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We measure the variation of the escape speed of the Galaxy across a range of$\sim$ 40 kpc in Galactocentric radius. The local escape speed is found to be$521^{+46}_{-30}\,\mathrm{km\,s^{-1}}$, in good agreement with other studies.We find that this has already fallen to $379^{+34}_{-28}\,\mathrm{km\,s^{-1}}$at a radius of 50 kpc. Through measuring the escape speed and its variation, weobtain constraints on the Galactic potential as a whole. In particular, thegradient in the escape speed with radius suggests that the total mass containedwithin 50 kpc is $29^{+7}_{-5}\times10^{10}\mathrm{M}_\odot$, implying arelatively light dark halo for the Milky Way. Our method represents a novel wayof estimating the mass of the Galaxy, and has very different systematics tomore commonly used models of tracers, which are more sensitive to the centralparts of the halo velocity distributions. Using our inference on the escapespeed, we then investigate the orbits of high-speed Milky Way dwarf galaxies.For each dwarf we consider, we predict small pericenter radii and large orbitaleccentricities. This naturally explains the large observed ellipticities of twoof the dwarfs, which are likely to have been heavily disrupted as they passedthrough pericenter.

On the Run: mapping the escape speed across the Galaxy with SDSS