By observing gravitational radiation from a binary black hole merger, the LIGO collaboration has simultaneously opened a new window on the universe and achieved the first direct detection of gravitational waves. Here this discovery is analyzed using concepts from introductory physics. Drawing upon Newtonian mechanics, dimensional considerations, and analogies between gravitational and electromagnetic waves, we are able to explain the principal features of LIGO's data and make order of magnitude estimates of key parameters of the event by inspection of the data. Our estimates of the black hole masses, the distance to the event, the initial separation of the pair, and the stupendous total amount of energy radiated are all in good agreement with the best fit values of these parameters obtained by the LIGO-VIRGO collaboration.

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17.
For the duration of the in-spiral, it is acceptable to treat the black holes as particles of fixed mass and the only relevant gravitational potential energy is the mutual potential energy of the two black holes, not their individual self-energy.
18.
The reader will notice that the total energy is one half the potential energy. This is an example of the virial theorem in classical mechanics, but students of introductory physics can derive the result by adding up all the contributions to the orbital energy. The potential energy is obviously −GMm/(r + R). The kinetic energy is given by (1/2)Iω2. Making use of Eq. (1) for ω and Eq. (4) for the moment of inertia leads quickly to the result quoted in Eq. (2) for the total energy.
19.

By way of comparison, electromagnetic radiation is predominantly produced by the changing electric or magnetic dipole moments. The quadrupole component matters only if the dipole moments of the radiating system vanish by symmetry. See Problem 5 in  Appendix B for more on electromagnetic dipole radiation.

20.

To obtain Eq. (11) first write Eq. (10) in the form f11/3df=3απ8/3(MG)5/3(1/c5)dt and integrate both sides. Take the lower limit on the time integral 0 and the upper limit as τ. The corresponding limits on the f integral are f1 and f2, respectively, yielding Eq. (11).

21.
By so doing we are approximating the total energy radiated by the energy radiated during the in-spiral process alone. Although the peak power is radiated during the merger, inspection of Fig. 1 suggests that the power radiated during in-spiral is indeed comparable to the total power radiated during the entire process, thereby justifying the estimate in Eq. (18).
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