Why is the gravitational potential energy of a system of multiple masses the sum of pairwise interactions?
Gravitational potential energy follows the superposition principle, where the total energy is the sum of the potential energies of all possible pairs (V = −Gm1m2r) due to the linear nature of gravitational force.
Ref: Halliday & Resnick, Fundamentals of Physics, 11th ed., Chapter 13: Gravitation.