Mathematical Problems in Engineering
Volume 2008 (2008), Article ID 763654, 14 pages
Research Article

Third-Body Perturbation in the Case of Elliptic Orbits for the Disturbing Body

R. C. Domingos,1 R. Vilhena de Moraes,1 and A. F. Bertachini De Almeida Prado2

1Department of Mathematics, Universidade Estadual Paulista (UNESP), Guaratinguetá, 12516-410, São Paulo, Brazil
2Instituto Nacional de Pesquisas Espaciais (INPE), São José dos Campos, 12227-010, São Paulo, Brazil

Received 1 November 2007; Accepted 7 April 2008

Academic Editor: Alexander P. Seyranian

Copyright © 2008 R. C. Domingos et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This work presents a semi-analytical and numerical study of the perturbation caused in a spacecraft by a third-body using a double averaged analytical model with the disturbing function expanded in Legendre polynomials up to the second order. The important reason for this procedure is to eliminate terms due to the short periodic motion of the spacecraft and to show smooth curves for the evolution of the mean orbital elements for a long-time period. The aim of this study is to calculate the effect of lunar perturbations on the orbits of spacecrafts that are traveling around the Earth. An analysis of the stability of near-circular orbits is made, and a study to know under which conditions this orbit remains near circular completes this analysis. A study of the equatorial orbits is also performed.