Four identical small spheres, each of mass m, are fixed at the corners of a square of side length a. The system is isolated in space far from other masses.
(a) Derive an expression, in terms of G, m, and a, for the total gravitational potential energy of the four-sphere configuration. Include interactions between all distinct pairs.
(b) Evaluate your expression numerically for m=5.0kg and a=0.10m. Express the result in joules.