Non-Central Forces in N-body Problems?

[0pt618]

For a 2-body system that is not under the influence of an external force, the forces on each body (assumed to be point particles) always point to the center of mass the 2-body system.

Does this still hold for general N-body problems, where N>2? Specifically, does the net force on each body point to the center of mass of the N-body system?

 

[A.T.]

No.

 

[0pt618]

Thanks A.T. - is there a classical counterexample?

 

[A.T.]

Thanks A.T. - is there a classical counterexample?

As posed, your assertion isn`t even true for all 2 particle systems. Two equal charges can have net forces away from the common COM, not towards it. For gravity consider 3 equal masses, two of which are very close together, the thrid one very far away.