{"id":1172,"date":"2017-12-20T00:05:29","date_gmt":"2017-12-20T05:05:29","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/?post_type=chapter&p=1172"},"modified":"2021-05-02T05:08:33","modified_gmt":"2021-05-02T09:08:33","slug":"28-8-collaborative-group-activities-questions-and-exercises","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/28-8-collaborative-group-activities-questions-and-exercises\/","title":{"raw":"28.7 Collaborative Group Activities, Questions and Exercises","rendered":"28.7 Collaborative Group Activities, Questions and Exercises"},"content":{"raw":"
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Collaborative Group Activities<\/h1>\r\n
    \r\n \t
  1. Suppose you developed a theory to account for the evolution of a large city such as New York City. Have your group discuss whether it would resemble the development of structure in the universe (as we have described it in this chapter). What elements of your model for New York City resemble the astronomers\u2019 model for the growth of structure in the universe? Which elements do not match?<\/li>\r\n \t
  2. Most astronomers believe that dark matter exists and is a large fraction of the total matter in the universe. At the same time, most astronomers do not believe that UFOs are evidence that we are being visited by aliens from another world. Yet astronomers have never actually seen either dark matter or a UFO. Why do you think one idea is widely accepted by scientists and the other is not? Which idea do you think is more believable? Give your reasoning.<\/li>\r\n \t
  3. Someone in your group describes the redshift surveys of galaxies to a friend, who says he\u2019s never heard of a bigger waste of effort. Who cares, he asks, about the large-scale structure of the universe? What is your group\u2019s reaction, and what reasons could you come up with for putting money into figuring out how the universe is organized?<\/li>\r\n \t
  4. The leader of a small but very wealthy country is obsessed by maps. She has put together a fabulous collection of Earth maps, purchased all the maps of other planets that astronomers have assembled, and now wants to commission the best possible map of the entire universe. Your group is selected to advise her. What sort of instruments and surveys should she invest in to produce a good map of the cosmos? Be as specific as you can.<\/li>\r\n \t
  5. Download a high-resolution image of a rich galaxy cluster from the Hubble Space Telescope (see the list of gravitational lens news stories in the \u201cFor Further Exploration\u201d section). See if your group can work together to identify gravitational arcs, the images of distant background galaxies distorted by the mass of the cluster. How many can you find? Can you identify any multiple images of the same background galaxy? (If anyone in the group gets really interested, there was a Citizen Science project called Spacewarps, where you could have help astronomers identify gravitational lenses on their images: https:\/\/spacewarps.org<\/a>\u00a0 \u00a0There are other citizen science project available at:\u00a0https:\/\/www.zooniverse.org\/projects?page=1&status=live<\/a> .)<\/li>\r\n \t
  6. You get so excited about gravitational lensing that you begin to talk about it with an intelligent friend who has not yet taken an astronomy course. After hearing you out, this friend starts to worry. He says, \u201cIf gravitational lenses can distort quasar images, sometimes creating multiple, or ghost, images of the same object, then how can we trust any point of light in the sky to be real? Maybe many of the stars we see are just ghost images or lensed images too!\u201d Have your group discuss how to respond. (Hint: Think about the path that the light of a quasar took on its way to us and the path the light of a typical star takes.)<\/li>\r\n \t
  7. The 8.4-meter Large Synoptic Survey Telescope (LSST at\u00a0https:\/\/www.lsst.org\/<\/a>), currently under construction atop Cerro Pach\u00f3n, a mountain in northern Chile, will survey the entire sky with its 3.2-gigapixel camera every few days, looking for transient, or temporary, objects that make a brief appearance in the sky before fading from view, including asteroids and Kuiper belt objects in our solar system, and supernovae and other explosive high-energy events in the distant universe. When it\u2019s fully operating sometime after 2021, the LSST will produce up to 30 terabytes of data every night.<\/em> (A terabyte is 1000 gigabytes, which is the unit you probably use to rate your computer or memory stick capacity.) With your group, consider what you think might be some challenges of dealing with that quantity of data every night in a scientifically productive but efficient way. Can you propose any solutions to those challenges?<\/li>\r\n \t
  8. Quasars are rare now but were much more numerous when the universe was about one-quarter of its current age. The total star formation taking place in galaxies across the universe peaked at about the same redshift. Does your group think this is a coincidence? Why or why not?<\/li>\r\n \t
  9. One way to see how well the ideas in astronomy (like those in this chapter) have penetrated popular culture is to see whether you can find astronomical words in the marketplace. A short web search for the term \u201cdark matter\u201d turns up both a brand of coffee and a brand of \u201cmuscle growth accelerator\u201d with that name. How many other terms used in this chapter can your group find in the world of products? (What\u2019s a really popular type of Android cell phone, for example?)<\/li>\r\n \t
  10. What\u2019s your complete address in the universe? Group members should write out their full address, based on the information in this chapter (and the rest of the book). After your postal code and country, you may want to add continent, planet, planetary system, galaxy, etc. Then each group member should explain this address to a family member or student not taking astronomy.<\/li>\r\n<\/ol>\r\n<\/section>
    \r\n

