{"id":293,"date":"2022-02-11T17:08:19","date_gmt":"2022-02-11T17:08:19","guid":{"rendered":"https:\/\/pressbooks.ccconline.org\/astronomy\/?post_type=chapter&#038;p=293"},"modified":"2022-04-26T22:58:24","modified_gmt":"2022-04-26T22:58:24","slug":"5-6-the-doppler-effect","status":"publish","type":"chapter","link":"https:\/\/pressbooks.ccconline.org\/astronomy\/chapter\/5-6-the-doppler-effect\/","title":{"raw":"5.6 The Doppler Effect","rendered":"5.6 The Doppler Effect"},"content":{"raw":"<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Learning Objectives<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p id=\"fs-id1168583400437\" class=\" \">By the end of this section, you will be able to:<\/p>\r\n\r\n<ul id=\"fs-id1163975574006\">\r\n \t<li>Explain why the spectral lines of photons we observe from an object will change as a result of the object\u2019s motion toward or away from us<\/li>\r\n \t<li>Describe how we can use the Doppler effect to deduce how fast astronomical objects are moving through space<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<p id=\"fs-id1163975575671\" class=\" \">The last two sections introduced you to many new concepts, and we hope that through those, you have seen one major idea emerge. 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.<\/p>\r\n\r\n<section id=\"fs-id1163974263930\" data-depth=\"1\">\r\n<h3 data-type=\"title\">Motion Affects Waves<\/h3>\r\n<p id=\"fs-id1163974366375\" class=\" \">In 1842, Christian\u00a0<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term218\" class=\"no-emphasis\" data-type=\"term\">Doppler<\/span>\u00a0first 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\u00a0<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term219\" data-type=\"term\">Doppler effect<\/span>, is illustrated in\u00a0Figure 5.22.<\/p>\r\n\r\n<div id=\"OSC_Astro_05_06_Doppler\" class=\"os-figure\">\r\n<figure data-id=\"OSC_Astro_05_06_Doppler\">\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"900\"]<img id=\"2\" src=\"https:\/\/openstax.org\/apps\/archive\/20210823.155019\/resources\/2e31d65d9eef6dd9d8a5fd17863d6d4d54e2cc02\" alt=\"This figure illustrates the Doppler effect. Part A shows even concentric rings representing waves moving over an observer. The center of the rings is labeled \u201cS\u201d for source, and from innermost to outermost the rings are labeled \u201c4\u201d, \u201c3\u201d, \u201c2\u201d, and \u201c1\u201d. An arrow points outward from the outmost ring, and is labeled \u201cto observer\u201d. Part B shows uneven concentric rings representing waves moving over three observers. The center of the rings is labeled \u201cS 4\u201d for source, and from innermost to outermost the rings are labeled \u201c4\u201d, \u201c3\u201d, \u201c2\u201d, and \u201c1\u201d. Labels \u201cS 3\u201d, \u201cS 2\u201d, and \u201cS 1\u201d are marked vertically above \u201cS 4\u201d, and represent the movement of the source \u201cto Observer A\u201d at the bottom of the outmost ring. \u201cTo observer B\u201d is labeled at the left, and \u201cto observer C\u201d at the top of the outmost ring.\" width=\"900\" height=\"528\" data-media-type=\"image\/jpeg\" \/> <strong>Figure\u00a05.22\u00a0<\/strong>Doppler Effect.\u00a0(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\u00a0A\u00a0and away from observer\u00a0C. Wave crest 1 was emitted when the source was at position S1, crest 2 at position S2, and so forth. Observer\u00a0A\u00a0sees waves compressed by this motion and sees a blueshift (if the waves are light). Observer\u00a0C\u00a0sees the waves stretched out by the motion and sees a redshift. Observer\u00a0B, whose line of sight is perpendicular to the source\u2019s motion, sees no change in the waves (and feels left out).[\/caption]<\/figure>\r\n<\/div>\r\n<p id=\"fs-id1163975706572\" class=\" \">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, [latex]\\lambda [\/latex], where [latex]\\lambda [\/latex] 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.<\/p>\r\n<p id=\"fs-id1163975352155\" class=\" \">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\u00a0<em data-effect=\"italics\">A<\/em>, this motion of the source has decreased the distance between crests\u2014it\u2019s squeezing the crests together, this observer might say.