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The Lambert W function and solutions to Kepler’s equation

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Abstract

This paper presents a method for the truncation of infinite Fourier–Bessel representations for functions requiring a solution to Kepler’s equation. Use is made of the Lambert W function to solve for the desired index that bounds the remainder terms of the series, within the prescribed tolerance. The enforcement of a maximum on the number of Bessel functions is also useful in truncating the Bessel functions themselves, resulting in an analytical representation of the solution to a desired tolerance, without the use of infinite series.

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  1. Department of Aerospace Engineering, TAMU 3141, Texas A&M University, College Station, TX, 77843-3141, USA

    Prasenjit Sengupta

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  1. Prasenjit Sengupta
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Correspondence to Prasenjit Sengupta.

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Sengupta, P. The Lambert W function and solutions to Kepler’s equation. Celestial Mech Dyn Astr 99, 13–22 (2007). https://doi.org/10.1007/s10569-007-9085-6

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  • DOI: https://doi.org/10.1007/s10569-007-9085-6

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