  The frequency of Galactic stellar encounters the Solar system experienced
depends on the local density and velocity dispersion along the orbit of the Sun
in the Milky Way galaxy. We aim at determining the effect of the radial
migration of the solar orbit on the rate of stellar encounters. As a first step
we integrate the orbit of the Sun backwards in time in an analytical potential
of the Milky Way. We use the present-day phase-space coordinates of the Sun,
according to the measured uncertainties. The resulting orbits are inserted in
an N-body simulation of the Galaxy, where the stellar velocity dispersion is
calculated at each position along the orbit of the Sun. We compute the rate of
Galactic stellar encounters by employing three different solar orbits
---migrating from the inner disk, without any substantial migration, and
migrating from the outer disk. We find that the rate for encounters within
$4\times10^5$ AU from the Sun is approximately 21, 39 and 63 Myr$^{-1}$,
respectively. The stronger encounters establish the outer limit of the
so-called parking zone, which is the region in the plane of the orbital
eccentricities and semi-major axes where the planetesimals of the Solar system
have been perturbed only by interactions with stars belonging to the Sun's
birth cluster. We estimate the outer edge of the parking zone at semi-major
axes of 250--1300 AU (the outward and inward migrating orbits reaching the
smallest and largest values, respectively), which is one order of magnitude
smaller than the determination made by Portegies Zwart & J\'ilkov\'a (2015). We
further discuss the effect of stellar encounters on the stability of the
hypothetical Planet 9.
