The problem of space flights safety arose with the beginning of the first launches of artificial Earth satellites. With expansion of the boundaries of space flights, the area of outer space that must be controlled to ensure flight safety is significantly increasing. In this study, we consider the possibility of capturing space objects into near-planetary space and further movement of these objects. Such statistical analysis is very important when planning the long-term flights. The objects of our research are both: the particles that came from deep space and the evolving asteroids of the Main asteroid belt. A special attention is paid to the evolution of the Griqua family of asteroids, which belong to the main asteroid belt, and move in orbital resonance with Jupiter.