Gaia EDR3 proper motions of Milky Way dwarfs I: 3D Motions and Orbits
  Based on Gaia Early Data Release 3 (EDR3), we estimate the proper motions for
46 dwarf spheroidal galaxies (dSphs) of the Milky Way. The uncertainties in
proper motions, determined by combining both statistical and systematic errors,
are smaller by a factor 2.5, when compared with Gaia Data Release 2. We have
derived orbits in four Milky Way potential models that are consistent with the
MW rotation curve, with total mass ranging from $2.8\times10^{11}$ $M_{\odot}$
to $15\times10^{11}$ $M_{\odot}$. Although the type of orbit (ellipse or
hyperbola) are very dependent on the potential model, the pericenter values are
firmly determined, largely independent of the adopted MW mass model. By
analyzing the orbital phases, we found that the dSphs are highly concentrated
close to their pericenter, rather than to their apocenter as expected from
Kepler's law. This may challenge the fact that most dSphs are Milky Way
satellites, or alternatively indicates an unexpected large number of
undiscovered dSphs lying very close to their apocenters. Between half and two
thirds of the satellites have orbital poles that indicate them to orbit along
the Vast Polar Structure (VPOS), with the vast majority of these co-orbiting in
a common direction also shared by the Magellanic Clouds, which is indicative of
a real structure of dSphs.
