{"id":1134,"date":"2017-12-19T23:27:44","date_gmt":"2017-12-20T04:27:44","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/?post_type=chapter&#038;p=1134"},"modified":"2020-04-22T21:09:49","modified_gmt":"2020-04-23T01:09:49","slug":"29-8-collaborative-group-activities-questions-and-exercises","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/chapter\/29-8-collaborative-group-activities-questions-and-exercises\/","title":{"raw":"29.9 Collaborative Group Activities, Questions and Exercises","rendered":"29.9 Collaborative Group Activities, Questions and Exercises"},"content":{"raw":"<section id=\"fs-id1163975491281\" class=\"group-activities\">\r\n<h1>Collaborative Group Activities.<\/h1>\r\n<ol id=\"fs-id1163975708743\">\r\n \t<li>This chapter deals with some pretty big questions and ideas. Some belief systems teach us that there are questions to which \u201cwe were not meant to know\u201d the answers. Other people feel that if our minds and instruments are capable of exploring a question, then it becomes part of our birthright as thinking human beings. Have your group discuss your personal reactions to discussing questions like the beginning of time and space, and the ultimate fate of the universe. Does it make you nervous to hear about scientists discussing these issues? Or is it exciting to know that we can now gather scientific evidence about the origin and fate of the cosmos? (In discussing this, you may find that members of your group strongly disagree; try to be respectful of others\u2019 points of view.)<\/li>\r\n \t<li>A popular model of the universe in the 1950s and 1960s was the so-called steady-state cosmology. In this model, the universe was not only the same everywhere and in all directions (homogeneous and isotropic), but also the same <em>at all times<\/em>. We know the universe is expanding and the galaxies are thinning out, and so this model hypothesized that new matter was continually coming into existence to fill in the space between galaxies as they moved farther apart. If so, the infinite universe did not have to have a sudden beginning, but could simply exist forever in a steady state. Have your group discuss your reaction to this model. Do you find it more appealing philosophically than the Big Bang model? Can you cite some evidence that indicates that the universe was not the same billions of years ago as it is now\u2014that it is not in a steady state?<\/li>\r\n \t<li>One of the lucky accidents that characterizes our universe is the fact that the time scale for the development of intelligent life on Earth and the lifetime of the Sun are comparable. Have your group discuss what would happen if the two time scales were very different. Suppose, for example, that the time for intelligent life to evolve was 10 times greater than the main-sequence lifetime of the Sun. Would our civilization have ever developed? Now suppose the time for intelligent life to evolve is ten times shorter than the main-sequence lifetime of the Sun. Would we be around? (This latter discussion requires considerable thought, including such ideas as what the early stages in the Sun\u2019s life were like and how much the early Earth was bombarded by asteroids and comets.)<\/li>\r\n \t<li>The grand ideas discussed in this chapter have a powerful effect on the human imagination, not just for scientists, but also for artists, composers, dramatists, and writers. Here we list just a few of these responses to cosmology. Each member of your group can select one of these, learn more about it, and then report back, either to the group or to the whole class.\r\n<ul id=\"fs-id1163974217055\">\r\n \t<li>The California poet Robinson Jeffers was the brother of an astronomer who worked at the Lick Observatory. His poem \u201cMargrave\u201d is a meditation on cosmology and on the kidnap and murder of a child: <a href=\"http:\/\/www.poemhunter.com\/best-poems\/robinson-jeffers\/margrave\/\">http:\/\/www.poemhunter.com\/best-poems\/robinson-jeffers\/margrave\/<\/a>.<\/li>\r\n \t<li>In the science fiction story \u201cThe Gravity Mine\u201d by Stephen Baxter, the energy of evaporating supermassive black holes is the last hope of living beings in the far future in an ever-expanding universe. The story has poetic description of the ultimate fate of matter and life and is available online at: <a href=\"http:\/\/www.infinityplus.co.uk\/stories\/gravitymine.htm\">http:\/\/www.infinityplus.co.uk\/stories\/gravitymine.htm<\/a>.<\/li>\r\n \t<li>The musical piece <em>YLEM<\/em> by Karlheinz Stockhausen takes its title from the ancient Greek term for primeval material revived by George Gamow. It tries to portray the oscillating universe in musical terms. Players actually expand through the concert hall, just as the universe does, and then return and expand again. See: <a href=\"http:\/\/www.karlheinzstockhausen.org\/ylem_english.htm\">http:\/\/www.karlheinzstockhausen.org\/ylem_english.htm<\/a>.<\/li>\r\n \t<li>The musical piece <em>Supernova Sonata<\/em> <a href=\"http:\/\/www.astro.uvic.ca\/~alexhp\/new\/supernova_sonata.html\">http:\/\/www.astro.uvic.ca\/~alexhp\/new\/supernova_sonata.html<\/a> by Alex Parker and Melissa Graham is based on the characteristics of 241 type Ia supernova explosions, the ones that have helped astronomers discover the acceleration of the expanding universe.