The 3D motions of stars in small galaxies beyond our own are minute and yet they are crucial for our understanding of the nature of gravity and dark matter. Even for the dwarf galaxy Sculptor which is one of the best studied systems and inferred to be strongly dark matter dominated, there are conflicting reports on its mean motion around the Milky Way and the 3D internal motions of its stars have never been measured. Here we report, based on data from the Gaia space mission and the Hubble Space Telescope, a new precise measurement of Sculptors mean proper motion. From this we deduce that Sculptor is currently at its closest approach to the Milky Way and moving on an elongated high-inclination orbit that takes it much farther away than previously thought. For the first time we are also able to measure the internal motions of stars in Sculptor. We find $sigma_{R}=11.5 pm 4.3$ km/s and $sigma_{T}=8.5pm3.2$ km/s along the projected radial and tangential directions, implying that the stars in our sample move preferentially on radial orbits as quantified by the anisotropy parameter, which we find to be $betasim 0.86^{+0.12}_{-0.83}$ at a location beyond the core radius. Taken at face value such a high radial anisotropy requires abandoning conventional models for the mass distribution in Sculptor. Our sample is dominated by metal-rich stars and for these we find $beta^{MR} sim 0.95^{+0.04}_{-0.27}$, a value consistent with multi-component models where Sculptor is embedded in a cuspy dark halo as expected for cold dark matter.
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