Derivation of Potentially Important Masses for Physics and Astrophysics by Dimensional Analysis
DOI : 10.3844/pisp.2017.24.29
Volume 8, Issue 1
The Hubble constant has been added in addition to the three fundamental constants (speed of light, gravitational constant and Planck constant) used by Max Planck, for derivation of the Planck mass by dimensional analysis. As a result, a general solution is found for the mass dimension expression m = γp m0, where m0 ≡ mp is the Planck mass, γ = 1.23×10-61 is a small dimensionless quantity and p is an arbitrary parameter in the interval [–1, 1]. The Planck mass mp = 2.17×10-8 kg, mass of the Hubble sphere MH ~ 1053 kg, minimum quantum of mass/energy mG = 2.68×10-69 kg, Weinberg mass mW = 1.08×10-28 kg, mass of hypothetical quantum gravity atom MG = 3.8×1012 kg, Eddington mass limit of stars ME = 6.6×1032 kg and some more masses potentially important for the physics and astrophysics represent particular solutions for values of p, expressed as fractions with small numerators and nominators.
© 2017 Dimitar Valev. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.