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Consider a system with a star and many planets. A non-interacting solar substitute system will have the star gravitational field as an external potential of quasi-planets. The quasi-planets are moving so they possess kinetic energy and are affected by the external potential and also the (average) inter-quasi-planet interactions. The many-body effect need to be accounted for in a known additional potential. As this last interaction is not explicitly known, approximations are needed.
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