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The Hubble constant, $H_{0}$, is the ratio of the recessional velocity of a galaxy to its distance. The Hubble constant is estimated to be 70 km/sec per million parsecs of distance. (One parsec is equal to 3.26 light years.) Based on this ratio, how many billions of light years away would a galaxy be if it had a recessional velocity of 300,000 km/sec?

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Answer:

14 billion light years away

Explanation:

v = Recessional velocity = 70km/s/million parsec

D = Proper distance

Hubble constant

[tex]70\ km/s=3260000\ ly\\\Rightarrow 1\ km/s=\dfrac{3260000}{70}\ ly[/tex]

From Hubble's law we have the relation

[tex]v=H_0D\\\Rightarrow D=\dfrac{v}{H_0}\\\Rightarrow D=\dfrac{3260000}{70}\times 300000}\\\Rightarrow D=13971428571.42857\ ly[/tex]

The distance in light years of the galaxy is 14 billion light years away

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