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tokens: et al. ( 2012 ) analysis does not apply. This result is obviously related to the apparent first-infall status of many of these galaxies. Among the galaxies for which the binding energy is well behaved, the Rocha et al. ( 2012 ) relation suggests infall times of ∼7 Gyr for Tri II (also see Carlin et al. 2017 ), Segue 2, and Willman 1; ∼8 Gyr for Draco II and Tuc III; and >12 Gyr for Ret II. Ret II has a higher binding energy than any of the Via Lactea 2 subhalos included in the Rocha et al. sample. 6.5. Implications for the Mass of the Milky Way As discussed in previous sections and shown in Figure 6 , a number of the target galaxies of this study appear to be very loosely bound and may be on their first orbital passage around the Milky Way, which would be an unexpected result. I showed in Section 5 that this problem can be alleviated if the mass of the Milky Way is larger than assumed in the default galpy MWPotential2014 model. Relatively large Milky Way masses have been advocated by some authors (e.g., Boylan-Kolchin et al. 2013 ), but if the mass of the Galaxy is large, that will tend to exacerbate issues such as the missing satellite problem (Klypin et al. 1999 ; Moore et al. 1999 ) and the too big to fail problem (Boylan-Kolchin et al. 2011 , 2012 ). The alternative explanation is that many of the ultra-faint satellites are on their first orbit because they formed in a Magellanic group (D’Onghia Lake 2008 ) that is now infalling into the Milky Way for the first time (Besla et al. 2007 ; Kallivayalil et al. 2013 ). However, if many of the currently known satellites were originally located around the LMC, that also has adverse consequences for the missing satellite problem, because the number of dwarfs formed around the Milky Way would be even smaller. Improved estimates of the Milky Way’s mass based on dynamical modeling of the kinematics of the satellite population provided here and by Gaia Collaboration et al. ( 2018b ) will be valuable for attempting to resolve this dilemma. 7. Summary and Conclusions I have presented Gaia DR2-based proper motions, space velocities, and Galactic orbits for 17 ultra-faint satellites of the Milky Way. I cross-match lists of member stars that are confirmed via spectroscopy or variable star pulsations with the Gaia DR2 catalog to determine the motion of each system across the sky. Thanks to the exquisite astrometric performance of Gaia , even with as few as ∼3 member stars brighter than g = 20 per satellite, the proper motions are determined with a typical precision of ∼0.1 mas yr −1 per coordinate. At a median distance of 35 kpc, the uncertainties on the tangential velocities are therefore ∼25 km s −1 . I find good agreement with the proper-motion measurements reported by Gaia Collaboration et al. ( 2018b ) for Boötes I and Leo I, as well as with HST measurements of Leo I (Sohn et al. 2013 ) and Ω Centauri (Libralato et al. 2018 ). The tangential velocities of the sample of ultra-faint dwarfs analyzed