<\/p>\r\n<p id=\"fs-id1163974375052\" class=\" \">In part (b), we show the situation from the perspective of three observers. The source is seen in four positions, [latex]{S_1}[\/latex], [latex]{S_2}[\/latex], [latex]{S_3}[\/latex], and [latex]{S_4}[\/latex], each corresponding to the emission of one wave crest. To observer\u00a0<em data-effect=\"italics\">A<\/em>, 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.)<\/p>\r\n<p id=\"fs-id1163975339496\" class=\" \">The situation is not the same for other observers. Let\u2019s look at the situation from the point of view of observer\u00a0<em data-effect=\"italics\">C<\/em>, located opposite observer\u00a0<em data-effect=\"italics\">A<\/em>\u00a0in 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\u00a0<em data-effect=\"italics\">B<\/em>, 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.<\/p>\r\n<p id=\"fs-id1163975294473\" class=\" \">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\u00a0<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term220\" data-type=\"term\">radial velocity<\/span>. Sideways motion does not produce such an effect. Observers between\u00a0<em data-effect=\"italics\">A<\/em>\u00a0and\u00a0<em data-effect=\"italics\">B<\/em>\u00a0would 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\u00a0<em data-effect=\"italics\">B<\/em>\u00a0and\u00a0<em data-effect=\"italics\">C<\/em>\u00a0would observe lengthening of the light waves that are along their line of sight.<\/p>\r\n<p id=\"fs-id1163975393928\" class=\" \">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.<\/p>\r\n\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nA nice example of this change in the sound of a train whistle can be heard at the end of the classic Beach Boys song \u201cCaroline, No\u201d on their album\u00a0<em data-effect=\"italics\">Pet Sounds<\/em>. To hear this sound, go to this\u00a0<a href=\"https:\/\/openstax.org\/l\/30BBtrain\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">YouTube<\/a>\u00a0version of the song. The sound of the train begins at approximately 2:20.\r\n\r\n<\/div>\r\n<\/div>\r\n<h3 data-type=\"title\">Color Shifts<\/h3>\r\n<p id=\"fs-id1163975575055\" class=\" \">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\u00a0<em data-effect=\"italics\">blueshift<\/em>\u00a0(since the end of the spectrum is really violet, the term should probably be\u00a0<em data-effect=\"italics\">violetshift<\/em>, 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\u00a0<em data-effect=\"italics\">redshift<\/em>. Because the Doppler effect was first used with visible light in astronomy, the terms \u201c<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term221\" class=\"no-emphasis\" data-type=\"term\">blueshift<\/span>\u201d and \u201c<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term222\" class=\"no-emphasis\" data-type=\"term\">redshift<\/span>\u201d 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.<\/p>\r\n<p id=\"fs-id1163975574693\" class=\" \">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<\/p>\r\n\r\n<math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mfrac><mrow><mtext>\u0394<\/mtext><mtext>\u03bb<\/mtext><\/mrow><mtext>\u03bb<\/mtext><\/mfrac><mo>=<\/mo><mfrac><mi>v<\/mi><mi>c<\/mi><\/mfrac><\/mrow><\/mrow><annotation-xml encoding=\"MathML-Content\"><mrow><mfrac><mrow><mtext>\u0394<\/mtext><mtext>\u03bb<\/mtext><\/mrow><mtext>\u03bb<\/mtext><\/mfrac><mo>=<\/mo><mfrac><mi>v<\/mi><mi>c<\/mi><\/mfrac><\/mrow><\/annotation-xml><\/semantics><\/math>where [latex]\\lambda[\/latex] is the wavelength emitted by the source, [latex]\\Delta \\lambda[\/latex] is the difference between [latex]\\lambda[\/latex] and the wavelength measured by the observer,\u00a0<em data-effect=\"italics\">c<\/em>\u00a0is the speed of light, and\u00a0<em data-effect=\"italics\">v<\/em>\u00a0is the relative speed of the observer and the source in the line of sight. The variable\u00a0<em data-effect=\"italics\">v<\/em>\u00a0is 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\u00a0[latex]v = c \\times \\frac{{\\Delta \\lambda }}{\\lambda }[\/latex].