Optimal aeroassisted orbital interception

Optimal trajectories are found for the interception of a target in circular, low-Earth orbit, by a vehicle which is initially in a higher orbit. The interceptor vehicle can use both conventional rocket propulsion and, if optimal or necessary. aerodynamic forces to change its orbit. The problem is solved using a direct method, collocation with nonlinear programming, in which the continuous optimal control problem is converted into a discrete problem. Both minimum-time and minimum-fuel trajectories are found. The sensitivity of the optimal trajectories to atmospheric heating-rate constraints is determined. An interesting result is that some minimum-time trajectories enter the atmosphere and use aerodynamic forces for orbit change even when there is sufficient propellant available to accomplish the interception ballistically.