  Motivated by the report of a possible new planetary member of the Solar
System, this work calculates cross sections for interactions between passing
stars and this proposed Planet Nine. Evidence for the new planet is provided by
the orbital alignment of Kuiper Belt objects, and other Solar System
properties, which suggest a Neptune-mass object on an eccentric orbit with
semimajor axis $a_9\approx400-1500$ AU. With such a wide orbit, Planet Nine has
a large interaction cross section, and is susceptible to disruption by passing
stars. Using a large ensemble of numerical simulations (several million), and
Monte Carlo sampling, we calculate the cross sections for different classes of
orbit-altering events: [A] scattering the planet into its proposed orbit from a
smaller orbit, [B] ejecting it from the Solar System from its current orbit,
[C] capturing the planet from another system, and [D] capturing a free-floating
planet. Results are presented for a range of orbital elements with planetary
mass $m_9=10M_{earth}$. Removing Planet Nine from the Solar System is the most
likely outcome. Specifically, we obtain ejection cross sections
$\sigma_{int}\sim5\times10^6$ AU$^2$ ($5\times10^4$ AU$^2$) for environments
corresponding to the birth cluster (field). With these cross sections, Planet
Nine is likely to be ejected if the Sun resides within its birth cluster longer
than $\Delta{t} \gtrsim 100$ Myr. The probability of ejecting Planet Nine due
to passing field stars is $\lesssim 3\%$ over the age of the Sun. Probabilities
for producing the inferred Planet Nine orbit are low $(\lesssim 5\%)$.
