"Skinny Milky Way, Please", says Sagittarius
  Motivated by recent observations of the Sagittarius stream, we devise a rapid
algorithm to generate faithful representations of the centroids of stellar
tidal streams formed in a disruption of a progenitor of an arbitrary mass in an
arbitrary potential. Our method works by releasing swarms of test particles at
the Lagrange points around the satellite and subsequently evolving them in a
combined potential of the host and the progenitor. We stress that the action of
the progenitor's gravity is crucial to making streams that look almost
indistinguishable from the N-body realizations, as indeed ours do. The method
is tested on mock stream data in three different Milky Way potentials with
increasing complexity, and is shown to deliver unbiased inference on the
Galactic mass distribution out to large radii. When applied to the observations
of the Sagittarius stream, our model gives a natural explanation of the
stream's apocentric distances and the differential orbital precession. We,
therefore, provide a new independent measurement of the Galactic mass
distribution beyond 50 kpc. The Sagittarius stream model favours a light Milky
Way with the mass 4.1 +/- 0.4 x 10^11 M_sun at 100 kpc, which can be
extrapolated to 5.6 +/- 1.2 x 10^11 M_sun at 200 kpc. Such a low mass for the
Milky Way Galaxy is in good agreement with estimates from the kinematics of
halo stars and from the satellite galaxies (once Leo I is removed from the
sample). It entirely removes the "Too Big To Fail Problem".
