# Procedures for solving Kepler's equation

@article{Odell1986ProceduresFS, title={Procedures for solving Kepler's equation}, author={A. W. Odell and Robert H. Gooding}, journal={Celestial mechanics}, year={1986}, volume={38}, pages={307-334} }

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 is entirely new. The new procedure operates with an iterative process that always gives fourth-order convergence and is taken to only two iterations. The error in the resulting solution then never exceeds 7×10−15 rad.

## 40 Citations

Solving Kepler's equation with high efficiency and accuracy

- Physics
- 1991

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…

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 for nearly parabolic orbits

- Physics
- 1996

We deal here with the efficient starting points for Kepler's equation in the special case of nearly parabolic orbits. Our approach provides with very simple formulas that allow calculating these…

Solution of Kepler’s Equation with Machine Precision

- Physics
- 2020

Abstract— An algorithm for the numerical solution of Kepler’s equation with machine precision is presented. The convergence of the iterative sequence of Newton’s method is proved for the indicated…

A cubic approximation for Kepler's equation

- Mathematics, Physics
- 1987

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…

Kepler Equation solver

- Computer Science
- 1995

Kepler's Equation is solved over the entire range of elliptic motion by a fifth-order refinement of the solution of a cubic equation, and requires only four transcendental function evaluations.

The hyperbolic Kepler equation (and the elliptic equation revisited)

- Physics, Mathematics
- 1988

A procedure is developed that, in two iterations, solves the hyperbolic Kepler's equation in a very efficient manner, and to an accuracy that proves to be always better than 10−20 (relative…

Sequential solution to Kepler’s equation

- Physics, Computer Science
- 2010

Seven sequential starter values for solving Kepler’s equation are proposed for fast orbit propagation and obtain improved accuracy at lower computational cost as compared to the best existing methods.

Numerical solution of the two-body problem for orbital motion is heavily dependent on efficient solution of Kepler's Equation

- Mathematics
- 1995

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…

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…

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