Imagine a rocket ship launched from Earth with enough fuel to allow it to accelerate to speeds comparable to the speed of light. As the ship's speed increased, a remarkable thing would happen (Figure 3.16). Passengers would notice that the light from the star system toward which they were traveling seemed to be getting bluer. In fact, all stars in front of the ship would appear bluer than normal, and the greater the ship's speed, the greater the color change would be. Furthermore, stars behind the vessel would seem redder than normal, while stars to either side would be unchanged in appearance. As the spacecraft slowed down and came to rest relative to Earth, all stars would resume their usual appearance. The travelers would have to conclude that the stars had changed their colors not because of any real change in their physical properties but because of the spacecraft's own motion.

Figure 3.16 Observers in a fast-moving spacecraft will see the stars ahead of them seem bluer than normal, while those behind are reddened. The stars have not changed their properties— the color changes are the result of the motion of the spacecraft relative to the stars.

This phenomenon is not restricted to electromagnetic radiation and fast-moving spacecraft. Waiting at a railroad crossing for an express train to pass, most of us have had the experience of hearing the pitch of the engine's horn shift from high shrill to low blare as the train approaches and then recedes. High-pitched sound (treble) has shorter wavelengths than low-pitched sound (bass); this change in wavelength is analogous to the color change observed by our space travelers. Indeed, if the train had a light atop its engine, we could, in principle, witness the light change color, from bluer than normal to redder than normal, as the train passed by. (In practice, however, the color variation would be impossible to discern because trains travel far too slowly for us to perceive the effect.)

This motion-induced change in the observed wavelength of any wave—be it electromagnetic (light) or acoustical (sound)—is known as the Doppler effect, in honor of Christian Doppler, the nineteenth-century Austrian physicist who first explained it. Note that in our example of the spaceship, the observer was in motion, whereas, in the train example, it was the source of the wave that was moving. For electromagnetic radiation, the result is the same in either case—only the relative motion of source and observer matters.

To understand how the Doppler effect occurs, imagine a wave moving from the place where it is generated toward an observer who is not moving with respect to the wave source, as shown in Figure 3.17(a). By counting the number of wave crests passing per unit time, the observer could determine the wavelength of the emitted wave. Suppose now that the wave source begins to move. As illustrated in Figure 3.17(b), because the source moves between the times of emission of one wave crest and the next, successive wave crests in the direction of motion of the source will be seen to be closer together than normal, whereas crests behind the source will be more widely spaced. An observer in front of the source will therefore measure a shorter wavelength than normal, while one behind will see a longer wavelength. (The numbers indicate successive wave crests emitted by the source and the location of the source at the instant each wave crest was emitted.)

Figure 3.17 (a) Wave motion from a source toward an observer at rest with respect to the source. The four numbered circles represent successive wave crests emitted by the source; at the instant shown, the fifth wave crest is just about to be emitted. As seen by the observer, the source is not moving, so the wave crests are just concentric spheres (shown here as circles). (b) Waves from a moving source tend to "pile up" in the direction of motion and be "stretched out" on the other side. (The numbered points indicate the location of the source at the instant each wave crest was emitted.) As a result, an observer situated in front of the source measures a shorter-than-normal wavelength— a blueshift— while an observer behind the source sees a redshift. In this diagram the source is shown in motion. However, the same general statements hold whenever there is any relative motion between source and observer.

The greater the relative speed of the source and the observer, the greater the observed change in wavelength. Furthermore, only motion along the line joining the source to the observer (called radial motion) contributes to the Doppler effect. Motion across the line of sight (known as transverse motion) has no effect on the perceived wavelength. In fact, Einstein's Theory of Relativity (see Chapter 22) implies that when the transverse velocity is comparable to the speed of light, a wavelength change, called the transverse Doppler shift, does occur. For most terrestrial and astronomical applications, however, this shift is negligibly small, and we will ignore it here. In terms of the net velocity of recession between source and observer (that is, the radial component of their relative velocity, with a positive value meaning that the two are moving apart, a negative value that they are approaching), the apparent wavelength (measured by the observer) is related to the true wavelength as follows:

In the case of electromagnetic radiation, the wave speed is the speed of light c. Because cis so large—300,000 km/s—the Doppler effect is extremely small for everyday terrestrial velocities. Even with its source receding at Earth's orbital speed of 30 km/s, a beam of blue light will be shifted by only 0.01 percent, from 400 nm to 400.04 nm—a very small change indeed, and one that the human eye cannot distinguish (but one that is easily detectable with modern instruments.)

The radiation measured by an observer situated in front of a moving source is said to be blueshifted, because blue light has a shorter wavelength than red light. Similarly, an observer situated behind the source will measure a longer-than-normal wavelength—the radiation is said to be redshifted. This terminology is used even for invisible radiation, for which "red" and "blue" have no meaning: any shift toward shorter wavelengths is called a blueshift, and any shift toward longer wavelengths is called a redshift. For example, ultraviolet radiation might be blueshifted into the X-ray part of the spectrum or redshifted into the visible, infrared radiation could be redshifted into the microwave range, and so on.

Astronomers can use the Doppler effect to measure the speed of any cosmic object along the line of sight simply by determining the extent to which its light is red- or blueshifted. The motions of nearby stars and distant galaxies—even the expansion of the universe itself—have all been measured in this way. Motorists stopped for speeding on the highway have experienced another, much more down-to-earth, application: police radar measures speed by means of the Doppler effect, as do the radar guns used to clock the velocity of a pitcher's fastball or a tennis player's serve. Notice, incidentally, that the Doppler effect depends only on the relative motion of source and observer; it does not depend on distance in any way.

In practice, it is hard to measure the Doppler shift of an entire blackbody curve, simply because it is widely spread over many wavelengths, making small shifts hard to determine with any accuracy. However, if the radiation were more narrowly defined and took up just a narrow "sliver" of the spectrum, then precise measurements of Doppler effect could be made. We will see in the next chapter that in many circumstances this is precisely what does happen, making the Doppler effect one of the observational astronomer's most powerful tools.

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