Efficiency of Solution Methods for Kepler’s Equation

This article discusses, in the case of eccentric orbits, some solution methods for Kepler's equation, for instance: Newton's method, Halley method and the solution by Fourire-Bessel expansion. The efficiency of solution methods is evaluated according to the number of iterations that each m...

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Published inApplied Mechanics and Materials Vol. 851; no. Advanced Materials, Structures and Mechanical Engineering II; pp. 587 - 592
Main Authors Romão, Estaner Claro, Nunes de Oliveira, João Francisco, Garcia, Roberta Veloso, Kuga, Hélio Koiti
Format Journal Article
LanguageEnglish
Published Zurich Trans Tech Publications Ltd 01.08.2016
Subjects
Eccentric orbits
Efficiency
Fourier-Bessel transformations
Iterative methods
Mathematical analysis
Newton methods
Tolerances
Kepler’s Equation
Halley Method
Fourier-Bessel Series Expansion
Newton Method
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Summary:This article discusses, in the case of eccentric orbits, some solution methods for Kepler's equation, for instance: Newton's method, Halley method and the solution by Fourire-Bessel expansion. The efficiency of solution methods is evaluated according to the number of iterations that each method needs to lead to a solution within the specified tolerance. The solution using Fourier-Bessel series is not an iterative method, however, it was analyzed the number of terms required to achieve the accuracy of the prescribed solution.
Bibliography:Selected, peer reviewed papers from the 3rd International Conference on Advanced Materials, Structures and Mechanical Engineering, May 20-22, 2016, Incheon, South Korea
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ISBN:9783038357063
3038357065
ISSN:1660-9336
1662-7482
1662-7482
DOI:10.4028/www.scientific.net/AMM.851.587