The formula for gravitational potential energy is just mgh (mass times gravitational acceleration times height), and g is just GM/r^2, so the potential energy of one black hole in the other's gravitational field would be GMm/r, which would be the same for the other, so the total gravitational potential energy would be twice that.
Also, the schwarzschild radius of a black hole is about 3km per solar mass (2e30 kg).
Which means that before their event horizons touch the two black holes should be separated by a distance of at least 65.1 km.
So, 2 * G * 14.2 * 7.5 * (2e30kg)^2 / 65.1 km is...
8.73e47 joules
divide by c^2:
9.7e30 kg or 4.86 solar mass
So the system actually had nearly 5 solar masses of gravitational potential energy in it, some of which was radiated away as gravitational waves.
You're just calculating how much kinetic energy the black holes had when they collided. This energy goes into the spin of the final black hole. The energy for the gravitational waves comes from loss of mass of the final black hole.
The formula for gravitational potential energy is just mgh (mass times gravitational acceleration times height), and g is just GM/r^2, so the potential energy of one black hole in the other's gravitational field would be GMm/r, which would be the same for the other, so the total gravitational potential energy would be twice that.
Also, the schwarzschild radius of a black hole is about 3km per solar mass (2e30 kg).
Which means that before their event horizons touch the two black holes should be separated by a distance of at least 65.1 km.
So, 2 * G * 14.2 * 7.5 * (2e30kg)^2 / 65.1 km is...
8.73e47 joules
divide by c^2:
9.7e30 kg or 4.86 solar mass
So the system actually had nearly 5 solar masses of gravitational potential energy in it, some of which was radiated away as gravitational waves.