  Most planetary systems are formed within stellar clusters, and these
environments can shape their properties. This paper considers scattering
encounters between solar systems and passing cluster members, and calculates
the corresponding interaction cross sections. The target solar systems are
generally assumed to have four giant planets, with a variety of starting
states, including circular orbits with the semimajor axes of our planets, a
more compact configuration, an ultra-compact state with multiple mean motion
resonances, and systems with massive planets. We then consider the effects of
varying the cluster velocity dispersion, the relative importance of binaries
versus single stars, different stellar host masses, and finite starting
eccentricities of the planetary orbits. For each state of the initial system,
we perform an ensemble of numerical scattering experiments and determine the
cross sections for eccentricity increase, inclination angle increase, planet
ejection, and capture. This paper reports results from over 2 million
individual scattering simulations. Using supporting analytic considerations,
and fitting functions to the numerical results, we find a universal formula
that gives the cross sections as a function of stellar host mass, cluster
velocity dispersion, starting planetary orbital radius, and final eccentricity.
The resulting cross sections can be used in a wide variety of applications. As
one example, we revisit constraints on the birth aggregate of our Solar System
due to dynamical scattering and find $N<10^4$ (consistent with previous
estimates).
