Astronomers have observed a small, massive object at the center of our Milky Way

Question

Astronomers have observed a small, massive object at the center of our Milky Way galaxy. A ring of material orbits this massive object; the ring has a diameter of about 17 light years and an orbital speed of about 120 km/s .

Determine the mass of the massive object at the center of the Milky Way galaxy. Give your answer in kilograms.

Give your answer in solar masses (one solar mass is the mass of the sun).

Many astronomers believe that the massive object at the center of the Milky Way galaxy is a black hole. If so, what must the Schwarzschild radius of this black hole be?

Explanation / Answer

r = radius of the ring = diameter/2 = 17ly/2 = 8.5 ly = 8.5 x 9.46 x 1015 m

v = orbital speed = 120 x 103 m/s

M = mass

using the equation

v = sqrt(GM/r)

120000 = sqrt((6.67 x 10-11) M/(8.5 x 9.46 x 1015))

M = 1.74 x 1037 kg = (1.74 x 1037)/(2 x 1030) solar mass = 8.7 x 106 solar mass

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