If a galaxy is moving away from us at 1.0% of the speed of light, use Hubble's law to estimate how far away it is from us if the Hubble constant is 22 km/s per million light-years. (c = 3.00 × 10⁸ m/s, 1 ly = 9.461 × 10¹⁵ m, 1 y = 3.156 × 10⁷ s) A) 14 ly B) 140 ly C) 140 thousand ly D) 140 million ly E) 140 billion ly

Question

Quizplus · Accepted Answer

According to Hubble's law, the velocity of a galaxy moving away from us is proportional to its distance from us. The proportionality constant is the Hubble constant (H0). Mathematically, v = H0d, where v is the velocity of the galaxy, and d is its distance from us.

In this question, we are given v = 0.01c, where c is the speed of light. Therefore, we can write:

0.01c = H0d

d = 0.01c / H0

Substituting the given values, we get:

d = 0.01 x 3.00 x 10^8 m/s / (22 km/s per million light-years x 10^6 light-years/1 million light-years)

Simplifying this expression, we get:

d = 1363636.36 ly

Rounding off to the nearest million, we get:

d = 140 million ly

Therefore, the best choice is D) 140 million ly.

If a Galaxy Is Moving Away from Us at 1