<\/li>\r\n \t<li>Gregory Benford\u2019s short story \u201cThe Final Now\u201d envisions the end of an accelerating open universe, and blends religious and scientific imagery in a very poetic way. Available free online at: <a href=\"http:\/\/www.tor.com\/stories\/2010\/03\/the-final-now.\">http:\/\/www.tor.com\/stories\/2010\/03\/the-final-now.<\/a><\/li>\r\n<\/ul>\r\n<\/li>\r\n \t<li>When Einstein learned about Hubble\u2019s work showing that the universe of galaxies is expanding, he called his introduction of the cosmological constant into his general theory of relativity his \u201cbiggest blunder.\u201d Can your group think of other \u201cbig blunders\u201d from the history of astronomy, where the thinking of astronomers was too conservative and the universe turned out to be more complicated or required more \u201coutside-the-box\u201d thinking?<\/li>\r\n<\/ol>\r\n<\/section><section id=\"fs-id1163974183185\" class=\"review-questions\">\r\n<h1>Review Questions<\/h1>\r\n<div class=\"exercise\"><section>\r\n<div class=\"problem\">\r\n<p id=\"fs-id1163974419414\"><strong>1:<\/strong> What are the basic observations about the universe that any theory of cosmology must explain?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163975571214\" class=\"exercise\"><section>\r\n<div class=\"problem\">\r\n<p id=\"fs-id1163974178048\"><strong>2:<\/strong> Describe some possible futures for the universe that scientists have come up with. What property of the universe determines which of these possibilities is the correct one?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"exercise\"><section>\r\n<div id=\"fs-id1163975770309\" class=\"problem\">\r\n<p id=\"fs-id1163975493844\"><strong>3:<\/strong> What does the term Hubble time mean in cosmology, and what is the current best calculation for the Hubble time?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974335761\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974230227\" class=\"problem\">\r\n\r\n<strong>4:<\/strong> Which formed first: hydrogen nuclei or hydrogen atoms? Explain the sequence of events that led to each.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163975660888\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163975531667\" class=\"problem\">\r\n<p id=\"fs-id1163974219597\"><strong>5:<\/strong> Describe at least two characteristics of the universe that are explained by the standard Big Bang model.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"exercise\"><section>\r\n<div id=\"fs-id1163974318299\" class=\"problem\">\r\n\r\n<strong>6:<\/strong> Describe two properties of the universe that are not explained by the standard Big Bang model (without inflation). How does inflation explain these two properties?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"exercise\"><section>\r\n<div class=\"problem\">\r\n<p id=\"fs-id1163974352585\"><strong>7:<\/strong> Why do astronomers believe there must be dark matter that is not in the form of atoms with protons and neutrons?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974318006\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163975705585\" class=\"problem\">\r\n\r\n<strong>8:<\/strong> What is dark energy and what evidence do astronomers have that it is an important component of the universe?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163976539387\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163976458316\" class=\"problem\">\r\n\r\n<strong>9:<\/strong> Thinking about the ideas of space and time in Einstein\u2019s general theory of relativity, how do we explain the fact that all galaxies outside our Local Group show a redshift?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163976748132\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163976407982\" class=\"problem\">\r\n<p id=\"fs-id1163976808195\"><strong>10:<\/strong> Astronomers have found that there is more helium in the universe than stars could have made in the 13.8 billion years that the universe has been in existence. How does the Big Bang scenario solve this problem?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"exercise\"><section>\r\n<div id=\"fs-id1163975708965\" class=\"problem\">\r\n\r\n<strong>11:<\/strong> Describe the anthropic principle. What are some properties of the universe that make it \u201cready\u201d to have life forms like you in it?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163976632102\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163976857420\" class=\"problem\">\r\n<p id=\"fs-id1163973141179\"><strong>12:<\/strong> Describe the evidence that the expansion of the universe is accelerating.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section><section id=\"fs-id1163974245207\" class=\"thought-questions\">\r\n<h1>Thought Questions<\/h1>\r\n<div id=\"fs-id1163975473448\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974284314\" class=\"problem\">\r\n<p id=\"fs-id1163975572404\"><strong>13:<\/strong> What is the most useful probe of the early evolution of the universe: a giant elliptical galaxy or an irregular galaxy such as the Large Magellanic Cloud? Why?