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The efficiency of a magnetic system of kinetic moment dumping in solving the problem of stabilizing Aist-2D spacecraft without using information on angular velocity is investigated. We defined the conditions under which the magnetic moment produced by electromagnets constitutes a useful control mechanical moment. Boundary conditions for preventing emergence of the parasitic moment are also defined. The paper presents the solution of the problem of forming the vector of the kinetic moment of the system “spacecraft + control moment gyro” according to the information on the vector of geomagnetic induction of the Earth. We defined the dependence of the time taken by the algorithm of angular speed reduction on the value and direction of the projections of the vector of spacecraft angular speeds at the time of algorithm actuation. The results obtained in the course of mathematical modeling and natural experiment on the spacecraft, the process of dumping angular speeds in providing the solution of the problem of attitude determination with the use of star sensors are compared.