Measurements of star motions at the center of the Andromeda Galaxy, also known as M31, show that stars about 3 light-years from the center are orbiting at a speed of 400 km/s. These stars are suspected to be orbiting a supermassive black hole. Use the orbital velocity law from Mathematical Insight 21.2 to estimate the mass of this black hole.

The mass is 6.81x10^37 kg

Explanation:

The orbital velocity is given as

Rearranging this equation gives

Here V is given as 400 km/s of 4 x10^5 m/s

R is given as 3 light years so R is given as  m

G is the gravitational constant whose value 6.67x10^-11

By putting the values

So the mass is 6.81x10^37 kg

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