In the quadrupole approximation of General Relativity in the weak-field limit, a time-varying quadrupole moment generates gravitational radiation. Binary orbits are one of the main mechanisms for producing gravitational waves and are the main sources and backgrounds for gravitational-wave detectors across the multi-band spectrum. In this Paper, we introduce additional contributions to the gravitational radiation from close binaries that arise from time-varying masses along with those produced by orbital motion. We derive phase-dependent formulae for these effects in the quadrupolar limit for binary point masses, which reduce to the formulae that Peters and Mathews (1963) derived when the mass of each component is taken to be constant. We show that gravitational radiation from mass variation can be orders of magnitude greater than that of orbital motion.
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