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tokens: ( 1963 ) with the origin located at the barycenter. There is an implicit perturbing force that induces the following accelerationwhich is implicit in the isotropic variation of the mass-losing body. This has been derived in several previous works (Hadjidemetriou 1963 , 1966a , 1966b ; Verhulst 1975 ). If the mass variation is anisotropic, i.e., either from nonconservative mass exchange and asymmetric ejecta, then the equation of motion will have an explicit perturbing force (e.g., Dosopoulou Kalogera 2016a , 2016b ). The orbital evolution can be described as an osculating orbit, which is the Keplerian orbit the binary would follow if the perturbation ceased immediately. The full set of equations for the time evolution of the osculating orbital elements from the isotropically varying mass are (e.g., Hadjidemetriou 1963 ) where the specific angular momentum is conserved, i.e., the quantity is a constant of the motion. Since there is no net force in the direction perpendicular to the orbital plane, , and the orbital motion thus remains coplanar. The mass variation causes the argument of periapsis to precess at a rate (see Equation 3 (c)). 3. Quadrupole Gravitational Radiation For eccentric Keplerian orbits, the orbital separation r between the binary masses obeysThe components of the mass quadrupole tensor I jk for an eccentric binary are where θ = ν + ω , which simplifies to θ = ν if the precession of the argument of periapsis is taken to be negligible. We can choose the initial θ to begin where ω = 0. For isotropic wind mass loss, the periapsis distance is constant, so . When including gravitational radiation reaction, the periapsis distance will indeed decrease, though one can take on timescales less than the mass-loss timescale when the GW coalescence timescale is much longer than the mass-loss timescale. The third time derivatives of the mass-quadrupole tensor components are If the periapsis precession is taken to be negligible, , then the first two terms of Equation 6 simplify to the canonical PM expressions. The additional terms in Equation 6 contain time derivatives of the masses of the binary, which may also be thought of as time derivatives of the binary’s chirp mass . Gravitational radiation carries away the orbital energy and angular momentum of the binary at the following rates where c is the speed of light and is the reduced (trace-free) quadrupole moment tensor . If we take the orbit to be circular, then the GW luminosity simplifies towhere the positive terms in Equation ( 8 ) correspond to GW energy loss from the orbit and the negative terms correspond to GW energy gain in the orbit. From the strain tensor in the transverse-traceless gauge,where is the luminosity distance to the source, the strain amplitude for a circular binary iswhere Ω is the angular frequency of the binary, . In the transverse-traceless gauge, the plus and cross polarizations of the strain are and . From Equation ( 10 ), we can define the following parameters