The opening up of space flights is going on with physical discoveries. One of them was a spinning object cyclic inversion revealed on the MIR space station classified in 1985. Later, the NASA International Space Station openly showed the same effect. This physical effect was an object of stare studying by physicists and mathematicians. They developed only approximated and numerical models on the level of assumptions. The inversion of the spinning objects in the condition of free flight is the subject of gyroscope theory. The mass of the spinning object at the orbital flight generates the system of the interrelated inertial torques that results from the action of the inertial torques produced by the curvilinear motion of the object around the earth. This system of the torques acting on the spinning object at an orbital flight manifests its cyclic inversions, which is the gyroscopic effects. The theory of the gyroscopic effects describes the method of application of the system of the inertial torques, the physics of all gyroscopic effects that manifested by any rotating objects under any condition of their motions.