What astronomers observed in the Hulse-Taylor Pulsar was a decrease in the orbital period of the two neutron stars.
From general relativity, it was possible to predict, mathematically, how the period ought to change in time as the binary system emitted gravitational energy during the time the orbits of the neutron stars were being 'circularized'.
The predicted, and deceptively simple, formula for the period change, dP/dt, can be found in the excellent book by Stuart Shapiro and Saul Teukolsky Black holes, white dwarfs and neutron stars, and it looks like this:
dP/dt = -1.202 x 10^-12 M (2.8278 - M)
where M = 1.41 solar masses...the mass of one of the neutron stars determined by observation and the application of Kepler's Laws. The units are in seconds of orbit period change per second.
The result is the predicted period change is dP/dt = -2.40 x 10^-12 and the observed value is -2.30 +/- 0.22 x 10^-12 seconds per second. This implies a better than 10 percent disagreement between theory and observation, and thereby proves that gravitational radiation leakage is the simplest explanation. No one has yet found a simpler explanation in terms of tidal friction or other non-relativity processes.
Return to Dr. Odenwald's Gravity page at the Astronomy Cafe Blog.