  The majority of stars form in star clusters and many are thought to have
planetary companions. We demonstrate that multi-planet systems are prone to
instabilities as a result of frequent stellar encounters in these star clusters
much more than single-planet systems. The cumulative effect of close and
distant encounters on these planetary systems are investigated using Monte
Carlo scattering experiments. We consider two types of planetary configurations
orbiting Sun-like stars: (i) five Jupiter-mass planets in the semi-major axis
range 1-42 AU orbiting a Solar mass star, with orbits that are initially
co-planar, circular, and separated by 10 mutual Hill radii, and (ii) the four
gas giants of our Solar system. Planets with short orbital periods are not
directly affected by encountering stars. However, secular evolution of
perturbed systems may result in the ejection of the innermost planets or in
physical collisions of the innermost planets with the host star, up to many
thousands of years after a stellar encounter. The simulations of the Solar
system-like systems indicate that Saturn, Uranus and Neptune are affected by
both direct interactions with encountering stars, as well as planet-planet
scattering. Jupiter, on the other hand, is almost only affected by direct
encounters with neighbouring stars, as its mass is too large to be
substantially perturbed by the other three planets. Our results indicate that
stellar encounters can account for the apparent scarcity of exoplanets in star
clusters, not only for those on wide-orbit that are directly affected by
stellar encounters, but also planets close to the star which can disappear long
after a stellar encounter has perturbed the planetary system.
