We analyse the orbital kinematics of the Milky Way (MW) satellite system utilizing the latest systemic proper motions for 38 satellites based on data from Gaia Data Release 2. Combining these data with distance and line-of-sight velocity measurements from the literature, we use a likelihood method to model the velocity anisotropy, $beta$, as a function of Galactocentric distance and compare the MW satellite system with those of simulated MW-mass haloes from the APOSTLE and Auriga simulation suites. The anisotropy profile for the MW satellite system increases from $betasim -2$ at $rsim20$ kpc to $betasim 0.5$ at $rsim200$ kpc, indicating that satellites closer to the Galactic centre have tangentially-biased motions while those farther out have radially-biased motions. The motions of satellites around APOSTLE host galaxies are nearly isotropic at all radii, while the $beta(r)$ profiles for satellite systems in the Auriga suite, whose host galaxies are substantially more massive in baryons than those in APOSTLE, are more consistent with that of the MW satellite system. This shape of the $beta(r)$ profile may be attributed to the central stellar disc preferentially destroying satellites on radial orbits, or intrinsic processes from the formation of the Milky Way system.
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