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In this paper, a study is made in the problem of the orbital control of an Earth´s satellite using the gravity of the Moon. The main objective is to study a technique to decrease the fuel consumption of a plane change maneuver to be performed in a satellite that is in orbit around the Earth. The main idea of this approach is to send the spacecraft to the Moon using a single impulsive maneuver, use the gravity field of the Moon to make the desired plane change of the trajectory, and then return the spacecraft to its nominal semi-major axis and eccentricity using a bi-impulsive Hohmann type maneuver. The spacecraft is assumed to start in a circular orbit in the plane of the lunar orbit around the Earth and the goal is to put it in a similar orbit that differs from the initial orbit only by the inclination. A description of the close approach maneuver is made in the three-dimensional space. Analytical equations based in the patched conics approximation are used to calculate the variation in velocity, angular momentum, energy and inclination of the spacecraft that realizes this maneuver. Then, several simulations are made to evaluate the savings involved

Orbital control of a satellite using the gravity of the Moon