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A maneuver called "Aero-Gravity Assisted" is known in the literature to increase the energy gains given by a close approach between a spacecraft and a planet using the atmosphere of the planet. In a sequence of studies related to this problem, the present paper studies close approaches between a spacecraft and the Earth, in situations where the passage is close enough to the surface of the Earth such that the spacecraft crosses its atmosphere. The dynamical model considers the atmosphere of the Earth, in terms of drag and lift, the gravitational fields of the Earth and the Sun, assumed to be points of mass, and the spacecraft. The Earth and the Sun are assumed to be in circular coplanar orbits around their common center of mass. The equations of motion are the ones given by the circular planar restricted three-body problem with the addition of the forces generated by the atmospheric drag and lift. The primary objective is to map the variations of energy of the orbits of the spacecraft due to this close approach. The results show how the atmosphere affects the trajectory of the spacecraft, generating situations where the variation of energy changes sign with respect to the gravity part of the maneuver or where they have a zero net result, based in the equilibrium

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In a swing-by maneuver, the variation of energy of the spacecraft is controlled by the angle, velocity, and distance of approach. These parameters are defined by the incoming trajectory, when the spacecraft is far from the planetary atmosphere. The passage of the spacecraft by the atmosphere generates aerodynamic forces, affecting its trajectory and giving new forms of control, which are functions of the attitude of the spacecraft. This maneuver is called aerogravity-assist maneuver. This control can change the direction and magnitude of aerodynamic forces. Previous results showed the influence of the lift-to-drag ratio and the effects of the application of impulses in this maneuver. However, the variations of energy due to the control that can be given by the bank angle have not been studied before, and this study constitutes the main new aspect of the present paper. In this research, it is implemented the classical methodology to calculate the variations of energy to analyze the effects of the bank angle in aerogravity-assist maneuvers. This analysis can identify regions of collisions and the variations of energy as a function of the bank angle, giving new alternatives to this maneuver that are not available in the literature.