The study of orbital maneuvers in space missions is a very important problem in astrodynamics. One of the options is the use of a “gravity assisted” maneuver, which is a technique where a spacecraft passes close to a celestial body and uses the gravity of this body to change its trajectory. There is also a more complex maneuver, when the passage by the celestial body is combined with the application of propulsion, either to give extra energy to the spacecraft or to help to satisfy other constraints required by the mission, like passing by a giving point or region in space. The main object of this study is to measure the efficiency of the application of a continuous thrust combined with the “gravity assisted” maneuver. The effect of this combination is analyzed using maps that give the energy variation of the spacecraft as function of the parameters related to the maneuver. The effects of the variations of the direction of the thrust are also studied. This type of combined maneuver may be used to give extra energy to the spacecraft and keeping control of the trajectory during the close approach to better position the spacecraft to complete the mission.