# 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} }

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.

## 68 Citations

The solution of Kepler's equation, III

- Physics
- 1987

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

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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

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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…

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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…

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- 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.

Error analysis for stationary one point iteration formulae of arbitrary order of convergence for solving universal Kepler's equation

- MathematicsAppl. Math. Comput.
- 2004

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