It works well enough for bodies in close proximity (and by close, I mean in the way that we're close to the sun, or something), but I think it falls apart in the face of general relativity because it means information is being passed from one body to another at a speed well exceeding the speed of light.
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Thats exactly right. Einstein defined equal times in spacetime through the synchronization of clocks at different locations via a pulse of light. The fact that you can't pass information any faster than the speed of light is an interesting side effect. Since equal times are defined around the time it takes a light pulse to go from one location to another, by sending information faster than the speed of light, you would be send it back in time (effectively time travel), which is impossible.
To use the sun example, if we did not continue rotating around the sun for 8 minutes, we would know the sun was gone before the light reaching us from it disappeared.
When considering this law in the context of quantum mechanics, things can get interesting. For example, the phenomenon of quantum entanglement is often misunderstood. It says that you can have two particles whose states will always be the same. Quantum mechanics says this will be true even if the particles are separated by a great distance (a phenomenon often called rather inappropriately quantum teleportation in popular magazines). Does this mean that I can move information faster than the speed of light, because if I change the state of a particle here, then an entangled one far away will reflect that change immediately? Nope. Heisenberg says that when I go to look at that entangled particle, it's state will simultaneously decompose with such probabilities that I didn't learn any information at all.
Cool stuff.
This also leads me to believe that gravitrons are not transferred between molecules to cause gravity. I would say that they are a more permanent feature of the atom. That would mean that their proximity to each other woudl cause gravity.
Personally, I'm satisfied with this explanation, because it's sufficient to model anything we want to. Physicists, though, have too much time on their hands...they are asking the question, how does one particle "know" that it is close to another particle and it is attracted to it? Which is a stupid question IMO.