A diffractive solar sail is an elegant concept for a propellantless spacecraft propulsion system that uses a large, thin, lightweight surface covered with a metamaterial film to convert solar radiation pressure into a net propulsive acceleration. The latter can be used to perform a typical orbit transfer both in a heliocentric and in a planetocentric mission scenario. In this sense, the diffractive sail, proposed by Swartzlander a few years ago, can be considered a sort of evolution of the more conventional reflective solar sail, which generally uses a metallized film to reflect the incident photons, studied in the scientific literature starting from the pioneering works of Tsander and Tsiolkovsky in the first decades of the last century. In the context of a diffractive sail, the use of a metamaterial film with a Littrow transmission grating allows for the propulsive acceleration magnitude to be reduced to zero (and then, the spacecraft to be inserted in a coasting arc during the transfer) without resorting to a sail attitude that is almost edgewise to the Sun, as in the case of a classical reflective solar sail. The aim of this work is to study the optimal (i.e., the rapid) transfer performance of a spacecraft propelled by a diffractive sail with a Littrow transmission grating (DSLT) in a three-dimensional heliocentric mission scenario, in which the space vehicle transfers between two assigned Keplerian orbits. Accordingly, this paper extends and generalizes the results recently obtained by the author in the context of a simplified, two-dimensional, heliocentric mission scenario. In particular, this work illustrates an analytical model of the thrust vector that can be used to study the performance of a DSLT-based spacecraft in a three-dimensional optimization context. The simplified thrust model is employed to simulate the rapid transfer in a set of heliocentric mission scenarios as a typical interplanetary transfer toward a terrestrial planet and a rendezvous with a periodic comet.
