Authors: Dimitar Valev
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•mP, where 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 m1 ≡ mP = 2.17×10^(-8) kg, mass of the Hubble sphere m2 ~ 10^53 kg, minimum quantum of mass/energy m3 = 2.68×10^(-69) kg, Weinberg mass m5 = 1.08×10^(-28) kg, Eddington mass limit of stars M3 = 6.6×10^32 kg, mass of hypothetical quantum gravity atom M2 = 3.8×10^12 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.
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