High precision spectrographs can enable not only the discovery of exoplanets, but can also provide a fundamental measurement in Galactic dynamics. Over about ten year baselines, the expected change in the line-of-sight velocity due to the Galaxys gravitational field for stars at $sim$ kpc scale distances above the Galactic mid-plane is $sim$ few - 10 cm/s, and may be detectable by the current generation of high precision spectrographs. Here, we provide theoretical expectations for this measurement based on both static models of the Milky Way and isolated Milky Way simulations, as well from controlled dynamical simulations of the Milky Way interacting with dwarf galaxies. We simulate a population synthesis model to analyze the contribution of planets and binaries to the Galactic acceleration signal. We find that while low-mass, long-period planetary companions are a contaminant to the Galactic acceleration signal, their contribution is very small. Our analysis of $sim$ ten years of data from the LCES HIRES/Keck precision radial velocity (RV) survey shows that slopes of the RV curves of standard RV stars agree with expectations of the local Galactic acceleration near the Sun within the errors, and that the error in the slope scales inversely as the square root of the number of observations. Thus, we demonstrate that a survey of stars with low intrinsic stellar jitter at kpc distances above the Galactic mid-plane for realistic sample sizes can enable a direct determination of the dark matter density.
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