The Hill Sphere is the region of gravitational dominance of a body in orbit around second body. Inside the Hill Sphere, an object can stably orbit one body; outside of the Hill Sphere, an object can escape from orbit. For example, the Earth can hold on to an object orbiting within its Hill Sphere but beyond that, the object would escape and go into its own orbit around the Sun (perhaps some day coming back to visit the Earth in some unfortunate way...). Calculate the radius of the Hill Sphere associated with the Earth. Express your answer in both in units of AU and Earth-Moon distance.