  Dark matter pervades the Solar System, free-streaming at the halo's local
Galactic orbital velocity and density. As these objects pass through the Solar
system, they perturb gravitationally, and thus very weakly, all nearby inertial
masses. Making use of this, we propose an approach to the direct detection of
dark matter at previously inaccessible intermediate masses (1e14 -- 1e20 gm).
Such mass scales are relevant for example for dark matter made of primordial
black holes or clumped matter in a sequestered sector. If such dark matter
exists it will be unambiguously detectable through its inelastic gravitational
interaction with the proposed Laser Interferometer Space Antenna (LISA)
experiment. We demonstrate the efficacy of this approach by studying the dark
matter signal in numerical simulations of the LISA data stream. A more
conservative approach -- to detect dark matter in the differential acceleration
power spectrum -- significantly underestimates the expected rates for LISA.
Interestingly, while the space-density of 1e15 gm DM objects would be
comparable to the space-density of asteroids of similar masses, such ``light
matter'' contaminants are readily detectable in reflected Solar light, allowing
for the elimination of the major background.
