Abstract: To clarify the controversy over Newton’s constant, GCODATA = 6.673(10)x10-11m3kg-1s-2 – offered e.g. through enlarging its uncertainty from 128 ppm to 1500 ppm in 1998 – the formula GAB = G(1-ΔmA/Am)-1 (1-ΔmB/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 ΔmA= Am-mIsotope,A. The formulae with the constant of nature G and for ΔmA 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 gn is the same gn= 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 ΔAMD =ΔmA/Am, the new theory predicts aside of hydrogen: a composition dependent GAB 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