[ChaseW (OP)]

I know if you compress a spring it will weigh more because of the stored elastic potential energy.  But how does this work for potential gravitational energy.  If I push a rock up a hill will it get heaver?  And for that matter will the earth also get heaver?  I would imagine this increase in weight would be insignificant but would it become relevant for launching things like rockets?  And now for the really hard question. If that is all true how much potential gravitational energy was created in the big bang and does this energy account for a significant portion of the “weight” we experience today?

[Mr. Scientist]

Gravitational energy will have an influence in a real sense. It is the potential gravity which gives rise to actual gravitational interactions.


Potential energy is the energy ready to make us by actual action of physical systems.

[lightarrow]

does potential gravitational energy have "weight"?
Yes, but it's negative:

http://www.negative-mass.com/
<<Calculation of the Mass Density of the Gravitational Field
...
Gravitational Case
...
Thus, the mass density of the gravitational field is:

M = -g²/8πGc²>>

[Mr. Scientist]

That last equation is derived from General Relativity, is it not?

[Kryptid]

I was a bit surprised when I read something related to this in Scientific American (or some similar magazine. I can't remember which one for sure). It said something to the effect that if you were to have two rocks a certain distance apart, and weighed them, that the weight you would get would be different than if those two rocks were closer together when you weighed them. I don't remember if they said if it would be more or less. I guess that goes back to gravitational potential energy.

[lightarrow]

That last equation is derived from General Relativity, is it not?

In that document that equation is derived with newtonian mechanics.