The differential equations of motion of a two-rotor gyroscopic system, when the center of suspension of this system is traveling on a geocentric sphere of radius R//1 and the system is in the Newtonian central-force field, are derived in this paper. Sufficien conditions of stability of a gyroscopic vertical located on an earth satellite are determined. The study is completed with allowance for the moments of inertia of all the elements included in the gyroscopic system.