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We present GaiaHub, a publicly available tool that combines $Gaia$measurements with $Hubble$ $Space$ $Telescope$ ($HST$) archival images toderive proper motions (PMs). It increases the scientific impact of bothobservatories beyond their individual capabilities. $Gaia$ provides PMs acrossthe whole sky, but the limited mirror size and time baseline restrict the bestPM performance to relatively bright stars. $HST$ can measure accurate PMs formuch fainter stars over a small field, but this requires two epochs ofobservation which are not always available. GaiaHub yields considerablyimproved PM accuracy compared to $Gaia$-only measurements, especially for faintsources $(G \gtrsim 18)$, requiring only a single epoch of $HST$ data observedmore than $\sim 7$ years ago (before 2012). This provides considerablescientific value especially for dynamical studies of stellar systems orstructures in and beyond the Milky Way (MW) halo, for which the member starsare generally faint. To illustrate the capabilities and demonstrate theaccuracy of GaiaHub, we apply it to samples of MW globular clusters (GCs) andclassical dwarf spheroidal (dSph) satellite galaxies. This allows us, e.g., tomeasure the velocity dispersions in the plane of the sky for objects out to andbeyond $\sim 100$ kpc. We find, on average, mild radial velocity anisotropy inGCs, consistent with existing results for more nearby samples. We observe acorrelation between the internal kinematics of the clusters and theirellipticity, with more isotropic clusters being, on average, more round. Ourresults also support previous findings that Draco and Sculptor dSph galaxiesappear to be radially anisotropic systems.

GaiaHub: A method for combining data from the Gaia and Hubble space telescopes to derive improved proper motions for faint stars