We propose a new mechanism to explain the physical cause of the empirical asymmetric reflectivity effect observed for the LAGEOS satellites. To reach this result we have modelled the reflection of the Sun's visible light from the four Germanium Cube Corner Retroreflectors of these laser-ranged satellites. The position of the cubes play a crucial role in defining the characteristics of the effect and its impact in the satellites orbit. We analyzed the long-term effects of the perturbation in the satellites eccentricity vector excitations and in their perigee rate. With the new model we have been able to reproduce the time evolution of LAGEOS eccentricity vector excitations and perigee rate as due to the empirical effect. In the case of LAGEOS II, the asymmetric reflectivity effect needs to be modelled with an analytical expression different from that for LAGEOS.