# On solving Kepler's equation

@article{Taff1989OnSK, title={On solving Kepler's equation}, author={Laurence G. Taff and Timothy A Brennan}, journal={Celestial Mechanics and Dynamical Astronomy}, year={1989}, volume={46}, pages={163-176} }

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 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 in both mean anomaly/eccentricity space and eccentric anomaly/eccentricity space, and finally the best and simplest starting value/solution…

## 22 Citations

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…

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.

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…

The Convergence of Newton–Raphson Iteration with Kepler's Equation

- Physics
- 1997

Conway (Celest. Mech. 39, 199–211, 1986) drew attention to the circumstance that when the Newton–Raphson algorithm is applied to Kepler's equation for very high eccentricities there are certain…

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.

Bounds on the Solution to kEPLER'S EQUATION:II. UNIVERSAL AND OPTIMAL STARTING POINTS

- Mathematics, Physics
- 1998

In this paper we find bounds on the solution to Kepler's equation for hyperbolic and parabolic motions. Two general concepts introduced here may be proved useful in similar numerical problems.…

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…

Optimal starters for solving the elliptic Kepler’s equation

- Computer Science, Physics
- 2013

The highly accurate starter given by Markley is considered in proposing an improvement of it for low to medium eccentricities and new optimal starters with respect to these measures are derived.

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.

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…

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Keywords: analyse ; methodes : numeriques ; equations : lineaires ; calcul : integral ; equations : differentielles Reference Record created on 2005-11-18, modified on 2016-08-08