Caption: A diagram illustrating the solution of an astrophysical self-gravitating multi-body system (AKA n-body system) by perturbation theory.
The procedure of perturbation theory for multi-body systems is as follows:
This gives an approximate solution to the real multi-body system.
Usually, the simplication is to treat each astro-body as part of a (gravitational) two-body system (for which an exact analytic solution exists).
The astronomical perturbations make the simplified multi-body system more like the real multi-body system and improve the approximate solution.