  Various approaches to quantum gravity, such as string theory, predict a
minimal measurable length and a modification of the Heisenberg Uncertainty
Principle near the Plank scale, known as the Generalized Uncertainty Principle
(GUP). Here we study the effects of GUP which preserves the rotational symmetry
of the spacetime, on the Kepler problem. By comparing the value of the
perihelion shift of the planet Mercury in Schwarzschild-de Sitter spacetime
with the resulted value of GUP, we find a relation between the minimal
measurable length and the cosmological constant of the spacetime. Now, if the
cosmological constant varies with time, we have a variable minimal length in
the spacetime. Finally, we investigate the effects of GUP on the stability of
circular orbits
