Even though materialistic atoms are having independent existence in this current accelerating universe, they are not allowing scientists and engineers to explore the secrets of gravity at atomic scale. This may be due to incomplete unification paradigm, inadequacy of known physics and technological difficulties etc. In this challenging scenario, one fundamental question to be answered is: Is Newtonian gravitational constant having a physical existence? We would like to suggest that, it’s a man created empirical constant and is having no physical existence. Clearly speaking, it’s not real but virtual. For understanding the secrets of large scale gravitational effects, scientists consider it as a physical constant. In the same way, each atomic interaction can be allowed to have its own gravitational constant. With further study, their magnitudes can be refined for a better understanding of the nature. Thinking in this way, we tried to fit the Newtonian gravitational constant. It’s estimated value seems to be 6.679855x10^(-11) m3/kg/sec2. Proceeding further, the famous radiation constants can be shown to be complex or secondary physical constants. By considering proton neutron stability, nuclear binding energy, nuclear charge radii, neutron life time, Fermi’s weak coupling constant and strong coupling constant, we are trying to understand the validity of the proposed three atomic gravitational constants. It needs further study.