  Very recently authors in [1] proposed a new Generalized Uncertainty Principle
(or GUP) with a linear term in Plank length. In this Letter the effect of this
linear term is studied perturbatively in the context of Keplerian orbits. The
angle by which the perihelion of the orbit revolves over a complete orbital
cycle is computed. The result is applied in the context of the precession of
the perihelion of Mercury. As a consequence we get a lower bound of the new
intermediate length scale offered by the GUP which is approximately 40 orders
of magnitude below Plank length.
