Celestial mechanics

, Volume 31, Issue 2, pp 95–107 | Cite as

The solution of Kepler's equation, I

  • J. M. A. Danby
  • T. M. Burkardt
Article
Received:
Accepted:

Abstract

Methods of iteration are discussed in relation to Kepler's equation, and various initial ‘guesses’ are considered, with possible strategies for choosing them. Several of these are compared; the method of iteration used in the comparisons has local convergence of the fourth order.

Keywords

Fourth Order Local Convergence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Burniston, E. E. and Siewart, C. E.: 1972, ‘An Exact Analytical Solution of Kepler's Equation’,Celest. Mech. 6, 294.Google Scholar
  2. Isaacson, E. and Keller, H. B.: 1966,Analysis of Numerical Methods, Wiley, New York, p. 102.Google Scholar
  3. Moulton, F. R.: 1914,An Introduction to Celestial Mechanics, MacMillan, New York.Google Scholar
  4. Ng, E. W.: 1979, ‘A General Algorithm for the Solution of Kepler's Equation for Elliptic Orbits’,Celest. Mech. 20, 243.Google Scholar
  5. Smith, G. R.: 1979, ‘A Simple Efficient Starting Value for the Iterative Solution of Kepler's Equation’,Cel. Mech. 19, 163.Google Scholar

Copyright information

© D. Reidel Publishing Company 1983

Authors and Affiliations

  • J. M. A. Danby
    • 1
  • T. M. Burkardt
  1. 1.North Carolina State UniversityUSA

Personalised recommendations