How does one calculate total potential energy for a particle of mass m?

[Alan Grayson]

IIRC, for R2 > R1, and the potential function going as 1/r, one can integrate from R1 to R2 to get the total added PE when moving against the gravity field between those distances. But the PE is undefined if we integrate from R = 0. If this is correct, it seems that the PE for a point mass is undefined, and it's therefore impossible to equate it with the rest energy of the gravitating mass, to get a total energy for the rest mass as zero. AG

[smitra]

You have to regularize the point mass. So you replace it with an object
of finite size and density. You can take the limit of the size to zero
for constant total mass at the end of the computations.

Saibal

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[Alan Grayson]

I was thinking of something similar. One has to start with a finite mass, say with a continuous mass distribution, and spherical, and use one of those theorems, Gauss or Green, to calculate the PE from its origin, to the surface, and then infinitely outward. IIRC, Brent once explained this, but I can't recall the details. AG