Reachable Domain for Spacecraft with a Single Impulse

This paper analyzes the reachable domain for spacecraft with a single fixed-magnitude impulse, and overapproximation of the reachable domain is provided for cases involving spacial impulse. A low impulse is assumed, implying elliptical trajectories and a bounded reachable domain. An equation is developed for the trajectory, with no restriction on the eccentricity of the initial elliptical orbit. A method is given to determine both the envelope of the ellipsoids of revolution containing the trajectories and the envelope of the planes containing the trajectories, with the intersection of these two envelopes found to be the upper bound on the reachable domain. The reachable domain is given for three scenarios for different missions, with several examples given to demonstrate the efficiency of this method.