# An improved algorithm due to laguerre for the solution of Kepler's equation

@article{Conway1986AnIA, title={An improved algorithm due to laguerre for the solution of Kepler's equation}, author={Bruce A. Conway}, journal={Celestial mechanics}, year={1986}, volume={39}, pages={199-211} }

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 higher-order Newton methods for the problem formulated in both conventional and universal variables and for both elliptic and hyperbolic orbits. In many thousands of trials the Laguerre method never failed to converge to the correct solution, even from exceptionally poor starting approximations. The non…

## 43 Citations

An Improved Algorithm For The Solution of Kepler 's Equation For An Elliptical Orbit

- Physics
- 2010

In this paper, a root finding method due to iterative method is used first to the solution of Kepler's equation for an elliptical orbit. Then the extrapolation technique in the form of Aitken Δ 2…

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…

AN EFFICIENT CODE TO SOLVE THE KEPLER ’ S EQUATION FOR ELLIPTIC AND HYPERBOLIC ORBITS

- Physics
- 2016

The Kepler equation for the elliptical motion, y− e siny = x, involves a nonlinear function depending on three parameters: the eccentric anomaly y ≡ E, the eccentricity e and the mean anomaly x ≡ M.…

An efficient code to solve the Kepler equation. Elliptic case

- Physics
- 2017

A new approach for solving Kepler equation for elliptical orbits is developed in this paper. This new approach takes advantage of the very good behaviour of the modified Newton?Raphson method when…

An efficient code to solve the Kepler equation

- Mathematics, PhysicsAstronomy & Astrophysics
- 2018

Context. This paper introduces a new approach for solving the Kepler equation for hyperbolic orbits. We provide here the Hyperbolic Kepler Equation–Space Dynamics Group (HKE–SDG), a code to solve the…

Dynamic discretization method for solving Kepler’s equation

- Computer Science
- 2006

This paper defines Kepler’s equation for the elliptical case and describes existing solution methods, and presents the dynamic discretization method and shows the results of a comparative analysis, demonstrating that, for the conditions of the tests, dynamicDiscretization performs the best.

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.

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.

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.

Robust resolution of Kepler’s equation in all eccentricity regimes

- Physics, Mathematics
- 2013

In this paper we discuss the resolution of Kepler’s equation in all eccentricity regimes. To avoid rounding off problems we find a suitable starting point for Newton’s method in the hyperbolic case.…

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