The Newtonian gravitational force can be derived from the Heisenberg uncertainty principle. In the realm of high-energy physics, it is necessary to replace the standard uncertainty principle by the generalized uncertainty principle (GUP). The generalized uncertainty principle can provide some corrections into the gravitational force. In this paper, we have applied the GUP to modify the gravitational force. The modified gravitational force has been applied to find the GUP corrections into Binet’s equation. The modified Binet’s equation has been used to study the advance of the perihelion of Mercury. It is shown that the GUP may provide the precession of Mercury’s perihelion in the context of Newtonian physics. The modified gravitational force can also be applied to find the modified Friedmann equation in which the correction terms may play the role of dark energy to provide an accelerating universe.
