A galaxy has a recessional velocity of 0-30c - Scottish Highers Physics - Question 5 - 2017

Hubble's Law states that the recessional velocity (v) is directly proportional to the distance (d) from the observer: v = H_0 d Where $H_0$ is the Hubble constant, approximately $70 ext{ km s}^{-1} ext{Mpc}^{-1}$ (or $7.0 × 10^{-18} ext{ s}^{-1}$ when converted).

Using the maximum recessional velocity: v = 30c = 30 × 3.0 × 10^8 ext{ m/s} = 9.0 × 10^9 ext{ m/s} Applying Hubble's Law:

d = rac{v}{H_0} = rac{9.0 × 10^9 ext{ m/s}}{7.0 × 10^{-18} ext{ s}^{-1}} Calculating this gives:

$d ≈ 1.286 imes 10^{17} ext{ m}$ Rounding this gives an approximate distance of $1.3 × 10^{17} ext{ m}$.

Based on the calculation, the predicted distance between Earth and the galaxy corresponds to option A: $1.3 × 10^{17} ext{ m}$.