Autonomous slewing of a spacecraft about a desired axis using reaction wheels permits a maximum slew rate without wheel saturation even with one wheel failure. The slew is carried out if the total angular momentum of the spacecraft is less than a momentum storage threshold determined from reaction wheel availability. The momentum threshold may be found as the radius of a sphere inscribed in a polyhedron in momentum space, the polyhedron based on the maximum single wheel capacity and the geometry of the reaction wheel system as well as the reaction wheel availability. The momentum available for the slew is determined from the total angular momentum and the availability of each reaction wheel. The slew rate magnitude and slew direction are based on the available momentum. The available momentum calculation may include factors to accommodate noise and model uncertainties, to prevent the slew from placing the total angular momentum into a state overly limiting the rate of a subsequent slew, and to avoid numerical problems.