Newton's Constant Isn't Constant

According to Newton’s law of gravity, two masses interact with each other via a central force which can be derived from the potential VN (r) = −Gm1m2/r where G is a universal constant known as Newton’s constant. Likewise, according to Coulomb’s law, two electrically charged particles with charges n1e and n2e interact via the central potential VCb (r) = αn1n2/r where e is the elementary charge and where α ≡ e/4π is nowadays referred to as the fine structure constant. Thus, in classical physics, the gravitational and the electrostatic interactions are described by exactly the same 1/r-law, and their respective coupling strengths are determined by the two universal constants G and α which enter the equations in an analogous fashion.