  Recent work in the literature has studied the restricted three-body problem
within the framework of effective-field-theory models of gravity. This paper
extends such a program by considering the full three-body problem, when the
Newtonian potential is replaced by a more general central potential which
depends on the mutual separations of the three bodies. The general form of the
equations of motion is written down, and they are studied when the interaction
potential reduces to the quantum-corrected central potential considered
recently in the literature. A recursive algorithm is found for solving the
associated variational equations, which describe small departures from given
periodic solutions of the equations of motion. Our scheme involves repeated
application of a 2 x 2 matrix of first-order linear differential operators.
