Question 3 (6 points).
Consider two inspiraling black holes with mass 10$M_\odot$, where $M_\odot$ is the mass of the sun. Assume
the system is located at the centre of our galaxy; let's call this distance to the black holes $r_{gal}$.
Assume that the initial separation is 100 $r_s$, where $r_s$ is the Schwarzschild radius. In the weak field
approximation, compute the gravitational wave amplitude $h(t)$ at the LIGO site as a function of
time, making use of the quadrupole radiation formula. Assume that we are seeing the system face
on. Then, using the formula for the radiated power derived in class, compute the gradual decay of
the orbital radius $r(t)$ (using Newtonian physics to relate the energy density radiated to the change
in the orbital radius). The approximations cease to be valid once $r(t)$ approaches $r_s$, so stop the
calculation before that point.
