Dynamical problems associated with the orbital motion of dust particles in strong gravitational and radiation fields are analyzed. The general relativistic equations for the motion of a single dust particle are derived, and the static, spherically symmetric situation described by the Schwarzschild metric is considered. Two sharply differentiated regions are tentatively discerned in relativistic dust rings. In the outer regions, dust particles evolve according to a derived expression, reemitting preferentially in a cone centered in the plane of motion, while in the inner ring the particles fall approaching radial geodesics near the speed of light.