# Formula for gravitational energy

#### wolram

Gold Member
i have looked on the net for a formula that would give me an idea
of how much gravitational energy verses other energies is given
of when a massive body is destroyed, is there such a formula?
or is it just that the mass of the body is converted into energy by
E=M^2 and the gravitational energy that, that the origonal body
exhibited?

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#### HallsofIvy

Homework Helper
I have no idea at all what this question means!

What do you mean by "gravitational energy"? Is there any reason to think that the energy contained in a body can be allocated to "gravity", "electricity", etc?

"or is it just that the mass of the body is converted into energy by
E=M^2" Typo here: E= M c^2.

Yes, there is not differentiation into "types" of energy.

#### Ambitwistor

Well, there's Newtonian gravitational potential energy (binding energy), which for a sphere of mass M and radius r is equal to,

U = 3/5 GM/r

This is the energy needed to separate all the matter in the Earth to infinity.

But this isn't the energy "released" by blowing up the Earth, it's the energy needed to blow up the Earth (so that the pieces will never come back together again).

#### wolram

Gold Member
not very well posed and typos also, maybe if i ask,
if two bodies collied and are totaly destroyed, gravitational
radiation is given out, "hopefully", how would the total amount of this radiation
be measured? i hope this makes more sence.

#### NateTG

Homework Helper
Originally posted by wolram
not very well posed and typos also, maybe if i ask,
if two bodies collied and are totaly destroyed, gravitational
radiation is given out, "hopefully", how would the total amount of this radiation
be measured? i hope this makes more sence.
Huh? If two collide, they are not totally destroyed. If you look at collisions, matter is rearranged, not destroyed.

If you're referring to a matter/antimatter reaction, you should still get gravitation from the cosmic rays that are formed from the colision.

#### Ambitwistor

Colliding bodies can emit gravitational radiation, but this effect is not really significant for anything less dense than a neutron star.

#### wolram

Gold Member
significant or not the LIGO project is attempting to detect GRAVITATIONAL
RADIATION, so how are the parameters set, i would WAG that less
than the origonal bodies "potential gravitational energy"
is converted into gravitational radiation, maybe 10% or less,
so has anyone who can understand my ramblings any idea of how
many "ERGs or what ever" of gravitational energy is release
when a mass is converted to energy?

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