For two particle system, the gravitational potential energy is given by

U = - GMm/r

For a three particle system, it is the sum of potential energies of all the possible pairs. This is expalined in terms of energy, but i am not able to understand in terms of work done by forces. When i try to bring in a third particle, the forces being vectors add up in vectors and the result is no where equal to he original one.

Explain for 3 or more particle system in terms of work done by forces or refer to any source which i can refer to.

Thank you.