Please make sure to answer thin question correctly. Astronomers have observed a

Question

Please make sure to answer thin question correctly.

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 160 km/s .

Part A

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

Express your answer using two significant figures.

Part B

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

Express your answer using two significant figures.

Part C

Observations of stars, as well as theories of the structure of stars, suggest that it is impossible for a single star to have a mass of more than about 50 solar masses. Can this massive object be a single, ordinary star?

no

Part D

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?

Express your answer using two significant figures.

in Meter

Part E

Would a black hole of this size fit inside the earth's orbit around the sun?

no

Part D

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?

Express your answer using two significant figures.

in Meter

Part E

Would a black hole of this size fit inside the earth's orbit around the sun?

Explanation / Answer

here,

diameter of the orbit , d = 17 light years

radius , r = 8.042 * 10^16 m

speed of thematerial , v = 160 km/s

v = 160000 m/s

part a)

let the mass of the object at centre be m

v^2 = G*m /r

160000^2 = 6.67 * 10^-11 * m /(8.042 * 10^16 )

m = 3.08 * 10^37 kg

the mass of the massive object is 3.08 * 10^37 kg

B)

1 solar mass = 1.989 * 10^30 kg

the mass of the massive object is 1.55 * 10^7 solar mass

C)

this massive object is not a single ordinary star

d)

rs = 2 * G * M /c^2

rs = 2 * 6.67 * 10^-11 * 3.08 * 10^37 /( 3 * 10^8)^2

rs = 4.57 * 10^10 m

the Schwarzschild radius of this black hole is 4.57 * 10^10 m

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