Astronomers can learn about the elements in stars and galaxies by decoding the information in
their spectral lines. There is a complicating factor in learning how to decode the message of
starlight, however. If a star is moving toward or away from us, its lines will be in a slightly different
place in the spectrum from where they would be in a star at rest. And most objects in the universe
do have some motion relative to the Sun.
Motion Affects Waves
In 1842, Christian Doppler first measured the effect of motion on waves by hiring a group of
musicians to play on an open railroad CAR as it was moving along the track. He then applied what
he learned to all waves, including light, and pointed out that if a light source is approaching or
receding from the observer, the light waves will be, respectively, crowded more closely together or
spread out. The general principle, now known as the Doppler effect, is illustrated in Figure
5.22.
Figure 5.22 Doppler Effect. (a) A source, S, makes waves whose numbered crests (1, 2, 3, and 4)
wash over a stationary observer. (b) The source S now moves toward observer A and away from
observer C. Wave crest 1 was emitted when the source was at position S1, crest 2 at position S2,
and so forth. Observer A sees waves compressed by this motion and sees a blueshift (if the waves
are light). Observer C sees the waves stretched out by the motion and sees a redshift. Observer B,
whose line of sight is perpendicular to the source’s motion, sees no change in the waves (and feels
left out).
In part (a) of the figure, the light source (S) is at rest with respect to the observer. The source
gives off a series of waves, whose crests we have labeled 1, 2, 3, and 4. The light waves spread
out evenly in all directions, like the ripples from a splash in a pond. The crests are
separated by a distance, λ, where λ is the wavelength. The observer, who happens to be
located in the direction of the bottom of the image, sees the light waves coming nice
and evenly, one wavelength apart. Observers located anywhere else would see the same
thing.
On the other hand, if the source of light is moving with respect to the observer, as seen in part (b),
the situation is more complicated. Between the time one crest is emitted and the next one is ready
to come out, the source has moved a bit, toward the bottom of the page. From the point of view of
observer A, this motion of the source has decreased the distance between crests—it’s squeezing the
crests together, this observer might say.
In part (b), we show the situation from the perspective of three observers. The source is seen
in four positions, S1, S2, S3, and S4, each corresponding to the emission of one wave
crest. To observer A, the waves seem to follow one another more closely, at a decreased
wavelength and thus increased frequency. (Remember, all light waves travel at the speed of
light through empty space, no matter what. This means that motion cannot affect the
speed, but only the wavelength and the frequency. As the wavelength decreases, the
frequency must increase. If the waves are shorter, more will be able to move by during each
second.)
The situation is not the same for other observers. Let’s look at the situation from the point of view
of observer C, located opposite observer A in the figure. For her, the source is moving away from
her location. As a result, the waves are not squeezed together but instead are spread out by the
motion of the source. The crests arrive with an increased wavelength and decreased frequency.
To observer B, in a direction at right angles to the motion of the source, no effect is
observed. The wavelength and frequency remain the same as they were in part (a) of the
figure.
We can see from this illustration that the Doppler effect is produced only by a motion toward or
away from the observer, a motion called radial velocity. Sideways motion does not produce such an
effect. Observers between A and B would observe some shortening of the light waves
for that part of the motion of the source that is along their line of sight. Observers
between B and C would observe lengthening of the light waves that are along their line of
sight.
You may have heard the Doppler effect with sound waves. When a train whistle or police siren
approaches you and then moves away, you will notice a decrease in the pitch (which is how human
senses interpret sound wave frequency) of the sound waves. Compared to the waves at rest, they
have changed from slightly more frequent when coming toward you, to slightly less frequent when
moving away from you.
Link to Learning
A nice example of this change in the sound of a train whistle can be heard at the end of the classic
Beach Boys song “Caroline, No” on their album PET Sounds. To hear this sound, go to this
YouTube (https://openstax.org/l/30BBtrain) version of the song. The sound of the train begins at
approximately 2:20.
Color Shifts
When the source of waves moves toward you, the wavelength decreases a bit. If the waves involved
are visible light, then the colors of the light change slightly. As wavelength decreases, they shift
toward the blue end of the spectrum: astronomers call this a blueshift (since the end
of the spectrum is really violet, the term should probably be violetshift, but blue is
a more common color). When the source moves away from you and the wavelength
gets longer, we call the change in colors a redshift. Because the Doppler effect was first
used with visible light in astronomy, the terms “blueshift” and “redshift” became well
established. Today, astronomers use these words to describe changes in the wavelengths of
radio waves or X-rays as comfortably as they use them to describe changes in visible
light.
The greater the motion toward or away from us, the greater the Doppler shift. If the
relative motion is entirely along the line of sight, the formula for the Doppler shift of light
is
where λ is the wavelength emitted by the source, Δλ is the difference between λ and the
wavelength measured by the observer, c is the speed of light, and v is the relative speed of the
observer and the source in the line of sight. The variable v is counted as positive if the velocity is
one of recession, and negative if it is one of approach. Solving this equation for the velocity, we
find
Link to Learning
Click-and-drag the object emitting waves or the object receiving waves in this simulator
(https://openstax.org/l/30doppsim) to experiment with the Doppler effect yourself. The plots
along the top show how the detected wavelengths change if the objects are approaching each other
or moving further apart.
If a star approaches or recedes from us, the wavelengths of light in its continuous spectrum appear
shortened or lengthened, respectively, as do those of the dark lines. However, unless its speed is
tens of thousands of kilometers per second, the star does not appear noticeably bluer or redder
than normal. The Doppler shift is thus not easily detected in a continuous spectrum and cannot
be measured accurately in such a spectrum. The wavelengths of the absorption lines
can be measured accurately, however, and their Doppler shift is relatively simple to
detect.
You may now be asking: if all the stars are moving and motion changes the wavelength of
each spectral line, won’t this be a disaster for astronomers trying to figure out what
elements are present in the stars? After all, it is the precise wavelength (or color) that tells
astronomers which lines belong to which element. And we first measure these wavelengths in
containers of gas in our laboratories, which are not moving. If every line in a star’s
spectrum is now shifted by its motion to a different wavelength (color), how can we be
sure which lines and which elements we are looking at in a star whose speed we do not
know?
Take heart. This situation sounds worse than it really is. Astronomers rarely judge the presence of
an element in an astronomical object by a single line. It is the pattern of lines unique
to hydrogen or calcium that enables us to determine that those elements are part of
the star or galaxy we are observing. The Doppler effect does not change the pattern
of lines from a given element—it only shifts the whole pattern slightly toward redder
or bluer wavelengths. The shifted pattern is still quite easy to recognize. Best of all,
when we do recognize a familiar element’s pattern, we get a bonus: the amount the
pattern is shifted can enable us to determine the speed of the objects in our line of
sight.
The training of astronomers includes much work on learning to decode light (and other
electromagnetic radiation). A skillful “decoder” can learn the temperature of a star, what elements
are in it, and even its speed in a direction toward us or away from us. That’s really an impressive
amount of information for stars that are light-years away.
Attribution
Access for free at openstax.org.
Bibliography
This article is a derivative work of the original 2022 CC BY 4.0 release identified in
[1].
[1] Andrew Fraknoi, David Morrison, and Sidney Wolff, “5.6 The Doppler Effect,” in Astronomy
2e. Houston, Texas: OpenStax, March 9, 2022. Original digital ISBN 978-1-951693-50-3. Original
textbook content licensed under the Creative Commons Attribution 4.0 International
License (CC BY 4.0), except where otherwise noted. Changes: converted to LaTeX for
PhysicsLibrary and Example 5.6 separated into a standalone entry. Access for free at
openstax.org.
