  Recent observations have shown the presence of extra-solar planets in
Galactic open stellar clusters, as in the Praesepe (M44). These systems provide
a favorable environment for planetary formation due to the high heavy-element
content exhibited by the majority of their population. The large stellar
density, and corresponding high close-encounter event rate, may induce strong
perturbations of planetary orbits with large semimajor axes. Here we present a
set of N-body simulations implementing a novel scheme to treat the tidal
effects of external stellar perturbers on planetary orbit eccentricity and
inclination. By simulating five nearby open clusters we determine the rate of
occurrence of bodies extracted from their parent stellar system by
quasi-impulsive tidal interactions. We find that the specific free-floating
planet production rate (total number of free-floating planets per unit of time,
normalized by the total number of stars) is proportional to the stellar density
of the cluster, with a constant of proportionality equal to (23 +/- 5)10^-6
pc^3 Myr^-1. For the Pleiades (M45) we predict that about 26% of stars should
have lost their planets. This raises the exciting possibility of directly
observing these wandering planets with the James Webb Space Telescope in the
NIR band. Assuming a surface temperature of the planet of 500 K, a
free-floating planet of Jupiter size inside the Pleiades would have a specific
flux @4.4 micron of approximately 400 nJy, which would lead to a very clear
detection (S/N of order 100) in only one hour of integration.
