A new solution approach via analytical approximation of the elliptic Kepler equation

摘要

A new analytical approach for constructing approximate solutions to the elliptic Kepler equation is proposed. We first establish a high-accuracy initial approximation using the piecewise Pade ' approximation, subsequently we apply the Schro center dot der method to further improve the accuracy of the initial approximation. In general, one Schro center dot der iteration is sufficient to obtain a highly accurate approximate solution. This is a direct method that requires only solving a cubic equation and evaluating two trigonometric functions. The approximate, analytical solutions are compared with solutions by other numerical procedures to prove the accuracy and effectiveness of the proposed approach.

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