# Chaotic behaviour in the newton iterative function associated with kepler's equation

@article{Stumpf1999ChaoticBI, title={Chaotic behaviour in the newton iterative function associated with kepler's equation}, author={L. Stumpf}, journal={Celestial Mechanics and Dynamical Astronomy}, year={1999}, volume={74}, pages={95-109} }

The chaotic behaviour observed when Newton's method is used to solve Kepler's equation is analysed using methods borrowed from chaos theory. The result of the analysis is compared with previous results. A sufficient condition for convergence of a given iterative function is presented and yields ranges of eccentricity and mean anomaly such that Newton's method applied to Kepler's equation will converge from an initial guess of π.

## 15 Citations

The dynamics of Kepler equation

- Physics, Geology
- 2003

It is well known that Kepler?s equation can be solved by means of an iterative
method defined, in a natural way, from the equation itself. This method yields to
the unique solution if the…

Improved First Estimates to the Solution of Kepler's Equation

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The manuscripts provides a novel starting guess for the solution of Kepler's equation for unknown eccentric anomaly E given the eccentricity e and the mean anomaly M of an elliptical orbit.

An efficient code to solve the Kepler equation. Elliptic case

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- 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…

Padé Approximation to the Solution of the Elliptical Kepler Equation

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- 2019

In orbital mechanics, the elliptical Kepler equation is a basic nonlinear equation which determines the eccentric anomaly of a planet orbiting the Sun. In this paper, Kepler’s equation has been…

Global convergence of Newton’s method on an interval

- MathematicsMath. Methods Oper. Res.
- 2004

Global convergence of the method is considered in the strong sense of convergence for any initial value in I and any feasible right-hand side and the class of functions for which the method converges globally is characterized.

Accurate analytical periodic solution of the elliptical Kepler equation using the Adomian decomposition method

- Physics, Geology
- 2017

A new analytical solution of the hyperbolic Kepler equation using the Adomian decomposition method

- Physics
- 2017

Métodos iterativos aplicados a la ecuación de Kepler

- Physics
- 2013

In this thesis we join two exciting areas such as astronomy, consisting of Kepler's equation, and numerical analysis, represented by iterative methods of solving equations. We investigate the…

Properties of Bessel Function Solution to Kepler’s Equation with Application to Opposition and Conjunction of Earth–Mars

- Physics, Geology
- 2016

Abstract In this article, a simple approach is suggested to calculate the approximate dates of opposition and conjunction of Earth and Mars since their opposition on August 28, 2003 (at perihelion of…

Chaotic Behavior in the Real Dynamics of a One Parameter Family of Functions

- Mathematics
- 2014

The chaotic behavior in the real dynamics of a one parameter family of nonlinear functions is studied in the present paper. For this purpose, the function f_λ(x)=λ=xe^x /( x - 1) λ ＞ 0, x ∈ R \ {1}…

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