# Binary Black Hole Inspiral

**Classical Mechanics**Level 4

Two black holes in a mutually orbiting binary system both have mass \(M\) and orbit at radius \(R\) to their center of rotation. What is magnitude of the rate of change of their radius (the rate at which they inspiral due to energy loss to gravitational radiation) in the Newtonian approximation?

Note: the power radiated in gravitational waves by an inspiraling binary is: \[P = -\frac25 \frac{G^4 M^5}{c^5 R^5}.\]