Extended renormalizations group analysis for quantum gravity and Newton’s gravitational constant

The conventional renormalization groups as applied in SU(5) GUT are adapted to the transfinite simplictic arithmetic of E–infinity theory. The resulting simple formalism yielded the exact quantum gravity inverse coupling for non-super symmetric and super symmetric unifications alike. Subsequently by means of analogy supported by Witten’s T-duality and black hole theory an accurate estimation of Newton’s constant of gravity is derived from what is basically the same formalism.