Advanced space transportation systems, such as the National Aerospace Plane or an Orbital Transfer Vehicle, have atmospheric maneuvering capabilities. For such vehicles the use of aeroassisted orbital transfer from a high Earth orbit to a low Earth orbit, with unpowered flight in the atmosphere, has the potential for significant fuel savings compared to exoatmospheric Hohmann transfer. However, to exploit the fuel savings that can be achieved by using the Earths atmosphere to reduce the vehicles energy, a guidance law is required, and it must be able to handle large unpredictable fluctuations in atmospheric density, on the order of ${pm}$50% relative to the 1962 US Standard Atmosphere. In this paper aeroassisted orbital transfer is considered as a differential game, with Nature controlling the atmosphere density to yield a worst case (min-max fuel required) atmosphere, from which the guaranteed playable set boundary are achieved. Inside the playable set, it is guaranteed that the vehicle achieves the optimal atmospheric exit condition for the minimum fuel consumption regardless of the atmospheric density variations.