Effects of atmospheric drag in swing-by trajectory

In this paper, we study the effects of the atmospheric drag in swing-by maneuvers. Our goal is to simulate a large variety of initial conditions for those orbits and study them according to the effects caused by this close approach. The practical importance of this topic is to allow mission designers to explore close approaches with planets, as well as to take advantage of the atmospheric effects, when it is possible. We use the well-known planar restricted circular three-body problem plus atmospheric drag as our model. We integrate numerically the equations of motion forward and backward in time, until the spacecraft is in a distance that we can neglect the planet's effect and consider the system formed by the Sun and the spacecraft as a two-body system. At these two points we can use the two body celestial mechanics to compute energy, angular momentum and the Jacobian constant before and after the close approach.