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Mathematical Problems in Engineering
Volume 2006 (2006), Article ID 13690, 13 pages

Changing inclination of earth satellites using the gravity of the moon

Divisão de Mecânica, Instituto Nacional de Pesquisas Espaciais, Avenida dos Astronautas 1758, São José dos Campos, São Paulo 12227-010, Brazil

Received 23 August 2005; Revised 14 April 2006; Accepted 18 April 2006

Copyright © 2006 Karla de Souza Torres and A. F. B. A. Prado. 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.


We analyze 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 satellite 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 satellite to its nominal semimajor axis and eccentricity using a bi-impulsive Hohmann-type maneuver. The satellite is assumed to start in a Keplerian 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 on the patched conics approach are used to calculate the variation in velocity, angular momentum, energy, and inclination of the satellite. Then, several simulations are made to evaluate the savings involved. The time required by those transfers is also calculated and shown.