Red Shift and Radial Velocity

recall the Doppler principle for radial velocities
demonstrate an understanding that light from distant galaxies is shifted to longer wavelengths (redshift)
use the equation: Δλ / λ = v / c to determine the radial velocity of a galaxy
demonstrate an understanding that for galaxies in the Local Group blueshift is possible

Imagine a racing car moving towards you very fast, passing you then moving away from you.

To the person driving the car the sound of the engine doesn't change but to you it does. This is because the sound waves coming from the engine are squashed together when the car is approaching you and so the frequency of the sound reaching you increases. When the car moves away from you the space between the waves is bigger so the frequency is lower. This is called the Doppler effect.

All stars emit light. If we look at the spectrum of the light (e.g. if we make it go through a prism) we see black lines. These are there because some of the light is absorbed by elements in the outer layers of the stars. The are called absorption lines.

If we compare light from nearby galaxies with light from galaxies much further away we can see a difference. The black lines are shifted towards the red end of the spectrum. Their wavelength is bigger than it should be. What does this mean?

Could it be something like the Doppler effect?     Are these galaxies moving away from us?    YES, and very fast.

By measuring the amount of red shift we can work out how quickly they are receding (moving away from us).

Imagine light coming from two galaxies, one not moving and the other moving away from us. See how the light from the moving galaxy is stretched as it moves away making its wavelength bigger.

To calculate the recession velocity we use the equation

where λ = the unshifted wavelength, λ = the bigger shifted wavelength so Δλ is the amount that it has shifted,

v = the recession velocity and c = the speed of light ( 3 x 10⁸ m/s or 300 million m/s)

Some galaxies close to ours in our Local Group, e.g. Andromeda, are actually moving towards us as there is a significant gravitational attraction. At some point in the future the Milky Way and Andromeda will merge and form a larger galaxy. Many large galaxies are the result of mergers of smaller galaxies. The light from Andromeda is actually blue shifted.

In the first example below I have shown how we can use the red shift of 21cm radio waves to calculate the velocity of different parts of our own galaxy relative to us.

Example 1

Hydrogen emits 21.106cm radio waves. These waves appear to have a wavelength of 21.133cm coming from a group of stars in a spiral arm in the Milky Way. Calculate how fast these stars are moving away from us.

Δλ = 21.133 - 21.106 = 1cm     so    Δλ ÷ λ₀  =  0.027 ÷ 21.106      v = (0.027 ÷ 21.106) x 300 million = 0.38 million m/s

Example 2

The Hydrogen Alpha line has a wavelength of 656nm. This line appears to be at 662nm in the light observed from a distant galaxy. Calculate the recession velocity of the galaxy.

Δλ = 662 - 656 = 6nm     so    Δλ ÷ λ₀  =  6 ÷ 656      v = (6 ÷ 656) x 300 million = 2.74 million m/s

Here is a rotating spiral galaxy. We can measure how fast it is rotating by measuring the red and blue shift of the light from either side.
(Red shift = moving away, blue shift = moving towards).

galaxy pic - NASA

If we know how big the galaxy is as well we can, using Newton's law of gravitation, calculate its mass. The problem is that using this calculation it works out that there is a lot more mass in the galaxy that we can actually see. Could it be that there is a lot of invisible matter in the galaxy, indeed in the Universe?