A method solving kepler's equation without transcendental function evaluations

Details A method solving kepler's equation without transcendental function evaluations A method solving kepler's equation without transcendental function evaluations

Sep 1996

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1996cemda..66..309f&link_type=abstract

Celestial Mechanics and Dynamical Astronomy, Volume 66, Issue 3, pp.309-319

Astronomy and Astrophysics

Astronomy

2

Kepler'S Equation, Newton-Raphson Method, Orbital Motion

Scientific paper

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.

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