  The recent discovery of free-floating planets and their theoretical
interpretation as celestial bodies, either condensed independently or ejected
from parent stars in tight clusters, introduced an intriguing possibility.
Namely, that some exoplanets are not condensed from the protoplanetary disk of
their parent star. In this novel scenario a free-floating planet interacts with
an already existing planetary system, created in a tight cluster, and is
captured as a new planet. In the present work we study this interaction process
by integrating trajectories of planet-sized bodies, which encounter a binary
system consisting of a Jupiter-sized planet revolving around a Sun-like star.
To simplify the problem we assume coplanar orbits for the bound and the
free-floating planet and an initially parabolic orbit for the free-floating
planet. By calculating the uncertainty exponent, a quantity that measures the
dependence of the final state of the system on small changes of the initial
conditions, we show that the interaction process is a fractal classical
scattering. The uncertainty exponent is in the range (0.2-0.3) and is a
decreasing function of time. In this way we see that the statistical approach
we follow to tackle the problem is justified. The possible final outcomes of
this interaction are only four, namely flyby, planet exchange, capture or
disruption. We give the probability of each outcome as a function of the
incoming planet's mass. We find that the probability of exchange or capture (in
prograde as well as retrograde orbits and for very long times) is
non-negligible, a fact that might explain the possible future observations of
planetary systems with orbits that are either retrograde or tight and highly
eccentric.
