The research is to study the formation of the Solar system and to obtain knowledge about the population of interplanetary space by celestial bodies. The reasons for interest in this topic are the study of outer space for practical purposes, understanding the reality of space threats, as well as the opportunity, using new knowledge about small bodies, to clarify the models of the evolution of the Solar system in General, planets and their environment in particular. The aim of this study is to search for trajectories of a small-mass celestial body, which, going into the zone of Jupiter influence, will reduce the initial parabolic velocity to a velocity close to circular relative to the Sun, creating dust accumulation zones in certain parts of the orbits. For this purpose, the solution algorithm and the corresponding software for numerical simulation of the problem are developed. On the basis of the perturbed Kepler problem, we studied the trajectories of small cosmic bodies arriving in the Solar system from deep space. Under the gravitational influence of Jupiter, particles change their speed, reducing it or increasing it. We are interested in the first option, where the particles slow down and move further into a circular orbit, becoming satellites of the Sun and forming areas of accumulation of dust particles in certain areas of the orbits. In this paper, a methodological approach is developed that allows us to qualitatively investigate the problem of celestial mechanics. In the process of numerical simulation, the system of differential equations of motion was solved by the Runge-Kutta method of the fifth order with automatic step selection. The software and hardware complex is implemented in the C language, the simulation was carried out in the CodeBlocks environment with the GNU GCC compiler. Visualization was carried out in AdvancedGrapher and Gnuplot. The main result of the research is that the problem was solved, the capture area – the zone from which bodies must move to get under the influence of Jupiter and continue further movement under the influence of the attraction of the Sun – were constructed numerically. The graphs that confirm the formation of clusters of small celestial bodies over a period of 250 years are presented, and the characteristic zones of their appearance in the Solar system are obtained. The graphs show visual images of trajectories, where you can trace the evolution of the orbits from the beginning to the end.