  Models of the dynamical evolution of the early solar system following the
dispersal of the gaseous protoplanetary disk have been widely successful in
reconstructing the current orbital configuration of the giant planets.
Statistically, some of the most successful dynamical evolution simulations have
initially included a hypothetical fifth giant planet, of ice giant mass, which
gets ejected by a gas giant during the early solar system's proposed
instability phase. We investigate the likelihood of an ice giant ejection event
by either Jupiter or Saturn through constraints imposed by the current orbits
of their wide-separation regular satellites Callisto and Iapetus respectively.
We show that planetary encounters that are sufficient to eject an ice giant,
often provide excessive perturbations to the orbits of Callisto and Iapetus
making it difficult to reconcile a planet ejection event with the current orbit
of either satellite. Quantitatively, we compute the likelihood of reconciling a
regular Jovian satellite orbit with the current orbit of Callisto following an
ice giant ejection by Jupiter of ~ 42% and conclude that such a large
likelihood supports the hypothesis of a fifth giant planet's existence. A
similar calculation for Iapetus reveals that it is much more difficult for
Saturn to have ejected an ice giant and reconcile a Kronian satellite orbit
with that of Iapetus (likelihood ~ 1%), although uncertainties regarding the
formation of Iapetus, on its unusual orbit, complicates the interpretation of
this result.
