The Supermassive Black Hole in M87 M87 is a massive elliptical galaxy in the Vir

Question

The Supermassive Black Hole in M87 M87 is a massive elliptical galaxy in the Virgo cluster, and contains a supermassive black hole at its center. The estimated mass of the M87 black hole is M_BH = 3.5 times 10^9 M_sun. A circumnuclear gas disk has been discovered in orbit around the M87 black hole, and the gas velocities have been measured at a radius of r = 10 pc (i.e., where r is measured relative to the black hole). How fast is this gas moving? Express your answer in km/s. At this radius, do you expect general relativistic effects to be important? Explain.

Explanation / Answer

From the given question,

The circumnuclear gas disk is in equilibrium due to two opposite forces.

m1= mass of circumnuclear gas disk

m2= mass of black hole

1pc = 3.08 x 1016m

Gravitational force = G m1m2/r2

Centrifugal force = m1v2/r

Equating both forces,

G m1m2/r2 = m1v2/r

v2= Gm2/r

=(6.67 x 10-11 x 3.5 x 109 x 2 x 1030)/(10 x 3.08 x 1016 )

=15.15 x 1011

v=1231222.6m/s

=1.23 x 106 m/s

(b) as this is close to speed of light ( 3 x 108), the relativistic effects are important.

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