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The second data release from the Gaia mission (DR2) provides a comprehensiveand unprecedented picture of the motions of astronomical sources in the planeof the sky, extending from the solar neighborhood to the outer reaches of theMilky Way. I present proper motion measurements based on Gaia DR2 for 17ultra-faint dwarf galaxies within 100 kpc of the Milky Way. I compile thespectroscopically-confirmed member stars in each dwarf bright enough for Gaiaastrometry from the literature, producing member samples ranging from 2 starsin Triangulum II to 68 stars in Bootes I. From the spectroscopic membercatalogs I estimate the proper motion of each system. I find good agreementwith the proper motions derived by the Gaia collaboration for Bootes I and LeoI. The tangential velocities for 14 of the 17 dwarfs are determined to betterthan 50 km/s, more than doubling the sample of such measurements for Milky Waysatellite galaxies. The orbital pericenters are well-constrained, with a medianvalue of 38 kpc. Only one satellite, Tucana III, is on an orbit passing within15 kpc of the Galactic center, suggesting that the remaining ultra-faint dwarfsare unlikely to have experienced severe tidal stripping. As a group, theultra-faint dwarfs are on high-velocity, eccentric, retrograde trajectories,with nearly all of them having space motions exceeding 370 km/s. In a low-mass(M_vir = 0.8 x 10^12 M_sun) Milky Way potential, eight out of the 17 galaxieslack well-defined apocenters and appear likely to be on their first infall,indicating that the Milky Way mass may be larger than previously estimated orthat many of the ultra-faint dwarfs are associated with the Magellanic Clouds.The median eccentricity of the ultra-faint dwarf orbits is 0.79, similar to thevalues seen in numerical simulations, but distinct from the rounder orbits ofthe more luminous dwarf spheroidals.

Gaia Proper Motions and Orbits of the Ultra-Faint Milky Way Satellites