  This work provides, at lower order, general analytical solutions for the
orbital separation, merging time, and orbital frequency of binary systems
emitting gravitational waves while being submitted to mass variations. Specific
features, depending on the exponent of the mass derivative, are investigated in
details. Two phenomenologically interesting cases are explicitly considered :
i) binaries formed by two light primordial black holes submitted to Hawking
evaporation and ii) bodies driven by a Bondi accretion of phantom dark energy.
It is shown that three different regimes arise, including an intricate
non-monotonic behaviour of the system. We study subtle imprints that could be
associated with those phenomena. A careful analysis of the conditions of
validity of the different hypotheses performed is finally carried out.
