  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, we
obtain constraints on the Galactic potential as a whole. In particular, the
gradient in the escape speed with radius suggests that the total mass contained
within 50 kpc is $29^{+7}_{-5}\times10^{10}\mathrm{M}_\odot$, implying a
relatively light dark halo for the Milky Way. Our method represents a novel way
of estimating the mass of the Galaxy, and has very different systematics to
more commonly used models of tracers, which are more sensitive to the central
parts of the halo velocity distributions. Using our inference on the escape
speed, we then investigate the orbits of high-speed Milky Way dwarf galaxies.
For each dwarf we consider, we predict small pericenter radii and large orbital
eccentricities. This naturally explains the large observed ellipticities of two
of the dwarfs, which are likely to have been heavily disrupted as they passed
through pericenter.
