Similarity and dimensional theory for galaxies: Explanation of long-known results of observations

A practical extension of the similarity and dimensional theory to the case of several similarity parameters is proposed. On this basis, for galaxies an explanation is given for the empirical correlations noticed in the last quarter of the 20th century: the Tully–Fisher relation, the concept of a fundamental plane, etc. For galaxies, apart from the virial, there is another similarity parameter whose choice is arbitrary. Here, it is introduced in the simplest form for an empirical determination:Π₁ = U ₀/U _d, U ₀ is the observed velocity, the scale U _d = (GL)^1/5, where L is the object luminosity, G is the gravitational constant.