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We determine the velocity vector of M31 with respect to the Milky Way and usethis to constrain the mass of the Local Group, based on HST proper-motionmeasurements presented in Paper I. We construct N-body models for M31 tocorrect the measurements for the contributions from stellar motions internal toM31. We also estimate the center-of-mass motion independently, using thekinematics of satellite galaxies of M31 and the Local Group. All estimates aremutually consistent, and imply a weighted average M31 heliocentric transversevelocity of (v_W,v_N) = (-125.2+/-30.8, -73.8+/-28.4) km/s. We correct for thereflex motion of the Sun using the most recent insights into the solar motionwithin the Milky Way. This implies a radial velocity of M31 with respect to theMilky Way of V_rad = -109.3+/-4.4 km/s, and a tangential velocity V_tan = 17.0km/s (<34.3 km/s at 1-sigma confidence). Hence, the velocity vector of M31 isstatistically consistent with a radial (head-on collision) orbit towards theMilky Way. We revise prior estimates for the Local Group timing mass, includingcorrections for cosmic bias and scatter. Bayesian combination with other massestimates yields M_LG = M_MW(vir) + M_M31(vir) = (3.17 +/- 0.57) x 10^12 solarmasses. The velocity and mass results imply at 95% confidence that M33 is boundto M31, consistent with expectation from observed tidal deformations.(Abridged)

The M31 Velocity Vector. II. Radial Orbit Towards the Milky Way and Implied Local Group Mass