    Review Questions<\/h1>\r\n
    \r\n
    \r\n\r\n1:<\/strong> How are distant (young) galaxies different from the galaxies that we see in the universe today?\r\n\r\n<\/div>\r\n<\/div>\r\n
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    2:<\/strong> What is the evidence that star formation began when the universe was only a few hundred million years old?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n\r\n3:<\/strong> Describe the evolution of an elliptical galaxy. How does the evolution of a spiral galaxy differ from that of an elliptical?\r\n\r\n<\/div>\r\n<\/div>\r\n
    \r\n
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    4:<\/strong> Explain what we mean when we call the universe homogeneous and isotropic. Would you say that the distribution of elephants on Earth is homogeneous and isotropic? Why?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    \r\n\r\n5:<\/strong> Describe the organization of galaxies into groupings, from the Local Group to superclusters.\r\n\r\n<\/div>\r\n<\/div>\r\n
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    \r\n\r\n6:<\/strong> What is the evidence that a large fraction of the matter in the universe is invisible?\r\n\r\n<\/div>\r\n<\/div>\r\n
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    \r\n\r\n7:<\/strong> When astronomers make maps of the structure of the universe on the largest scales, how do they find the superclusters of galaxies to be arranged?\r\n\r\n<\/div>\r\n<\/div>\r\n
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    8:<\/strong> How does the presence of an active galactic nucleus in a starburst galaxy affect the starburst process?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section>

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    Thought Questions<\/h1>\r\n
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    9:<\/strong> Describe how you might use the colour of a galaxy to determine something about what kinds of stars it contains.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    10:<\/strong> Suppose a galaxy formed stars for a few million years and then stopped (and no other galaxy merged or collided with it). What would be the most massive stars on the main sequence after 500 million years? After 10 billion years? How would the colour of the galaxy change over this time span? (Refer to Evolution from the Main Sequence to Red Giants<\/a>.)<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    11:<\/strong> Given the ideas presented here about how galaxies form, would you expect to find a giant elliptical galaxy in the Local Group? Why or why not? Is there in fact a giant elliptical in the Local Group?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
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    12:<\/strong> Can an elliptical galaxy evolve into a spiral? Explain your answer. Can a spiral turn into an elliptical? How?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    13:<\/strong> If we see a double image of a quasar produced by a gravitational lens and can obtain a spectrum of the galaxy that is acting as the gravitational lens, we can then put limits on the distance to the quasar. Explain how.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    14:<\/strong> The left panel of the Hubble Ultra Deep Field<\/a> shows a cluster of yellow galaxies that produces several images of blue galaxies through gravitational lensing. Which are more distant\u2014the blue galaxies or the yellow galaxies? The light in the galaxies comes from stars. How do the temperatures of the stars that dominate the light of the cluster galaxies differ from the temperatures of the stars that dominate the light of the blue-lensed galaxy? Which galaxy\u2019s light is dominated by young stars?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    15:<\/strong> Suppose you are standing in the centre of a large, densely populated city that is exactly circular, surrounded by a ring of suburbs with lower-density population, surrounded in turn by a ring of farmland. From this specific location, would you say the population distribution is isotropic? Homogeneous?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
    \r\n\r\n16:<\/strong> Astronomers have been making maps by observing a slice of the universe and seeing where the galaxies lie within that slice. If the universe is isotropic and homogeneous, why do they need more than one slice? Suppose they now want to make each slice extend farther into the universe. What do they need to do?\r\n\r\n<\/div>\r\n<\/div>\r\n
    \r\n
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    17:<\/strong> Human civilization is about 10,000 years old as measured by the development of agriculture. If your telescope collects starlight tonight that has been traveling for 10,000 years, is that star inside or outside our Milky Way Galaxy? Is it likely that the star has changed much during that time?<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    18:<\/strong> Given that only about 5% of the galaxies visible in the Hubble Deep Field are bright enough for astronomers to study spectroscopically, they need to make the most of the other 95%. One technique is to use their colours and apparent brightnesses to try to roughly estimate their redshift. How do you think the inaccuracy of this redshift estimation technique (compared to actually measuring the redshift from a spectrum) might affect our ability to make maps of large-scale structures such as the filaments and voids shown in the Sloan Digital Survey shown in this earlier section and reproduced in thumbnail size below<\/a>?<\/p>\r\n\"\"\r\n\r\n<\/div>\r\n<\/div>\r\n<\/section>

