An efficient code to solve the Kepler equation. Elliptic case

Raposo Pulido, Virginia and Pelaez Alvarez, Jesus (2017). An efficient code to solve the Kepler equation. Elliptic case. "Montly Notice of the Royal Astronomical Society", v. 467 (n. 2); pp. 1702-1713. ISSN 0035-8711. https://doi.org/10.1093/mnras/stx138.

Description

Title: An efficient code to solve the Kepler equation. Elliptic case
Author/s:
  • Raposo Pulido, Virginia
  • Pelaez Alvarez, Jesus
Item Type: Article
Título de Revista/Publicación: Montly Notice of the Royal Astronomical Society
Date: May 2017
ISSN: 0035-8711
Volume: 467
Subjects:
Freetext Keywords: Methods: numerical, space vehicles, celestial mechanics
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Física Aplicada a las Ingenierías Aeronáutica y Naval
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

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 the initial seed is close to the looked for solution. To determine a good initial seed the eccentric anomaly domain [0, ?] is discretized in several intervals and for each one of these intervals a fifth degree interpolating polynomial is introduced. The six coefficients of the polynomial are obtained by requiring six conditions at both ends of the corresponding interval. Thus the real function and the polynomial have equal values at both ends of the interval. Similarly relations are imposed for the two first derivatives. In the singular corner of the Kepler equation, M smaller than 1 and 1 ? e close to zero an asymptotic expansion is developed. In most of the cases, the seed generated leads to reach machine error accuracy with the modified Newton?Raphson method with no iterations or just one iteration. This approach improves the computational time compared with other methods currently in use.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainESP2013-41634-PUnspecifiedUnspecifiedDynamic analysis, advanced orbit propagation and simulation of complex space systems

More information

Item ID: 50318
DC Identifier: http://oa.upm.es/50318/
OAI Identifier: oai:oa.upm.es:50318
DOI: 10.1093/mnras/stx138
Official URL: https://academic.oup.com/mnras/article-abstract/467/2/1702/2929272?redirectedFrom=PDF
Deposited by: Memoria Investigacion
Deposited on: 16 Nov 2018 09:22
Last Modified: 16 Nov 2018 09:22
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