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 \dot { N } _ { o } ( total number of free-floating planets per unit of time , normalized by the total number of stars ) is proportional to the stellar density \rho _ { \star } of the cluster : \dot { N } _ { o } = \alpha \rho _ { \star } , with \alpha = ( 23 \pm 5 ) \times 10 ^ { -6 } { pc ^ { 3 } } { Myr } ^ { -1 } .
For the Pleiades ( M45 ) we predict that \sim 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 \sim 500 K , a free-floating planet of Jupiter size inside the Pleiades would have a specific flux of F _ { \nu } ( 4.4 \mu m ) \approx 4 \times 10 ^ { 2 } nJy , which would lead to a very clear detection ( S / N \sim 100 ) in only one hour of integration .