I'm not sure what you're going to need to assume to solve this, but the moon in orbit around the earth isn't an inertial reference frame (it's not moving on a straight trajectory), so that special relativity would have problems if you tried to figure out reference frames. Also, distances contract in the direction you're moving, not in the direction perpendicular to it. Unless the moon and earth are getting much closer together, would you need to calculate how that distance changes? Do you have enough information to solve the problem if you just assume the Earth and moon aren't moving at all?