The Sagittarius dwarf spheroidal galaxy , the closest satellite galaxy of the Milky Way , has survived for many orbits about the Galaxy .
Extant numerical calculations modeled this galaxy as a system with a centrally-concentrated mass profile , following the light , and found that it should lose more than one-half of its mass every 2–4 orbits and be completely disrupted long before now .
Apparently the Sagittarius dwarf spheroidal , and by implication other dSph galaxies , do not have a centrally-concentrated profile for their dark matter .
We develop a model in which the stars of the Sgr dwarf are embedded in a constant-density dark matter halo , representing the core of a tidally-limited system , and show that this is consistent with its survival .
We present new photometric and kinematic observations of the Sagittarius dwarf spheroidal and show these data are consistent with this explanation for the continued existence of this galaxy .
The Sagittarius dwarf is being tidally distorted and is tidally limited , but is not disrupted as yet .
The corresponding minimum total mass is 10 ^ { 9 } { M _ { \odot } } , while the central mass to visual light ratio \sim 50 in Solar units .

Our new photographic photometry allows the detection of main-sequence stars of the Sagittarius dwarf over an area of 22 ^ { \circ } \times 8 ^ { \circ } .
The Sagittarius dwarf is prolate , with axis ratios \sim 3:1:1 .
For an adopted distance of 16 \pm 2 { kpc } from the Galactic center on the opposite side of the Galaxy to the Sun , the major axis is \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } \hss } \raise 2.0 pt% \hbox { $ \mathchar 318 $ } } 9 { kpc } long and is aligned approximately normal to the plane of the Milky Way Galaxy , roughly following the coordinate line \ell = 5 ^ { \circ } .

The central velocity dispersion of giant stars which are members of the Sagittarius dwarf is 11.4 \pm 0.7 { km s ^ { -1 } } and is consistent with being constant over the face of the galaxy .
The gradient in mean line-of-sight velocity with position along the major axis , dv / db , is \sim 0 { km s ^ { -1 } } /degree in the central regions and increases in amplitude to dv / db = -3 { km s ^ { -1 } } /degree over the outermost three degrees for which we have data .
A first measurement of the proper motion of Sgr determines the component of its space velocity parallel to its major axis to be 250 \pm 90 { km s ^ { -1 } } , directed towards the Galactic Plane .
We model these kinematic data to determine the orbit of the Sagittarius dwarf .
Our best fit model has an orbital period of \mathrel { \hbox to 0.0 pt { \lower 3.0 pt \hbox { $ \mathchar 536 $ } \hss } \raise 2.0 pt% \hbox { $ \mathchar 316 $ } } 1 { Gyr } and has the Sagittarius dwarf spheroidal close to perigalacticon .
This period is shorter , by about a factor of \lower 2.15 pt \hbox { $ \buildrel > \over { \sim } $ } 10 , than the age of the bulk of its stellar population .