Gravitational radiation damping and the three-body problem

Abstract

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 center-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, $m\omega=2n\Omega$, where $m$ and $n$ are relatively prime integers and $\omega$ and $\Omega$ are the angular frequencies of the binary orbit and third mass orbit, 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 the average while its angular momentum changes during the resonance.