Derivation of Potentially Important Masses for Physics and Astrophysics by Dimensional Analysis

Abstract

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 = γ^p m₀, where m₀ ≡ m_p 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 m_p = 2.17×10^-8 kg, mass of the Hubble sphere M_H ~ 10⁵³ kg, minimum quantum of mass/energy m_G = 2.68×10^-69 kg, Weinberg mass m_W = 1.08×10^-28 kg, mass of hypothetical quantum gravity atom M_G = 3.8×10¹² kg, Eddington mass limit of stars M_E = 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.