The galaxies are present at such a large distance from the Earth that the motion of galaxies cannot be observed through a telescope. No observable change in the position will be detected even if we observe any galaxy throughout life. Then, you must be wondering how the speed of the galaxy is measured by astronomers?
The speed of the galaxy is measured by observing the light spectrum coming from the distant galaxy. The properties of spectrum change due to the motion of galaxy with respect to the Earth. In other words, you can say that the spectrum contains the information about the motion of galaxy. The Doppler Effect is used to determine the speed of the galaxy.
You must have observed that the sound of Horn of rail engine is different when it is approaching as compared to the situation when it is moving away. When the engine is approaching you, the sound is shriller (sharper) as compared to the engine moving away because the frequency of sound increases as the source moves towards the observer and decreases as it moves away from the observer. This is called Doppler Effect.
The Doppler Effect is also observed for light. When the source of light moves away from the observer the wavelength increases and the frequency decreases. Since the red light has the largest wavelength in the visible spectrum, the increase in wavelength is interpreted as the shift of wavelength towards the red end of the spectrum. That is why it is also called red shift. The galaxies moving away from the Earth will appear redder than their actual color.
The opposite happens for the galaxy moving towards the observer, the wavelength decreases, and the frequency increases. The decrease in wavelength is interpreted as the shift of wavelength towards the blue end of the visible spectrum. That is why it is also called blue shift. The galaxies moving towards the Earth will appear bluer than their actual color.
Relation between change in wavelength and speed of galaxy
The speed of galaxy is related to the change in wavelength of light by the following relation:
Here, λ = rest wavelength, λ’ = observed wavelength, c = velocity of light, v = velocity of galaxy.
(λ’- λ)/λ is also called rest shift. Then,
the velocity of galaxy = redshift x velocity of light
The light from the distant galaxy is observed through the spectrometer which spreads the light into a spectrum. The lines of high intensity can be easily observed which are usually due to hydrogen, oxygen and other elements found in the galaxies. The red line of hydrogen (H-alpha) can be easily identified due to high intensity then the wavelength of this red line is calculated which gives us λ’ for the red line of hydrogen.
The wavelength of the red line of hydrogen in rest frame in the lab is also calculated which gives us λ. Now the redshift and velocity of the galaxy can be calculated from the above formula.
Line = H alpha
Rest wavelength, λ = 6562.8 A
Observed wavelength, λ’ = 8100 A
Red shift = 0.234
Velocity of galaxy = red shift x velocity of light
= 7.03 x 104 km/s.