  Saturn's moon Iapetus has an orbit in a transition region where the Laplace
surface is bending from the equator to the orbital plane of Saturn. The orbital
inclination of Iapetus to the local Laplace plane is ~8 deg, which is
unexpected, because the inclination should be ~0 if Iapetus formed from a
circumplanetary disk on the Laplace surface. It thus appears that some process
has pumped up Iapetus's inclination while leaving its eccentricity near zero
(e=0.03 at present). Here we examined the possibility that Iapetus's
inclination was excited during the early solar system instability when
encounters between Saturn and ice giants occurred. We found that the dynamical
effects of planetary encounters on Iapetus's orbit sensitively depend on the
distance of the few closest encounters. In four out of ten instability cases
studied here, the orbital perturbations were too large to be plausible. In one
case, Iapetus's orbit was practically unneffected. In the remaining five cases,
the perturbations of Iapetus's inclination were adequate to explain its present
value. In three of these cases, however, Iapetus's eccentricity was excited to
0.1-0.25, and it is not clear whether it could have been damped to its present
value (0.03) by some subsequent process (e.g., tides and dynamical friction
from captured irregular satellites do not seem to be strong enough). Our
results therefore imply that only 2 out of 10 instability cases (~20%) can
excite Iapetus's inclination to its present value (~30% of trials lead to >5
deg) while leaving its orbital eccentricity low.