\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nClick-and-drag the object emitting waves or the object receiving waves in this\u00a0<a href=\"https:\/\/openstax.org\/l\/30doppsim\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">simulator<\/a>\u00a0to 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.\r\n\r\n<\/div>\r\n<\/div>\r\nIf 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.\r\n<p id=\"fs-id1163974226844\" class=\" \">You may now be asking: if all the stars are moving and motion changes the wavelength of each spectral line, won\u2019t 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\u2019s 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?<\/p>\r\n<p id=\"fs-id1163975535992\" class=\" \">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\u00a0<em data-effect=\"italics\">pattern<\/em>\u00a0of 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\u2014it 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\u2019s 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.<\/p>\r\n<p id=\"fs-id1163975661689\" class=\" \">The training of astronomers includes much work on learning to decode light (and other electromagnetic radiation). A skillful \u201cdecoder\u201d 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\u2019s really an impressive amount of information for stars that are light-years away.<\/p>\r\n\r\n<\/section>\r\n<div class=\"textbox\">This book was adapted from the following: Fraknoi, A., Morrison, D., &amp; Wolff, S. C. (2016). 5.6 The Doppler Effect. In <i>Astronomy<\/i>. OpenStax. https:\/\/openstax.org\/books\/astronomy\/pages\/5-6-the-doppler-effect under a <a href=\"http:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Creative Commons Attribution License 4.0<\/a><\/div>\r\n<div>Access the entire book for free at <a href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction\">https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction<\/a><\/div>","rendered":"<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Learning Objectives<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<p id=\"fs-id1168583400437\" class=\"\">By the end of this section, you will be able to:<\/p>\n<ul id=\"fs-id1163975574006\">\n<li>Explain why the spectral lines of photons we observe from an object will change as a result of the object\u2019s motion toward or away from us<\/li>\n<li>Describe how we can use the Doppler effect to deduce how fast astronomical objects are moving through space<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<p id=\"fs-id1163975575671\" class=\"\">The last two sections introduced you to many new concepts, and we hope that through those, you have seen one major idea emerge. 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.<\/p>\n<section id=\"fs-id1163974263930\" data-depth=\"1\">\n<h3 data-type=\"title\">Motion Affects Waves<\/h3>\n<p id=\"fs-id1163974366375\" class=\"\">In 1842, Christian\u00a0<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term218\" class=\"no-emphasis\" data-type=\"term\">Doppler<\/span>\u00a0first 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\u00a0<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term219\" data-type=\"term\">Doppler effect<\/span>, is illustrated in\u00a0Figure 5.22.<\/p>\n<div id=\"OSC_Astro_05_06_Doppler\" class=\"os-figure\">\n<figure data-id=\"OSC_Astro_05_06_Doppler\">\n<figure style=\"width: 900px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" id=\"2\" src=\"https:\/\/openstax.org\/apps\/archive\/20210823.155019\/resources\/2e31d65d9eef6dd9d8a5fd17863d6d4d54e2cc02\" alt=\"This figure illustrates the Doppler effect. Part A shows even concentric rings representing waves moving over an observer. The center of the rings is labeled \u201cS\u201d for source, and from innermost to outermost the rings are labeled \u201c4\u201d, \u201c3\u201d, \u201c2\u201d, and \u201c1\u201d. An arrow points outward from the outmost ring, and is labeled \u201cto observer\u201d. Part B shows uneven concentric rings representing waves moving over three observers. The center of the rings is labeled \u201cS 4\u201d for source, and from innermost to outermost the rings are labeled \u201c4\u201d, \u201c3\u201d, \u201c2\u201d, and \u201c1\u201d. Labels \u201cS 3\u201d, \u201cS 2\u201d, and \u201cS 1\u201d are marked vertically above \u201cS 4\u201d, and represent the movement of the source \u201cto Observer A\u201d at the bottom of the outmost ring. \u201cTo observer B\u201d is labeled at the left, and \u201cto observer C\u201d at the top of the outmost ring.