Binary stars are common . While only those with small separations may exchange gas with one another , even the widest binaries interact with their gaseous surroundings . Drag forces and accretion rates dictate how these systems are transformed by these interactions . We perform three-dimensional hydrodynamic simulations of Bondi-Hoyle-Lyttleton flows , in which a binary moves supersonically relative to a homogeneous medium , using the adaptive mesh refinement code FLASH . We simulate a range of values of the initial semi-major axis of the orbit relative to the gravitational focusing impact parameter of the pair . When the binary separation is less than the gravitational focusing impact parameter , the pair orbits within a shared bow shock . When the pair is wider , each object has an individual bow-shock structure . The long-term evolution of the binary is determined by the timescales for accretion , slowing of the center of mass , and orbital inspiral . We find a clear hierarchy of these timescales ; a binary ’ s center-of-mass motion is slowed over a shorter timescale than the pair inspirals or accretes . In contrast to previous analytic predictions , which assume an unperturbed background medium , we find that the timescale for orbital inspiral is proportional to the semi-major axis to the 0.19 \pm 0.01 power . This positive scaling indicates that gaseous drag forces can drive binaries either to coalescence or to the critical separation at which gravitational radiation dominates their further evolution . We discuss the implications of our results for binaries embedded in the interstellar medium , active galactic nuclei disks , and common envelope phases .