# 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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