Mathematical Problems in Engineering
Volume 2009 (2009), Article ID 159287, 10 pages
Research Article

Controlling the Eccentricity of Polar Lunar Orbits with Low-Thrust Propulsion

1Grupo de Dinâmica Orbital & Planetologia, UNESP, Universidade Estadual Paulista, Avenida Ariberto Pereira da Cunha, 333, CEP, 12516-410, Guaratinguetá, SP, Brazil
2Instituto Nacional de Pesquisas Espaciais—INPE, Avenida dos Astronautas 1752, CEP, 12227-010, São José dos Campos-SP, Brazil
3Instituto de Física, Universidade de Brasília—UnB, CP 04455, CEP, 70919-970, Brasília, DF, Brazil

Received 30 July 2009; Accepted 31 December 2009

Academic Editor: A. F. B. De Almeida Prado

Copyright © 2009 O. C. Winter 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.


It is well known that lunar satellites in polar orbits suffer a high increase on the eccentricity due to the gravitational perturbation of the Earth. That effect is a natural consequence of the Lidov-Kozai resonance. The final fate of such satellites is the collision with the Moon. Therefore, the control of the orbital eccentricity leads to the control of the satellite's lifetime. In the present work we study this problem and introduce an approach in order to keep the orbital eccentricity of the satellite at low values. The whole work was made considering two systems: the 3-body problem, Moon-Earth-satellite, and the 4-body problem, Moon-Earth-Sun-satellite. First, we simulated the systems considering a satellite with initial eccentricity equals to 0.0001 and a range of initial altitudes between 100 km and 5000 km. In such simulations we followed the evolution of the satellite's eccentricity. We also obtained an empirical expression for the length of time needed to occur the collision with the Moon as a function of the initial altitude. The results found for the 3-body model were not significantly different from those found for the 4-body model. Secondly, using low-thrust propulsion, we introduced a correction of the eccentricity every time it reached the value 0.05. These simulations were made considering a set of different thrust values, from 0.1 N up to 0.4 N which can be obtained by using Hall Plasma Thrusters. In each run we measured the length of time, needed to correct the eccentricity value (from e=0.04 to e=0.05). From these results we obtained empirical expressions of this time as a function of the initial altitude and as a function of the thrust value.