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    Figuring for Yourself<\/h1>\r\n
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    19:<\/strong> Using the information from the example about galaxy distribution in the earlier section, 28.3<\/a>, how much fainter an object<\/strong> <\/span>will you have to be able to measure in order to include the same kinds of galaxies in your second survey? Remember that the brightness of an object varies as the inverse square of the distance.\u00a0 The first survey was of a sphere of 30 million light years in radius and the second survey was of a sphere with a radius of 60 million light years or twice the radius.<\/strong><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    20:<\/strong> Using the information from the example about galaxy distribution in the earlier section, 28.3<\/a>, if galaxies are distributed homogeneously, how many times more of them would you expect to count on your second survey?\u00a0\u00a0The first survey was of a sphere of 30 million light years in radius and the second survey was of a sphere with a radius of 60 million light years or twice the radius.<\/strong>\u00a0 \u00a0 \u00a0The example shows you how to calculate the increase in volume.\u00a0 Hint:\u00a0 If the volume was twice as big you would see two times more galaxies.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    21:<\/strong> Using the information from the example about galaxy distribution in the earlier section, 28.3<\/a>, how much longer will it take you to do your second survey?\u00a0The first survey was of a sphere of 30 million light years in radius and the second survey was of a sphere with a radius of 60 million light years or twice the radius.<\/strong>\u00a0 Assume that the instrument you are using stays the same -- it keeps counting galaxies at the same rate.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    22:<\/strong> Galaxies are found in the \u201cwalls\u201d of huge voids; very few galaxies are found in the voids themselves. The text says that the structure of filaments and voids has been present in the universe since shortly after the expansion began 13.8 billion years ago. In science, we always have to check to see whether some conclusion is contradicted by any other information we have. In this case, we can ask whether the voids would have filled up with galaxies in roughly 14 billion years. Observations show that in addition to the motion associated with the expansion of the universe, the galaxies in the walls of the voids are moving in random directions at typical speeds of 300 km\/s. At least some of them will be moving into the voids. How far into the void will a galaxy move in 14 billion years? Is it a reasonable hypothesis that the voids have existed for 14 billion years? Remember that the voids typically have a diameter of 150 million light years that 1 light-year = 9.46 x 1015<\/sup> m that 1 hear = 3.15 x 107<\/sup> seconds and speed = distance \/time.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

