A FAST PROCEDURE SOLVING KEPLERS EQUATION FOR ELLIPTIC CASE

The bisection method was applied to localize a solution of Kepler's eq uation in an extended form where the Newton-Raphson and some other met hods are not always stable. This localizer was combined with a variati on of the Newton-Raphson method where trigonometric functions are eval uated by Taylor series expansions. As a result, we developed a procedu re solving the extended Kepler's equation. It is roughly twice as fast as Halley's method and more for other existing schemes. This signific antly speeds up Encke's method applied to orbital elements (Fukushima 1996a). Also, even in solving the original Kepler's equation, it is 20 % faster than the author's former method (Fukushima 1996b). (C) 1996 A merican Astronomical Society.