I was thinking about how a compressed spring weighs more than the same spring uncompressed, and it got me wondering about the earth and moon system. Basically, if you separate the two and weigh them individually, the sum is not going to weigh as much as if you weighed them as a system because of the potential energy bound in the gravitational field. Well, this potential energy has mass too, right? Which means if we want to calculate completely how the earth and moon interact, we have to take a third mass into consideration. However, this third mass (I'll just call it the field) interacts itself with the earth and moon, and this interaction is itself another potential (or simply modifies the field from what we assumed it was)! It seems to me this recursive process goes unto infinity, so you can't really calculate the interacting system directly -- you have to iterate and converge onto the correct solution. Is this right? Or am I way off base?