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    23:<\/strong> You can calculate the velocity, the distance, and thus the \"look-back time\" of the most distant galaxies.\u00a0 The Doppler shift gives the velocity and that velocity with the Hubble-Lemaitre law gives us the distance away.\u00a0 If you look back in the Sloan Digital Sky Survey image]<\/a> you can see that the redshift \"z\" is given on the graph.\u00a0 Confirm for yourself by looking at the diagram that the redshift for those most distant galaxies is 0.14.\u00a0 That means that \u0394\u03bb \/ \u03bb = 0.14 or the redshift is 14%.\u00a0 The Doppler formula for velocity v = c ( \u0394\u03bb \/ \u03bb ) so first calculate the recession speed of those distant galaxies.\u00a0 Then use the\u00a0 Hubble law where v<\/em> = H<\/em> \u00d7 d<\/em>, where d<\/em> is the distance to a galaxy and H =\u00a0 (22 km\/s) \/ 1 million light years\u00a0 to find the distance.\u00a0 In other words d = v \/ H.\u00a0 Take the v from the first part of this question and divide by H to get the distance.\u00a0 For these low velocities, you can neglect relativistic effects.\u00a0 \u00a0The Sloan Digital Survey was shown in this earlier section and reproduced in thumbnail size below <\/a>\u00a0 \u00a0The answer is given below.<\/p>\r\n\"\"\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
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    24:<\/strong> Assume that dark matter is uniformly distributed throughout the Milky Way, not just in the outer halo but also throughout the bulge and in the disk, where the solar system lives. How much dark matter would you expect there to be inside the solar system? Would you expect that to be easily detectable? Hint: For th e radius of the Milky Way\u2019s dark matter halo, use R<\/em> = 300,000 light-years; for the solar system\u2019s radius, use 100 AU; and start by calculating the ratio of the two volumes.<\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
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    25:<\/strong> The simulated box of galaxy filaments and superclusters shown in the previous section<\/a> stretches across 1 billion light-years. If you were to make a scale model where that box covered the core of a university campus, say 1 km, then how big would the Milky Way Galaxy be? How far away would the Andromeda galaxy be in the scale model?\u00a0 You can do this -- it is a ratio problem.\u00a0 \u00a0If 1 km = 1 billion light years, then how big would the Milky Way Galaxy be?\u00a0 Remember that the Milky Way galaxy is about 50,000 light years while the Andromeda Galaxy is about 2.5 million light years away.\u00a0 \u00a0 The picture of the box is reproduced here in thumbnail size.<\/p>\r\n\"\"\r\n\r\n<\/div>\r\n<\/div>\r\n

    \r\n
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    26:<\/strong> The first objects to collapse gravitationally after the Big Bang might have been globular cluster-size galaxy pieces, with masses around 106<\/sup> solar masses. Suppose you merge two of those together, then merge two larger pieces together, and so on, Lego-style, until you reach a Milky Way mass, about 1012<\/sup> solar masses. How many merger generations would that take, and how many original pieces? (Hint: Think in powers of 2.)<\/p>\r\n\r\n<\/div>\r\n \r\n

    Answers 22:\u00a0<\/strong>Travelling at 300 km\/s the distance it would travel in 14 billion years can be found from distance = speed x time = (300 km\/s) ( 14 x 109<\/sup> years) ( 3.15 x 107<\/sup> sec\/year ) = 1.32 x1023<\/sup> m.\u00a0 1 light year = 9.46x1015<\/sup> m so this distance = 1.4 x 107<\/sup> light-years = 14 x1 0 6<\/sup> light-years =\u00a0 14 million light years.\u00a0 AS the voids are typically 150 million light years there would still be lots of empty space.\u00a0 The galaxies would only be 10% of the way into the void so they would NOT have filled up the void.<\/div>\r\n
    Answers 23:<\/strong> A redshift of 0.14 means the velocity from Doppler = 4.2 x 10 7<\/sup> m\/s = 4.2 x 10 4<\/sup> km\/s.\u00a0 \u00a0Hubble's law give us d = v\/ H = (4.2 x 104<\/sup> m\/s ) \/\u00a0 (22 km\/s \/ million light years) = 1.9 x 103<\/sup> million light years = 1.9 x 109<\/sup> light-years = 1.9 billion light-years.\u00a0 \u00a0So the \"look back time\" = 1.9 billion years.\u00a0 Our universe is believed to be about 14 billion years old.<\/div>\r\n<\/div>\r\n
    <\/div>\r\n
    \r\n\r\n \r\n\r\n \r\n\r\n<\/div>\r\n<\/section>","rendered":"
    \n

