Q4PE - College Physics (Urone)

Question

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

Step-by-Step Solution

Answer

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

Step 1: 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.

Step 2: Evaluating the direction

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

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

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