A cubic approximation for Kepler's equation

Details A cubic approximation for Kepler's equation A cubic approximation for Kepler's equation

Sep 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987cemec..40..329m&link_type=abstract

Celestial Mechanics, Volume 40, Issue 3-4, pp. 329-334

Physics

9

Scientific paper

The author derives a new method to obtain an approximate solution for Kepler's equation. By means of an auxiliary variable it is possible to obtain a starting approximation correct to about three figures. A high order iteration formula then corrects the solution to high precision at once. The method can be used for all orbit types, including hyperbolic. To obtain this solution the trigonometric or hyperbolic functions must be evaluated only once.

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