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10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Age of the universe <a href="#" class="mark-page-favorite pull-right" data-pid="834" title="Mark as favorite" onclick="return false;"><i class="fa fa-star-o"></i></a> </h1> <ol class="breadcrumb"> <li><a href="../../../physics.html"><i class="fa fa-home"></i></a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../823/astrophysics.html">Astrophysics</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Age of the universe</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 10 minutes"><i class="fa fa-clock-o"></i> 10'</span> </ol> <article id="main-article"> <p><img alt="" src="../../astro/ruler-1.jpg" style="float: left; width: 225px; height: 150px;">We can calculate an estimate for the age of the universe based on the velocity at which galaxies are receding from our observations.</p> <hr class="hidden-separator"> <div class="panel panel-turquoise panel-has-colored-body"> <div class="panel-heading"> <div> <p>Key Concepts</p> </div> </div> <div class="panel-body"> <div> <p>The cosmic scale factor is defined as the size of the universe at a given time relative to its size now.</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(z={R\over R_0} -1\)</span></p> <ul> <li><span class="math-tex">\(z\)</span> is the factor by which the universe has expanded in size (dimensionless)</li> <li><span class="math-tex">\(R\)</span> is the size of the universe at time <span class="math-tex">\(t\)</span></li> <li><span class="math-tex">\(R_0\)</span> is the size of the universe now</li> </ul> </div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Essentials</p> </div> </div> <div class="panel-body"> <div> <p><img alt="" src="../../astro/hubble.jpg" style="float: left; width: 202px; height: 150px;">Hubble's law is based on analysis of observational data from thousands of galaxies. It states that the recessional velocity of galaxies is approximately proportional to their distance from Earth.</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(v=H_0d\)</span></p> <ul> <li><span class="math-tex">\(v\)</span> is the recessional velocity (kms<sup>-1</sup>)</li> <li><span class="math-tex">\(H_0\)</span> is the Hubble constant (=68 kms<sup>-1</sup>Mpc<sup>-1</sup>)</li> <li><span class="math-tex">\(d\)</span> is the distance from Earth (Mpc)</li> </ul> </div> <hr class="hidden-separator"> <p><img alt="" src="../../astro/age-of-universe.jpg" style="float: right; width: 300px; height: 200px;">We can use Hubble's law to calculate the age of the universe, by calculating the time over which the universe would have expanded to reach its current size.</p> <p>NB: time = distance / speed</p> <p><span class="math-tex">\(T\approx {d\over v}\)</span></p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(T\approx {1\over H_0}\)</span></p> <ul> <li><span class="math-tex">\(T\)</span> is the age of the universe</li> <li><span class="math-tex">\(H_0\)</span> is the Hubble constant (=68 kms<sup>-1</sup>Mpc<sup>-1</sup>)</li> </ul> </div> <hr class="hidden-separator"> <div class="video-embed vimeo"><iframe allow="accelerometer; autoplay; encrypted-media; gyroscope; picture-in-picture" allowfullscreen="" mozallowfullscreen="" webkitallowfullscreen="" height="420" width="100%" src="https://player.vimeo.com/video/358639930"></iframe></div> <p>Converting all of the necessary units gives an estimate of the age of the universe as 14.4 billion years. This is based on the assumption that the universe has expanded at a constant rate.</p> <p><img alt="" src="../../astro/type-1a.jpg" style="float: left; width: 220px; height: 220px;">However, observations of <em>type 1a supernovae</em> suggest that the unvierse is, in fact, accelerating in its expansion.</p> <p>A type 1a supernova is an example of a <em>standard candle</em> with known luminosity. Using redshift to determine the distance of a type 1a supernova from Earth, we can calculate the expected apparent brightness.</p> <p>The apparent brightness of distant type 1a supernovae is lower than calculated, which suggests that their distance from us is larger than expected. The universe has expanded at an increasing rate in the time since the light left the supernova!</p> <p>The accelerating expansion of the universe is hypothesized as being a result of <em>dark energy</em>.</p> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="panel panel-has-colored-body panel-green"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Test Yourself</p> </div> </div> <div class="panel-body"> <div> <p><i>Use flashcards to practise your recall.