# How do astronomers measure the speed of the Galaxy? The Andromeda Galaxy is moving towards us with relative speed 225 Km/s (Credit: NASA/JPL-Caltech)

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.

# Doppler Effect

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.

# Red Shift

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.

# Blue Shift

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:

(λ’-λ)/λ=v/c

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

# Observation

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.

# Example

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.

##### Reference

http://www.cfa.harvard.edu/seuforum/galSpeed/

http://astro.wku.edu/astr106/Hubble_intro.html

http://www.ifa.hawaii.edu/users/acowie/class05/home9_sol.html

## 8 thoughts on “How do astronomers measure the speed of the Galaxy?”

1. Alena Simon Peter says:

For the time I was able to understand, how Doppler effect is used to measure speed of galaxies. Wonderful, accurate and precise explanation and description.

2. amir says:

thanks, that was great.

3. leku jordan says:

it has widen my knowledge about the topic and i understood it more

4. Nayan Trivedi says:

True, but much more complicated.
The best measure that we have is redshift from a SN1a within a galaxy. That is very accurate (within 0.1%), but only to about 250 Mpc. For from 150 to 250 Mpc compensating using special relativity is good enough. After that, you need to start compensating for “proper recessional velocity” using general relativity with the assumption of a few omega parameters.

However, Isn’t it true that getting accurate measures of distance and velocity are very difficult, especially past a few hundred Mpc. It is even difficult to choose the right survey data since most surveys vary significantly from one another. This is all part of the Hubble value issue.
Your views on this?

1. Anil Kumar says:

I work in Experimental High Energy Physics specifically in neutrino physics and do not have much idea about the details of astronomical measurements. But I would like to highlight few of my views regarding distance and velocity measurement:

The above concept of Doppler shift assumes that the shift in wavelength is only caused by the relative velocity of the source and receivers. The medium is assumed to be non-disturbing like the vacuum. But the interstellar space is filled with stellar remnants in low density which may cause scattering and change wavelength making it difficult to measure the Doppler shift accurately.

The gravitational shift also needs to be considered which will change the wavelength and may cause false Doppler shift. The gravitational shift can be caused by visible objects or dark matter also.

For small distances, these effects can be ignored but for large distances, these effects will accumulate to give you large errors in the measurements. We may also need to worry the validity of physics laws at such large distances. Does the same physics laws apply at so large distances? What if the gravitation force falls as not square of distance but a fractionally different than square ( maybe 2.00000000000001 or so for example). This difference in physics laws will not be visible at normal distances but may come into the picture at very large distances.

5. Aprilia says:

thats good, do you have any reference?

6. Barry says:

Interesting, but how do you measure the rotational speed of a galaxy? I would assume that if the galaxy was perfectly aligned side on to us you would subtract the wavelength of the side rotating away from us from the wavelength of the side rotating towards us? If that’s correct would it just be another mathematical correction needed to adjust for a galaxy rotating at an angle?