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home / study / science / physics / questions and answers / astronomers have observed a small, massive object ... Your question has been answered! Rate it below. Let us know if you got a helpful answer. . 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 10 light years and an orbital speed of about 250 km/s .

a) 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?

b) Would a black hole of this size fit inside the earth's orbit around the sun? yes or no

Explanation / Answer

solution:

Turn 10 light years to metres (multiply 3x10^8m/s by the number of seconds in 10 years).

2. if the the speed is 250km/s, change to m/s (multiply by 1000).

3. The centripetal force, mv²/r, on a mass m of the the orbiting material equals the gravitational force, GmM/r², from the central object of mass M. So:
GmM/r² = mv²/r
GM/r = v²
M = rv²/G
C) Schwarzschild radius = GM/c² (same formula as above with v = c).

Rschwar  =(6.67*10-11)(5.972*1024) /(3*108)2 =4.42mm

this is very small and can fit inside earth's orbit

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