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This paper presents the development of an analytical model for the force and torque developed by a Reaction Sphere for satellite attitude control. The Reaction Sphere is a magnetic bearings spherical motor whose rotation axis can be electronically controlled. The actuator is composed of an 8-pole permanent magnet spherical rotor and a 20-pole stator. Force and torque models are derived by solving the Laplace equation and applying the Lorentz force law. Using the linear superposition principle, the expression of the force and torque is formulated in matrix form. The developed models are validated through an open loop measurement campaign as well as by finite element simulations. Experimental results confirmed the validity of both the force and torque analytical models.