Redshift and Blueshift Explained - How We Know Disance to Far-Off Objects

Last Updated January 10, 2019 by . First Published in 2009.

846 words, estimated reading time 3 minutes.

Cosmology Series
  1. What is Cosmology and the Big Bang Theory
  2. The Physics Governing the Universe
  3. What is Light? How To Measure the Speed of Light?
  4. Redshift and Blueshift Explained - How We Know Disance to Far-Off Objects
  5. What is the Cosmic Microwave Background Radiation?
  6. Expansion of the Universe, Cosmic Scale Factor and Hubble's Law
Redshift and Blueshift Explained - How We Know Disance to Far-Off Objects

Redshift and Blueshift are visible effects of the Doppler effect which you may have heard when a siren approaches and passes you by.

Redshift is an increase in the wavelength of light coming from an object due to its motion away from Earth. Blueshift is the opposite, a decrease in wavelength due to its motion towards Earth.

Redshift and Blueshift are visible effects of the Doppler effect. You have probably witnessed the Doppler effect yourself. The best example is a siren coming towards you fast. As it approaches the siren is a much higher pitch than when it passes and is moving away from you. This corresponds with an increase in frequency. This is demonstrated in the video below.

The same thing happens with light. As an object moves towards us the wavelength is altered so that it shifts towards the blue end of the spectum. As the object moves away from us the light is "stretched" towards the red. The shifts we can observe occur in the change of position in the spectral lines.

Redshift and Blueshift
Redshift and Blueshift

History of Redshift and Blueshift

The Doppler effect is named after Christian Andreas Doppler who offered the first known physical explanation for the phenomenon in 1842. The hypothesis was tested and confirmed for sound waves by the Dutch scientist Christoph Hendrik Diederik Buys Ballot in 1845.

The first doppler redshift was described in 1848 by French physicist Armand-Hippolyte-Louis Fizeau, who pointed to the shift in spectral lines seen in stars as being due to the Doppler effect. The effect is sometimes called the "Doppler-Fizeau effect". In 1868, British astronomer William Huggins was the first to determine the velocity of a star moving away from the Earth by this method.

In 1871, optical redshift was confirmed when the phenomenon was observed in Fraunhofer lines using solar rotation, about 0.1 Å in the red. In 1901 Aristarkh Belopolsky verified optical redshift in the laboratory using a system of rotating mirrors.

Looking for Redshift in Spectra

The spectrum of light coming from a distant object can be measured through spectroscopy. To determine the redshift features in the spectrum (such as absorption lines, emission lines, or other variations in light intensity) are searched for and if found compared with known features in the spectrum of various elements. A very common element in space is hydrogen.

Absorption lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to absorption lines in the optical spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decr
Absorption lines in the optical spectrum of a supercluster of distant galaxies (right), as compared to absorption lines in the optical spectrum of the Sun (left). Arrows indicate redshift. Wavelength increases up towards the red and beyond (frequency decr

In the diagram above you can see two spectra. One from out Sun (a known spectra - we know each of the absorption lines) and one from a supercluster of distant galaxies. When we compare the two we see a correlation between the Hydrogen lines of the Sun and of the distant galaxies, the only difference is that the absorption lines in the galaxies are all moved up (towards the red). This indicates a redshift and we can tell that the galaxies are moving away from us (or we are moving away from the galaxies).

Calculation of Redshift and Blueshift

Once we find a known spectral line we can work out it's wavelength in the spectra. We can then use this to calculate the exact redshift.

From the graphic above we can take the Hydrogen Alpha emission line at 656.2 nm. We can then calculate the wavelength from the observed spectra based on the spectrum (for this example the observed line is at 675 nm). We can then use a simple equation to calculate the redshift value.

Equation 27 - Redshift

Plugging in our values for the observed wavelengths gives:

Redshift example working
Redshift example working
Equation 28 - Redshift example working

z is a dimensionless quantity that is traditionally used. A positive value of z indicates redshift, a negative value represents blueshift.

Calculating Speed and Distance from Redshift

Now we know the redshift of a distant object, we can work out its speed. This is done using the formula:

z = v/c

This equation is actually an approximation that is only valid to describe the redshift of galaxies when the recession velocity v is much smaller than the velocity of light c.

Now we know the speed the object is moving towards or away from us, we can further derive the distance using the Hubble relation. The Hubble relation is a (locally) linear correlation between the redshift of a galaxy and its distance from the Milky Way.

v = H_0 d

Where v is the velocity and H0 is the Hubble constant. We can then solve this for d.

d = v / H_0

Solving the redshift equation for v gives v = z c which we can combine into the Hubble equation which further gives:

d = z {c}/H_0

Which is how we can calculate distance to an object given its redshift value.

Example Redshifts

Currently the objects with the highest known redshifts are galaxies. The most reliable redshifts are from spectroscopic data and the highest confirmed spectroscopic redshift of a galaxy is that of IOK-1 at a redshift z = 6.96.

The most distant observed gamma ray burst is GRB 080913, which had a redshift of 6.7.


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  1. TR

    On Friday 6th of October 2017, Trevor said

    Just saying there does not appear to be any adjustment for the effect of gravity.....why
  2. MK

    On Wednesday 5th of December 2012, Mo King said

    The red and blue-shift in relation to photons seems to be grossly misused for the determination of stellar motion.Gravity lensing is a phenomena caused by the slingshot effect around gravity bodies whereby the photons gain energy but not speed, which has the effect of shortening the wavelength to a higher energy band thus negating the use for measurement of large interstellar distances. The wavelength of all radiation can be increased or decreased in space by any and all large gravity bodies, therefore its use in distance measurement is nonsensical.Lastly the radiation over large distances will dissipate its energies effecting a red shift regardless of direction (towards or away). MoK
  3. NJ

    On Tuesday 22nd of May 2012, Nicholas Jessup said

    1. What are the Negative Aspects of Red Shift2. Are there other pieces of evidence that show the universe is changing besides red shift.
  4. AX

    On Saturday 21st of April 2012, Axel said

    we can also say z=v/c, where c is the speed of light and v is the velocity of the source. From this we can calculate how fast the object is moving away or towards us.
    1. Lonewolf Online

      On Thursday 14th of June 2012, Lonewolf Online  Post Author replied

      True, but that equation only works in a non-relativistic Universe. For a unrelativistic speeds it is <em>nearly</em> right.