Hubble's law: Estimate the speed of a galaxy away from us if it is 10 billion light-years from us and 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) 0.1c B) 0.3c C) 0.5c D) 0.7c E) 0.9c

Question

Quizplus · Accepted Answer

Hubble's law states that the speed $v$ at which a galaxy moves away from us is directly proportional to its distance $d$ from us, given by $v = H_0 \times d$, where $H_0$ is the Hubble constant. Given $d = 10$ billion light-years and $H_0 = 22$ km/s per million light-years, we first convert distance to the same unit as $H_0$, which is million light-years: $10$ billion light-years = $10,000$ million light-years. Then, $v = 22 \, \text{km/s} \times 10,000 = 220,000$ km/s. To find this speed as a fraction of the speed of light $c$, we convert $c$ to km/s: $c = 3.00 \times 10^8$ m/s = $3.00 \times 10^5$ km/s. Thus, $v/c = 220,000 / 300,000 = 0.73$, which is approximately $0.7c$, making option D correct.

Hubble's Law: Estimate the Speed of a Galaxy Away from Us