  We have computed trajectories, distances and times of closest approaches to
the Sun by stars in the Solar neighbourhood with known position, radial
velocity and proper motions. For this purpose we have used a full potential
model of the Galaxy that reproduces the local z-force, the Oort constants, the
local escape velocity, and the rotation curve of the Galaxy. From our sample we
constructed initial conditions, within observational uncertainties, with a
Monte Carlo scheme for the twelve most suspicious candidates because of their
small tangential motion. We find that the star Gliese 710 will have the closest
approach to the Sun, with a distance of approximately 0.34 pc at 1.36 Myr in
the future. We show that the effect of a flyby with the characteristics of
Gliese 710 on a 100 AU test particle disk representing the Solar system is
negligible. However, since there is a lack of 6D data for a large percentage of
stars in the Solar neighbourhood, closer approaches may exist. We calculate
parameters of passing stars that would cause noticeable effects on the Solar
disk. Regarding the birth cloud of the Sun, we performed experiments to
reproduce roughly the observed orbital parameters such as eccentricities and
inclinations of the Kuiper Belt. It is known now that in Galactic environments,
such as stellar formation regions, the stellar densities of new born stars, are
high enough to produce close encounters within 200 AU. Moreover, in these
Galactic environments, the velocity dispersion is relatively low, typically
approximately 1-3 km s-1.We find that with a velocity dispersion of
approximately 1 km s-1 and an approach distance of about 150 AU, typical of
these regions, we obtain approximately the eccentricities and inclinations seen
in the current Solar system. Simple analytical calculations of stellar
encounters effects on the Oort cloud are presented.
