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Second Order Perturbations of Elliptic Elements with Respect to the Initial Ones

Published online by Cambridge University Press:  12 April 2016

F.J. Marco Castillo ,
M.J. Martínez Usó  and
J.A. López Ortí
F.J. Marco Castillo
Affiliation:
Depto de Matemáticas, Universitat Jaume I, Castellón, SPAIN
M.J. Martínez Usó
Affiliation:
Depto de Matemática Aplicada, ESTII, Universidad Politécnica de Valencia, SPAIN
J.A. López Ortí
Affiliation:
Depto de Matemáticas, Universitat Jaume I, Castellón, SPAIN

Abstract

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The following paper is devoted to the theoretical exposition of the obtention of second order perturbations of elliptic elements and is a follow-up of previous papers (Marco et al., 1996; Marco et al., 1997) where the hypothesis was made that the matrix of the partial derivatives of the orbital elements with respect to the initial ones is the identity matrix at the initial instant only. So, we must compute them through the integration of Lagrange planetary equations and their partial derivatives.

Such developments have been applied to the individual corrections of orbits together with the correction of the reference system through the minimization of a quadratic form obtained from the linearized residual. In this state two new targets emerged:

  1. 1. To be sure that the most suitable quadratic form was to be considered.

  2. 2. To provide a wider vision of the behavior of the different orbital parameters in time.

Both aims may be accomplished through the consideration of the second order partial derivatives of the elliptic orbital elements with respect to the initial ones.

Type
Extended Abstracts
Information
International Astronomical Union Colloquium , Volume 172: Impact of Modern Dynamics in Astronomy , 1999 , pp. 453 - 454
Copyright
Copyright © Kluwer 1999

References

Marco, F.J., López, J.A., Martínez, M.J.: 1996, A time-dependent extension to Btouwer’s method of orbital elements correction. Dynamics, Ephemerides and Astrometry of the Solar System, pp.199–202 CrossRefGoogle Scholar
Marco, F.J., López, J.A., Martínez, M.J.: 1997, Temporal variations of perturbed elliptic elements: A semi-analytical approach, Celest. Mec., 68, 193–198 Google Scholar
Simon, J.L.: 1988, Calcul des dérivées premières et secondes des équations de Lagrange par analyse harmonique, Astron. Astrophys., 175, 303–308 Google Scholar