Envelopes of Spacecraft Trajectories with a Single Impulse

This paper analyzes reachable domains of spacecraft using a single impulsive maneuver. In particular, compact expressions are obtained of the envelopes of spacecraft trajectories in closed form, in both cases of either radial or tangential impulse. Suitable bounds are enforced on the magnitude of the velocity variation to obtain an elliptic transfer trajectory after the maneuver with a pericenter radius greater than the primary body’s radius. Three different cases are investigated: (1) the impulse point is fixed and the velocity variation may be varied; (2) a fixed impulse magnitude and free maneuver point; (3) both free impulse point and magnitude. Finally, some mission scenarios are analyzed to show the effectiveness of the proposed analytical method.