  At least 10-15% of nearby sun-like stars have known Jupiter-mass planets. In
contrast, very few planets are found in mature open and globular clusters such
as the Hyades and 47 Tuc. We explore here the possibility that this dichotomy
is due to the post-formation disruption of planetary systems associated with
the stellar encounters in long-lived clusters. One supporting piece of evidence
for this scenario is the discovery of freely floating low-mass objects in star
forming regions. We use two independent numerical approaches, a hybrid Monte
Carlo and a direct $N$-body method, to simulate the impact of the encounters.
We show that the results of numerical simulations are in reasonable agreement
with analytical determinations in the adiabatic and impulsive limits. They
indicate that distant stellar encounters generally do not significantly modify
the compact and nearly circular orbits. However, moderately close stellar
encounters, which are likely to occur in dense clusters, can excite planets'
orbital eccentricity and induce dynamical instability in systems which are
closely packed with multiple planets. We compute effective cross sections for
the dissolution of planetary systems and show that, for all initial
eccentricities, dissolution occurs on time scales which are longer than the
dispersion of small stellar associations, but shorter than the age of typical
open and globular clusters. Although it is much more difficult to disrupt
short-period planets, close encounters can excite modest eccentricity among
them, such that subsequent tidal dissipation leads to orbital decay, tidal
inflation, and even disruption of the close-in planets.