\" width=\"900\" height=\"528\" data-media-type=\"image\/jpeg\" \/><figcaption class=\"wp-caption-text\"><strong>Figure\u00a05.22\u00a0<\/strong>Doppler Effect.\u00a0(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\u00a0A\u00a0and away from observer\u00a0C. Wave crest 1 was emitted when the source was at position S1, crest 2 at position S2, and so forth. Observer\u00a0A\u00a0sees waves compressed by this motion and sees a blueshift (if the waves are light). Observer\u00a0C\u00a0sees the waves stretched out by the motion and sees a redshift. Observer\u00a0B, whose line of sight is perpendicular to the source\u2019s motion, sees no change in the waves (and feels left out).<\/figcaption><\/figure>\n<\/figure>\n<\/div>\n<p id=\"fs-id1163975706572\" class=\"\">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, [latex]\\lambda[\/latex], where [latex]\\lambda[\/latex] 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.<\/p>\n<p id=\"fs-id1163975352155\" class=\"\">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\u00a0<em data-effect=\"italics\">A<\/em>, this motion of the source has decreased the distance between crests\u2014it\u2019s squeezing the crests together, this observer might say.<\/p>\n<p id=\"fs-id1163974375052\" class=\"\">In part (b), we show the situation from the perspective of three observers. The source is seen in four positions, [latex]{S_1}[\/latex], [latex]{S_2}[\/latex], [latex]{S_3}[\/latex], and [latex]{S_4}[\/latex], each corresponding to the emission of one wave crest. To observer\u00a0<em data-effect=\"italics\">A<\/em>, 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.)<\/p>\n<p id=\"fs-id1163975339496\" class=\"\">The situation is not the same for other observers. Let\u2019s look at the situation from the point of view of observer\u00a0<em data-effect=\"italics\">C<\/em>, located opposite observer\u00a0<em data-effect=\"italics\">A<\/em>\u00a0in 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\u00a0<em data-effect=\"italics\">B<\/em>, 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.<\/p>\n<p id=\"fs-id1163975294473\" class=\"\">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\u00a0<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term220\" data-type=\"term\">radial velocity<\/span>. Sideways motion does not produce such an effect. Observers between\u00a0<em data-effect=\"italics\">A<\/em>\u00a0and\u00a0<em data-effect=\"italics\">B<\/em>\u00a0would 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\u00a0<em data-effect=\"italics\">B<\/em>\u00a0and\u00a0<em data-effect=\"italics\">C<\/em>\u00a0would observe lengthening of the light waves that are along their line of sight.<\/p>\n<p id=\"fs-id1163975393928\" class=\"\">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.<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<p>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 \u201cCaroline, No\u201d on their album\u00a0<em data-effect=\"italics\">Pet Sounds<\/em>. To hear this sound, go to this\u00a0<a href=\"https:\/\/openstax.org\/l\/30BBtrain\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">YouTube<\/a>\u00a0version of the song. The sound of the train begins at approximately 2:20.<\/p>\n<\/div>\n<\/div>\n<h3 data-type=\"title\">Color Shifts<\/h3>\n<p id=\"fs-id1163975575055\" class=\"\">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\u00a0<em data-effect=\"italics\">blueshift<\/em>\u00a0(since the end of the spectrum is really violet, the term should probably be\u00a0<em data-effect=\"italics\">violetshift<\/em>, 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\u00a0<em data-effect=\"italics\">redshift<\/em>. Because the Doppler effect was first used with visible light in astronomy, the terms \u201c<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term221\" class=\"no-emphasis\" data-type=\"term\">blueshift<\/span>\u201d and \u201c<span id=\"9d6442f2-71bf-4ed3-9a37-1723bb846e0e_term222\" class=\"no-emphasis\" data-type=\"term\">redshift<\/span>\u201d 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.