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Compact binaries are within the reach of gravitational and electromagneticwave detectors, and are important for our understanding of astrophysicalenvironments and the composition of compact objects. There is a vast body ofwork devoted to the evolution of such binaries in background media, such as incommon-envelope evolution, accretion disks and dark matter mini-spikes. Here,we explore further gravitationally-bound binaries evolving within anenvironment. We show that dissipative effects such as gravitational drag andaccretion impart a momentum to the center of mass of asymmetric binaries. Wenumerically evolve the binaries in a Newtonian setup and show that, dependingon the medium density, the center of mass can accelerate to high speeds -- insome cases $300\, {\rm km/s}$ or more -- during inspiral, with potentiallyobservable signatures. Our numerical results are fully consistent with an\textit{analytical} result for the CM evolution at first order in the mediumdensity.

Drifting through the medium: kicks and self-propulsion of binaries within accretion disks and other environments