Abstract
An analysis of delta-velocity Earth-gravity-assist (D V-EGA) trajectories is carried out by using an indirect optimization method. In comparison to previous literature, the eccentricity of the Earth’ s orbit is taken into account, and simplifying assumptions, concerning the position and direction of velocity impulses, are removed. However, the focus is on the application of the theory of optimal control to complex interplanetary missions and D V-EGA trajectories are only illustrative examples. In particular, it is shown that the optimization of this kind of mission, according to the patched-conic approximation, can be obtained by considering only the two-body problem equations in the heliocentric frame. The necessary optimum conditions for the Earth e yby are extended to consider a minimum-height constraint, which is frequently required in this maneuver. The procedure is also capable of recognizing when a numerical solution is only suboptimal and a powered e yby could improve the mission.
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