The Study of the Asymmetric Multiple Encounters Problem and Its Application to Obtain Jupiter Gravity Assisted Maneuvers

The Multiple Encounters Problem is described in the literature as the problem of finding trajectories for a spacecraft that leaves from a mother planet, describes a trajectory in the interplanetary space, and then goes back to the mother planet. The present paper extends the literature and the departure and arrival angles of the spacecraft are generalized to be nonsymmetrical. The solutions are shown in terms of the true ( ) and eccentric anomaly ( ). The velocity variation ( ) required for the transfer is also shown. Then, this study is generalized to consider the possibility that the spacecraft makes a close approach with the mother planet to change its energy in the return trip. The velocity ( ) and energy variation ( ) due to this passage are obtained. The topics studied here can be applied in missions that leave and come back to the Earth, with the goal of studying the interplanetary space, as well as for missions whose objective is to make an alteration in the energy of the space vehicle through a swing-by with the mother body.