    Collaborative Group Activities<\/h1>\n
      \n
    1. Suppose you developed a theory to account for the evolution of a large city such as New York City. Have your group discuss whether it would resemble the development of structure in the universe (as we have described it in this chapter). What elements of your model for New York City resemble the astronomers\u2019 model for the growth of structure in the universe? Which elements do not match?<\/li>\n
    2. Most astronomers believe that dark matter exists and is a large fraction of the total matter in the universe. At the same time, most astronomers do not believe that UFOs are evidence that we are being visited by aliens from another world. Yet astronomers have never actually seen either dark matter or a UFO. Why do you think one idea is widely accepted by scientists and the other is not? Which idea do you think is more believable? Give your reasoning.<\/li>\n
    3. Someone in your group describes the redshift surveys of galaxies to a friend, who says he\u2019s never heard of a bigger waste of effort. Who cares, he asks, about the large-scale structure of the universe? What is your group\u2019s reaction, and what reasons could you come up with for putting money into figuring out how the universe is organized?<\/li>\n
    4. The leader of a small but very wealthy country is obsessed by maps. She has put together a fabulous collection of Earth maps, purchased all the maps of other planets that astronomers have assembled, and now wants to commission the best possible map of the entire universe. Your group is selected to advise her. What sort of instruments and surveys should she invest in to produce a good map of the cosmos? Be as specific as you can.<\/li>\n
    5. Download a high-resolution image of a rich galaxy cluster from the Hubble Space Telescope (see the list of gravitational lens news stories in the \u201cFor Further Exploration\u201d section). See if your group can work together to identify gravitational arcs, the images of distant background galaxies distorted by the mass of the cluster. How many can you find? Can you identify any multiple images of the same background galaxy? (If anyone in the group gets really interested, there was a Citizen Science project called Spacewarps, where you could have help astronomers identify gravitational lenses on their images: https:\/\/spacewarps.org<\/a>\u00a0 \u00a0There are other citizen science project available at:\u00a0https:\/\/www.zooniverse.org\/projects?page=1&status=live<\/a> .)<\/li>\n
    6. You get so excited about gravitational lensing that you begin to talk about it with an intelligent friend who has not yet taken an astronomy course. After hearing you out, this friend starts to worry. He says, \u201cIf gravitational lenses can distort quasar images, sometimes creating multiple, or ghost, images of the same object, then how can we trust any point of light in the sky to be real? Maybe many of the stars we see are just ghost images or lensed images too!\u201d Have your group discuss how to respond. (Hint: Think about the path that the light of a quasar took on its way to us and the path the light of a typical star takes.)<\/li>\n
    7. The 8.4-meter Large Synoptic Survey Telescope (LSST at\u00a0https:\/\/www.lsst.org\/<\/a>), currently under construction atop Cerro Pach\u00f3n, a mountain in northern Chile, will survey the entire sky with its 3.2-gigapixel camera every few days, looking for transient, or temporary, objects that make a brief appearance in the sky before fading from view, including asteroids and Kuiper belt objects in our solar system, and supernovae and other explosive high-energy events in the distant universe. When it\u2019s fully operating sometime after 2021, the LSST will produce up to 30 terabytes of data every night.<\/em> (A terabyte is 1000 gigabytes, which is the unit you probably use to rate your computer or memory stick capacity.) With your group, consider what you think might be some challenges of dealing with that quantity of data every night in a scientifically productive but efficient way. Can you propose any solutions to those challenges?<\/li>\n
    8. Quasars are rare now but were much more numerous when the universe was about one-quarter of its current age. The total star formation taking place in galaxies across the universe peaked at about the same redshift. Does your group think this is a coincidence? Why or why not?<\/li>\n
    9. One way to see how well the ideas in astronomy (like those in this chapter) have penetrated popular culture is to see whether you can find astronomical words in the marketplace. A short web search for the term \u201cdark matter\u201d turns up both a brand of coffee and a brand of \u201cmuscle growth accelerator\u201d with that name. How many other terms used in this chapter can your group find in the world of products? (What\u2019s a really popular type of Android cell phone, for example?)<\/li>\n
    10. What\u2019s your complete address in the universe? Group members should write out their full address, based on the information in this chapter (and the rest of the book). After your postal code and country, you may want to add continent, planet, planetary system, galaxy, etc. Then each group member should explain this address to a family member or student not taking astronomy.<\/li>\n<\/ol>\n<\/section>\n
      \n

