Abstract
In the earlier published papers the authors suggested that, “Magnitude of the unified force can be assumed to be equal to the classical or astrophysical force limit . Strength of any interaction can be defined as the ratio of the operating force magnitude and the magnitude of . If strength of the Schwarzschild interaction is assumed to be unity, then weak interaction strength seems to be ‘squared Avogadro number’ times less than the Schwarzschild interaction. The characteristic atomic force can be represented by â€. Thinking in this way, atomic gravitational constant can be expressed as  With current atomic physical constants and with the assumed two new grand unified back ground numbers analytically - value of  can be fixed for 10 digits and can be verified. Inverse of the strong coupling constant can be considered as the ‘natural logarithm of square root of ratio of gravitational and electromagnetic force ratio of down quark mass where the operating gravitational constant is squared Avogadro number times the gravitational constant’. Finally an attempt is made to fit and understand the mystery of Up and Down quarks, nuclear stability, and nuclear binding energy. For medium and heavy atomic nuclides, at the stable mass number, nuclear binding energy seems to be equal to the sum of rest energy of  up quarks and  down quarks.
Highlights
From final unification point of view, it is very much essential to couple the universal gravitational constant with the elementary physical constants
For medium and heavy atomic nuclides, at the stable mass number, nuclear binding energy seems to be equal to the sum of rest energy of 2Z up quarks and Z down quarks
From the above relations it is reasonable to say that, 1) If it is true that c and G are fundamental physical constants
Summary
From final unification point of view, it is very much essential to couple the universal gravitational constant with the elementary physical constants. & Sivaram C 1993), (Recami E 1994), (Dine, Michael 2007), (Roberto Onofrio 2013) In this context, readers may go through the authors published papers By introducing two new back ground unified numbers x , y , in the published paper the authors expressed their views Lakshminarayana 2014) on final unification and proposed three characteristic relations for connecting, fitting and verifying the Newtonian gravitational constant in a unified approach via the Avogadro number N A. The topics covered and reviewed are: Schwarzschild interaction strength, meaning of strength of interaction in atomic physics, significance of Avogadro number, fitting of the gravitational constant, muon an tau rest masses, strong coupling constant, fine structure ratio, reduced Planck’s constant, rest masses of Up &.
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