Geometrical framework as seen by an observatory comoving with S₁. The position vector ξ, the position vector of S₀, x(t) and the position of S₁ in S₁, x_O′(t), are shown in green. Here the system attached to the reference frame S₁ has been zoomed to show the quantities defined in the text better, but it is supposed to be the smaller in mass and dimension and is orbiting around an inertial major system attached to S₀. The blue shadow represents the generic external environment attached to S₀-system in which the S₁-system is embedded. The position vector of S₀, once at the surface of the galaxy, Σ, take the scale radius value ∥ ξ ∥ _Σ = r_s (doted red orange circle). The scale radius is generally a function of time r_s = r_s(t) and it varies as a consequence of the gravitational external field that the galaxy experiences along its orbit around the major galaxy centred in S₀. In the non-inertial reference frame, S₁ the velocity v = v(t) (red arrow aligned with ) of the fluid impacting the galaxy (i.e. the negative of the velocity of the stellar system in S₀) forms an angle θ with the position vector ξ, (with notation for the smaller angle between two, three-dimensional vectors). The acceleration (violet arrow) inclusive of the apparent effect forced due to the non-inertial character of S₁ forms an angle with the position vector. An observer comoving with S₁ sees the inertial reference frame S₀ changing position at different times t − Δt,t or t + Δt as well as the rotation of S₀ axes.