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163975825548\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163975413162\" class=\"problem\">\r\n\r\n<strong>14:<\/strong> What are the advantages and disadvantages of using quasars to probe the early history of the universe?\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974639103\" class=\"exercise\"><section>\r\n<div class=\"problem\">\r\n<p id=\"fs-id1163975481424\"><strong>15:<\/strong> Would acceleration of the universe occur if it were composed entirely of matter (that is, if there were no dark energy)?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163975590978\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974375113\" class=\"problem\">\r\n<p id=\"fs-id1163975441589\"><strong>16:<\/strong> Suppose the universe expands forever. Describe what will become of the radiation from the primeval fireball. What will the future evolution of galaxies be like? Could life as we know it survive forever in such a universe? Why?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974412327\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974188449\" class=\"problem\">\r\n<p id=\"fs-id1163975451006\"><strong>17:<\/strong> Some theorists expected that observations would show that the density of matter in the universe is just equal to the critical density. Do the current observations support this hypothesis?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974340636\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163975837957\" class=\"problem\">\r\n<p id=\"fs-id1163974343925\"><strong>18:<\/strong> There are a variety of ways of estimating the ages of various objects in the universe. Describe two of these ways, and indicate how well they agree with one another and with the age of the universe itself as estimated by its expansion.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974411668\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974258533\" class=\"problem\">\r\n<p id=\"fs-id1163974194108\"><strong>19:<\/strong> Since the time of <span class=\"no-emphasis\">Copernicus<\/span>, each revolution in astronomy has moved humans farther from the centre of the universe. Now it appears that we may not even be made of the most common form of matter. Trace the changes in scientific thought about the central nature of Earth, the Sun, and our Galaxy on a cosmic scale. Explain how the notion that most of the universe is made of dark matter continues this \u201cCopernican tradition.\u201d<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974393618\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974550087\" class=\"problem\">\r\n<p id=\"fs-id1163972000574\"><strong>20:<\/strong> The anthropic principle suggests that in some sense we are observing a special kind of universe; if the universe were different, we could never have come to exist. Comment on how this fits with the Copernican tradition described in the earlier in this textbook.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163975840606\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974431259\" class=\"problem\">\r\n<p id=\"fs-id1163974176647\"><strong>21:<\/strong> Penzias and Wilson\u2019s discovery of the Cosmic Microwave Background (CMB) is a nice example of scientific <em>serendipity<\/em>\u2014something that is found by chance but turns out to have a positive outcome. What were they looking for and what did they discover?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974541815\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974184170\" class=\"problem\">\r\n<p id=\"fs-id1163975741498\"><strong>22:<\/strong> Construct a timeline for the universe and indicate when various significant events occurred, from the beginning of the expansion to the formation of the Sun to the appearance of humans on Earth.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section><section id=\"fs-id1163974220018\" class=\"figuring-for-yourself\">\r\n<h1>Figuring for Yourself<\/h1>\r\n<div id=\"fs-id1163974343982\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163975472994\" class=\"problem\">\r\n<p id=\"fs-id1163975638730\"><strong>23:<\/strong> Suppose the Hubble constant were not 22 but 33 km\/s per million light-years. Then what would the critical density be?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163975581676\" class=\"exercise\"><section>\r\n<div class=\"problem\">\r\n<p id=\"fs-id1163974264853\"><strong>24:<\/strong> Assume that the average galaxy contains 10<sup>11<\/sup><em>M<\/em><sub>Sun<\/sub> and that the average distance between galaxies is 10 million light-years. Calculate the average density of matter (mass per unit volume) in galaxies. What fraction is this of the critical density we calculated in the chapter?<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974406483\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974273046\" class=\"problem\">\r\n<p id=\"fs-id1163974172674\"><strong>25:<\/strong> The CMB contains roughly 400 million photons per m<sup>3<\/sup>. