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Reading on wikipedia about Faddeev equations, I've come across the notion of three-body force. The article which describes this type of force doesn't give me any understanding what it is about.

My questions are: does every three-body problem have such force? Or are e.g. classical celestial three-body problems free of it? If it's not in every three-body problem, then what classes of problems do have it?

Also, does such a force violate principle of superposition for forces?

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Please do however remember the following line from the link you yourself have cited:

In general, if the behaviour of a system of more than two objects cannot be described by the two-body interactions between all possible pairs, as a first approximation, the deviation is mainly due to a three-body force.

Hence, it can be seen that, initially, when people were thinking of many-body problems, they encountered terms in the mathematical formulation which they later termed as many body forces. Incidentally, they were discovered in strong interactions and were a result of gluon mediation. In the celestial scale hence, you would need to have a similar mediating phenomena/theory to explain any physically valid three body force.

Also related: N-body forces in classical mechanics

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