</i></p> <div class="tib-flashcard"><a class="show-flashcards btn btn-success btn-xs-block btn-block " data-levels="1" data-mode="Normal" data-topics="839" data-subject-id="6" data-n-flashcards="6" style="text-align:center">Show flashcards</a></div><hr> <p><i>Use quizzes to practise application of theory.</i> </p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#e0c1ec1a"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="e0c1ec1a"> <div class="modal-dialog" style="width: 95vw; max-width: 960px"> <div class="modal-content"> <div class="modal-header slide-quiz-title"> <h4 class="modal-title" style="width: 100%;"> Cosmology <strong class="q-number pull-right"> <span class="counter">1</span>/<span class="total">1</span> </strong> </h4> </div> <div class="modal-body p-xs-3"> <div class="slide-quiz" data-stats="6-336-834" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>The early universe was opaque because...</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>photons did not have enough energy to pass through</span></label> </p><p><label class="radio"> <input type="radio"> <span>it was so dense</span></label> </p><p><label class="radio"> <input type="radio"> <span>the gravitational field was so big</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>photons were continually <span class="scayt-misspell-word" data-scayt-word="ionising" data-wsc-lang="en_US">ionising atoms</span></span></label> </p></div><div class="q-explanation"><p>In the early stages of the universe, photons had enough energy to <span class="scayt-misspell-word" data-scayt-word="ionise" data-wsc-lang="en_US">ionise</span> newly formed atoms.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>At what temperature did photons in the early universe stop <span class="scayt-misspell-word" data-scayt-word="ionising" data-wsc-lang="en_US">ionising</span> atoms?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>6000 K</span></label> </p><p><label class="radio"> <input type="radio"> <span>2.73 K</span></label> </p><p><label class="radio"> <input type="radio"> <span>300 K</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>3000 K</span></label> </p></div><div class="q-explanation"><p>The cosmic microwave background is now a temperature of 2.73 K.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The graph shows the spectrum of cosmic microwave background radiation.</p><p style="text-align: center;"><img alt="" src="../../astro/cmb.png" style="width: 300px; height: 200px;"></p><p>The temperature is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>1 mK</span></label> </p><p><label class="radio"> <input type="radio"> <span>0 K</span></label> </p><p><label class="radio"> <input type="radio"> <span>3000 K</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>2.73 K</span></label> </p></div><div class="q-explanation"><p>3000 K was the original temperature before the expansion of CMB radiation. The peak wavelength can be used to determine the temperature today:</p><p><span class="math-tex">\(T = {0.0029\over λ_\text{peak}}\)</span></p><p>Using 1 mm, we obtain an answer of 2.9 K so must choose the closest.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows two galaxies photographed with the same telescope from the Earth.</p><p style="text-align: center;"><img alt="" height="192" src="../../astro/screenshot-2019-08-18-at-07.31.45.png" width="342"></p><p>If the distance to A is 9 Mpc, the distance to B is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>18 Mpc</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>27 Mpc</span></label> </p><p><label class="radio"> <input type="radio"> <span>54 Mpc</span></label> </p><p><label class="radio"> <input type="radio"> <span>3 Mpc</span></label> </p></div><div class="q-explanation"><p>For small angles (i.e. those subtended by galaxies at great distance from Earth!), the angular width of a body is proportional to its width. B has an angular width approximately one third of A.</p><p>The distance away is inversely proportional to angular width, so B is three times further from Earth than A.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>The image shows three spectra. The top one is from a stationary source. A and B are the spectra from two galaxies. Wavelength increases from left to right.