The planet Mercury rotates 3 times about its axis while it revolves 2 times about the Sun Internet source 2025,  so that Mercury offers opposite sides to the Sun after each consecutive revolution. This was unexpected by astronomers. Indeed, they thought that a planet as close to the sun as Mercury always ought to offer the same side to the Sun because of tidal forces; so that 1 rotation of the planet occurs during 1 revolution. Bouncing off radar waves from Mercury in 1965 taught them the truth, see Asimov (1972). I shall characterize the two possibilities as the 1.5/1-mode and the 1/1-mode respectively. This paper introduces a model in which the tidal deformation of a planet is simulated by visco-elastic springs subject to the gravitational field of the Sun. It turns out that both modes may occur. The model can be shown to exhibit other modes upon a change of its visco-elastic properties: \(\tfrac{n}{2}/1\) with n being any integer greater than 1. Thus the ratio of the mean angular velocities of rotation and revolution might be said to be “quantized.”