Abstract: To clarify the controversy over Newton’s constant, G^CODATA = 6.673(10)x10^-11m³kg^-1s^-2 – offered e.g. through enlarging its uncertainty from 128 ppm to 1500 ppm in 1998 – the formula G_AB = G(1-Δm_A/Am)^-1 (1-Δm_B/Bm)^-1 is presented for the gravitational force between two isotopes with the mass numbers A and B, containing a constant m = 1.006727885(8) amu and a new defined mass defect Δm_A= Am-m_Isotope,A. The formulae with the constant of nature G and for Δm_A emerge from the Unified Field consisting of the electromagnetic and of the covariant gravitational field with gravitational charges. The gravitational charge of the electron + proton system and of neutron g_n is the same g_n= gm with G = g² /4. From available experiments with copper G = 6.576(6)x10^-11m³kg^-1s^-2 is determined. With G and with the empirical known mass number dependent Δ_A^MD =Δm_A/Am, the new theory predicts aside of hydrogen: a composition dependent G_AB in a range of ~ 0.7 % (observed is 0.74 %). The relative difference of inertial and gravitational mass of a body is 0.78 % and the Universality of Free Fall is violated in this order. A fall experiment with Li and Fe must directly show a measurable Δa/a 0.33%. The basic hypothesis of UFF was stated by Philoponus and Galileo Galilei and was taken over by Albert Einstein for the General Relativity Theory and for the gravity.

PACS Numbers: 04.20.Cv, 04.80.Cc, 06.20.Jr, 12.10.-g

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Non-equivalence of inertial and gravitational mass