# Kepler Equation solver

@article{Markley1995KeplerES, title={Kepler Equation solver}, author={F. Landis Markley}, journal={Celestial Mechanics and Dynamical Astronomy}, year={1995}, volume={63}, pages={101-111} }

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 transcendental function evaluations: a square root, a cube root, and two trigonometric functions. The maximum relative error of the algorithm is less than one part in 1018, exceeding the capability of double-precision computer arithmetic. Roundoff errors in double-precision implementation of the algorithm are…

## 27 Citations

A method solving kepler's equation without transcendental function evaluations

- Mathematics
- 1996

We developed two approximations of the Newton-Raphson method. The one is a sort of discretization, namely to search an approximate solution on pre-specified grid points. The other is a Taylor series…

An analytic investigation into the behavior of Kepler’s equation1

- Mathematics
- 2008

Kepler’s Equation is solved over the entire range of elliptic and parabolic motion. Global solution accuracy is maintained by defining four M-e plane solution sub-domains. Three computational methods…

Solving Kepler's equation CORDIC-like

- Mathematics, Physics
- 2018

Context. Many algorithms to solve Kepler's equations require the evaluation of trigonometric or root functions.
Aims. We present an algorithm to compute the eccentric anomaly and even its cosine and…

Accurate Kepler equation solver without transcendental function evaluations

- Mathematics
- 2013

The goal for the solution of Kepler’s equation is to determine the eccentric anomaly accurately, given the mean anomaly and eccentricity. This paper presents a new approach to solve this very well…

Appropriate Starter for Solving the Kepler's Equation

- Computer Science
- 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.

CORDIC-like method for solving Kepler’s equation

- Astronomy & Astrophysics
- 2018

Context. Many algorithms to solve Kepler’s equations require the evaluation of trigonometric or root functions.
Aims. We present an algorithm to compute the eccentric anomaly and even its cosine and…

Solving Kepler’s Equation using Bézier curves

- Mathematics
- 2007

This paper presents a non-iterative approach to solve Kepler’s Equation, M = E − e sin E, based on non-rational cubic and rational quadratic Bézier curves. Optimal control point coordinates are first…

Solving Kepler’s equation using implicit functions

- Mathematics
- 2014

A new approach to solve Kepler’s equation based on the use of implicit functions is proposed here. First, new upper and lower bounds are derived for two ranges of mean anomaly. These upper and lower…

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…

QUASI CONSTANT-TIME ORBIT PROPAGATION WITHOUT SOLVING KEPLER'S EQUATION 1

- Physics
- 2008

Efficient methods for solving Kepler’s equation, a transcendental equation relating orbital position as a function of time, have been studied for centuries and generated a vast literature. This paper…

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