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Mathematical Problems in Engineering
Volume 2015, Article ID 382340, 14 pages
Research Article

Study of Some Strategies for Disposal of the GNSS Satellites

1Instituto Nacional de Pesquisas Espaciais (INPE), 1758 Avenida dos Astronautas, 12227-010 São José dos Campos, SP, Brazil
2Universidade Estadual Paulista (UNESP), 1515 Avenida 24A, Caixa Postal 178, 13500-970 Rio Claro, SP, Brazil

Received 3 June 2014; Accepted 15 August 2014

Academic Editor: Chaudry M. Khalique

Copyright © 2015 Diogo Merguizo Sanchez 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.


The complexity of the GNSS and the several types of satellites in the MEO region turns the creation of a definitive strategy to dispose the satellites of this system into a hard task. Each constellation of the system adopts its own disposal strategy; for example, in the American GPS, the disposal strategy consists in changing the altitude of the nonoperational satellites to 500 km above or below their nominal orbits. In this work, we propose simple but efficient techniques to discard satellites of the GNSS by exploiting Hohmann type maneuvers combined with the use of the resonance to increase its orbital eccentricity, thus promoting atmospheric reentry. The results are shown in terms of the increment of velocity required to transfer the satellites to the new orbits. Some comparisons with direct disposal maneuvers (Hohmann type) are also presented. We use the exact equations of motion, considering the perturbations of the Sun, the Moon, and the solar radiation pressure. The geopotential model was considered up to order and degree eight. We showed the quantitative influence of the sun and the moon on the orbit of these satellites by using the method of the integral of the forces over the time.