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Journal of Applied Mathematics
Volume 2012 (2012), Article ID 479093, 15 pages
Research Article

Matched Asymptotic Expansions to the Circular Sitnikov Problem with Long Period

1High Temperatures Department, Instituto de Innovación en Minería y Metalurgia, Ahumada 341, 8320181 Santiago, Chile
2Department of Physics, Universidad Gabriela Mistral, Avenida Ricardo Lyon 1177, Santiago, Chile

Received 3 August 2012; Revised 22 November 2012; Accepted 23 November 2012

Academic Editor: Roberto Barrio

Copyright © 2012 Marco Rosales-Vera. 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 circular Sitnikov problem is revisited, using matched asymptotic expansions. In the case of large oscillation periods, approximate analytical expressions for the period and the orbit of the third body are found. The results are compared with those described in the literature and show that the movement of the third body can be well described by two analytical solutions, the inner and outer solutions.