Source of Gravitational Energy

[poverlord]

I have been thinking a bit about gravity in the classical Newtonian sense. So we know that the gravitational potential energy is inversely proportial to the distance that an object is from the object it is being attracted to. Thus if we form spheres of equal distance from a certain object we can assign to each sphere a total energy proportional to its distance from the object because we will be essentially multiplying a function of order 1/r with one of order r^2. This means that the potential energy on a sphere increases as one reaches infinity. It is obvious then that the gravitational field has a nearly infinite supply of potential energy. My question is, where does all this energy come from? Does Einstein's theory account for this?

 

[tiny-tim]

welcome to pf!

hi poverlord! welcome to pf!

you're confusing gravitational potential with gravitational potential energy

gravitational potential (GP) is potential energy (PE) per charge …

ie if a charge of q is at a GP of 1/r, then its PE is q/r

you're suggesting that the total GP for a sphere of area 4πr² would be 4πr² times 1/r, = 4πr, which -> to ∞ as r -> ∞

but that sort-of assumes you have an infinite charge distributed over the whole sphere!

 

[poverlord]

Thanks for the reply. If I understood you correctly, you mean that in order for there to be energy on a sphere, we need to have charges on that sphere otherwise we will have nothing to speak of. I guess there must be some confusion somewhere. What I actually meant by this is that if we consider the gravitational field itself and try to measure its energy. I think that this energy within the gravitational field itself is measured by the potential energy that it imparts on the object that is placed at a certain distance from the object generating that field. Of course, the gravitational field must have energy since it has the capacity to move stuff about. And we know that its capacity to move things about can be fully measured by the potential energy it imparts on an object. This is how I concluded that the energy on a "sphere" increases as the sphere becomes larger. Thus you should not interpret the word "sphere" as referring to a real sphere but to a spherical slice of the gravitational field itself and the amount of energy that sphere can impart on particles that can be present upon it.

 

[tiny-tim]

… if we consider the gravitational field itself and try to measure its energy. I think that this energy within the gravitational field itself is measured by the potential energy that it imparts on the object that is placed at a certain distance from the object generating that field.

no, just as the energy density of the electric field E is proportional to the field squared (force-per-charge squared, E²), so the (Newtonian) energy density of the gravitational field can be defined as proportional to the field squared (force-per-mass squared) …

in other words: the energy density of the gravitational field is proportional to 1/r⁴, whose integral over all space is finite!

(for some details, see http://en.wikipedia.org/wiki/Gravitational_energy#Newtonian_mechanics")

 

[poverlord]

Thank you for the clarification.