Optimal three-dimensional heliocentric solar-sail rendezvous transfer trajectories

This study is concerned with the problem of optimization of the control, in the sense of high speed of response, for minimum time rendezvous transfer of sail-spacecraft between heliocentric, inclined, elliptic orbits. The angles defining the orientation of the sail (assumed to be perfectly reflecting and flat) with respect to sunlight are the control variables. The analysis employs a two-body inverse square force model and an inverse square variation of solar pressure with heliocentric distance. The formulation is attempted through a set of autonomous variables related to the angular momentum, eccentricity vector and the direction cosines of the unit normal to the ecliptic plane. The optimal strategy is pursued by conversion to a two-point boundary value problem and its solution by the application of the Controlled Random Search optimization technique. Illustrations are mainly attempted for Earth-Mercury orbit transfer.