Period Shift in Hulse-Taylor Binaries

Classical Mechanics Level pending

Suppose an inspiraling black hole binary system is at radius \(R_0\) at time \(t=0\), and that the radius of the binary changes as:

\[\frac{dR}{dt} = -\frac{\kappa}{R^3}\]

for some constant \(\kappa\). What is the period shift in the rotation of the binary as a function of time, noting that the frequency of rotation in a Hulse-Taylor binary is: \[\Omega = \left(\frac{GM}{4R^3}\right)^{1/2}?\]

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