Solving Kepler's equation with high efficiency and accuracy |
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| Authors: | Albert Nijenhuis |
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| Institution: | (1) Department of Mathematics, University of Pennsylvania, 19104 Philadelphia, PA;(2) Department of Mathematics, University of Washington, 98195 Seattle, WA;(3) 13727 41st Ave. NE, 98125 Seattle, WA, U.S.A. |
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| Abstract: | We present a method for solving Kepler's equation for elliptical orbits that represents a gain in efficiency and accuracy compared with those currently in use. The gain is obtained through a starter algorithm which uses Mikkola's ideas in a critical range, and less costly methods elsewhere. A higher-order Newton method is used thereafter. Our method requires two trigonometric evaluations. |
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| Keywords: | Two-body problem Kepler's equation numerical method |
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