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

Effect of GUP on the Kepler problem and a variable minimal length