I Need help with some calculations with gravitational waves

[Meerio]

I have some questions about the first discovery paper that was released about gravitational waves, especially some of the maths.

How did they:
1. Calculate the masses of the black holes that merged
2. Calculate the energy radiated away in gravitational waves
3. Calculate how far away the event happened

(I assume the third can be calculated with a formula that involves amplitude, but I am yet to find the right formula's for any of these)

Sorry if this is easily solvible but I couldn't find the answers myself.

Paper: https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.116.061102

 

[Jonathan Scott]

I think this is probably how it was done:
1. As mentioned in the paper, the frequency and rate of change of frequency determine the "chirp mass" which gives the basic mass scale. Numeric modelling based on General Relativity with varying parameters is used to recreate the shape of the wave form in figure 2 to give the likely individual masses.
2. The radiated energy is estimated using General Relativity from a model of the merger given the identified masses.
3. The amplitude of the signal is compared with the theoretical amplitude at a given distance for that amount of energy to establish the approximate distance.

 

[Meerio]

Thank you very much if anyone knows whether this is true or not please confirm!

 

[snorkack]

What is the angle between the orbital plane of the binary hole, and the direction to Earth?

 

[Jonathan Scott]

There seems to be a lot more detail in a later paper "Properties of the Binary Black Hole Merger GW150914" here:
https://dcc.ligo.org/public/0122/P1500218/014/PhysRevLett.116.241102.pdf