Gravitational Radiation Reaction in the Binary Pulsar and the Quadrupole-Formula Controversy

The evolution of the orbit of a binary pulsar under the action of gravitational radiation reaction is calculated. No approximation is made of weak gravity inside the individual stars; the details of the orbital motion are given directly (to order $c^{-5\mathrm{}}$ and $G^3$). The calculation reveals no acceleration of the center of mass of the system, and a secular decrease of the time of return to periastron. The quantitative results agree both with the well-known "quadrupole formula" and with observations.