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Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 740460, 24 pages
Research Article

Nonsphericity of the Moon and Near Sun-Synchronous Polar Lunar Orbits

1UNESP—Universidade Estadual Paulista, CEP 12516-410, Guaratinguetá-SP, Brazil
2Division of Space Mechanics and Control—INPE, CEP 12227-010, São José dos Campos, SP, Brazil

Received 30 July 2009; Revised 28 October 2009; Accepted 3 December 2009

Academic Editor: Tadashi Yokoyama

Copyright © 2009 Jean Paulo dos Santos Carvalho 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.


Herein, we consider the problem of a lunar artificial satellite perturbed by the nonuniform distribution of mass of the Moon taking into account the oblateness () and the equatorial ellipticity (sectorial term ). Using Lie-Hori method up to the second order short-period terms of the Hamiltonian are eliminated. A study is done for the critical inclination in first and second order of the disturbing potential. Coupling terms due to the nonuniform distribution of mass of the Moon are analyzed. Numerical simulations are presented with the disturbing potential of first and second order is. It an approach for the behavior of the longitude of the ascending node of a near Sun-synchronous polar lunar orbit is presented.