The M31 Velocity Vector. III. Future Milky Way-M31-M33 Orbital
  Evolution, Merging, and Fate of the Sun
  We study the future orbital evolution and merging of the MW-M31-M33 system,
using a combination of collisionless N-body simulations and semi-analytic orbit
integrations. Monte-Carlo simulations are used to explore the consequences of
varying the initial phase-space and mass parameters within their observational
uncertainties. The observed M31 transverse velocity implies that the MW and M31
will merge t = 5.86 (+1.61-0.72) Gyr from now, after a first pericenter at t =
3.87 (+0.42-0.32) Gyr. M31 may (probability p=41%) make a direct hit with the
MW (defined here as a first-pericenter distance less than 25 kpc). Most likely,
the MW and M31 will merge first, with M33 settling onto an orbit around them.
Alternatively, M33 may make a direct hit with the MW first (p=9%), or M33 may
get ejected from the Local Group (p=7%). The MW-M31 merger remnant will
resemble an elliptical galaxy. The Sun will most likely (p=85%) end up at
larger radius from the center of the MW-M31 merger remnant than its current
distance from the MW center, possibly further than 50 kpc (p=10%). The Sun may
(p=20%) at some time in the next 10 Gyr find itself moving through M33 (within
10 kpc), but while dynamically still bound to the MW-M31 merger remnant. The
arrival and possible collision of M31 (and possibly M33) with the MW is the
next major cosmic event affecting the environment of our Sun and solar system
that can be predicted with some certainty. (Abridged)
