Galactic Redshift

In space, the Doppler effect of light can be observed when spectra of distant stars and galaxies are observed, this is known as:
- Redshift if the object is moving away from the Earth
  - The wavelength is increasing but the frequency is decreasing
- Blueshift if the object is moving towards the Earth
  - The wavelength is decreasing but the frequency is increasing

red-and-blue-shift

Stars and galaxies can be red or blueshifted to an observer on Earth

Redshift is defined as:

The fractional increase in wavelength (or decrease in frequency) due to the source and observer receding from each other

Redshift can be observed by comparing the light spectrum produced from a close object, such as our Sun, with that of a distant galaxy
- The light from the distant galaxy is shifted towards the red end of the spectrum (compared to the Sun's spectra)
- This provides evidence that the universe is expanding

Comparing the light spectrum produced from the Sun and a distant galaxy, downloadable IGCSE & GCSE Physics revision notes

Comparing the light spectrum produced by the Sun with light from a distant galaxy

Positive and Negative Velocities

If the speed of the galaxy relative to Earth is positive then the galaxy is moving towards the Earth
- This is the case when the observed frequency f₀ is greater than the reference frequency f

If the speed of the galaxy relative to Earth is negative then the galaxy is moving away from the Earth
- This is the case when the observed frequency f₀ is less than the reference frequency f

An Expanding Universe

After the discovery of Doppler redshift, astronomers began to realize that almost all the galaxies in the universe are receding
This led to the idea that the space between the Earth and the galaxies must be expanding
This expansion stretches out the light waves as they travel through space, shifting them towards the red end of the spectrum

Expanding Universe Balloon

The expansion of the universe can be compared to dots on an inflating balloon

As the balloon is inflated, the dots all move away from each other
In the same way, as the rubber stretches when the balloon is inflated, space itself is stretching out between galaxies
Just like the dots, the galaxies move away from each other, however, they themselves do not move

Another observation from looking at the light spectra produced by distant galaxies is that the greater the distance to the galaxy, the greater the redshift
- This means that the greater the degree of redshift, the faster the galaxy is moving away from Earth

5-12-5-redshifts-of-galaxies_ocr-al-physics

The further a galaxy is from Earth, the greater its redshift tends to be

Hubbles-law, IGCSE & GCSE Physics revision notes

The furthest galaxies appear to be redshifted the most and are receding the fastest

Worked example

The spectra below show dark absorption lines against a continuous visible spectrum.

Redshift, downloadable AS & A Level Physics revision notes

A particle line in the spectrum of light from a source in the laboratory has a frequency of 4.570 × 10¹⁴ Hz. The same line in the spectrum of light from a distant galaxy has a frequency of 4.547 × 10¹⁴ Hz.

Calculate the speed of the distant galaxy in relation to the Earth. State whether it is moving towards or away from the Earth.

Answer:

Step 1: Write down the known quantities

Observed frequency, f₀ = 4.547 × 10¹⁴ Hz
Reference (source) frequency, f = 4.570 × 10¹⁴ Hz
Shift in frequency, Δf = observed − source = (4.547 – 4.570) × 10¹⁴ = –2.3 × 10¹² Hz
Speed of light, c = 3.0 × 10⁸ m s^–1

Step 2: Write down the Doppler redshift equation

$\frac{∆ f}{f} = \frac{f_{0} - f}{f} \approx \frac{v}{c}$

Step 3: Rearrange for speed v, and calculate

$v = \frac{c Δ f}{f} = \frac{(3.0 \times 10^{8}) \times (- 2.3 \times 10^{12})}{4.570 \times 10^{14}}$ = –1.5 × 10⁶ m s^–1

Step 4: Write a concluding sentence

The velocity is negative, so the source is moving away from the Earth
OR
The observed frequency is less than the source frequency, therefore, there is a decrease in frequency, so the source is receding, or moving away, from the Earth at 1.5 × 10⁶ m s^–1

Examiner Tip

Keep travel of the minus signs in your calculation, as this gives you information about whether the object is moving away or towards the observer.

The speed of light is given in your data booklet, you will not need to memorise this value.

Galactic Redshift (HL IB Physics)

Revision Note