  Are dwarf spheroidal galaxies dark matter dominated? We present N-body
simulations of the interaction between the Milky Way and its closest companion,
the Sagittarius dwarf spheroidal galaxy, constrained by new kinematic, distance
and surface density observations detailed in a companion paper. It is shown
that there is no possible self-consistent solution to the present existence of
the Sagittarius dwarf if its distribution of luminous matter traces the
underlying distribution of mass. The luminous component of the dwarf galaxy
must therefore be shielded within a small dark matter halo. Though at present
we are unable to construct a fully self-consistent model that includes both the
stellar and dark matter components, it is shown numerically that it is possible
that a pure dark matter model, approximating the dark matter halo deduced for
the Sagittarius dwarf from analytical arguments, may indeed survive the
Galactic tides.
  The orbit of the Sagittarius dwarf galaxy around the Milky Way is considered,
taking into account the perturbative effects of the Magellanic Clouds. It is
shown that at the present time, the orbital period must be short, ~ 0.7 Gyr;
the initial orbital period for a 10^9 Solar mass model will have been ~ 1 Gyr.
It is found that a close encounter with the Magellanic Clouds may have occured,
though the chances of such an interaction affecting the orbit of the
Sagittarius dwarf galaxy is negligible.

Astrophysics