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Gravitational Waves on the Back of an Envelope


Schutz,  Bernard F.
Astrophysical Relativity, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;
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Schutz, B. F. (1984). Gravitational Waves on the Back of an Envelope. American Journal of Physics, 52(5), 412-419. doi:10.1119/1.13627.

Using only Newtonian gravity and a little special relativity we calculate most of the important effects of gravitational radiation, with results very close to the predictions of full general relativity theory. Used with care, this approach gives helpful back-of-the-envelope derivations of important equations and estimates, and it can help to teach gravitational wave phenomena to undergraduates and others not expert in general relativity. We use it to derive the following: the quadrupole approximation for the amplitude h of gravitational waves; a simple upper bound on h in terms of the Newtonian gravitational field of the source; the energy flux in the waves, the luminosity of the source (called the ``quadrupole formula''), and the radiation reaction in the source; order-of-magnitude estimates for radiation from supernovae and binary star systems; and the rate of change of the orbital period of the binary pulsar system. Where our simple results differ from those of general relativity we quote the relativistic ones as well. We finish with a derivation of the principles of detecting gravitational waves, and we discuss the principal types of detectors under construction and the major limitations on their sensitivity.