### Applications of Gravitational Model of Possible Final Unification in both Large & Small Scale Physics

#### Abstract

Considering two pseudo gravitational constants assumed to be connected with proton and electron, we make an attempt to fit the Newtonian gravitational constant. In this semi- empirical approach, proton-electron mass ratio, reduced Planck’s constant and root-mean-square radius of proton seem to play a crucial role. In this approach, a change in 18^{th} decimal place of the root mean square radius of proton seems to change the 14^{th} decimal place of the Newtonian gravitational constant. It may be noted that, with reference to the operating force magnitudes, protons and electrons cannot be considered as ‘black holes’. But electrons and protons can be assumed to follow the relations that black holes generally believed to follow where the proposed pseudo gravitational constants take the role of the Newtonian gravitational constant. Proceeding further, by combining the views of S.W. Hawking and Abhas Mithra, melting temperatures of proton, electron and quark soup can be estimated. The two characteristic supporting points to be noted are: 1) Neutron star’s mass limit can be understood very easily with the square root of the ratio of gravitational constant associated with proton and the Newtonian gravitational constant; and 2) Square root of the ratio of gravitational constant associated with electron and the Newtonian gravitational constant is matching with Avogadro number by 99%.