We measure the variation of the escape speed of the Galaxy across a range of \sim 40 { \mathrm { 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 { \mathrm { 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 { \mathrm { kpc } } is 29 ^ { +7 } _ { -5 } \times 10 ^ { 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 .