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Introduction. A constant increase in the amount of space debris already constitutes a significant threat to satellites in nearEarth orbits, starting with the trajectory of their launch vehicle injection. Problem Statement. Design and development of various modern methods of protection against space debris requires knowledge of the statistical characteristics of the distribution of the kinematic parameters of the simultaneous motion of a launch vehicle injecting satellite and a group of space debris objects in the area of its trajectory. Purpose. Development of a mathematical model of a launch vehicle rendezvous with a group of observable orbital debris while injecting a satellite into near-earth orbits with an altitude of up to 2100 km and an inclination from 45 to 90 degrees.  Materials and Methods. The following methods are used in the research: analysis, synthesis, comparison, simulation modeling, statistical processing of experimental results, approximation, correlation analysis, and the least squares method.  Results. The simultaneous motion of a launch vehicle and a group of space debris objects has been studied. The distributions of relative distance, relative velocity, angle of encounter, and moments of time of approach of a launch vehicle to a group of the observed space debris at a relative distance of less than 5 km have been obtained. The dependence of the average rendezvous concentration on the distribution of space debris across the average altitude of the orbit and the inclination of the target orbit of the launch vehicle has been determined. The dependence of the average probability of rendezvous in the launch on the inclination of the target orbit, the number of orbital debris, and the relative distance of the rendezvous has been determined. Conclusions. The obtained mathematical model of rendezvous of a launch vehicle with a group of observed orbital debris can be used while designing means of cleaning the near-Earth space and systems to protect modern satellite launch vehicles from orbital debris. In addition, the results of the research can be used to assess the impact of unobserved orbital debris on the flight of a launch vehicle.

Launch Vehicle Rendezvous to Catalogued Orbital Debris while Injecting into Highly-Inclined Orbits