuis, A.: 1991, Solving Kepler's Equation with High Efficiency and Accuracy, Celest. Mech. 51, 319–330.
Odell, A. W. and Gooding, R. H.: 1986, Procedures for Solving Kepler's Equation, Celest. Mech. 38, 307–334.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fukushima, T. A method solving kepler's equation without transcendental function evaluations. Celestial Mech Dyn Astr 66, 309–319 (1996). https://doi.org/10.1007/BF00049384
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00049384