Close encounters of a rotating star with planets in parabolic orbits of
  varying inclination and the formation of Hot Jupiters
  (abbreviated) We extend the theory of close encounters of a planet on a
parabolic orbit with a star to include the effects of tides induced on the
central rotating star. Orbits with arbitrary inclination to the stellar
rotation axis are considered. We obtain results both from an analytic treatment
and numerical one that are in satisfactory agreement. These results are applied
to the initial phase of the tidal circularisation problem. We find that both
tides induced in the star and planet can lead to a significant decrease of the
orbital semi-major axis for orbits having periastron distances smaller than 5-6
stellar radii (corresponding to periods $\sim 4-5$ days after the
circularisation has been completed) with tides in the star being much stronger
for retrograde orbits compared to prograde orbits. We use the simple Skumanich
law for the stellar rotation with its rotational period equal to one month at
the age of 5Gyr. The strength of tidal interactions is characterised by
circularisation time scale, $t_{ev}$ defined as a time scale of evolution of
the planet's semi-major axis due to tides considered as a function of orbital
period $P_{obs}$ after the process of tidal circularisation has been completed.
We find that the ratio of the initial circularisation time scales corresponding
to prograde and retrograde orbits is of order 1.5-2 for a planet of one Jupiter
mass and $P_{obs}\sim $ four days. It grows with the mass of the planet, being
of order five for a five Jupiter mass planet with the same $P_{orb}$. Thus, the
effect of stellar rotation may provide a bias in the formation of planetary
systems having planets on close orbits around their host stars, as a
consequence of planet-planet scattering, favouring systems with retrograde
orbits. The results may also be applied to the problem of tidal capture of
stars in young stellar clusters.
