An Analysis of Flight Dynamics of a Space Debris Collector Transferring from its Orbital Plane to the Orbital Plane of a Debris Fragment

A space debris collector and a debris fragment move along random noncoplanar orbits ranging from 400 to 2000 km in height. The space collector leaves the base station, transfers into the orbital plane of a debris fragment, aligns itself with and approaches the fragment, grabs it and returns to the base station. The execution time of the flight mission is 24 hours. This paper examines only the stage when the debris collector transfers from its orbital plane to the fragment’s orbital plane. Dampening is provided by repeated activation of a cruise propulsion unit with the thrust of no less than 20000 N and the fuel specific impulse of no less than 15000 m/s. An analysis of dynamics of the orbital flight is performed by numerically integrating the equations of orbital movement of the debris collector and the debris fragment using the fourth order Runge-Kutta methods. The change of the scalar product sign of the vector of the orbit area integral of the debris fragment and the radius-vector of the debris collector is the criterion for intersecting the final orbit plane. Fuel depletion and the nonsphericity of the Earth’s gravitational field in the second zonal harmonic are taken into account, and an example of the calculations is given. Convergence estimates for the integration procedure with regard to the final orbit inclination relative to the orbit’s eccentricity are provided.

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