Right, but this dipole solution will neglect the perturbation of the third body on whatever is creating the dipole. Fair enough, because we expect the effect t

Right, but this dipole solution will neglect the perturbation of the third body on whatever is creating the dipole. Fair enough, because we expect the effect to be tiny. But still you would have to unpack that dipole approximation to figure out if this perturbation will slowly change it in ways that do something significant in the long run.