  We use a N--body/hydrodynamic simulation to forecast the future encounter
between the Milky Way and the Andromeda galaxies, given current observational
constraints on their relative distance, relative velocity, and masses. Allowing
for a comparable amount of diffuse mass to fill the volume of the Local Group,
we find that the two galaxies are likely to collide in a few billion years -
within the Sun's lifetime. During the the interaction, there is a chance that
the Sun will be pulled away from its present orbital radius and reside in an
extended tidal tail. The likelihood for this outcome increases as the merger
progresses, and there is a remote possibility that our Sun will be more tightly
bound to Andromeda than to the Milky Way before the final merger. Eventually,
after the merger has completed, the Sun is most likely to be scattered to the
outer halo and reside at much larger radii (>30 kpc). The density profiles of
the stars, gas and dark matter in the merger product resemble those of
elliptical galaxies. Our Local Group model therefore provides a prototype
progenitor of late--forming elliptical galaxies.
