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

Abstract

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. In the present paper the assumptions made in the literature are extended, and the departure and arrival angles of the spacecraft are generalized to be non-symmetrical, which means that the departure and arrival true anomaly of the spacecraft are not symmetrical with respect to the line of apsis of the spacecraft. The solutions are found and shown in terms of the true (n) and eccentric anomaly (h). The velocity variation (DV) 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. Then, the velocity (DV) and energy variation (DE) due to this passage is also obtained and shown. 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 which objective is to make an alteration in the energy of the space vehicle through a swing-by with the mother body, like in a maneuver that needs to move a spacecraft that is around Jupiter to another location in the Solar System or beyond. So, the present paper combines the study of gravity assisted maneuvers with the so called Multiple Encounters Problem. (AU)