Can impact craters on the moon act like giant radio telescopes?
Interesting idea. I think the answer is both yes and no -- yes with a manufactured dish but no in the crater's raw state.
The Arecibo telescope sits in a natural crater, but adds a dish which has a couple of important things required by a radio dish:
- a radio-reflective surface
- a specific curvature, classically parabolic, but also shaped
- low surface roughness typically in the order of mm to µm for radio frequencies we're interested in. See http://en.wikipedia.org/wiki/Ruze%27s_Equation
- a receiver close to the reflective surface (focal length), a satellite would probably be beyond the focal point
- probably some some other things, but that's probably enough.
Edit: Added #4
Could rovers feasibly resurface a naturally nearly spherical Lunar crater to an Arecibo type telescope, by moving the Lunar soil around a bit and then burning it to a precision glassy surface by focusing Solar light on it at incredible heat? Does that sound as a possible technology this century, or is it conceptually physically just wrong? Does it make more sense to just fold out or build our own parabolic dishes from scratch over there?
Actually the Arecibo dish is spherical, not parabolic, because it's steered by moving the detector, not the dish. Reference: https://en.wikipedia.org/wiki/Arecibo_Observatory
LocalFluff -- another interesting idea, but it may be easier to just install a pre-fab surface. Have a look at Spektr-R.
A satellite couldn't be used. There are no Luna Stationary orbits. There are the Earth-Moon Lagrange points, but all are much to high, and inconveniently positioned. The receiver would be part of the telescope, just as at Arecibo. A satellite could be used as a relay, to transmit data back to Earth.