Annotation: The mathematic modeling was performed of the flight of light-class three-stage launch vehicle injecting a payload into sun-synchronous orbit of 700 km altitude and a cluster of observed space debris objects in the conditions of dynamically changing cataloged space situation. It is shown that as the launch moment becomes closer, the cataloged space situation is ascertained, which leads to the constant change of the quantity of hazardous space debris objects observed in the vicinity of launch vehicle trajectory and to the change of the parameters of their approach to the launch vehicle: minimal relative distance, relative velocity, rendezvous angle and launch moment for which hazardous approach is revealed. The hazardous approaches for the launch vehicle trajectory under consideration are more often observed with the relative velocities of more than 8 km/s and rendezvous angles less than 90 deg and their variations within the launch window do not exceed 1.2 m/s and 0.035 deg respectively. In this case, the histograms of distribution of relative distance, relative velocity, and rendezvous angle from catalog to catalog vary insignificantly. The distribution of hazardous approaches in launch time within launch window is not uniform, the regions are observed with low quantity of hazardous approaches and with high quantity. The hazard of launch vehicle collision with observed space debris objects in a launch is confirmed. In all, in the launch day time window under consideration, more than ten hazardous approaches are revealed, for two of them the approach to minimal distance of less than 1 km is predicted. This testifies to the necessity of taking measures to increase safety of launch vehicle flight through observed space debris cluster. In order to increase Ukrainian launch vehicles miss ion safety in the conditions of near space pollution, it is proposed to create the system of pre -flight space analysis, whose tasks are periodic analysis of space situation not less than once in a day, revealing of hazardous approaches, determination of their parameters, and preparation of data to make decision on launch time.

Annotation: This article considers the problem of determination of propulsion system solid fuel burn-out time in the extraatmospheric flight segment taking the apparent acceleration and apparent speed measured by the inertial navigation system. Correlation analysis of the realized and nominal dependencies of the apparent acceleration and apparent speed of the launch vehicle on relative operating time of the propulsion system is suggested to be used to forecast the fuel burn-out time. In order to improve the accuracy of the forecast, and to decrease the amplitude and vibration rate of its results several channels simultaneously are suggested to be used for calculations with subsequent majority voting and digital filtration. As a result of the study, the procedure to forecast the time of solid fuel burn-out in the launch vehicle propulsion system in flight has been developed. Operability of the suggested procedure has been verified using the mathematical simulation of the launch vehicle flight for two operating modes of the propulsion system different from the nominal ones. Based on the statistical processing of the deviations of the predicted time of solid fuel burn-out versus the realized one it was determined that the forecast based on the results of apparent acceleration measurement has the greatest accuracy with the minimal number of operations. Suggested procedure is easily realized as the multistage adaptive algorithm and can be used in the guidance system of the solid-propellant launch vehicle in the extra-atmospheric flight segment for the numerical forecast of the reachable terminal parameters of flight, definition of command vector and development of the relevant thrust vector control commands.