<\/p>\n<p id=\"fs-id1163975574693\" class=\"\">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<\/p>\n<p><math display=\"block\" xmlns=\"http:\/\/www.w3.org\/1998\/Math\/MathML\"><semantics><mrow><mrow><mfrac><mrow><mtext>\u0394<\/mtext><mtext>\u03bb<\/mtext><\/mrow><mtext>\u03bb<\/mtext><\/mfrac><mo>=<\/mo><mfrac><mi>v<\/mi><mi>c<\/mi><\/mfrac><\/mrow><\/mrow><annotation-xml encoding=\"MathML-Content\"><mrow><mfrac><mrow><mtext>\u0394<\/mtext><mtext>\u03bb<\/mtext><\/mrow><mtext>\u03bb<\/mtext><\/mfrac><mo>=<\/mo><mfrac><mi>v<\/mi><mi>c<\/mi><\/mfrac><\/mrow><\/annotation-xml><\/semantics><\/math>where [latex]\\lambda[\/latex] is the wavelength emitted by the source, [latex]\\Delta \\lambda[\/latex] is the difference between [latex]\\lambda[\/latex] and the wavelength measured by the observer,\u00a0<em data-effect=\"italics\">c<\/em>\u00a0is the speed of light, and\u00a0<em data-effect=\"italics\">v<\/em>\u00a0is the relative speed of the observer and the source in the line of sight. The variable\u00a0<em data-effect=\"italics\">v<\/em>\u00a0is 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\u00a0[latex]v = c \\times \\frac{{\\Delta \\lambda }}{\\lambda }[\/latex].<\/p>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<h3 class=\"textbox__title\">Link to Learning<\/h3>\n<\/header>\n<div class=\"textbox__content\">\n<p>Click-and-drag the object emitting waves or the object receiving waves in this\u00a0<a href=\"https:\/\/openstax.org\/l\/30doppsim\" target=\"_blank\" rel=\"noopener nofollow noreferrer\">simulator<\/a>\u00a0to 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.<\/p>\n<\/div>\n<\/div>\n<p>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.<\/p>\n<p id=\"fs-id1163974226844\" class=\"\">You may now be asking: if all the stars are moving and motion changes the wavelength of each spectral line, won\u2019t 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\u2019s 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?<\/p>\n<p id=\"fs-id1163975535992\" class=\"\">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\u00a0<em data-effect=\"italics\">pattern<\/em>\u00a0of 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\u2014it 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\u2019s 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.<\/p>\n<p id=\"fs-id1163975661689\" class=\"\">The training of astronomers includes much work on learning to decode light (and other electromagnetic radiation). A skillful \u201cdecoder\u201d 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\u2019s really an impressive amount of information for stars that are light-years away.<\/p>\n<\/section>\n<div class=\"textbox\">This book was adapted from the following: Fraknoi, A., Morrison, D., &amp; Wolff, S. C. (2016). 5.6 The Doppler Effect. In <i>Astronomy<\/i>. OpenStax. https:\/\/openstax.org\/books\/astronomy\/pages\/5-6-the-doppler-effect under a <a href=\"http:\/\/creativecommons.org\/licenses\/by\/4.0\/\" target=\"_blank\" rel=\"noopener noreferrer\">Creative Commons Attribution License 4.0<\/a><\/div>\n<div>Access the entire book for free at <a href=\"https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction\">https:\/\/openstax.org\/books\/astronomy\/pages\/1-introduction<\/a><\/div>\n","protected":false},"author":33,"menu_order":6,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-293","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":253,"_links":{"self":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/293","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/users\/33"}],"version-history":[{"count":8,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/293\/revisions"}],"predecessor-version":[{"id":827,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/293\/revisions\/827"}],"part":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/parts\/253"}],"metadata":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapters\/293\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/media?parent=293"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/pressbooks\/v2\/chapter-type?post=293"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/contributor?post=293"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.ccconline.org\/astronomy\/wp-json\/wp\/v2\/license?post=293"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}