Efficiency of Solution Methods for Kepler’s Equation

João Francisco Nunes de Oliveira; Roberta Veloso Garcia; Hélio Koiti Kuga; Estaner Claro Romão

doi:10.4028/www.scientific.net/AMM.851.587

Paper Titles

Study on Methods for Improving LMD End Effect
p.559

Study of 3D Tolerance Modeling Method for Complex Feature Geometric Variations
p.567

Processing Method for End Effect of Local Mean Decomposition Based on Extreme Point and Distant
p.574

Research on Positioning Algorithm Based on the Gaussian Distribution Function and Partial Estimation of the Fusion Theory
p.582

Efficiency of Solution Methods for Kepler’s Equation
p.587

Analysis and Implementation for the RPG Boxing Game
p.595

Personalized Ring Design and Rapid Manufacturing Based on Reverse Engineering and 3D Printing
p.599

Information Feedback for Human Motor Skill Transferring System Using Augmented Reality
p.603

Study of XML Indexing Structure Based on XISS
p.611

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 851Efficiency of Solution Methods for Kepler’s...

Efficiency of Solution Methods for Kepler’s Equation

Abstract:

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.

You might also be interested in these eBooks

Advanced Materials, Structures and Mechanical Engineering II

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 851)

Pages:

587-592

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.851.587

Citation:

Cite this paper

Online since:

August 2016

Authors:

João Francisco Nunes de Oliveira*, Roberta Veloso Garcia, Hélio Koiti Kuga, Estaner Claro Romão

Keywords:

Fourier-Bessel Series Expansion, Halley Method, Kepler’s Equation, Newton Method

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] J. M. A. Danby, T. M. Burkardt, in: The Solution of Kepler's Equation, I, Celestial Mech. 31 (1983) 95-107.

Google Scholar

[2] R. H. Battin, in: An Introduction to the Mathematics and Methods of Astrodynamics, Revised Edition, published by American Institute of Aeronautics and Astronautics, Inc. (1968).

Google Scholar

[3] W. Gander, in: On Halley's Iteration Method, The American Mathematical Montly, 92(2) (1985) 131-134.

Google Scholar

[4] P. Colwell, in: Bessel Functions and Kepler's Equation, The American Mathematical Montly, 99, (1) (1992) 45-48.

Google Scholar