The diagram shows the spectral lines in the light from two galaxies as well as the same spectral lines in the light from a laboratory source. How is Galaxy A moving relative to Earth? How is Galaxy B moving relative to Earth? Which galaxy is moving faster relative to Earth?
So we can see that we’ve got spectral lines from two galaxies in the diagram: the labelled Galaxy A and Galaxy B. As well as this, we’ve got the same spectral lines from a laboratory source. So that obviously has to be back here on Earth. And that’s also labelled in the diagram.
Now, since the laboratory source is on Earth, that means that it cannot be moving relative to Earth because it’s on Earth. Therefore, the spectral lines that we find from the laboratory source are in a way our reference spectral lights. This is because these are the spectral lines that we would expect from a source that’s not moving at all relative to Earth. In other words, its stationary relative to Earth.
We also know that any source moving away from us will have its spectral lines redshifted. Conversely, any source moving towards us will have its spectral lines blueshifted. What do those things mean though? What does it mean for something to be redshifted or blueshifted?
Well, let’s look at redshifted first. All it means is that if something is moving away from us, then its spectral lines will move towards the red end of the spectrum. Same thing with blueshift, if something is moving towards us, then the spectral lines will move towards the blue end of the spectrum.
So what we need to do in this question is to see how the spectral lines from Galaxy A and B compared to those from the laboratory source. So let’s do that now. Let’s start with this pair of spectral lines. They’re spaced a certain distance apart. And we can see that same spectral lines signature in both of these spectra here — in Galaxy A and B. They are the same spectral lines. However, we can clearly see that this pair of spectral lines has been shifted towards the red end in both Galaxy A spectrum and Galaxy B spectrum.
And this is true for the other spectral lines as well. This one, for example, starts out roughly about here. And it’s been shifted to about here for the Galaxy A spectrum. It’s been shifted even further to the right for the Galaxy B spectrum. And in fact, we can do this kind of thing for all the spectral lines. This ends up making the diagram a bit messy, but we can essentially see that every single spectral line has been shifted towards the right for both Galaxies A and B.
So let’s focus our attention on the spectral line we’ve labelled in orange — this first one on the left here. It starts out at this frequency. And it gets shifted towards the red end of the spectrum, which is towards the right for Galaxy A, by a small amount. In other words, the spectral line is redshifted. Therefore, the galaxy emitting the spectrum must be moving away from Earth. And so we know that Galaxy A is moving away from Earth.
Now, the same thing is true for Galaxy B, except this time, it’s a lot more redshifted. So Galaxy B must also be moving away from Earth. But if they’re both moving away, then why had they different amounts of redshift on each of the spectra? Well, the amount of redshift or in other words how much the spectrum is shifted towards the red end depends on the speed at which the galaxy is moving away from the Earth.
Larger redshift means the galaxies moving away from the Earth much faster. Smaller redshift means the galaxies moving away from the Earth slightly more slowly. So because the redshift on Galaxy B is much bigger than the redshift on Galaxy A, we know that Galaxy B is moving away faster from the Earth or in other words Galaxy B is moving faster relative to Earth.