      Review Questions<\/h1>\n
      \n
      \n

      1:<\/strong> How are distant (young) galaxies different from the galaxies that we see in the universe today?<\/p>\n<\/div>\n<\/div>\n

      \n
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      2:<\/strong> What is the evidence that star formation began when the universe was only a few hundred million years old?<\/p>\n<\/div>\n<\/div>\n

      \n
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      3:<\/strong> Describe the evolution of an elliptical galaxy. How does the evolution of a spiral galaxy differ from that of an elliptical?<\/p>\n<\/div>\n<\/div>\n

      \n
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      4:<\/strong> Explain what we mean when we call the universe homogeneous and isotropic. Would you say that the distribution of elephants on Earth is homogeneous and isotropic? Why?<\/p>\n<\/div>\n<\/div>\n

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      5:<\/strong> Describe the organization of galaxies into groupings, from the Local Group to superclusters.<\/p>\n<\/div>\n<\/div>\n

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      6:<\/strong> What is the evidence that a large fraction of the matter in the universe is invisible?<\/p>\n<\/div>\n<\/div>\n

      \n
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      7:<\/strong> When astronomers make maps of the structure of the universe on the largest scales, how do they find the superclusters of galaxies to be arranged?<\/p>\n<\/div>\n<\/div>\n

      \n
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      8:<\/strong> How does the presence of an active galactic nucleus in a starburst galaxy affect the starburst process?<\/p>\n<\/div>\n<\/div>\n<\/section>\n

      \n

      Thought Questions<\/h1>\n
      \n
      \n

      9:<\/strong> Describe how you might use the colour of a galaxy to determine something about what kinds of stars it contains.<\/p>\n<\/div>\n<\/div>\n

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      10:<\/strong> Suppose a galaxy formed stars for a few million years and then stopped (and no other galaxy merged or collided with it). What would be the most massive stars on the main sequence after 500 million years? After 10 billion years? How would the colour of the galaxy change over this time span? (Refer to Evolution from the Main Sequence to Red Giants<\/a>.)<\/p>\n<\/div>\n<\/div>\n

      \n
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      11:<\/strong> Given the ideas presented here about how galaxies form, would you expect to find a giant elliptical galaxy in the Local Group? Why or why not? Is there in fact a giant elliptical in the Local Group?<\/p>\n<\/div>\n<\/div>\n

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      12:<\/strong> Can an elliptical galaxy evolve into a spiral? Explain your answer. Can a spiral turn into an elliptical? How?<\/p>\n<\/div>\n<\/div>\n

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      13:<\/strong> If we see a double image of a quasar produced by a gravitational lens and can obtain a spectrum of the galaxy that is acting as the gravitational lens, we can then put limits on the distance to the quasar. Explain how.<\/p>\n<\/div>\n<\/div>\n

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      14:<\/strong> The left panel of the Hubble Ultra Deep Field<\/a> shows a cluster of yellow galaxies that produces several images of blue galaxies through gravitational lensing. Which are more distant\u2014the blue galaxies or the yellow galaxies? The light in the galaxies comes from stars. How do the temperatures of the stars that dominate the light of the cluster galaxies differ from the temperatures of the stars that dominate the light of the blue-lensed galaxy? Which galaxy\u2019s light is dominated by young stars?<\/p>\n<\/div>\n<\/div>\n

      \n
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      15:<\/strong> Suppose you are standing in the centre of a large, densely populated city that is exactly circular, surrounded by a ring of suburbs with lower-density population, surrounded in turn by a ring of farmland. From this specific location, would you say the population distribution is isotropic? Homogeneous?<\/p>\n<\/div>\n<\/div>\n

