Abstract
In this chapter we focus on time-optimal transfers from a geostationary orbit to a sample of Natural Earth Satellites (NES) for a spacecraft using low thrust propulsion. Based on prior work we first analyze rendezvous missions in a vicinity of the Earth–Moon $$L1$$ equilibrium point, using a range of low thrusts from 0.2N to 1.0N. As a first approach, we approximate the dynamics of the spacecraft subject to the gravitational field of the Earth and the Moon by the planar restricted three-body model, before considering the spatial restricted three-body model. The time optimal control strategies are calculated using classical indirect methods of optimal control based on the Pontryagin Maximum Principle. We verify the local optimality of the corresponding trajectories using second order conditions.
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