M giants recovered from the Two Micron All-Sky Survey ( 2MASS ) have recently been used to map the position and velocity distributions of tidal debris from the Sagittarius ( Sgr ) dwarf spheroidal galaxy entirely around the Galaxy .
We compare this data set to both test particle orbits and N-body simulations of satellite destruction run within a variety of rigid Milky Way potentials and find that the mass of the Milky Way within 50 kpc of its center should be 3.8 - 5.6 \times 10 ^ { 11 } M _ { \odot } in order for any Sgr orbit to simultaneously fit the velocity gradient in the Sgr trailing debris and the apocenter of the Sgr leading debris .
Orbital pole precession of young debris and leading debris velocities in regions corresponding to older debris provide contradictory evidence in favor of oblate/prolate Galactic halo potentials respectively , leading us to conclude that the orbit of Sgr has evolved over the past few Gyr .
In light of this discrepancy , we consider constraints from the younger portions of the debris alone within three models of the flattening of the Galactic potential ( q = 0.90/1.0/1.25 , i.e .
oblate/spherical/prolate ) in our further N-body simulations .

Based upon the velocity dispersion and width along the trailing tidal stream we estimate the current bound mass of Sgr to be M _ { Sgr } = 2 - 5 \times 10 ^ { 8 } M _ { \odot } independant of the form of the Galactic potential ; this corresponds to a range of mass to light ratios ( M / L ) _ { Sgr } = 14 - 36 ( M / L ) _ { \sun } for the Sgr core .
Models with masses in this range best fit the apocenter of leading Sgr tidal debris when they orbit with a radial period of roughly 0.85 Gyr and have periGalactica and apoGalactica of about 15 kpc and 60 kpc respectively .
These distances will scale with the assumed distance to the Sgr dwarf and the assumed depth of the Galactic potential .
The density distribution of debris along the orbit in these models is consistent with the M giant observations , and debris at all orbital phases where M giants are obviously present is younger ( i.e .
was lost more recently from the satellite ) than the typical age of a Sgr M giant star .