Where Does the Radiated Energy Come From in a Gravitational Collision?

[dtfroedge]

Presume there are two massive bodies in open space, having zero relative velocity, and having the same space ambient temperature. That is, the incoming and out-flowing black body radiation is balanced and the temperature is unchanging. Presume these bodies become gravitationally attracted, and fall together. On impact the temperature will rise, and then the excess thermal energy will be radiated away, returning to the ambient state. By both Newtonian and Relativistic mechanics, the total rest mass is equal to the sum of the rest mass of the two combined bodies. (Black Hole theory depends on it.)
The question is, from whence did the radiated energy come?

 

[Stonebridge]

From the gravitational potential they had when in space.
This was converted to kinetic energy when they started to move towards each other.
The k.e. was converted into heat in the inelastic collision, and the heat was radiated away.

 

[NeuronsAtWork]

This is certainly not my area of expertise and I am quite probably wrong, but it would seem that the kinetic energy of the bodies, built up as they fell toward each other through the force of gravity could be released as heat energy if this were considered a partially inelastic collision. It's a good question, and I'd love to be corrected on this if I'm wrong...

 

[NeuronsAtWork]

Update: Stonebridge, you beat me to it, but at least it looks as if I was thinking along the correct lines...

 

[Stonebridge]

I should have added that some of the (kinetic) energy could have been used to deform the masses when they merged; depending on how they actually did that. So that the original source was the gravitational p.e. - though it won't have all been converted into the radiated energy. There would be some losses on the way!

 

[dtfroedge]

Remember, any energy associated with the gravitational field is part of the mass, and is all accounted for after the particles are merged.

 

[russ_watters]

Remember, any energy associated with the gravitational field is part of the mass, and is all accounted for after the particles are merged.

I don't see a question in there (and it doesn't sound right anyway...)...what are you getting at?

 

[dtfroedge]

There was a quantity of energy radiated away, yet the entire e=mc^2 is still there

 

[Dale]

the total rest mass is equal to the sum of the rest mass of the two combined bodies.

Remember, any energy associated with the gravitational field is part of the mass, and is all accounted for after the particles are merged.

There was a quantity of energy radiated away, yet the entire e=mc^2 is still there

Actually, all of this is incorrect. The mass of any bound system is always less than the mass of the unbound constituents. This is called the "mass deficit" and is related to the binding energy of the system. It is really only significant for nuclear binding, but it applies to the other forces also. Your specific scenario is described in the 3rd paragraph in the Mass Deficit section of the Wikipedia article on Binding Energy: http://en.wikipedia.org/wiki/Binding_energy

 

[dtfroedge]

Actually, all of this is incorrect. The mass of any bound system is always less than the mass [/url]

DaleSpam
You're right, very good.

 

[russ_watters]

I am impatiently waiting for a point here, dtfroedge.