A METHOD SOLVING KEPLERS EQUATION FOR HYPERBOLIC CASE

We developed a method to solve Kepler's equation for the hyperbolic ca se. The solution interval is separated into three regions; F << 1, F a pproximate to 1, and F >> 1. For the region F is large, we transformed the variable from F to exp F and applied the Newton method to the tra nsformed equation. For the region F is small, we expanded the equation with respect to F and applied the Newton method to the approximated e quations. For the middle region, we adopted a discretization of the Ne wton method and used the Taylor series expansion for the evaluation of transcendental functions (Fukushima, 1997). Numerical measurements sh owed that, in the case of Intel Pentium processor, the new method is m ore than 3.7 times as fast as the combination of a fourth order correc tion formula(Fukushima, 1997) and Roy's starting procedure (Roy, 1988) and others.