ABSTRACT
General Relativity predicts that the emission of gravitational waves affects the orbital motion of compact binary systems: the orbit shrinks and the orbital period decreases in time. This chapter shows how the orbital period, the orbital distance, and the Keplerian frequency of a binary system composed of two compact objects change in time, due to the emission of gravitational waves. This expression has to be considered as an average over several wavelengths. Since the emission frequency is twice the orbital frequency, one wavelength is emitted in half a period; thus averaging over several wavelengths corresponds to averaging in time over several periods. On September 14th, 2015 the interferometric antennas of the experiment LIGO, located in Livingston and in Hanford detected the gravitational wave signal emitted in the coalescence of two black holes.
