Consider a thin uniform spherical layer of mass M and radius R. The potential energy of gravitational interaction of matter forming this shell is

$-\frac{1}{2} \frac{GM^2}{R}$

Let us consider the shell when a mass m is already piled on it by the agency.

If V is the potential on the shell, then

$V=-\frac{Gm}{R}$

To add a mass dm further we have

dW = Vdm

$\Rightarrow dW=-\frac{Gm}{R} dm $

$\Rightarrow W=-\frac{G}{R} \int\limits_0^{M} mdm$

$\Rightarrow W=-\frac{1}{2} \frac{GM^2}{R}$

= Potential Energy of Interaction.