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- Does the work done in separating two masses increase their mass in accordance with e=mc^2

If I start with two, otherwise isolated, masses M and m initially together and do work to separate them then the work done, I assume, goes into the gravitational binding energy between them. Will the system of mass M and m have increased in mass due to this in accordance with e=mc^2?

I believe yes as it is broadly analogous to chemical or nuclear binding.

If I am wrong please provide some pointers in the right direction.

Thanks Andrew

PS this is not a homework question I am 70 and not formally studying it's for personal interest.

I believe yes as it is broadly analogous to chemical or nuclear binding.

If I am wrong please provide some pointers in the right direction.

Thanks Andrew

PS this is not a homework question I am 70 and not formally studying it's for personal interest.