PX158 - J3 - weighing galaxies

the orbital velocities appear constant right out to the limit of observations
most of the mass is "unseen", known as "dark matter"
stars are on circular orbits, balance force from gravity with centripetal force:

\begin{aligned} \frac{G M m_{s}}{R^{2}} & = \frac{m_{s} v^{2}}{R} \\ M & = \frac{v^{2} R}{G} \end{aligned}

eg: mass interior to the orbit of the sun in milky way:
- $v_{⊙} = 230 k m s^{- 1}$ , $R_{⊙} = 8 k p c$
$M_{M W} \approx 10^{11} M_{⊙}$
stars at the edge of the galaxy show similar velocities, giving

M_{M W} \approx 10^{12} M_{⊙}

this is far in excess of all baryonic matter
there lies a supermassive blackhole (SMBH) in the centre of most galaxies
eg: $M 84$ shows $v \approx 400 k m s^{- 1}$ at $R = 8 p c$
$M \approx 2 \times 10^{8} M_{⊙}$
in $2019$ , SMBH was observed in radio spectrum