An Efficient Iterative Method for Solving the Elliptical Kepler’s Equation

2021 ◽  
Vol 7 (2) ◽  
Author(s):  
O. González-Gaxiola ◽  
S. Hernández-Linares
Keyword(s):  
Iterative Method ◽  
Kepler's Equation ◽  
Kepler’S Equation

Efficiency of Solution Methods for Kepler’s Equation

2016 ◽  
Vol 851 ◽  
pp. 587-592
Author(s):  
João Francisco Nunes de Oliveira ◽  
Roberta Veloso Garcia ◽  
Hélio Koiti Kuga ◽  
Estaner Claro Romão
Keyword(s):  
Iterative Method ◽  
Newton’S Method ◽  
Newton's Method ◽  
Kepler's Equation ◽  
Eccentric Orbits ◽  
Kepler’S Equation ◽  
Solution Methods ◽  
Number Of Iterations

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.

Solution of Kepler’s Equation with Machine Precision

2020 ◽  
Vol 64 (12) ◽  
pp. 1060-1066
Author(s):  
M. K. Abubekerov ◽  
N. Yu. Gostev
Keyword(s):  
Machine Precision ◽  
Kepler's Equation ◽  
Kepler’S Equation

The solution of Kepler's equation, II

1983 ◽  
Vol 31 (3) ◽  
pp. 317-328 ◽  
Author(s):  
T. M. Burkardt ◽  
J. M. A. Danby
Keyword(s):  
Kepler's Equation ◽  
Kepler’S Equation

A note on ?Kepler's equation?

1997 ◽  
Vol 51 (1) ◽  
pp. 59-65 ◽  
Author(s):  
Jacques Dutka
Keyword(s):  
Kepler's Equation ◽  
Kepler’S Equation

Sequential solution to Kepler’s equation

2010 ◽  
Vol 108 (1) ◽  
pp. 59-72 ◽  
Author(s):  
Jeremy J. Davis ◽  
Daniele Mortari ◽  
Christian Bruccoleri
Keyword(s):  
Kepler's Equation ◽  
Kepler’S Equation ◽  
Sequential Solution
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