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An efficient code to solve the Kepler equation
Research Areas
  • Aeronautical engineering
A new approach for solving Kepler equation for elliptical orbits is developed in this paper. This new approach takes advantage of the very good behavior of the modified Newton-Raphson method (or Laguerre 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 twelve 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 polinomial 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 small and e close to unity) 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.
kepassa2015 : Key Topics in Orbit Propagation Applied to Space Situational Awareness
Toulouse (France)
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  • 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
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Cofinanciación del MINECO en el marco del Programa INNCIDE 2011 (OTR-2011-0236)
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