</p><p style="text-align: center;"><img alt="" height="243" src="../../astro/screenshot-2019-08-18-at-07.48.42.png" width="340"></p><p>The ratio <span class="math-tex">\(\text{speed}_A \over \text{speed}_B\)</span> is approximately:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(10\)</span></span></label></p><p><label class="radio"> <input class="c" type="radio"> <span><span class="math-tex">\(1\over2\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(2\)</span></span></label></p><p><label class="radio"> <input type="radio"> <span><span class="math-tex">\(1\over10\)</span></span></label></p></div><div class="q-explanation"><p>Speed is proportional to <span class="math-tex">\(Δλ\)</span>. The shift in wavelength for B is approximately twice that of A. Therefore, B is travelling at twice the speed of A.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>This <span class="scayt-misspell-word" data-scayt-word="Algodoo" data-wsc-lang="en_US">Algodoo</span> simulation represents particles moving after an explosion.</p><p style="text-align: center;"><img alt="" height="359" class="gifffer" data-gifffer="/media/physics/astro/bigbang.gif" width="359"></p><p>If the speed of the pink ball is 20 ms<sup>-1</sup>, the speed of the yellow ball is approximately:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>1 ms<sup>-1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>10 ms<sup>-1</sup></span></label> </p><p><label class="radio"> <input type="radio"> <span>20 ms<sup>-1</sup></span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>4 ms<sup>-1</sup></span></label> </p></div><div class="q-explanation"><p>The pink ball has traveled 5x further so must have 5x the speed.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>This <span class="scayt-misspell-word" data-scayt-word="Algodoo" data-wsc-lang="en_US">Algodoo</span> simulation represents particles moving after an explosion.</p><p style="text-align: center;"><img alt="" height="228" class="gifffer" data-gifffer="/media/physics/astro/bigbang.gif" width="228"><img alt="" height="224" src="../../astro/screenshot-2019-08-18-at-09.12.24.png" width="245"></p><p>The graph shows the velocity of a selection of balls plotted against their distance from the <span class="scayt-misspell-word" data-scayt-word="centre" data-wsc-lang="en_US">centre</span>.</p><p>The time after the explosion is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>1 s</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>0.1 s</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.01 s</span></label> </p><p><label class="radio"> <input type="radio"> <span>10 s</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(\text{time}={\text{distance}\over\text{speed}}\Rightarrow \text{time} ={1\over \text{gradient}}\)</span></p><p>Converting the distance into m, we find the gradient is 10 s<sup>-1</sup>.</p><p>NOTE: The correct answer can be obtained by finding the gradient without converting the units and noticing the dimensions.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div><div class="exercise shadow-bottom"><div class="q-question"><p>Measurements of the red shift of type Ia supernovae in distant galaxies leads to the conclusion that...</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>the universe isn't expanding</span></label> </p><p><label class="radio"> <input type="radio"> <span>the expansion of the universe is constant</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>the universe is expanding at an increasing rate</span></label> </p><p><label class="radio"> <input type="radio"> <span>the expansion of the universe is slowing down</span></label> </p></div><div class="q-explanation"><p>Dark energy is thought to be the reason. This is different to dark matter, which pulls the universe together under gravity.</p></div><div class="slide-q-actions"><button class="btn btn-default btn-sm btn-xs-block text-xs-center check"><i class="fa fa-check-square-o"></i> Check</button></div></div> </div> </div> <div class="modal-footer slide-quiz-actions"> <div class=""> <div class="pull-left pull-xs-none mb-xs-3"> <button class="btn btn-default d-xs-none btn-prev"> <i class="fa fa-arrow-left"></i> Prev </button> </div> <div class="pull-right pull-xs-none"> <button class="btn btn-success btn-xs-block text-xs-center btn-results" style="display: none"> <i class="fa fa-bar-chart"></i> Check Results </button> <button class="btn btn-default d-xs-none btn-next"> Next <i class="fa fa-arrow-right"></i> </button> <button class="btn btn-default btn-xs-block text-xs-center btn-close" data-dismiss="modal" style="display: none"> Close </button> </div> </div> </div> </div> </div></div> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="834"> <div class="panel-heading">MY PROGRESS</div> <div class="panel-body understanding-rate"> <div class="msg"></div> <label class="label-lg">Self-assessment</label><p>How much of <strong>Age of the universe</strong> have you understood?