Center Ngc

se the orbital velocity law to calculate the mass of the central black hole.?

The molecular clouds circling the center of the active galaxy NGC 4258 orbit at a speed of about 1,000 km/s, with an orbital radius of 0.49 light-year = 4.8 * 10^15 meters. Use the orbital velocity law to calculate the mass of the central black hole. Give your answer both in kilograms and in solar masses (1M(sun) = 2.0 * 10^30 kg).

a = GM/r^2 … gravitational acceleration
a = v^2/r …. centripetal acceleration

GM/r^2 = a = v^2/r
M = v^2 r/G

G = 6.67×10^-11 m^3 / kg s^2
v = 1,000,000 m/s
r = 4.8×10^15 m

M = 7.2 x10^37 kg
or
M = 3.6×10^7 M(sun)

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