Observatorio de I+D+i UPM

Memorias de investigación
Research Publications in journals:
An efficient code to solve the Kepler equation. Elliptic case
Year:2017
Research Areas
  • Space science,
  • Aeronautical engineering
Information
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.
International
Si
JCR
Si
Title
Montly notice of the royal astronomical society
ISBN
0035-8711
Impact factor JCR
4,961
Impact info
Volume
467
10.1093/mnras/stx138
Journal number
2
From page
1702
To page
1713
Month
SIN MES
Ranking
Participants
  • Autor: Virginia Raposo Pulido (UPM)
  • Autor: Jesus Pelaez Alvarez (UPM)
Research Group, Departaments and Institutes related
  • Creador: Grupo de Investigación: Dinámica Espacial (SDG-UPM)
  • Departamento: Física Aplicada a Las Ingenierías Aeronáutica y Naval
S2i 2020 Observatorio de investigación @ UPM con la colaboración del Consejo Social UPM
Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
Cofinanciación del MINECO en el marco del Programa INNPACTO (IPT-020000-2010-22)