</p><div class="slider-container text-center"><div id="self-assessment-slider" class="sib-slider self-assessment " data-value="1" data-percentage=""></div></div> <label class="label-lg">My notes</label> <textarea name="page-notes" class="form-control" rows="3" placeholder="Write your notes here..."></textarea> </div> <div class="panel-footer text-xs-center"> <span id="last-edited" class="mb-xs-3"> </span> <div class="actions mt-xs-3"> <button id="save-my-progress" type="button" class="btn btn-sm btn-primary text-center btn-xs-block"> <i class="fa fa-fw fa-floppy-o"></i> Save </button> </div> </div></div> <div id="modal-feedback" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <h4 class="modal-title">Feedback</h4> <button type="button" class="close hidden-xs hidden-sm" data-dismiss="modal" aria-label="Close"> <span aria-hidden="true">×</span> </button> </div> <div class="modal-body"> <div class="errors"></div> <p><strong>Which of the following best describes your feedback?</strong></p> <form method="post" style="overflow: hidden"> <div class="form-group"> <div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Recommendation"> Recommend</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Problem"> Report a problem</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Improvement"> Suggest an improvement</label></div><div class="radio"><label style="color: #121212;"><input type="radio" name="feedback-type" value="Other"> Other</label></div> </div> <hr> <div class="row"> <div class="col-md-6"> <div class="form-group"> <label for="feedback-name">Name</label> <input type="text" class="form-control" name="feedback-name" placeholder="Name" value=" "> </div> </div> <div class="col-md-6"> <div class="form-group"> <label for="feedback-email">Email address</label> <input type="email" class="form-control" name="feedback-email" placeholder="Email" value="@airmail.cc"> </div> </div> </div> <div class="form-group"> <label for="feedback-comments">Comments</label> <textarea class="form-control" name="feedback-comments" style="resize: vertical;"></textarea> </div> <input type="hidden" name="feedback-ticket" value="082b9c9c4ae3624d"> <input type="hidden" name="feedback-url" value="https://studyib.net/physics/page/834/age-of-the-universe"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> <div id="fc-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"><div class="modal-dialog" role="document"><div class="modal-content"><div class="modal-header" style="background-color: #fafafa;"><div class="row" style="width: 100%;"><div class="col-md-12 tags-heading"><div style="display: flex; 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</textarea></div><div class="modal-footer p-xs-3"><button type="button" class="btn btn-sm btn-primary btn-xs-block save-notes"><i class="fa fa-fw fa-pencil"></i>Save</button><button type="button" class="btn btn-sm btn-default btn-xs-block mx-xs-0" data-dismiss="modal" aria-label="Close">Close</button></div></div></div></div><div id="report-problem-sm-modal" class="modal fade overlay-modal report-problem" tabindex="-1" role="dialog"><div class="modal-dialog modal-sm" role="document"><div class="modal-content"><div class="modal-header p-xs-3"><h4 class="modal-title text-center my-xs-2">Report a problem for flashcard <span class="fc-viewer-id"></span></h4></div><div class="modal-body p-xs-3"><div class="msg"></div><div class="form-group mb-xs-0"><textarea class="form-control issue-description p-xs-3" rows="8"></textarea></div></div><div class="modal-footer p-xs-3"><button type="button" class="btn btn-sm btn-primary text-center btn-xs-block mb-xs-3 disabled send-report"><i class="fa fa-fw fa-paper-plane"></i>Send</button><button type="button" class="btn btn-sm btn-default text-center btn-xs-block mx-xs-0" data-dismiss="modal" aria-label="Close">Close</button></div></div></div></div> <div id="fcgame-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"> <div class="modal-dialog modal-lg modal-dialog-fcgame" role="document"> <div class="modal-content mc-flashcard modal-content-fcgame"> <div class="modal-header" style="background-color: #fafafa;"> <div class="row text-center" style="width: 100%;"> <div class="col-md-12"> <div style="display: flex; justify-content: space-between; align-items: center;"> <div class="text-left"> Your time: <span class="chronometer c-mobile" id="chronometer">00:00:</span> <span class="chronometer msec c-mobile" id="chronometer-msec">000</span> <br> Your best time: <span class="chronometer c-mobile" id="best-record"></span> </div> <button type="button" class="close" data-dismiss="modal" aria-label="Close"> <span 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