Powered aero-gravity-assist maneuvers considering lift and drag around the Earth

The goal of this research is to study the energy variations in trajectories of a spacecraft that performs a powered aero-gravity-assist maneuver considering the effects of the lift and drag forces around the Earth. It means that the spacecraft makes a passage by the Earth that is close enough to get effects from the atmosphere. Besides those effects, an impulse is applied to the spacecraft when it is passing by the periapsis of the trajectory, which also helps to modify its trajectory. It is varied the ballistic coefficient, lift to drag ratio, magnitude and direction of the impulse and the angle of approach of the maneuver. The mathematical model assumes that a spacecraft comes from an orbit around the Sun, traveling under the restricted three-body problem dynamics, makes a close approach passing inside the atmosphere of the Earth and then goes back to another orbit around the Sun, which is different from the initial orbit. The initial position and velocity of the spacecraft are given according to the usual pure gravity-assisted parameters, using the angle of approach and the perigee altitude and velocity. The energy is measured before and after the passage. The equations of motion are numerically integrated using a Runge–Kutta–Fehlberg 7/8 method. For the numerical examples, the perigee altitude is fixed in 120 km and the velocity at this point is fixed in 0.5 canonical units, which is near 14.89 km/s.