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 13 light-years and an orbital speed of about 120 km/s. Part A.) Determine the mass M of the massive object at the center of the Milky Way Galaxy. Give your answer in kilograms. Part B.) Give your answer in solar masses (one solar mass is the mass of the sun). Express your answer in units of solar masses. Part C.) 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 RSRS of this black hole be? Express your answer in meters.

Answer 1

Given : The ring has a diameter of about 13 light-years and an orbital speed of about 120 km/s.

• Radius of ring = 13/2 = 6.5 ly = 6.5ly * (9.461*10^15 m) => Radius= 6.15 * 10^16 m
• Orbital speed, v = 120 km/s = 1.2 * 10^5 m/s.

Part(A) Here, we can use the assumption that a ring-shaped accretion disk around the galaxy center's black hole (formally known as Sagittarius A*) is circular, and therefore, we can use the circular orbit equations.

To find the mass of Sagittarius A*, we will use the following equation:

Part (B) : To determine how big it is relative to the Sun, we'll just divide it by the book's data for the Sun's mass,

Part (C) : We can calculate Schwarzschild radius using equation,

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=> Since Earth's orbital radius is Roe = 1.5 * 10^11 m So, we conclude that this object can fit inside Earth's orbital radius since Rs < Roe.

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