If the only force exerted on a star far from the center of the Galaxy (r = 7.40 ✕ 1020 m) is the gravitational force exerted by the ordinary matter (Mord = 1.90 ✕ 1041 kg), find the speed of the star. Assume a circular orbit and assume all the Galaxy's matter is concentrated at the center.

Respuesta :

Answer:

The value is  [tex]v = 1.309*10^{5}\ m/s[/tex]

Explanation:

The radius is [tex]r = 7.40 *10^{20} \  m[/tex]

The mass of the ordinary matter is [tex]M_{rod} =  1.90 *10^{41}\  kg[/tex]

Generally the speed of the star is mathematically represented as

         [tex]v = \sqrt{\frac{G * M}{r} }[/tex]

Here G is the gravitational constant with a value

        [tex]G = 6.67384 * 10^{-11}[/tex]

So

      [tex]v = \sqrt{\frac{6.67384 * 10^{-11} * 1.90 *10^{41}}{7.40 *10^{20}} }[/tex]

=>    [tex]v = 1.309*10^{5}\ m/s[/tex]

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