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien\u2019s law, the peak wave length in <strong>nanometers<\/strong> is given by <span class=\"MJX_Assistive_MathML\" role=\"presentation\">\u03bb<sub>max<\/sub>=3\u00d710<sup>6 <\/sup>\/ T where T is the temperature in kelvin.\u00a0\u00a0<\/span> In metres, Wein's law is written as <span class=\"MJX_Assistive_MathML\" role=\"presentation\">\u03bb<sub>max<\/sub>=3\u00d710<sup>-3\u00a0<\/sup>\/ T\u00a0 . <\/span>Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters.\u00a0 Remember that 1 nano = 10 <sup>-9<\/sup> .\u00a0 \u00a0(Answer:\u00a0 1.1 x 10<sup>6<\/sup> nm = 1.1 x 10<sup>-3<\/sup> m.)<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163975655088\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163975433445\" class=\"problem\">\r\n<p id=\"fs-id1163975741435\"><strong>26:<\/strong> Following up on the question above calculate the energy of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in the exercise above.\u00a0 The energy of a photon is given by <span class=\"MJX_Assistive_MathML\" role=\"presentation\">E=hc \/ \u03bb,\u00a0<\/span>where <em>h<\/em> is Planck\u2019s constant and is equal to 6.626 \u00d7 10<sup>\u201334<\/sup> J \u00d7 s, <em>c<\/em> is the speed of light in m\/s, and \u03bb is the wavelength in m.\u00a0 (Answer: 1.8 x 10 <sup>-22<\/sup> J)<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974369405\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163974220870\" class=\"problem\">\r\n<p id=\"fs-id1163975544550\"><strong>27:<\/strong> Continuing the thinking in the two exercises above,\u00a0 calculate the energy in a cubic meter of space, multiply the energy per photon calculated by the number of photons per cubic meter given above.<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div class=\"exercise\"><section>\r\n<div id=\"fs-id1163974361252\" class=\"problem\">\r\n\r\n<strong>28:<\/strong> Continuing the thinking in the last three exercises, convert this energy to an equivalent in mass, use Einstein\u2019s equation <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>. Hint: Divide the energy per m<sup>3<\/sup> calculated in the exercise above by the speed of light squared. Check your units; you should have an answer in kg\/m<sup>3<\/sup>. Now compare this answer with the critical density. Your answer should be several powers of 10 smaller than the critical density. In other words, you have found for yourself that the contribution of the CMB photons to the overall density of the universe is much, much smaller than the contribution made by stars and galaxies.\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163975727734\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163975361222\" class=\"problem\">\r\n<p id=\"fs-id1163974195725\"><strong>29:<\/strong> There is still some uncertainty in the Hubble constant. (a) Current estimates for H range from about 68 km\/s per megaparsecs to 74 km\/s per megaparsecs.\u00a0 Assume that the Hubble constant has been constant since the Big Bang. What is the possible range in the ages of the universe? Use the equation in the text, <span class=\"MJX_Assistive_MathML\" role=\"presentation\">T<sub>0<\/sub>= 1 \/ H,<\/span> and make sure you use consistent units. (b) Twenty years ago, estimates for the Hubble constant ranged from 50 to 100 km\/s per megaparsecs. What are the possible ages for the universe from those values? Can you rule out some of these possibilities on the basis of other evidence?\u00a0 (Answers: a) 1.44 x 10<sup>10<\/sup> years, 1.32 x 10<sup>10<\/sup> years,\u00a0 b) 1.96 x 10<sup>10<\/sup> years, 9.78 x 10<sup>9<\/sup> years)<\/p>\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<div id=\"fs-id1163974171126\" class=\"exercise\"><section>\r\n<div id=\"fs-id1163975658340\" class=\"problem\">\r\n\r\n<strong>30:<\/strong> It is possible to derive the age of the universe given the value of the Hubble constant and the distance to a galaxy, again with the assumption that the value of the Hubble constant has not changed since the Big Bang. Consider a galaxy at a distance of 400 million light-years receding from us at a velocity, <em>v<\/em>. If the Hubble constant is 20 km\/s per million light-years, what is its velocity? How long ago was that galaxy right next door to our own Galaxy if it has always been receding at its present rate? Express your answer in years. Since the universe began when all galaxies were very close together, this number is a rough estimate for the age of the universe.\u00a0 (Answer: velocity =\u00a0 H<sub>o<\/sub> d =\u00a0 8000 km\/s ,\u00a0 time = distance \/ velocity\u00a0 =. 4.5 x 10 <sup>17<\/sup> sec = 14 billion years\u00a0 \u00a0or simpler time = age of universe = 1 \/ H<sub>o<\/sub> = 4.5 x 10<sup>17<\/sup> s = 14 billion years)\r\n\r\n<\/div>\r\n<\/section><\/div>\r\n<\/section>\r\n<div>\r\n<h2><\/h2>\r\n<\/div>","rendered":"<section id=\"fs-id1163975491281\" class=\"group-activities\">\n<h1>Collaborative Group Activities.