Inside MOND: Testing Gravity with Stellar Accelerations

We quantify the differences between stellar accelerations in disk galaxies formed in a MONDian universe relative to galaxies with the identical baryonic matter distributions and a fitted cold dark matter halo. In a Milky Way-like galaxy the maximal transverse acceleration is $\mathcal{O}({10}^{-9})$ arcseconds per year per decade, well beyond even the most optimistic extrapolations of current capabilities. Conversely, the maximum difference in the line-of-sight acceleration is $\mathcal{O}(1)$ centimetre per second per decade at solar distances from the galactic centre. This level of precision is within reach of plausible future instruments.