Exercise 13.39 Astronomers have observed a small, massive object at the center o

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Exercise 13.39

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 18 light years and an orbital speed of about 110 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.

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Part B

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

Express your answer using two significant figures.

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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?

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Correct

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.

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Exercise 13.39

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 18 light years and an orbital speed of about 110 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.

M=   kg  

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Part B

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

Express your answer using two significant figures.

M=   mS  

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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?

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? yes no

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Correct

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.

RS=   m

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Explanation / Answer

radius of orbit, r = d/2

= 18/2

= 9 light years

= 9*365*24*60*60*3*10^8 m

= 8.51*10^16 m

v = 110 km/s

= 110*10^3 m/s

orbital time period, T = 2*pi*r/v

= 2*pi*8.51*10^16/(110*10^3)

= 4.86*10^12 s

a)
let M is the massive object at the center of the milkyway galaxy.

use, T = 2*pi*r^(3/2)/sqrt(G*M)

T^2 = 4*pi^2*r^3/(G*M)

==> M = 4*pi^2*r^3/(G*T^2)

= 4*pi^2*(8.51*10^16)^3/(6.67*10^-11*(4.86*10^12)^2)

= 1.54*10^37 kg

b) M = 1.54*10^37/(1.99*10^30) ms

= 7.74*10^6*ms

c) No

d) Rs = 2*G*M/c^2

= 2*6.67*10^-11*1.54*10^37/(3*10^8)^2

= 2.28*10^10 m

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