<\/h1>\n<ol id=\"fs-id1163975708743\">\n<li>This chapter deals with some pretty big questions and ideas. Some belief systems teach us that there are questions to which \u201cwe were not meant to know\u201d the answers. Other people feel that if our minds and instruments are capable of exploring a question, then it becomes part of our birthright as thinking human beings. Have your group discuss your personal reactions to discussing questions like the beginning of time and space, and the ultimate fate of the universe. Does it make you nervous to hear about scientists discussing these issues? Or is it exciting to know that we can now gather scientific evidence about the origin and fate of the cosmos? (In discussing this, you may find that members of your group strongly disagree; try to be respectful of others\u2019 points of view.)<\/li>\n<li>A popular model of the universe in the 1950s and 1960s was the so-called steady-state cosmology. In this model, the universe was not only the same everywhere and in all directions (homogeneous and isotropic), but also the same <em>at all times<\/em>. We know the universe is expanding and the galaxies are thinning out, and so this model hypothesized that new matter was continually coming into existence to fill in the space between galaxies as they moved farther apart. If so, the infinite universe did not have to have a sudden beginning, but could simply exist forever in a steady state. Have your group discuss your reaction to this model. Do you find it more appealing philosophically than the Big Bang model? Can you cite some evidence that indicates that the universe was not the same billions of years ago as it is now\u2014that it is not in a steady state?<\/li>\n<li>One of the lucky accidents that characterizes our universe is the fact that the time scale for the development of intelligent life on Earth and the lifetime of the Sun are comparable. Have your group discuss what would happen if the two time scales were very different. Suppose, for example, that the time for intelligent life to evolve was 10 times greater than the main-sequence lifetime of the Sun. Would our civilization have ever developed? Now suppose the time for intelligent life to evolve is ten times shorter than the main-sequence lifetime of the Sun. Would we be around? (This latter discussion requires considerable thought, including such ideas as what the early stages in the Sun\u2019s life were like and how much the early Earth was bombarded by asteroids and comets.)<\/li>\n<li>The grand ideas discussed in this chapter have a powerful effect on the human imagination, not just for scientists, but also for artists, composers, dramatists, and writers. Here we list just a few of these responses to cosmology. Each member of your group can select one of these, learn more about it, and then report back, either to the group or to the whole class.\n<ul id=\"fs-id1163974217055\">\n<li>The California poet Robinson Jeffers was the brother of an astronomer who worked at the Lick Observatory. His poem \u201cMargrave\u201d is a meditation on cosmology and on the kidnap and murder of a child: <a href=\"http:\/\/www.poemhunter.com\/best-poems\/robinson-jeffers\/margrave\/\">http:\/\/www.poemhunter.com\/best-poems\/robinson-jeffers\/margrave\/<\/a>.<\/li>\n<li>In the science fiction story \u201cThe Gravity Mine\u201d by Stephen Baxter, the energy of evaporating supermassive black holes is the last hope of living beings in the far future in an ever-expanding universe. The story has poetic description of the ultimate fate of matter and life and is available online at: <a href=\"http:\/\/www.infinityplus.co.uk\/stories\/gravitymine.htm\">http:\/\/www.infinityplus.co.uk\/stories\/gravitymine.htm<\/a>.<\/li>\n<li>The musical piece <em>YLEM<\/em> by Karlheinz Stockhausen takes its title from the ancient Greek term for primeval material revived by George Gamow. It tries to portray the oscillating universe in musical terms. Players actually expand through the concert hall, just as the universe does, and then return and expand again. See: <a href=\"http:\/\/www.karlheinzstockhausen.org\/ylem_english.htm\">http:\/\/www.karlheinzstockhausen.org\/ylem_english.htm<\/a>.<\/li>\n<li>The musical piece <em>Supernova Sonata<\/em> <a href=\"http:\/\/www.astro.uvic.ca\/~alexhp\/new\/supernova_sonata.html\">http:\/\/www.astro.uvic.ca\/~alexhp\/new\/supernova_sonata.html<\/a> by Alex Parker and Melissa Graham is based on the characteristics of 241 type Ia supernova explosions, the ones that have helped astronomers discover the acceleration of the expanding universe.<\/li>\n<li>Gregory Benford\u2019s short story \u201cThe Final Now\u201d envisions the end of an accelerating open universe, and blends religious and scientific imagery in a very poetic way. Available free online at: <a href=\"http:\/\/www.tor.com\/stories\/2010\/03\/the-final-now.\">http:\/\/www.tor.com\/stories\/2010\/03\/the-final-now.<\/a><\/li>\n<\/ul>\n<\/li>\n<li>When Einstein learned about Hubble\u2019s work showing that the universe of galaxies is expanding, he called his introduction of the cosmological constant into his general theory of relativity his \u201cbiggest blunder.