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Journal of Applied Mathematics
Volume 2012, Article ID 489849, 18 pages
Research Article

Analytical and Semi-Analytical Treatment of the Satellite Motion in a Resisting Medium

1Department of Applied Mathematics, Faculty of Applied Science, Taibah University, Al-Madina-Al Munawwarah, Saudi Arabia
2Department of Mathematics, Faculty of Science, Tanta University, Tanta, Egypt
3Department of Mathematics, Faculty of Science, Taibah University, Al-Madina-Al Munwwarah, Saudi Arabia
4Department of Astronomy, Faculty of Science, Cairo University, Cairo 12613, Egypt

Received 11 August 2011; Revised 8 October 2011; Accepted 17 October 2011

Academic Editor: Pablo González-Vera

Copyright © 2012 S. E. Abd El-Bar and F. A. Abd El-Salam. 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 orbital dynamics of an artificial satellite in the Earth's atmosphere is considered. An analytic first-order atmospheric drag theory is developed using Lagrange's planetary equations. The short periodic perturbations due to the geopotential of all orbital elements are evaluated. And to construct a second-order analytical theory, the equations of motion become very complicated to be integrated analytically; thus we are forced to integrate them numerically using the method of Runge-Kutta of fourth order. The validity of the theory is checked on the already decayed Indian satellite ROHINI where its data are available.