There is no general solution to the problem of determining the motion of three or more bodies moving under their mutual gravitation. Here we consider a restricted case of the three-body problem in which the mass of one of the bodies, P, is much smaller than that of the other two masses, which are called the primaries.

In this case we neglect the effect of P on the primaries which therefore move in known fixed orbits. The body P moves in the time dependent, gravitational field of the primaries.