  Here, we continue this research with a detailed study of their past and
future motion during previous and next orbital periods under the perturbing
action of our Galactic environment. At all stages of our dynamical study, we
precisely propagate in time the observational uncertainties of cometary orbits.
For the first time in our calculations, we fully take into account individual
perturbations from all known stars or stellar systems that closely (less than
3.5 pc) approach the Sun during the cometary motion in the investigated time
interval of several million years. This is done by means of a direct numerical
integration of the N-body system comprising of a comet, the Sun and 90
potential stellar perturbers. We show a full review of various examples of
individual stellar action on cometary motion. We conclude that perturbations
from all known stars or stellar systems do not change the overall picture of
the past orbit evolution of long-period comets (LPCs).The future motion of them
might be seriously perturbed during the predicted close approach of Gliese 710
star but we do not observe significant energy changes. The importance of
stellar perturbations is tested on the whole sample of 108 comets investigated
by us so far and our previous results, obtained with only Galactic
perturbations included, are fully confirmed.We present how our results can be
used to discriminate between dynamically new and old near-parabolic comets and
discuss the relevance of the so-called Jupiter-Saturn barrier phenomenon.
Finally, we show how the Oort spike in the 1/a-distribution of near-parabolic
comets is built from both dynamically new and old comets. We also point out
that C/2007 W1 seems to be the first serious candidate for interstellar
provenience.
