CFP last date
20 June 2024
Reseach Article

Appropriate Starter for Solving the Kepler’s Equation

by Reza Esmaelzadeh, Hossein Ghadiri
International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 89 - Number 7
Year of Publication: 2014
Authors: Reza Esmaelzadeh, Hossein Ghadiri
10.5120/15517-4394

Reza Esmaelzadeh, Hossein Ghadiri . Appropriate Starter for Solving the Kepler’s Equation. International Journal of Computer Applications. 89, 7 ( March 2014), 31-38. DOI=10.5120/15517-4394

@article{ 10.5120/15517-4394,
author = { Reza Esmaelzadeh, Hossein Ghadiri },
title = { Appropriate Starter for Solving the Kepler’s Equation },
journal = { International Journal of Computer Applications },
issue_date = { March 2014 },
volume = { 89 },
number = { 7 },
month = { March },
year = { 2014 },
issn = { 0975-8887 },
pages = { 31-38 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume89/number7/15517-4394/ },
doi = { 10.5120/15517-4394 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:08:38.982358+05:30
%A Reza Esmaelzadeh
%A Hossein Ghadiri
%T Appropriate Starter for Solving the Kepler’s Equation
%J International Journal of Computer Applications
%@ 0975-8887
%V 89
%N 7
%P 31-38
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This article, focuses on the methods that have been used for solving the Kepler's equation for thirty years, then Kepler's equation will be solved by Newton-Raphson's method. For increasing the stability of Newton's method, various guesses studied and the best of them introduced base on minimum number repetition of algorithm. At the end, after studying various guesses base on time of Implementation, one appropriate choice first guesses that increase the isotropy and decrease the time of Implementation of solving is introduced.

References
  1. R. H. Battin. 2001. An Introduction to the Mathematics and Methods of Astrodynamics. Revised Edition, AIAA education series, pp. 160.
  2. P. Colwell. 1993. Solving Kepler equation over three centuries. Willmann-Bell, Ins.
  3. H. D. Curtis. 2010. Orbital Mechanics for engineering students. 2nded, Elsevier Aerospace Engineering Series p 163, pp. 168-170.
  4. Mikkola. 1987. A cubic approximation for Kepler's equation. Celestial Mech 40. pp. 329-334.
  5. Markley. 1995. Kepler equation solver. Celestial Mech Dyn Astr 63. pp. 101-111.
  6. S. A. Feinstein, C. A. McLaughlin. 2006. Dynamic discretization method for solving Kepler's equation. Celestial Mech Dyn Astr 96. pp. 49-62.
  7. D. Mortari, A. Clocchiatti. 2007. Solving Kepler's equation using Bezier curves. Celestial Mech Dyn Astr 99. pp. 45-57.
  8. J. T. Betts. 2010. Practical Methods for Optimal Control and Estimation Using Nonlinear Programming. Second Edition, Siam, Philadelphia. pp. 3.
  9. Edward W . NG. 1979. A general algorithm for the solution of Kepler's equation for elliptic orbits. Celestial Mech 20. pp. 243-249.
  10. Smith. 1979. A simple efficient staring value for the iterative solution of Kepler's equation. Celestial Mech 19. pp. 163-166.
  11. J. M. A. Danby, T. M. Burkardt . T. M. 1983. The solution of Kepler's equation, I. Celestial Mech 31. pp. 95-107.
  12. J. M. A. Danby. 1987. The solution of Kepler's equation, III. Celestial Mech 40. pp. 303-312.
  13. R. A. Serafin. 1986. Bounds on the solution to Kepler's equation. Celestial Mech 38. pp. 111-121.
  14. B. A. Conway. 1986. An improved algorithm due to laguerre for the solution of Kepler's equation. Celestial Mech 39. pp. 199-211.
  15. A. W. Odell, R. H. Gooding. 1986. Procedures for solving Kepler's equation. Celestial Mech 38. pp. 307-344.
  16. L. G. Taff, T. A. Brenan. 1989. On solving Kepler's equation. Celestial Mech Dyn Astr 46. pp. 163-176.
  17. Nijenhuis. 1991. Solving Kepler's equation with high efficiency and accuracy. Celestial Mech Dyn Astr 51. pp. 319-330.
  18. Chobotov. 1996. Orbital Mechanics. 2nded, AIAA education series.
  19. D. A. Vallado. 2001. Fundamentals of Astrodynamics and Application. Space Technology Series, McGraw-Hill. pp. 211, pp. 230-244.
  20. E. D. Charles, J. B. Tatum. 1998. The convergence of Newton-Raphson iteration with Kepler's equation. Celestial Mech Dyn Astr 69. pp. 357-372.
  21. A. Tewari. 2006. Atmospheric and space flight dynamics. Birkhauser. pp. 105.
Index Terms

Computer Science
Information Sciences

Keywords

Kepler's equation initial guesses iterative solution Newton -Raphson method