PX158 - K5 - density of the universe

\begin{aligned} \frac{1}{2} m v_{c}^{2} & = \frac{G M m}{R} \\ v_{c}^{2} & = \frac{2 G M}{R} \\ v_{c} & = H_{0} R \\ M & = \frac{4}{3} π R^{3} ρ_{c} \\ H_{0}^{2} R^{2} & = \frac{8}{3} π R^{2} G ρ_{c} \\ ρ_{c} & = \frac{3 H_{0}^{2}}{8 π G} \\ = 9.47 \times 10^{- 27} k g m^{- 3} \\ \approx 6 H a t o m s m^{- 3} \end{aligned}

where, $M =$ mass of the universe in a sphere of radius, $R$ ; $v_{c} =$ critical recessional velocity

the calculated value is about twenty times higher than the actual density as observed (baryonic matter)
therefore, only $\sim 5 %$ of $ρ_{c}$ is baryonic, $25 %$ is dark matter, $70 %$ is unknown
in the $1990 s$ , astronomers found 'dark energy' existed from supernova surveys, which can account for the $70 %$ of $ρ_{c}$
this is causing the expansion of the universe to accelerate