The use of aerodynamic forces to assist in certain orbital transfers can greatly reduce the fuel consumption as compared with corresponding all-propulsive transfers. Therefore, in seeking minimum fuel trajectories, aeroassisted transfers need to be investigated. A review of the current literature indicates that such problems have been solved almost exclusively via optimal control theory formulations that result in continuously varying control laws. The use of a piecewise-constant strategy allows the controls to vary to a degree necessary to affect changes in the desired state dependent parameters while simplifying the optimization process. In the process of searching for a tool to produce numerical results, the current research investigates three candidate methods of solving the parameter optimization problem of minimum fuel aeroassisted orbital transfer with piecewise-constant controls. A method based on implicitly integrating the state trajectory is chosen over methods which analytically and explicitly integrate the state trajectory. The implicit method offers improved performance over the explicit method while presenting a more correct solution than the analytic method. The analytic method is shown to suffer from approximations that lead to undesirable solutions. Analytic expressions for the characteristic velocities of Hohmann and idealized aeroassisted transfers are presented and compared. For a large number of transfers from high Earth orbit to low Earth orbit, the aeroassisted mode requires less fuel. Numerical results are presented for minimum fuel transfer from geosynchronous Earth orbit to low earth orbit for a variety of control strategies. The piecewise-constant strategies are seen to provide solutions which are comparable to those found via optimal control theory. / Master of Science