  We study the evolution of possible progenitors of Sgr dSph}using several
numerical N-body simulations of different dwarf spheroidal galaxies both with
and without dark matter, as they orbit the Milky Way. The barionic and dark
components of the dwarfs were made obeying a Plummer and NFW potentials of one
million particles respectively. The Milky Way was modeled like a tree-component
rigid potential and the simulations were performed using a modified Gadget-2
code. We found that none of the simulated galaxies without dark matter
reproduced the physical properties observed in Sgr dSph, suggesting that, at
the beginning of its evolution, Sgr dSph might have been immersed in a dark
matter halo.
  The simulations of progenitors immersed in dark matter halos suggest that Sgr
dSph at its beginning might have been an extended system, i.e. its Plummer
radius could have had a value approximated to 1.2 kpc or higher; furthermore,
this galaxy could have been immersed in a dark halo with a mass higher than
10^8 solar masses. These results are important for the construction of a model
of the formation of Sgr dSph.
