Gravitational radiation damping and the three-body problem

A model of three-body motion is developed which includes the effects of gravitational radiation reaction. The radiation reaction due to the emission of gravitational waves is the only post-Newtonian effect that is included here. For simplicity, all of the motion is taken to be planar. Two of the masses are viewed as a binary system, and the third mass, whose motion will be a fixed orbit around the centre-of-mass of the binary system, is viewed as a perturbation. This model aims to describe the motion of a relativistic binary pulsar that is perturbed by a third mass. Numerical integration of this simplified model reveals that, given the right initial conditions and parameters, one can see resonances. These ( m , n ) resonances are defined by the resonance condition,   mω =2 n Ω  , where m and n are relatively prime integers, and ω and Ω are the angular frequencies of the binary orbit and third mass orbit (around the centre-of-mass of the binary), respectively. The resonance condition consequently fixes a value for the semimajor axis of the binary orbit for the duration of the resonance; therefore the binary energy remains constant on average, while its angular momentum changes during the resonance.