Optimization of Biimpulsive Trajectories in the Earth-Moon Restricted Three-Body System

• Published in: Journal of guidance, control, and dynamics control, and dynamics, 2005-03, Vol.28 (2), p.209-216
• Main Authors: Mengali, Giovanni, Quarta, Alessandro A
• Format: Article
• Language: English
• Subjects: Aerospace engineering; Applied sciences; Computer science; control theory; systems; Control theory. Systems; Earth-Moon trajectories; Exact sciences and technology; Instruments, apparatus, components and techniques common to several branches of physics and astronomy; Optimal control; Optimization; Physics; Spaceborne and space research instruments, apparatus and components (satellites, space vehicles, etc.); Three body problem; Trajectory optimization; Velocity
• ISSN: 0731-5090; 1533-3884
• DOI: 10.2514/1.7702

The problem is addressed of transferring a spacecraft from a low Earth to a low lunar orbit in a planar circular restricted three-body framework. A closed-form approximate expression for the total velocity variation is developed under the assumption of minimum DeltaV biimpulsive maneuvers. This approximation quantifies the link between the transfer orbit energy and the minimum DeltaV needed to complete the maneuver, but it gives no information on the corresponding mission time. This last problem is addressed in a systematic framework using an optimization process, and the total DeltaV is minimized with the constraint that a maximum transfer time is not exceeded. Using a set of mission data taken from the literature, it is found that almost equivalent DeltaV and transfer times (compared to a weak stability boundary approach) are obtained without the use of solar perturbations. More important, a consistent methodology is proposed to exploit fully the fundamental tradeoff between the time of flight and the required DeltaV.