We present a comparison of semianalytic models of the phase-space structure of tidal debris with measurements of average distances, velocities, and surface densities of stars associated with the Sagittarius dwarf galaxy, compiled from all observations reported since its discovery in 1994. We find that several interesting features in the data can be explained by these models. The properties of stars about ±10°–15° away from the center of Sgr—in particular, the orientation of material perpendicular to Sgr's orbit and the kink in the velocity gradient—are consistent with those expected for unbound material stripped during the most recent pericentric passage ~50 Myr ago. The break in the slope of the surface density seen by Mateo, Olszewski, & Morrison at b ~ -35° can be understood as marking the end of this material. However, the detections beyond this point are unlikely to represent debris in a trailing streamer, torn from Sgr during the immediately preceding passage ~0.7 Gyr ago, as the surface density of this streamer would be too low compared with observations in these regions. The low-b detections are more plausibly explained by a leading streamer of material that was lost more that 1 Gyr ago and has wrapped all the way around the Galaxy to intercept the line of sight. The distance and velocity measurements at b = -40° reported by Majewski et al. in a companion paper also support this hypothesis. We determine debris models with these properties on orbits that are consistent with the currently known positions and velocities of Sgr in Galactic potentials with halo components that have circular velocities vcirc = 140–200 km s-1. In all cases, the orbits oscillate between ~12 and ~40 kpc from the Galactic center with radial time periods of 0.55–0.75 Gyr. The best match to the data is obtained in models where Sgr currently has a mass of ~109 M☉ and has orbited the Galaxy for at least the last 1 Gyr, during which time it has reduced its mass by a factor of 2–3, or luminosity by an amount equivalent to ~10% of the total luminosity of the Galactic halo. These numbers suggest that Sgr is rapidly disrupting and unlikely to survive beyond a few more pericentric passages. These conclusions are only tentative, because they rely heavily on the less certain measurements of debris properties far from the center of Sgr. However, they demonstrate the immense potential for using debris to determine Sgr's dynamical history in great detail.
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