If a galaxy is receding from us at 0.10c. Use Hubble's law to estimate the distance to this galaxy if the Hubble constant is 22 km/s per million light-years. (c = 3.00 × 10⁸m/s, 1 ly = 9.461 × 10¹⁵ m, 1 y = 3.156 × 10⁷ s) A) 1.4 × 10⁹ ly B) 6.6 × 10⁵ ly C) 6.6 × 10⁵ Mly D) 2.2 Mly E) 1.4 × 10⁷ Mly

Question

Quizplus · Accepted Answer

Hubble's Law states that the recessional velocity of a galaxy is proportional to its distance from us, with a proportionality constant called the Hubble constant.

Using the formula:

v = H_0 × d

where v is the recessional velocity, d is the distance, and H_0 is the Hubble constant.

Substituting the given values:

0.10c = 22 km/s/Mly × d

Converting the terms to the same units:

0.10 × 3.00 × 10^8 m/s = 22 km/s × (d/10^6 ly)

Simplifying:

d = (0.10 × 3.00 × 10^8 m/s × 10^6 ly) / (22 km/s) = 1.36 × 10^19 m = 1.36 × 10^9 Mly

Therefore, the distance to the galaxy is approximately 1.4 × 10^19 meters or 1.4 × 10^9 million light-years, which is closest to option A: 1.4 × 10^19 ly.

If a Galaxy Is Receding from Us at 0