Question

On average, how far away are galaxies that are moving away from us at$2.0\mathrm{\%}$of the speed of light?

Short answer

The direction is obtained as: $d=300\mathrm{M}\mathrm{l}\mathrm{y}$.

Step-by-step solution

Recession velocity

The recession velocity for a galaxy is given by,

$v=H_{o}d$

Here$H_o$is the Hubble constant and$d$is the distance to the galaxy.

Evaluating the direction

Galaxies are moving away from $2\mathrm{\%}\mathrm{c}$at distance.

$\begin{array}{c}d=\frac{v}{H_0}\\ =\frac{0.2\times 3\times 10^8\mathrm{m}/\mathrm{s}}{20\mathrm{k}\mathrm{m}/\mathrm{s}\mathrm{M}\mathrm{l}\mathrm{y}}\\ =300\mathrm{M}\mathrm{l}\mathrm{y}\end{array}$

Therefore, the distance of the galaxies that are moving away from us at $2\mathrm{\%}$ of the speed of the light is $300\mathrm{M}\mathrm{l}\mathrm{y}$.