Dark matter comprises the bulk of the matter in the Universe, but its particle nature and cosmological origin remain mysterious. Knowledge of the dark matter density distribution in the Milky Way Galaxy is crucial both to our understanding of the standard cosmological model and for grounding direct and indirect searches for the particles comprising dark matter. Current measurements of Galactic dark matter content rely on model assumptions to infer the forces acting upon stars from the distribution of observed velocities. Here, we propose to apply the precision radial velocity method, optimized in recent years for exoplanet astronomy, to measure the change in the velocity of stars over time, thereby providing a direct probe of the local gravitational potential in the Galaxy. Using numerical simulations, we develop a realistic strategy to observe the differential accelerations of stars in our Galactic neighborhood with next-generation telescopes, at the level of 10-8 cm /s2 . Our simulations show that detecting accelerations at this level with an ensemble of 103 stars requires the effect of stellar noise on radial velocity measurements to be reduced to <10 cm /s . The measured stellar accelerations may then be used to extract the local dark matter density and morphological parameters of the density profile.
