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. 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 (Δ ) 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 (Δ ) and energy variation (Δ ) 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.

Study of collision probability considering a non-uniform cloud of space debris

“…The standard maneuver can be identified by the following three parameters: r ap , the minimum distance between the fragment and the Earth during the closest approach; v − inf and v + inf , the velocities of the particle with respect to the Earth, before and after the passage, respectively; v 2 , the Earth velocity around the Sun; δ, half of the angle of the curvature due to the close approach; and , the angle of approach, that is, the angle between the line connecting the primaries and the periapsis of the close approach trajectory. The velocity and orbital elements of m 2 are changed by the close approach with the Earth (Formiga and Prado 2015;dos Santos et al 2013). The orbital elements of each fragment with respect to the Sun before the maneuver are semi-major axis (a), eccentricity (e), energy (E) and angular momentum (C).…”

Rendezvous maneuvers using genetic algorithm

“…In this particular case transfer of a spacecraft from one body back to the same body (Santos et al, 2012b). The literature is extensive with respect to the problems involving transfer orbits and optimal spacecraft maneuvers (Prussing, 1979;Santos et al, 2011, Santos et al, 2012aand 2012bSantos et. al, 2013).…”