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When heavenly bodies are made up of tiny atoms, it is imperative to find the correlations that might exist among ‘atoms’ and ‘heavenly body’ as a whole. In this context, by considering three virtual gravitational constants assumed to be associated with the three atomic interactions i.e. (electromagnetic, strong and weak interactions) and by considering four basic semi empirical (reference) relations pertaining to the four gravitational constants, a bold attempt is made to estimate the Newtonian gravitational constant (GN). Its fitted and recommended values are 6.679855x10-(11) m3/kg/sec2 and 6.67408x10-(11) m3/kg/sec2 respectively and error is -0.08653%. As current unification paradigm is failing in estimating (GN) from atomic and nuclear physical constants, our work can be recommended for further study.