  Evidence of exoplanets with orbits that are misaligned with the spin of the
host star may suggest that not all bound planets were born in the
protoplanetary disk of their current planetary system. Observations have shown
that free-floating Jupiter-mass objects can exceed the number of stars in our
galaxy, implying that capture scenarios may not be so rare. To address this
issue, we construct a three-dimensional simulation of a three-body scattering
between a free-floating planet and a star accompanied by a Jupiter-mass bound
planet. We distinguish between three different possible scattering outcomes,
where the free-floating planet may get captured after the interaction with the
binary, remain unbound, or "kick-out" the bound planet and replace it. The
simulation was performed for different masses of the free-floating planets and
stars, as well as different impact parameters, inclination angles and approach
velocities. The outcome statistics are used to construct an analytical
approximation of the cross section for capturing a free-floating planet by
fitting their dependence on the tested variables. The analytically approximated
cross section is used to predict the capture rate for these kinds of objects,
and to estimate that about 1\% of all stars are expected to experience a
temporary capture of a free-floating planet during their lifetime. Finally, we
propose additional physical processes that may increase the capture statistics
and whose contribution should be considered in future simulations.

Earth and Planetary Astrophysics