Is it possible to exhaust all ore on a planet or moon?

A while back I managed to land on a class D asteroid, and divert its orbit to Kerbin's. There I used it to supply my orbital refueling station. After a while though, I received a message stating that I had exhausted all resources on the asteroid.

I now have sent missions to Eve, and have started to mine Gilly (which is basically a large, captured asteroid). Of course, I remembered what happened with the asteroid I had a Kerbin, so I started to wonder...

Is it possible to mine all available resources on Gilly?

Or on any other moon or planet, for that matter?

Solution 1:

No, it's not possible. Only asteroids have a finite amount of ore, as mentioned on the wiki.