A 2MASS All-Sky View of the Sagittarius Dwarf Galaxy: IV. Modeling the Sagittarius Tidal Tails

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 x 10^11 Msun 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. 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 x 10^8 Msun 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.