Non-Central Forces in N-body Problems?

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In N-body problems, the net force on each body does not necessarily point to the center of mass of the system. This contrasts with 2-body systems, where forces typically direct towards the center of mass. Counterexamples exist, such as two equal charges that experience forces away from their common center of mass. Additionally, in a gravitational scenario with three equal masses, two masses close together can have a third mass far away, affecting the net forces. Thus, the behavior of forces in N-body systems can be complex and does not always align with the center of mass concept.
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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?
 
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Thanks A.T. - is there a classical counterexample?
 
0pt618 said:
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.
 
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