Authors: Casper Spanggaard
A definition of G is derived using the product of two Planck point masses and a definition of hbar based on the speed of light in vacuum and geometry. The theoretical value of G is found to be 6.74981057667161 x 10^-11 m^3 kg^-1 s^-2 yielding a relative accuracy error of the CODATA 2010 G-value of -1.1255%. One experiment resulted in a value with a smaller relative accuracy error than the CODATA 2010 G-value of -0.5098%. Both rest and relativistic mass product equations are derived. These equations relate the relative spacetime spin frequency w_s, the relative orbital frequency w_o and (relativistic equation only) the Lorentz factor y describing relative linear speed of two bodies to the mass product. The Planck mass is a special case mass with w_sw_o = w_planck^2 = 1 s^-2. The theoretical value of the Planck mass was found to be 2.16039211144077 x 10^-8 kg. The relative accuracy error of the CODATA 2010 Planck mass value is 0.7461%. This error is attributed to use of the different definition of hbar. When derived from both hbar and G constants as well as the rest mass product equation, three kilogram unit definition candidates are all inconsistent. The candidate derived from the rest mass product equation is the only candidate that has equal second and meter exponents suggesting a kind of symmetry. This definition is considered the nominal kilogram unit definition. The other two candidates are considered to be artifacts of the hbar and G constants.
Comments: 4 Pages. Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
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