**Authors:** U .V . S. Seshavatharam, S. Lakshminarayana

In the atomic or nuclear space, till today no one measured the value of the gravitational constant. To bring down the planck mass scale to the observed elementary particles mass scale a large scale factor is required. Ratio of planck mass and electron mass is close to $\textrm{Avogadro number}/8 \pi\cong N/8 \pi$. The idea of strong gravity originally referred specifically to mathematical approach of Abdus Salam of unification of gravity and quantum chromo-dynamics, but is now often used for any particle level gravity approach. In this connection it is suggested that, key conceptual link that connects the gravitational force and non-gravitational forces is - the classical force limit $\left(\frac{c^{4} }{G} \right)$. For mole number of particles, if strength of gravity is $\left(N.G\right),$ any one particle's weak force magnitude is $F_{W} \cong \frac{1}{N} \cdot \left(\frac{c^{4} }{N.G} \right)\cong \frac{c^{4} }{N^{2} G} $. Ratio of `classical force limit' and `weak force magnitude' is $N^{2} $. This is another significance of Avogadro number. If $R_0\cong 1.21$ fermi is the nuclear charge radius, to a very good accuracy it is noticed that in Hydrogen atom, ratio of total energy of electron and nuclear potential is equal to the electromagnetic and gravitational force ratio of electron where the operating gravitational constant is $N^2G_C$ but not $G_C.$ Square root of ratio of strong and weak force magnitudes can be expressed as $2 \pi \ln\left(N^2\right).$ With the defined strong and weak force magnitudes observed elementary particles masses and their magnetic moments can be generated. Interesting application is that: characteristic building block of the cosmological ‘dark matter’ can be quantified in terms of fundamental physical constants. No extra dimensions are required in this new approach.

**Comments:** 32 Pages. To be published in the Hadronic journal.

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[v1] 2011-12-08 09:40:32

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