Gravitational waves on the back of an envelope, Bernhard F. Schutz, Am. J. Phys. 52(5), May 1984
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 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 (called the "quadrupole formula"); and the the radiation reaction in the source; order-of-magnitude estimates for radiation from supernovae and binary star systems; and the rate of the orbit of the binary pulsar system. Where our simple results differ from those of general relativity we quote the relativistic ones as well. We finish our derivation of the principles of detecting gravitational waves, and we discuss the principle types of detectors under construction and a major limitations on their sensitivity.