Optimal Spacecraft Orbit Design for Inertial Alignment with Ground Telescopes

This paper addresses the orbit design and translational control problems for a new class of astrophysics missions that require regular periods of accurate alignment between a ground-based sensor, a space-based instrument, and an inertial target such as a star or galaxy. These problems must be solved to enable novel missions such as the Earth-Orbiting Starshade, which uses a 100m starshade with extremely large ground telescopes to image earth-like exoplanets with an effective inner working angle of only 50 milliarcseconds. The orbit design and control problems for these missions are challenging because the spacecraft must perform autonomous accurate formation-flying with a telescope that is not in orbit while satisfying multiple requirements on the optical and orbit configurations. To meet this need, this paper includes four contributions to the state-of-the-art. First, analytical constraints on key design variables are derived to guarantee the existence of regular observation opportunities that satisfy all mission requirements. Second, the delta-v cost of the station-keeping maneuvers required to maintain alignment between the sensor, instrument, and target is derived in closed-form as a function of the location of the target, the latitude of the sensor, and the start time and duration of the observation. This derivation provides simple design rules to minimize the delta-v cost of observations. Also, it is demonstrated that chemical propulsion is required to counteract the relative acceleration between the sensor and instrument for scientifically useful observation durations. Third, a novel four-impulse maneuver scheme is proposed to minimize the delta-v cost of reconfiguring the orbit to enable observations of multiple targets. It is found that the proposed maneuver scheme can reduce the total delta-v required for a large reconfiguration by up to 44 % compared to simply rotating the orbit plane. Finally, it is demonstrated that a distributed mission architecture can reduce the propellant required to observe each target by several hundred kilograms. Overall, this paper provides a novel orbit design that enables new science missions that require real-time cooperation between ground-based sensors and space-based instruments, providing sensing capabilities that are infeasible with any other mission architecture.