      \n
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      16:<\/strong> Astronomers have been making maps by observing a slice of the universe and seeing where the galaxies lie within that slice. If the universe is isotropic and homogeneous, why do they need more than one slice? Suppose they now want to make each slice extend farther into the universe. What do they need to do?<\/p>\n<\/div>\n<\/div>\n

      \n
      \n

      17:<\/strong> Human civilization is about 10,000 years old as measured by the development of agriculture. If your telescope collects starlight tonight that has been traveling for 10,000 years, is that star inside or outside our Milky Way Galaxy? Is it likely that the star has changed much during that time?<\/p>\n<\/div>\n<\/div>\n

      \n
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      18:<\/strong> Given that only about 5% of the galaxies visible in the Hubble Deep Field are bright enough for astronomers to study spectroscopically, they need to make the most of the other 95%. One technique is to use their colours and apparent brightnesses to try to roughly estimate their redshift. How do you think the inaccuracy of this redshift estimation technique (compared to actually measuring the redshift from a spectrum) might affect our ability to make maps of large-scale structures such as the filaments and voids shown in the Sloan Digital Survey shown in this earlier section and reproduced in thumbnail size below<\/a>?<\/p>\n

      \"\"<\/p>\n<\/div>\n<\/div>\n<\/section>\n

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      Figuring for Yourself<\/h1>\n
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      19:<\/strong> Using the information from the example about galaxy distribution in the earlier section, 28.3<\/a>, how much fainter an object<\/strong> <\/span>will you have to be able to measure in order to include the same kinds of galaxies in your second survey? Remember that the brightness of an object varies as the inverse square of the distance.\u00a0 The first survey was of a sphere of 30 million light years in radius and the second survey was of a sphere with a radius of 60 million light years or twice the radius.<\/strong><\/p>\n<\/div>\n<\/div>\n

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      20:<\/strong> Using the information from the example about galaxy distribution in the earlier section, 28.3<\/a>, if galaxies are distributed homogeneously, how many times more of them would you expect to count on your second survey?\u00a0\u00a0The first survey was of a sphere of 30 million light years in radius and the second survey was of a sphere with a radius of 60 million light years or twice the radius.<\/strong>\u00a0 \u00a0 \u00a0The example shows you how to calculate the increase in volume.\u00a0 Hint:\u00a0 If the volume was twice as big you would see two times more galaxies.<\/p>\n<\/div>\n<\/div>\n

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      21:<\/strong> Using the information from the example about galaxy distribution in the earlier section, 28.3<\/a>, how much longer will it take you to do your second survey?\u00a0The first survey was of a sphere of 30 million light years in radius and the second survey was of a sphere with a radius of 60 million light years or twice the radius.<\/strong>\u00a0 Assume that the instrument you are using stays the same — it keeps counting galaxies at the same rate.<\/p>\n<\/div>\n<\/div>\n

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      22:<\/strong> Galaxies are found in the \u201cwalls\u201d of huge voids; very few galaxies are found in the voids themselves. The text says that the structure of filaments and voids has been present in the universe since shortly after the expansion began 13.8 billion years ago. In science, we always have to check to see whether some conclusion is contradicted by any other information we have. In this case, we can ask whether the voids would have filled up with galaxies in roughly 14 billion years. Observations show that in addition to the motion associated with the expansion of the universe, the galaxies in the walls of the voids are moving in random directions at typical speeds of 300 km\/s. At least some of them will be moving into the voids. How far into the void will a galaxy move in 14 billion years? Is it a reasonable hypothesis that the voids have existed for 14 billion years? Remember that the voids typically have a diameter of 150 million light years that 1 light-year = 9.46 x 1015<\/sup> m that 1 hear = 3.15 x 107<\/sup> seconds and speed = distance \/time.<\/p>\n<\/div>\n<\/div>\n