\u201d Can your group think of other \u201cbig blunders\u201d from the history of astronomy, where the thinking of astronomers was too conservative and the universe turned out to be more complicated or required more \u201coutside-the-box\u201d thinking?<\/li>\n<\/ol>\n<\/section>\n<section id=\"fs-id1163974183185\" class=\"review-questions\">\n<h1>Review Questions<\/h1>\n<div class=\"exercise\">\n<section>\n<div class=\"problem\">\n<p id=\"fs-id1163974419414\"><strong>1:<\/strong> What are the basic observations about the universe that any theory of cosmology must explain?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163975571214\" class=\"exercise\">\n<section>\n<div class=\"problem\">\n<p id=\"fs-id1163974178048\"><strong>2:<\/strong> Describe some possible futures for the universe that scientists have come up with. What property of the universe determines which of these possibilities is the correct one?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"exercise\">\n<section>\n<div id=\"fs-id1163975770309\" class=\"problem\">\n<p id=\"fs-id1163975493844\"><strong>3:<\/strong> What does the term Hubble time mean in cosmology, and what is the current best calculation for the Hubble time?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974335761\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974230227\" class=\"problem\">\n<p><strong>4:<\/strong> Which formed first: hydrogen nuclei or hydrogen atoms? Explain the sequence of events that led to each.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163975660888\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163975531667\" class=\"problem\">\n<p id=\"fs-id1163974219597\"><strong>5:<\/strong> Describe at least two characteristics of the universe that are explained by the standard Big Bang model.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"exercise\">\n<section>\n<div id=\"fs-id1163974318299\" class=\"problem\">\n<p><strong>6:<\/strong> Describe two properties of the universe that are not explained by the standard Big Bang model (without inflation). How does inflation explain these two properties?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"exercise\">\n<section>\n<div class=\"problem\">\n<p id=\"fs-id1163974352585\"><strong>7:<\/strong> Why do astronomers believe there must be dark matter that is not in the form of atoms with protons and neutrons?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974318006\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163975705585\" class=\"problem\">\n<p><strong>8:<\/strong> What is dark energy and what evidence do astronomers have that it is an important component of the universe?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163976539387\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163976458316\" class=\"problem\">\n<p><strong>9:<\/strong> Thinking about the ideas of space and time in Einstein\u2019s general theory of relativity, how do we explain the fact that all galaxies outside our Local Group show a redshift?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163976748132\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163976407982\" class=\"problem\">\n<p id=\"fs-id1163976808195\"><strong>10:<\/strong> Astronomers have found that there is more helium in the universe than stars could have made in the 13.8 billion years that the universe has been in existence. How does the Big Bang scenario solve this problem?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"exercise\">\n<section>\n<div id=\"fs-id1163975708965\" class=\"problem\">\n<p><strong>11:<\/strong> Describe the anthropic principle. What are some properties of the universe that make it \u201cready\u201d to have life forms like you in it?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163976632102\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163976857420\" class=\"problem\">\n<p id=\"fs-id1163973141179\"><strong>12:<\/strong> Describe the evidence that the expansion of the universe is accelerating.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<section id=\"fs-id1163974245207\" class=\"thought-questions\">\n<h1>Thought Questions<\/h1>\n<div id=\"fs-id1163975473448\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974284314\" class=\"problem\">\n<p id=\"fs-id1163975572404\"><strong>13:<\/strong> What is the most useful probe of the early evolution of the universe: a giant elliptical galaxy or an irregular galaxy such as the Large Magellanic Cloud? Why?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163975825548\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163975413162\" class=\"problem\">\n<p><strong>14:<\/strong> What are the advantages and disadvantages of using quasars to probe the early history of the universe?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974639103\" class=\"exercise\">\n<section>\n<div class=\"problem\">\n<p id=\"fs-id1163975481424\"><strong>15:<\/strong> Would acceleration of the universe occur if it were composed entirely of matter (that is, if there were no dark energy)?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163975590978\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974375113\" class=\"problem\">\n<p id=\"fs-id1163975441589\"><strong>16:<\/strong> Suppose the universe expands forever. Describe what will become of the radiation from the primeval fireball. What will the future evolution of galaxies be like? Could life as we know it survive forever in such a universe? Why?