If two masses come togther, what is the resultant mass?

[RobertsMrtn]

Supposing we have two objects of masses m1 and m2 repeated by a large distance and sufficiently distant from any other masses or gravitational fields.

The masses are not moving relative to each other initially.
The masses will eventually move together by their mutual gravitational attraction to form another mass which we will call m3.

What will be the mass of m3?

The reader may initially reply m1+m2.

However there is a problem here. The masses will have kinetic energy when they collide which will be released as heat or radiation.

Where does this energy come from?

According to the laws of conservation of mass / energy and mass / energy equivalence, will the resultant mass m3 be less than m1+m2? Will the energy released come from the resultant mass according to e=mc^2 or e=m (if we put c=1)?

 

[justwild]

If the masses have been kept apart at an environment such that no other physical interaction except the mutual gravitational interaction between the masses exists...then...it follows that the masses are having a finite potential energy...And this potential energy is the source of kinetic energy...which eventually the source of heat and other radiations and also the sound...

So in accordance with the law of conservation of mass and energy, m3 is equal to m1+m2

It appears that you have messed up the theory of relativity and the gravitation...

 

[xAxis]

Since you want to include all effects, then I guess the best method would be this: as both objects are initialy at rest, calculate the energy E = (m1 + m2)c^2 + Ep. where Ep is potential energy of the system.
Then after collision measure the energy radiated as heat + deformation.
The rest energy content then convert to mass.

 

[RobertsMrtn]

potential energy

To say that a mass m1 of a distance d from another mass m2 has potential energy was always the way it was taught in my physics class. However this seems a bit of a cop out.
If a mass is created somewhere in the universe, what is its potential energy? You would have to conclude that this will depend on the values an positions of all other mass in the universe.

 

[HallsofIvy]

One of the things that you should have learned is that potential energy is always "relative" a given "0" point. I can talk about the potential energy of an object at the top of a cliff relative to the base of the cliff (mgh where m is the mass of the object and h is the height of the cliff) or relative to the top of the cliff (mg(0)= 0). That is, we can always add or subtract a constant from potential energy without changing the physical situation. Yes, potential energy is "relative" to the positions of all other objects but you do not need to know them to assign a value to potential energy.