Mathematical Problems in Engineering
Volume 2011 (2011), Article ID 187478, 19 pages
Research Article

Planetary Satellite Orbiters: Applications for the Moon

1Universidade Estadual Paulista (UNESP), 12 516-410 Guaratinguetá, SP, Brazil
2Instituto de Ciência e Tecnologia, Universidade Federal de São Paulo (UNIFESP), 12 331-280 São José dos Campos, SP, Brazil
3Division of Space Mechanics and Control, INPE, 12 227-010 São José dos Campos, SP, Brazil

Received 2 August 2010; Revised 9 February 2011; Accepted 17 March 2011

Academic Editor: E. E. N. Macau

Copyright © 2011 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.


Low-altitude, near-polar orbits are very desirable as science orbits for missions to planetary satellites, such as the Earth's Moon. In this paper, we present an analytical theory with numerical simulations to study the orbital motion of lunar low-altitude artificial satellite. We consider the problem of an artificial satellite perturbed by the nonuniform distribution of the mass of the Moon ( 𝐽 2 𝐽 5 , 𝐽 7 , and 𝐶 2 2 ). The conditions to get frozen orbits are presented. Using an approach that considers the single-averaged problem, we found families of periodic orbits for the problem of an orbiter travelling around the Moon, where frozen orbits valid for long periods of time are found. A comparison between the models for the zonal and tesseral harmonics coefficients is presented.