# Gravitational potential energy of multi particle system

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.

• A similar question was asked yesterday. physics.stackexchange.com/questions/509916/… You have to distiguish between force, energy and potential. – fwgb Oct 25 '19 at 17:00
• The vectors don't have to be added up. They can be worked with separately – R.W. Bird Oct 25 '19 at 17:25
• In a given example, we can only choose one path along which the third mass is brought from infinity and the two forces need not lie along that path leading to components – sheshin Oct 25 '19 at 17:49
• If you can calculate the forces you can calculate the potential energy. – Eli Oct 25 '19 at 18:16
• Can you show me how to do it? – sheshin Oct 26 '19 at 1:52