Kepler Equation solver

@article{Markley1995KeplerES,
  title={Kepler Equation solver},
  author={F. Landis Markley},
  journal={Celestial Mechanics and Dynamical Astronomy},
  year={1995},
  volume={63},
  pages={101-111}
}
  • F. Markley
  • Published 1 May 1995
  • Mathematics
  • Celestial Mechanics and Dynamical Astronomy
Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation. This method is not iterative, and requires only four transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 1018, exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are… 
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References

SHOWING 1-10 OF 12 REFERENCES
A cubic approximation for Kepler's equation
We derive a new method to obtain an approximate solution for Kepler's equation. By means of an auxiliary variable it is possible to obtain a starting approximation correct to about three figures. A
Procedures for solving Kepler's equation
We review starting formulae and iteration processes for the solution of Kepler's equation, and give details of two complete procedures. The first has been in use for a number of years, but the second
Solving Kepler's equation with high efficiency and accuracy
We present a method for solving Kepler's equation for elliptical orbits that represents a gain in efficiency and accuracy compared with those currently in use. The gain is obtained through a starter
On solving Kepler's equation
Intrigued by the recent advances in research on solving Kepler's equation, we have attacked the problem too. Our contributions emphasize the unified derivation of all known bounds and several
An improved algorithm due to laguerre for the solution of Kepler's equation
A root-finding method due to Laguerre (1834–1886) is applied to the solution of the Kepler problem. The speed of convergence of this method is compared with that of Newton's method and several
The solution of Kepler's equation, I
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
An introduction to the mathematics and methods of astrodynamics
Part 1 Hypergeometric Functions and Elliptic Integrals: Some Basic Topics In Analytical Dynamics The Problem of Two Bodies Two-Body Orbits and the Initial-Value Problem Solving Kepler's Equation
The general Kepler equation and its solutions
My father K. Stumpff (1947, 1949, 1951, 1959, 1962) developed a transcendental equation which replaces the original Kepler equation but is valid for all types of orbits. Other advantages over the
The solution of Kepler's equation, II
Starting values for the iterative solution of Kepler's equation are considered for hyperbolic orbits, and for generalized versions of the equation, including the use of universal variables.
The solution of Kepler's equation, III
Recently proposed methods of iteration and initial guesses are discussed, including the method of Laguerre-Conway. Tactics for a more refined initial guess for use with universal variables over a
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