Proper Motions, Orbits, and Tidal Influences of Milky Way Dwarf Spheroidal Galaxies

We measure systemic proper motion of 52 dwarf spheroidal (dSph) satellite galaxies of the Milky Way (MW). We combine {\it Gaia} EDR3 astrometry with accurate photometry and utilize a probabilistic mixture model to determine the systemic proper motions and identify likely dSph members. For the 46 dSphs with literature line-of-sight velocities we compute orbits in both a MW and a combined MW + Large Magellanic Cloud (LMC) potential and identify likely LMC satellites. For these orbits, we Monte Carlo sample over the observational uncertainties for each dSph as well as the uncertainties in the MW and LMC potentials. We explore orbital parameters and previously used diagnostics for probing the MW tidal influence on the dSph population. We find that signatures of tidal influence by the MW are easily seen by comparing a dSph's pericenter and its average density relative to the MW at its pericenter. dSphs with large ellipticity show a preference for their orbital direction to align with their major axis even if they do not have a small pericenter. We compare the radial orbital phase of our dSph sample to subhalos in MW-like $N$-body simulations and find that the distributions are similar and that there is not an excess of satellites near their pericenter. With future {\it Gaia} data releases, we find that the orbital precision of most dSphs will be limited by uncertainties in distance and/or the MW potential rather than proper motion precision. Finally, we provide our membership lists to enable community follow-up.