Gravitational radiation reaction in the binary pulsar and the quadrupole-formula controversy

The orbital motion of a binary pulsar system is investigated analytically. The two-body problem is reduced to a one-body problem, which is solved while terms of the order c to the -5th are disregarded; then the full problem is solved to the order G cubed by the variation of arbitrary constants, an aproach based on earlier work by Bel et al. (1981), Damour and Deruelle (1981), and Damour (1982, 1983). The isolated Schwarzschild mass' of each compact object is employed, rather than the integral of a Newtonian density, and the derivation does not involve quadrupole moment, energy flux at infinity, balance equations, energy, angular momentum, or radiation-damping force. No acceleration of the system center of mass is found, and the quantitative calculations of the secular decrease in the periastron-return time are shown to agree with the 'quadrupole formula' and with the secular acceleration of the orbital motion of PSR 1913+16 observed by Taylor et al. (1979).