Hubble's law: 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

Using Hubble's law:

v = H*d

where v is the recessional velocity of the galaxy, H is the Hubble constant, and d is the distance to the galaxy.

We are given that v = 0.01c, where c is the speed of light.

We are also given that H = 22 km/s per million light-years.

Converting c and H into the same units:

c = 3.00 x 10^8 m/s = 9.461 x 10^15 m/yr

H = 22 km/s per million light-years = (22 km/s) * (1 million light-years / 9.461 x 10^15 m) = 2.33 x 10^-18 s^-1

Substituting into Hubble's law:

0.01c = 2.33 x 10^-18 d

Solving for d:

d = (0.01c) / (2.33 x 10^-18) = 4.29 x 10^21 m = 4.29 x 10^14 ly

Therefore, the galaxy is approximately 140 million light-years away from us.

Hubble's Law: If a Galaxy Is Moving Away from Us