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      23:<\/strong> You can calculate the velocity, the distance, and thus the “look-back time” of the most distant galaxies.\u00a0 The Doppler shift gives the velocity and that velocity with the Hubble-Lemaitre law gives us the distance away.\u00a0 If you look back in the Sloan Digital Sky Survey image]<\/a> you can see that the redshift “z” is given on the graph.\u00a0 Confirm for yourself by looking at the diagram that the redshift for those most distant galaxies is 0.14.\u00a0 That means that \u0394\u03bb \/ \u03bb = 0.14 or the redshift is 14%.\u00a0 The Doppler formula for velocity v = c ( \u0394\u03bb \/ \u03bb ) so first calculate the recession speed of those distant galaxies.\u00a0 Then use the\u00a0 Hubble law where v<\/em> = H<\/em> \u00d7 d<\/em>, where d<\/em> is the distance to a galaxy and H =\u00a0 (22 km\/s) \/ 1 million light years\u00a0 to find the distance.\u00a0 In other words d = v \/ H.\u00a0 Take the v from the first part of this question and divide by H to get the distance.\u00a0 For these low velocities, you can neglect relativistic effects.\u00a0 \u00a0The Sloan Digital Survey was shown in this earlier section and reproduced in thumbnail size below <\/a>\u00a0 \u00a0The answer is given below.<\/p>\n

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      24:<\/strong> Assume that dark matter is uniformly distributed throughout the Milky Way, not just in the outer halo but also throughout the bulge and in the disk, where the solar system lives. How much dark matter would you expect there to be inside the solar system? Would you expect that to be easily detectable? Hint: For th e radius of the Milky Way\u2019s dark matter halo, use R<\/em> = 300,000 light-years; for the solar system\u2019s radius, use 100 AU; and start by calculating the ratio of the two volumes.<\/p>\n<\/div>\n<\/div>\n

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      25:<\/strong> The simulated box of galaxy filaments and superclusters shown in the previous section<\/a> stretches across 1 billion light-years. If you were to make a scale model where that box covered the core of a university campus, say 1 km, then how big would the Milky Way Galaxy be? How far away would the Andromeda galaxy be in the scale model?\u00a0 You can do this — it is a ratio problem.\u00a0 \u00a0If 1 km = 1 billion light years, then how big would the Milky Way Galaxy be?\u00a0 Remember that the Milky Way galaxy is about 50,000 light years while the Andromeda Galaxy is about 2.5 million light years away.\u00a0 \u00a0 The picture of the box is reproduced here in thumbnail size.<\/p>\n

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      26:<\/strong> The first objects to collapse gravitationally after the Big Bang might have been globular cluster-size galaxy pieces, with masses around 106<\/sup> solar masses. Suppose you merge two of those together, then merge two larger pieces together, and so on, Lego-style, until you reach a Milky Way mass, about 1012<\/sup> solar masses. How many merger generations would that take, and how many original pieces? (Hint: Think in powers of 2.)<\/p>\n<\/div>\n

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      Answers 22:\u00a0<\/strong>Travelling at 300 km\/s the distance it would travel in 14 billion years can be found from distance = speed x time = (300 km\/s) ( 14 x 109<\/sup> years) ( 3.15 x 107<\/sup> sec\/year ) = 1.32 x1023<\/sup> m.\u00a0 1 light year = 9.46×1015<\/sup> m so this distance = 1.4 x 107<\/sup> light-years = 14 x1 0 6<\/sup> light-years =\u00a0 14 million light years.\u00a0 AS the voids are typically 150 million light years there would still be lots of empty space.\u00a0 The galaxies would only be 10% of the way into the void so they would NOT have filled up the void.<\/div>\n
      Answers 23:<\/strong> A redshift of 0.14 means the velocity from Doppler = 4.2 x 10 7<\/sup> m\/s = 4.2 x 10 4<\/sup> km\/s.\u00a0 \u00a0Hubble’s law give us d = v\/ H = (4.2 x 104<\/sup> m\/s ) \/\u00a0 (22 km\/s \/ million light years) = 1.9 x 103<\/sup> million light years = 1.9 x 109<\/sup> light-years = 1.9 billion light-years.\u00a0 \u00a0So the “look back time” = 1.9 billion years.\u00a0 Our universe is believed to be about 14 billion years old.<\/div>\n<\/div>\n
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