Silva, Aurea A.Prado, Antonio F. B. A.Winter, Othon Cabo [UNESP]2014-05-272014-05-272007-12-01International Astronautical Federation - 58th International Astronautical Congress 2007, v. 7, p. 4384-4390.http://hdl.handle.net/11449/70162In the present work we show the expressions of the gravitational potential of homogeneous bodies with non-spherical three-dimensional shapes in order to study the trajectories around these bodies. The potentials of a prolate and an oblate ellipsoids with different values of semi-major axis are presented. Their results are validated with a test using a spherical body in order to guarantee the approximation of any body as a polyhedral model of the body. With these expressions we study trajectories of a point of mass around the three-dimensional bodies and the results indicated that there is a group of orbits around those bodies and the polyhedral form of the object does work very well. Copyright IAF/IAA. All rights reserved.4384-4390engOrbitsThree dimensionalTrajectoriesGravitational potentialsMajor axesPolyhedral modelsSpherical bodiesSpheresTrabalho apresentado em eventoAcesso aberto2-s2.0-5494910247009600245756472580000-0002-4901-3289