Astronomers have a mathematical model for the orbital speed of the stars as a fu

Question

Astronomers have a mathematical model for the orbital speed of the stars as a function of their distance x from the center of the galaxy. It is: v(x) = (350x)/(1 + x2)(3/4)
where the parameter x = 1 for 10,000 light years, x = 2 for 20,000 light years, x = 3 for 30,000 light years and so on. For example, at a distance of 10,000 light years, the rotational speed of a star is, v(1) = (350(1))/(1 + (1)2)3/4 = 350/2(3/4) = 208 kilometers / sec. The radius of the galaxy M-101 is about 90,000 light years. How fast are stars at this radius orbiting the center?

1 light year = 9.5 x 1012 km

1 year = 3.15 x 107 sec

Explanation / Answer

The radius of the galaxy M-101 is about 90,000 light years

The parameter x =9 for 90,000 light years

v(x) = (350x)/(1 + x2)(3/4)
v(9) = (350x9)/(1 + 92)(3/4)

= 115.598 kilometers / sec

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