We specify the range to which perturbations penetrate a planetesimal system. Such perturbations can originate from massive planets or from encounters with other stars. The latter can have an origin in the star cluster in which the planetary system was born, or from random encounters once the planetary system has escaped its parental cluster. The probability of a random encounter, either in a star cluster or in the Galactic field depends on the local stellar density, the velocity dispersion and the time spend in that environment. By adopting order of magnitude estimates we argue that the majority of planetary systems born in open clusters will have a {\em Parking zone}, in which planetesimals are affected by encounters in their parental star cluster but remain unperturbed after the star has left the cluster. Objects found in this range of semi-major axis and eccentricity preserve the memory of the encounter that last affected their orbits, and they can therefore be used to reconstruct this encounter. Planetary systems born in a denser environment, such as in a globular cluster are unlikely to have a Parking zone. We further argue that some planetary systems may have a {\em Frozen zone}, in which orbits are not affected either by the more inner massive planets or by external influences. Objects discovered in this zone will have preserved information about their formation in their orbital parameters.

4 pages, accepted for publication in MNRAS