  Recent studies of solar system formation suggest that the solar system's
giant planets formed and migrated in the protoplanetary disk to reach resonant
orbits with all planets inside 15 AU from the Sun. After the gas disk's
dispersal, Uranus and Neptune were likely scattered by gas giants, and
approached their current orbits while dispersing the transplanetary disk of
planetesimals, whose remains survived to this time in the region known as the
Kuiper belt. Here we performed N-body integrations of the scattering phase
between giant planets in an attempt to determine which initial states are
plausible. We found that the dynamical simulations starting with a resonant
system of four giant planets have a low success rate in matching the present
orbits of giant planets, and various other constraints (e.g., survival of the
terrestrial planets). The dynamical evolution is typically too violent, if
Jupiter and Saturn start in the 3:2 resonance, and leads to final systems with
fewer than four planets. Several initial states stand out in that they show a
relatively large likelihood of success in matching the constraints. Some of the
statistically best results were obtained when assuming that the solar system
initially had five giant planets and one ice giant, with the mass comparable to
that of Uranus and Neptune, was ejected to interstellar space by Jupiter. This
possibility appears to be conceivable in view of the recent discovery of a
large number free-floating planets in interstellar space, which indicates that
planet ejection should be common.
