  The determination of the birth radius of the Sun is important to understand
the evolution and consequent disruption of the Sun's birth cluster in the
Galaxy. Motivated by this fact, we study the motion of the Sun in the Milky Way
during the last 4.6 Gyr in order to find its birth radius. We carried out orbit
integrations backward in time using an analytical model of the Galaxy which
includes the contribution of spiral arms and a central bar. We took into
account the uncertainty in the parameters of the Milky Way potential as well as
the uncertainty in the present day position and velocity of the Sun. We find
that in general the Sun has not migrated from its birth place to its current
position in the Galaxy (R_\odot). However, significant radial migration of the
Sun is possible when: 1) The 2:1 Outer Lindblad resonance of the bar is
separated from the corrotation resonance of spiral arms by a distance ~1 kpc.
2) When these two resonances are at the same Galactocentric position and
further than the solar radius. In both cases the migration of the Sun is from
outer regions of the Galactic disk to R_\odot, placing the Sun's birth radius
at around 11 kpc. We find that in general it is unlikely that the Sun has
migrated significantly from the inner regions of the Galactic disk to R_\odot.
