Question

If a galaxy is\({\rm{500 Mly}}\)away from us, how fast do we expect it to be moving and in what direction?

Short answer

The direction is obtained as: \({\rm{1}}{{\rm{0}}^{\rm{4}}}\,{\rm{km/s}}\) away from us.

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

Using the Hubble's red shift formula, we then obtain as:

\(\begin{align}{}v & = {H_0}d\\ & = {\rm{ 20}}\,{\rm{km/sMly}} \times {\rm{500}}\,{\rm{Mly}}\\ &= {\rm{ 1}}{{\rm{0}}^{\rm{4}}}\,{\rm{km/s}}\end{align}\)

Therefore, the direction is: \({\rm{1}}{{\rm{0}}^{\rm{4}}}\,{\rm{km/s}}\) away from us.