I recently read about a proposed liquid mirror telescope to be constructed on the moon. My question is one of mechanics, hence this not being in the astronomy section. My question is regarding the shape of the surface of a rotating liquid. The design will have a dish containing a thin layer of mercury (~1mm) which will be rotated to generate a parabolic shape. Is the curve of a rotating liquid affected by the shape of its container? I suppose if it is thin enough, the friction between the liquid and its container would have an effect on the shape of this curve. If the liquid is sufficiently deep (i.e., the effect of friction on the container has a negligible effect on the surface) i would imagine that a rotation would produce a purely parabolic shape since the horizontal force would be proportional to the square of its velocity, whereas the vertical force is constant. If my logic is correct, why does the design of this mirror require a thin liquid layer?