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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 347835, 12 pages
Research Article

GPS Satellites Orbits: Resonance

1Department of Geomatic, Federal University of Paraná (UFPR), 81531-909 Curitiba, PR, Brazil
2UNESP-Univ Estadual Paulista, Guaratinguetá, CEP 12516-410, SP, Brazil

Received 29 July 2009; Accepted 28 September 2009

Academic Editor: Antonio Prado

Copyright © 2009 Luiz Danilo Damasceno Ferreira and Rodolpho Vilhena de Moraes. 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 perturbations due to resonant geopotential harmonics on the semimajor axis of GPS satellites are analyzed. For some GPS satellites, secular perturbations of about 4 m/day can be obtained by numerical integration of the Lagrange planetary equations considering in the disturbing potential the main secular resonant coefficients. Amplitudes for long-period terms due to resonant coefficients are also exhibited for some hypothetical satellites orbiting in the neighborhood of the GPS satellites orbits. The results are important to perform orbital maneuvers of GPS satellites such that they stay in their nominal orbits. Also, for the GPS satellites that are not active, the long-period effects due to the resonance must be taken into account in the surveillance of the orbital evolutions of such debris.