Abstract
We developed a method to solve Kepler’s equation for the hyperboliccase. The solution interval is separated into three regions; F ≪ 1, F≈ 1, F ≫ 1. For the region F is large, we transformed the variablefrom F to exp F and applied the Newton method to the transformed equation.For the region F is small, we expanded the equation with respect to F andapplied the Newton method to the approximated equations. For the middleregion, we adopted a discretization of the Newton method and used the Taylorseries expansion for the evaluation of transcendental functions (Fukushima,1997). Numerical measurements showed that, in the case of Intel Pentiumprocessor, the new method is more than 3.7 times as fast as the combinationof a fourth order correction formula (Fukushima, 1997) and Roy’sstarting procedure (Roy, 1988) and others.
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