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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 explained 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.

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  • $\begingroup$ A similar question was asked yesterday. physics.stackexchange.com/q/509916 You have to distiguish between force, energy and potential. $\endgroup$
    – JHT
    Commented Oct 25, 2019 at 17:00
  • $\begingroup$ The vectors don't have to be added up. They can be worked with separately $\endgroup$
    – R.W. Bird
    Commented Oct 25, 2019 at 17:25
  • $\begingroup$ 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 $\endgroup$
    – sheshin
    Commented Oct 25, 2019 at 17:49
  • $\begingroup$ If you can calculate the forces you can calculate the potential energy. $\endgroup$
    – Eli
    Commented Oct 25, 2019 at 18:16
  • $\begingroup$ Can you show me how to do it? $\endgroup$
    – sheshin
    Commented Oct 26, 2019 at 1:52

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Not only for 3 particle system but for any system(minimum 2 particles) following definition is valid:-

The change in potential energy of a system is defined as the negative of work done by the internal conservative forces of the system

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