A Procedure Solving the Extended Kepler's Equation for the Hyperbolic Case

Details A Procedure Solving the Extended Kepler's Equation for the Hyperbolic Case A Procedure Solving the Extended Kepler's Equation for the Hyperbolic Case

May 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997aj....113.1920f&link_type=abstract

Astronomical Journal v.113, p.1920

Astronomy and Astrophysics

Astronomy

5

Methods: Numerical, Celestial Mechanics

Scientific paper

The bisection method to localize the solution of a nonlinear equation [Fukushima (1996, M, 112, 2858)] was extended to handle a long sequence of bisections in a concise manner. This was done by means of the addition theorem of transcendental functions appearing in the equation. The localizer extended was combined with a variation of Newton's method where the functions are evaluated by their Taylor series expansions. As its application, we developed a procedure solving an extended form of Kepler's equation for the hyperbolic case. Our procedure is robust and fast. It finds sufficiently precise solutions even when Danby's starter [1988, Fundamentals of Celestial Mechanics, 2nd Ed. (Willmann-Bell, Richmond, VA), Section 6.9] fails. For typical cases, it requires less CPU time than that for evaluating the equation itself for an arbitrary argument.

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