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974412327\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974188449\" class=\"problem\">\n<p id=\"fs-id1163975451006\"><strong>17:<\/strong> Some theorists expected that observations would show that the density of matter in the universe is just equal to the critical density. Do the current observations support this hypothesis?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974340636\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163975837957\" class=\"problem\">\n<p id=\"fs-id1163974343925\"><strong>18:<\/strong> There are a variety of ways of estimating the ages of various objects in the universe. Describe two of these ways, and indicate how well they agree with one another and with the age of the universe itself as estimated by its expansion.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974411668\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974258533\" class=\"problem\">\n<p id=\"fs-id1163974194108\"><strong>19:<\/strong> Since the time of <span class=\"no-emphasis\">Copernicus<\/span>, each revolution in astronomy has moved humans farther from the centre of the universe. Now it appears that we may not even be made of the most common form of matter. Trace the changes in scientific thought about the central nature of Earth, the Sun, and our Galaxy on a cosmic scale. Explain how the notion that most of the universe is made of dark matter continues this \u201cCopernican tradition.\u201d<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974393618\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974550087\" class=\"problem\">\n<p id=\"fs-id1163972000574\"><strong>20:<\/strong> The anthropic principle suggests that in some sense we are observing a special kind of universe; if the universe were different, we could never have come to exist. Comment on how this fits with the Copernican tradition described in the earlier in this textbook.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163975840606\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974431259\" class=\"problem\">\n<p id=\"fs-id1163974176647\"><strong>21:<\/strong> Penzias and Wilson\u2019s discovery of the Cosmic Microwave Background (CMB) is a nice example of scientific <em>serendipity<\/em>\u2014something that is found by chance but turns out to have a positive outcome. What were they looking for and what did they discover?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974541815\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974184170\" class=\"problem\">\n<p id=\"fs-id1163975741498\"><strong>22:<\/strong> Construct a timeline for the universe and indicate when various significant events occurred, from the beginning of the expansion to the formation of the Sun to the appearance of humans on Earth.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<section id=\"fs-id1163974220018\" class=\"figuring-for-yourself\">\n<h1>Figuring for Yourself<\/h1>\n<div id=\"fs-id1163974343982\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163975472994\" class=\"problem\">\n<p id=\"fs-id1163975638730\"><strong>23:<\/strong> Suppose the Hubble constant were not 22 but 33 km\/s per million light-years. Then what would the critical density be?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163975581676\" class=\"exercise\">\n<section>\n<div class=\"problem\">\n<p id=\"fs-id1163974264853\"><strong>24:<\/strong> Assume that the average galaxy contains 10<sup>11<\/sup><em>M<\/em><sub>Sun<\/sub> and that the average distance between galaxies is 10 million light-years. Calculate the average density of matter (mass per unit volume) in galaxies. What fraction is this of the critical density we calculated in the chapter?<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974406483\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974273046\" class=\"problem\">\n<p id=\"fs-id1163974172674\"><strong>25:<\/strong> The CMB contains roughly 400 million photons per m<sup>3<\/sup>. The energy of each photon depends on its wavelength. Calculate the typical wavelength of a CMB photon. Hint: The CMB is blackbody radiation at a temperature of 2.73 K. According to Wien\u2019s law, the peak wave length in <strong>nanometers<\/strong> is given by <span class=\"MJX_Assistive_MathML\" role=\"presentation\">\u03bb<sub>max<\/sub>=3\u00d710<sup>6 <\/sup>\/ T where T is the temperature in kelvin.\u00a0\u00a0<\/span> In metres, Wein&#8217;s law is written as <span class=\"MJX_Assistive_MathML\" role=\"presentation\">\u03bb<sub>max<\/sub>=3\u00d710<sup>-3\u00a0<\/sup>\/ T\u00a0 . <\/span>Calculate the wavelength at which the CMB is a maximum and, to make the units consistent, convert this wavelength from nanometers to meters.\u00a0 Remember that 1 nano = 10 <sup>-9<\/sup> .\u00a0 \u00a0(Answer:\u00a0 1.1 x 10<sup>6<\/sup> nm = 1.1 x 10<sup>-3<\/sup> m.)