How far is a galaxy from Earth if it is receding from Earth at a speed of 0.1c? A)3.0 $\times$ 10²⁰ m B)1.0 $\times$ 10²² m C)1.2 $\times$ 10²⁵ m D)3.0 $\times$ 10²⁸ m E)1.0 $\times$ 10³⁰ m

Question

Quizplus · Accepted Answer

According to Hubble's law, the recession velocity of a galaxy is proportional to its distance from Earth. The constant of proportionality is known as the Hubble constant, which is approximately 70 km/s/Mpc. So, for every megaparsec (Mpc) of distance, a galaxy will recede from us at 70 km/s. Using the conversion factor 1 Mpc = 3.086 x 10^19 km, we can calculate the distance of the galaxy as follows:

velocity = Hubble constant x distance
0.1c = 70 km/s/Mpc x distance
distance = 0.1c / (70 km/s/Mpc) = 1.43 x 10^9 Mpc

Converting this to meters, we get:

1.43 x 10^9 Mpc x 3.086 x 10^22 m/Mpc = 1.2 x 10^32 m

Therefore, the best choice is C, 1.2 x 10^32 m.

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