2009 Brazilian Symposium on Aerospace Eng. & Applications 3 rd CTA-DLR Workshop on Data Analysis & Flight Control Copyright © 2009 by AAB September 14-16, 2009, S. J. Campos, SP, Brazil USING LOW THRUST PROPULSION TO ORBIT CONTROL OF THE LUNAR POLAR SATELLITES Othon Cabo Winter Décio Cardozo Mourão São Paulo State University – UNESP, Av. Ariberto Pereira da Cunha, 333, CP 205, CEP 12516-410, Guaratinguetá - SP - Brazil Cristiano Fiorillo Melo National Institute for Space Research – INPE, Av. dos Astronautas, 1752, CEP 12227-010, São José dos Campos – SP - Brazil Elbert Einstein Nehrer Macau National Institute for Space Research – INPE, Av. dos Astronautas, 1752, CEP 12227-010, São José dos Campos – SP – Brazil José Leonardo Ferreira University of Brasília – UNB, CEP 70919-970, Brasília – DF – Brazil Jean Paulo dos Santos Carvalho São Paulo State University – UNESP, Av. Ariberto Pereira da Cunha, 333, CP 205, CEP 12516-410, Guaratinguetá - SP - Brazil Abstract. 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 100km and 5000km. 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 0.1N up to 0.4N 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. Keywords: lunar polar orbit, kozai resonance, low thrusters propulsions 1. INTRODUCTION Recently, several nations presented plans to reach the Moon. Satellites have been launched and many more are planned for following years (see for instance Foing & Ehrenfreund (2008). The expectations are that in the near future there will be a lunar base. The lunar poles are particularly of interest since seems to be where water can be found. Therefore, long living satellites in polar lunar orbits will be needed. It is well known that lunar satellites in polar orbits suffer a strong gravitational perturbation from the Earth. That effect is a natural consequence of the Lidov-Kozai resonance. It is well known that the Lidov-Kozai resonance introduces equilibrium configurations. In the case of lunar polar orbits disturbed by the Earth's gravitational field, this can be used as an advantage to implement constellations of satellites with elliptic highly inclined orbits (Ely (2005); Ely & Lieb (2006)). On the other hand it causes instability for near circular highly inclined orbits. Wytrzyszczak et al. (2007) studied the regular and chaotic motion of geosynchronous satellites disturbed by the Moon's gravitational field. They found that the chaotic nature of high inclination satellites is caused due to the significant eccentricity growth caused by the Lidov-Kozai resonance. Similarly, the final fate of polar lunar near circular satellites is the collision with the Moon. Therefore, the control of the orbital eccentricity leads to the control of the satellite's lifetime. In this paper we purpose the control of the eccentricity, using a electrical thruster, similar of that is in development at the University of Brasília. Electric propulsion is basically a technique of space propulsion which evolves the conversion of electrical power into the kinetic power or thrust of the exhaust beam of ionized particles. The ability to obtain high exaust velocities with ionized particles enables plasma thrusters o perform high specific impulse mission in space (Ferreira, 2008). The main goal of the thruster that is being developed at the University of Brasília is the use of a permanent magnet, saving energy during the mission. Preliminary results in the laboratory show that is possible to