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We determine the velocity vector of M31 with respect to the Milky Way and use this to constrain the mass of the Local Group, based on HST proper-motion measurements presented in Paper I. We construct N-body models for M31 to correct the measurements for the contributions from stellar motions internal to M31. We also estimate the center-of-mass motion independently, using the kinematics of satellite galaxies of M31 and the Local Group. All estimates are mutually consistent, and imply a weighted average M31 heliocentric transverse velocity of (vW, vN) = (-125. 2+/-30. 8, -73. 8+/-28. 4) km/s. We correct for the reflex motion of the Sun using the most recent insights into the solar motion within the Milky Way. This implies a radial velocity of M31 with respect to the Milky Way of Vᵣad = -109. 3+/-4. 4 km/s, and a tangential velocity Vₜan = 17. 0 km/s (<34. 3 km/s at 1-sigma confidence). Hence, the velocity vector of M31 is statistically consistent with a radial (head-on collision) orbit towards the Milky Way. We revise prior estimates for the Local Group timing mass, including corrections for cosmic bias and scatter. Bayesian combination with other mass estimates yields MLG = MMW (vir) + MM31 (vir) = (3. 17 +/- 0. 57) x 10¹2 solar masses. The velocity and mass results imply at 95% confidence that M33 is bound to M31, consistent with expectation from observed tidal deformations. (Abridged)
Marel et al. (Fri,) studied this question.