We present a dynamical measurement of the tangential motion of the Andromeda system, the ensemble consisting of the Andromeda Galaxy (M31) and its satellites. The system is modelled as a structure with cosmologically-motivated velocity dispersion and density profiles, and we show that our method works well when tested using the most massive substructures in high-resolution Lambda Cold Dark Matter simulations. Applied to the sample of 40 currently-known galaxies of this system, we find a value for the transverse velocity of 164.4 +/- 61.8 km/s (v_East = -111.5 +/- 70.2 km/s and v_North = 99.4 +/- 60.0 km/s), significantly higher than previous estimates of the proper motion of M31 itself. This result has significant implications on estimates of the mass of the Local Group, as well as on its past and future history.
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