# The solution of Kepler's equation, I

```@article{Danby1983TheSO,
title={The solution of Kepler's equation, I},
author={J. M. Anthony Danby and T. M. Burkardt},
journal={Celestial mechanics},
year={1983},
volume={31},
pages={95-107}
}```
• Published 1 October 1983
• Physics
• Celestial mechanics
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.
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
The solution of Kepler's equation, II
• Physics, Mathematics
• 1983
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.
Procedures for solving Kepler's equation
• Mathematics
• 1986
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
Efficiency of Solution Methods for Kepler’s Equation
• Physics
• 2016
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
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
Homotopy Solutions of Kepler's Equations
• Physics
• 1996
Kepler's Equation is solved using an integrative algorithm developed using homotropy theory. The solution approach is applicable to both elliptic and hyperbolic forms of Kepler's Equation. The
The solution of the generalized Kepler's equation
• Physics
• 2018
In the context of general perturbation theories, the main problem of the artificial satellite analyses the motion of an orbiter around an Earth-like planet, only perturbed by its equatorial bulge or
Appropriate Starter for Solving the Kepler's Equation
• Physics
• 2014
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, and one appropriate choice first guesses that increase the isotropy and decrease the time of Implementation of solving is introduced.
On solving Kepler's equation
• Physics, Geology
• 1989
This work attacks Kepler's equation with the unified derivation of all known bounds and several starting values, a proof of the optimality of these bounds, a very thorough numerical exploration of a large variety of starting values and solution techniques, and finally the best and simplest starting value/solution algorithm: M + e and Wegstein's secant modification of the method of successive substitutions.

## References

SHOWING 1-3 OF 3 REFERENCES
A simple, efficient starting value for the iterative solution of Kepler's equation
A simple starting value for the iterative solution of Kepler's equation in the elliptic case is presented. This value is then compared against five other starting values for 3750 test cases. In
An exact analytical solution of Kepler's equation
• Physics
• 1972
Complex-variable analysis is used to develop an exact solution to Kepler's equation, for both elliptic and hyperbolic orbits. The method is based on basic properties of canonical solutions to
A general algorithm for the solution of Kepler's equation for elliptic orbits
An efficient algorithm is presented for the solution of Kepler's equationf(E)=E−M−e sinE=0, wheree is the eccentricity,M the mean anomaly andE the eccentric anomaly. This algorithm is based on simple