  Tsiganis et al. (2005) have proposed that the current orbital architecture of
the outer solar system could have been established if it was initially compact
and Jupiter and Saturn crossed the 2:1 orbital resonance by divergent
migration. The crossing led to close encounters among the giant planets, but
the orbital eccentricities and inclinations were damped to their current values
by interactions with planetesimals. Brunini (2006) has presented widely
publicized numerical results showing that the close encounters led to the
current obliquities of the giant planets. We present a simple analytic argument
which shows that the change in the spin direction of a planet relative to an
inertial frame during an encounter between the planets is very small and that
the change in the obliquity (which is measured from the orbit normal) is due to
the change in the orbital inclination. Since the inclinations are damped by
planetesimal interactions on timescales much shorter than the timescales on
which the spins precess due to the torques from the Sun, especially for Uranus
and Neptune, the obliquities should return to small values if they are small
before the encounters. We have performed simulations using the symplectic
integrator SyMBA, modified to include spin evolution due to the torques from
the Sun and mutual planetary interactions. Our numerical results are consistent
with the analytic argument for no significant remnant obliquities.

Astrophysics