  The main aim of this paper is to report two new detections of tidal debris in
the northern stream of the Sagittarius dwarf galaxy located at 45 arcdeg and 55
arcdeg from the center of galaxy. Our observational approach is based on deep
color-magnitude diagrams, that provides accurate distances, surface brightness
and the properties of stellar population of the studied region of this tidal
stream. The derived distances for these tidal debris wraps are 45 kpc and 54
kpc respectively.We also confirm these detections with numerical simulations of
the Sagittarius dwarf plus the Milky Way. The model reproduces the present
position and velocity of the Sagittarius main body and presents a long tidal
stream formed by tidal interaction with the Milky Way potential. This model is
also in good agreement with the available observations of the Sagittarius tidal
stream. We also present a method for estimating the shape of the Milky Way halo
potential using numerical simulations. From our simulations we obtain an
oblateness of the Milky Way dark halo potential of 0.85, using the current
database of distances and radial velocities of the Sagittarius tidal stream.
The color-magnitude diagram of the apocenter of Sagittarius shows that this
region of the stream shares the complex star formation history observed in the
main body of the galaxy. We present the first evidence for a gradient in the
stellar population along the stream, possibly correlated with its different
pericenter passages. (abridged)
