  Recently it was shown that quantum corrections to the Newton potential can
explain the rotation curves in spiral galaxies without introducing the Dark
Matter halo. The unique phenomenological parameter $\al\nu$ of the theory grows
with the mass of the galaxy. In order to better investigate the mass-dependence
of $\al\nu$ one needs to check the upper bound for $\al\nu$ at a smaller scale.
Here we perform the corresponding calculation by analyzing the dynamics of the
Laplace-Runge-Lenz vector. The resulting limitation on quantum corrections is
quite severe, suggesting a strong mass-dependence of $\al\nu$.
