If a galaxy is moving away from us at $1.0 \%$ of the speed of light, how far away is it from us if $H = 20 \frac { \mathrm { km } / \mathrm { s } } { \mathrm { Mly } } ? \left( c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } \right)$
A) 150 thousand ly
B) 150 billion ly
C) 200 million ly
D) 150 million ly
E) $150 \mathrm { ly }$

Question

Quizplus · Accepted Answer

The galaxy's velocity away from us is $1.0\%$ of the speed of light, $c$, which is $0.01 \times 3.00 \times 10^8 \, \text{m/s} = 3.00 \times 10^6 \, \text{m/s}$. Using Hubble's Law, $v = H \times d$, where $v$ is the velocity, $H$ is the Hubble constant, and $d$ is the distance. Rearranging for $d$, we get $d = \frac{v}{H}$. Substituting the given values, $d = \frac{3.00 \times 10^6 \, \text{m/s}}{20 \, \text{km/s/Mly}}$. Since $1 \, \text{km} = 10^3 \, \text{m}$, we convert the velocity to km/s to match the units of $H$, getting $d = \frac{3.00 \times 10^3 \, \text{km/s}}{20 \, \text{km/s/Mly}} = 150 \, \text{Mly}$.

If a Galaxy Is Moving Away from Us At 1.0%1.0 \%1.0%

If a Galaxy Is Moving Away from Us At $1.0 \%$