Precomputation and interpolation of the matrizant for starshade slewing

Operation of a space-based telescope and starshade pair promises to enable direct imaging of exoplanets. After selecting an orbit in Sun-Earth space for the telescope, trajectory design for the starshade relative to the telescope becomes important. Maximizing science yield under constraints on propellant and time requires large-scale schedule optimization of which candidate stars are observed and at what time. One of the most basic steps in such a mission design optimization is evaluating an objective function for a proposed mission schedule. Propellant use during the slewing of the starshade to obscure a star for observation is one vital component of such an objective function. We propose a novel method to quickly compute estimates of the propellant cost for slewing a starshade between observation positions. Existing methods for computation of relative transfer trajectories either require costly numerical integration of a high-dimensional system of variational equations at run time, or rely on dimension reduction and interpolation that may give coarse estimates of propellant use. We propose the precomputation of state transition matrix solutions to the variational equations at intervals along the trajectory of the telescope. With only a few matrix multiplications as well as linear interpolation or a much shortened numerical integration, we can accurately calculate a linear approximation of the transfer.