<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163975655088\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163975433445\" class=\"problem\">\n<p id=\"fs-id1163975741435\"><strong>26:<\/strong> Following up on the question above calculate the energy of a typical photon. Assume for this approximate calculation that each photon has the wavelength calculated in the exercise above.\u00a0 The energy of a photon is given by <span class=\"MJX_Assistive_MathML\" role=\"presentation\">E=hc \/ \u03bb,\u00a0<\/span>where <em>h<\/em> is Planck\u2019s constant and is equal to 6.626 \u00d7 10<sup>\u201334<\/sup> J \u00d7 s, <em>c<\/em> is the speed of light in m\/s, and \u03bb is the wavelength in m.\u00a0 (Answer: 1.8 x 10 <sup>-22<\/sup> J)<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974369405\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163974220870\" class=\"problem\">\n<p id=\"fs-id1163975544550\"><strong>27:<\/strong> Continuing the thinking in the two exercises above,\u00a0 calculate the energy in a cubic meter of space, multiply the energy per photon calculated by the number of photons per cubic meter given above.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div class=\"exercise\">\n<section>\n<div id=\"fs-id1163974361252\" class=\"problem\">\n<p><strong>28:<\/strong> Continuing the thinking in the last three exercises, convert this energy to an equivalent in mass, use Einstein\u2019s equation <em>E<\/em> = <em>mc<\/em><sup>2<\/sup>. Hint: Divide the energy per m<sup>3<\/sup> calculated in the exercise above by the speed of light squared. Check your units; you should have an answer in kg\/m<sup>3<\/sup>. Now compare this answer with the critical density. Your answer should be several powers of 10 smaller than the critical density. In other words, you have found for yourself that the contribution of the CMB photons to the overall density of the universe is much, much smaller than the contribution made by stars and galaxies.<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163975727734\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163975361222\" class=\"problem\">\n<p id=\"fs-id1163974195725\"><strong>29:<\/strong> There is still some uncertainty in the Hubble constant. (a) Current estimates for H range from about 68 km\/s per megaparsecs to 74 km\/s per megaparsecs.\u00a0 Assume that the Hubble constant has been constant since the Big Bang. What is the possible range in the ages of the universe? Use the equation in the text, <span class=\"MJX_Assistive_MathML\" role=\"presentation\">T<sub>0<\/sub>= 1 \/ H,<\/span> and make sure you use consistent units. (b) Twenty years ago, estimates for the Hubble constant ranged from 50 to 100 km\/s per megaparsecs. What are the possible ages for the universe from those values? Can you rule out some of these possibilities on the basis of other evidence?\u00a0 (Answers: a) 1.44 x 10<sup>10<\/sup> years, 1.32 x 10<sup>10<\/sup> years,\u00a0 b) 1.96 x 10<sup>10<\/sup> years, 9.78 x 10<sup>9<\/sup> years)<\/p>\n<\/div>\n<\/section>\n<\/div>\n<div id=\"fs-id1163974171126\" class=\"exercise\">\n<section>\n<div id=\"fs-id1163975658340\" class=\"problem\">\n<p><strong>30:<\/strong> It is possible to derive the age of the universe given the value of the Hubble constant and the distance to a galaxy, again with the assumption that the value of the Hubble constant has not changed since the Big Bang. Consider a galaxy at a distance of 400 million light-years receding from us at a velocity, <em>v<\/em>. If the Hubble constant is 20 km\/s per million light-years, what is its velocity? How long ago was that galaxy right next door to our own Galaxy if it has always been receding at its present rate? Express your answer in years. Since the universe began when all galaxies were very close together, this number is a rough estimate for the age of the universe.\u00a0 (Answer: velocity =\u00a0 H<sub>o<\/sub> d =\u00a0 8000 km\/s ,\u00a0 time = distance \/ velocity\u00a0 =. 4.5 x 10 <sup>17<\/sup> sec = 14 billion years\u00a0 \u00a0or simpler time = age of universe = 1 \/ H<sub>o<\/sub> = 4.5 x 10<sup>17<\/sup> s = 14 billion years)<\/p>\n<\/div>\n<\/section>\n<\/div>\n<\/section>\n<div>\n<h2><\/h2>\n<\/div>\n","protected":false},"author":9,"menu_order":10,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1134","chapter","type-chapter","status-publish","hentry"],"part":854,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/1134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/users\/9"}],"version-history":[{"count":14,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/1134\/revisions"}],"predecessor-version":[{"id":1180,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/1134\/revisions\/1180"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/parts\/854"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapters\/1134\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/media?parent=1134"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/pressbooks\/v2\/chapter-type?post=1134"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/contributor?post=1134"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/astronomy1105\/wp-json\/wp\/v2\/license?post=1134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}