  The Nice model of the dynamical instability and migration of the giant
planets can explain many properties of the present Solar System, and can be
used to constrain its early architecture. In the jumping-Jupiter version of the
Nice model, required from the terrestrial planet constraint and dynamical
structure of the asteroid belt, Jupiter has encounters with an ice giant. Here
we study the survival of the Galilean satellites in the jumping-Jupiter model.
This is an important concern because the ice-giant encounters, if deep enough,
could dynamically perturb the orbits of the Galilean satellites, and lead to
implausible results. We performed numerical integrations where we tracked the
effect of planetary encounters on the Galilean moons. We considered three
instability cases from Nesvorny & Morbidelli (2012) that differed in the number
and distribution of encounters. We found that in one case, where the number of
close encounters was relatively small, the Galilean satellite orbits were not
significantly affected. In the other two, the orbital eccentricities of all
moons were excited by encounters, Callisto's semimajor axis changed, and, in a
large fraction of trials, the Laplace resonance of the inner three moons was
disrupted. The subsequent evolution by tides damps eccentricities and can
recapture the moons in the Laplace resonance. A more important constraint is
represented by the orbital inclinations of the moons, which can be excited
during the encounters and not appreciably damped by tides. We find that one
instability case taken from Nesvorny & Morbidelli (2012) clearly fails this
constraint. This shows how the regular satellites of Jupiter can be used to set
limits on the properties of encounters in the jumping-Jupiter model, and help
us to better understand how the early Solar System evolved.
