Analysis of the Orbital Approach Dynamics of the Space Debris Collector to the Fragment of Debris by the Method of Thrust Reversal with Interruption

The debris collector and a debris fragment move along random noncoplanar orbits in the altitude range of 400--2000 km. The thrust of the promising engine is 5000--25 000 N, the specific impulse of the promising fuel is not lower than 20 000 m/s. The remaining fuel after approach is not less than the specified. The debris collector undocks from the base station, transfers from its orbital plane to the debris fragment orbital plane, performs phasing, approaches the fragment, grabs it and returns to the base station. The paper considers only the stage of orbital approach. The duration of the entire flight mission is limited to one day. The phasing time is insufficient, therefore, at the start time of the orbital approach, the distance to the target is ~ 100 km, the relative velocity is ~ 1 km/s. On the other hand, for reliable and safe grabbing of a debris fragment, it is necessary to provide a distance of ~ 1 m and a relative velocity of ~ 1 m/s. It is shown that this can be achieved by approach using the method of thrust reversal with interruption. An effective algorithm of approach with target is proposed. An analysis of the orbital approach dynamics was performed by joint numerical integration of the orbital motion equations of the debris collector and the debris fragment by the 4th-order Runge --- Kutta method. Approach is performed in 6 cycles. In each cycle, the engine turns on three times. Two cycles are performed by sustainer engines, four cycles are performed by auxiliary engines of lower thrust. The fuel depletion and the non-sphericity of the Earth's gravitational field according to the 2nd zonal harmonic are taken into account. Calculation example is considered. Convergence estimates of the integration procedure by the resultant distance to the target and the resultant relative velocity are given. Resultant orbital approach is oscillation process with heavy damping. Damping is ensured by multiple firings of the sustainer (auxiliary) engine

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