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The Scientific World Journal
Volume 2013, Article ID 136528, 16 pages
Research Article

A Comparison of Averaged and Full Models to Study the Third-Body Perturbation

1Federal University of ABC (UFABC), Rua Santa Adélia, 166 Bairro Bangu, 09.210-170 Santo André, SP, Brazil
2National Institute of Research Space (INPE), Avenida dos Astronautas, 1758 Jd da Granja, 12227-010 São José dos Campos, SP, Brazil

Received 8 August 2013; Accepted 17 September 2013

Academic Editors: M. Balasubramaniam and G. Martínez

Copyright © 2013 Carlos Renato Huaura Solórzano and Antonio Fernando Bertachini de Almeida Prado. 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.


The effects of a third-body travelling in a circular orbit around a main body on a massless satellite that is orbiting the same main body are studied under two averaged models, single and double, where expansions of the disturbing function are made, and the full restricted circular three-body problem. The goal is to compare the behavior of these two averaged models against the full problem for long-term effects, in order to have some knowledge of their differences. The single averaged model eliminates the terms due to the short period of the spacecraft. The double average is taken over the mean motion of the satellite and the mean motion of the disturbing body, so removing both short period terms. As an example of the methods, an artificial satellite around the Earth perturbed by the Moon is used. A detailed study of the effects of different initial conditions in the orbit of the spacecraft is made.