Optimization of Impulsive Europa Capture Trajectories using Primer Vector Theory

Abstract

The optimization of impulsive, three-dimensional transfer trajectories to capture at Europa is investigated. Two initial conditions are considered: a halo orbit in the vicinity of Europa, and a resonant orbit around Jupiter. Primer vector theory is utilized to determine the number of impulses and the gradient information needed for this highly nonlinear, many revolution optimization problem. A custom multi-shooting algorithm is developed to mitigate the extreme sensitivities from long flight times through regions dominated by chaotic dynamics. New equations are derived to inform decisions to keep or remove small intermediate maneuvers. Optimization of previously generated, near-optimal halo-to-capture transfers verifies that an energetic-based minimum ΔV provides a good initial measure of optimality. For the resonant boundary scenario, a new 3D periodic orbit is generated that incorporates natural transfers between a resonant orbit and a halo orbit. The intermediate halo orbit enables phase-free connection of the capture and resonant phases. The end-to-end transfers successfully converge to quasi-ballistic, manifold-like trajectories.