Question

On average, how far away are galaxies that are moving away from us at\({\rm{2}}{\rm{.0 \% }}\)of the speed of light?

Short answer

The direction is obtained as: \(d{\rm{ = 300 Mly}}\).

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 \({\rm{2\% c}}\)at distance.

\(\begin{array}{c}d = \frac{v}{{{H_0}}}\\ = {\rm{ }}\frac{{{\rm{0}}{\rm{.2 \times 3 \times 1}}{{\rm{0}}^{\rm{8}}}\,{\rm{m/s}}}}{{{\rm{20 km/sMly}}}}\\ = {\rm{ 300 Mly}}\end{array}\)

Therefore, the distance of the galaxies that are moving away from us at \(2\% \) of the speed of the light is \(300\,{\rm{Mly}}\).