# Special & General Relativity Questions and Answers

## What does the equation look like that shows how gravitational radiation is lost from the binary pulsar system?

What astronomers observed in the Hulse-Taylor Pulsar was a 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 formula for the period change, P-dot, 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:

P-dot = -1.202 x 10^-12 M2 (2.8278 - M2)where M2 = 1.41 solar masses...the mass of one of the neutron stars determined by observation and the application of Kepler's Laws. The result is the predicted period change is p-dot = -2.40 x 10^-12 and the observed value is -2.30 +/- 0.22 x 10^-12. This implies a better than 10 percent disagreement between theory and observation, and thereby proves that gravitational radiation leakage is the simplest explanation.

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All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the NASA Astronomy Cafe, part of the NASA Education and Public Outreach program.