The redshift of a distant galaxy is 0.014 - Scottish Highers Physics - Question 9 - 2019

Hubble's law states that the recessional velocity of a galaxy (v) is proportional to its distance (d) from us, represented by the formula:

$v = H_0 imes d$

where:

• $H_0$ is the Hubble constant (approximately 70 km/s/Mpc).

To use this formula, we first need to convert the redshift (z) into the velocity. The relationship between redshift and velocity is:

$v = z imes c$

where $c$ is the speed of light (approximately 3 x 10^8 m/s). For our redshift of 0.014, the velocity $v$ becomes:

$v = 0.014 imes 3 imes 10^8 ext{ m/s} = 4.2 imes 10^6 ext{ m/s}.$

Using the Hubble constant ($H_0 = 70 ext{ km/s/Mpc} = 2.27 imes 10^{-18} ext{ s}^{-1}$), we can find the distance $d$:

ightarrow d ext{ (in meters)}.$$ Calculating this gives: $$d ext{ (in m)} ext{ approximately } 1.84 imes 10^{22} ext{ m},$$ which we will express in the given options. This converts to about 1.83 x 10^10 m, which corresponds to option B.