File "cepheid-variable-stars.html"
Path: /StudyIB/physics/page/833/cepheid-variable-starshtml
File size: 50.33 KB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html><html lang="EN"><head> <script>(function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start': new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0], j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src= 'https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f); })(window,document,'script','dataLayer','GTM-PZBWZ8J');</script> <title>Cepheid variable stars</title><!-- Removed by WebCopy --><!--<base href="/">--><!-- Removed by WebCopy --><meta http-equiv="x-ua-compatible" content="IE=Edge"><meta charset="utf-8"><meta name="viewport" content="width=device-width, initial-scale=1"><link href="../../../css/bootstrap.flatly.min.css" rel="stylesheet" media="screen"><link rel="stylesheet" href="../../../fonts/awesome/css/font-awesome.min.css"><link href="../../../js/jquery-fancybox/jquery.fancybox.min.css" type="text/css" rel="stylesheet"><link rel="stylesheet" href="../../../css/style.min.css?v=202301301645"><meta name="robots" content="index, follow"><meta name="googlebot" content="noarchive"><meta prefix="og: http://ogp.me/ns#" property="og:title" name="og:title" content="StudyIB Physics: Cepheid variable stars"> <meta prefix="og: http://ogp.me/ns#" property="og:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta prefix="og: http://ogp.me/ns#" property="og:description" name="og:description" content="Cepheid variable stars, a pulsing star following the red giant stage, act as standard candles."> <meta prefix="og: http://ogp.me/ns#" property="og:url" name="og:url" content="https://studyib.net/physics/page/833/cepheid-variable-stars"> <meta prefix="og: http://ogp.me/ns#" property="og:site_name" name="og:site_name" content="StudyIB - Your IB learning companion"> <meta prefix="og: http://ogp.me/ns#" property="og:locale" name="og:locale" content="en"> <meta prefix="og: http://ogp.me/ns#" property="og:type" name="og:type" content="website"> <meta name="description" content="Cepheid variable stars, a pulsing star following the red giant stage, act as standard candles."> <meta name="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="keywords" content="StudyIB, Physics, Site overview, Self-study, Videos, Virtual tutor, Practices, Multiple Choice, IB, IBDP, InThinking, International Baccalaureate, Revision, Revision websites, Student Sites, Students, Learning, Guidance, Exam, Questions"> <meta itemprop="name" content="StudyIB Physics: Cepheid variable stars"> <meta itemprop="description" content="Cepheid variable stars, a pulsing star following the red giant stage, act as standard candles."> <meta itemprop="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:card" content="summary_large_image"> <meta name="twitter:title" content="StudyIB Physics: Cepheid variable stars"> <meta name="twitter:description" content="Cepheid variable stars, a pulsing star following the red giant stage, act as standard candles."> <meta name="twitter:image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="twitter:creator" content="@inthinker"><link rel="stylesheet" href="../../../css/snippets.min.css?v=202209111300"><link rel="stylesheet" href="../../../css/article.min.css?v=202211221000"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick.min.css"><link rel="stylesheet" type="text/css" href="../../../js/slick-carousel/slick-theme.min.css"><link rel="stylesheet" type="text/css" href="../../../css/flashcards/flashcards.min.css?v=202211221000"><link rel="stylesheet" href="../../../css/flashcards/magic.min.css"><style type="text/css">button.gifffer img { margin-bottom: 40px !important; }</style><style type="text/css">.filter-sl-only { display: none; }</style><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script src="../../../js/ifvisible.min.js"></script><script>ifvisible.setIdleDuration(300);</script><link rel="apple-touch-icon-precomposed" sizes="57x57" href="../../../img/favicon/apple-touch-icon-57x57.png"> <link rel="apple-touch-icon-precomposed" sizes="114x114" href="../../../img/favicon/apple-touch-icon-114x114.png"> <link rel="apple-touch-icon-precomposed" sizes="72x72" href="../../../img/favicon/apple-touch-icon-72x72.png"> <link rel="apple-touch-icon-precomposed" sizes="144x144" href="../../../img/favicon/apple-touch-icon-144x144.png"> <link rel="apple-touch-icon-precomposed" sizes="60x60" href="../../../img/favicon/apple-touch-icon-60x60.png"> <link rel="apple-touch-icon-precomposed" sizes="120x120" href="../../../img/favicon/apple-touch-icon-120x120.png"> <link rel="apple-touch-icon-precomposed" sizes="76x76" href="../../../img/favicon/apple-touch-icon-76x76.png"> <link rel="apple-touch-icon-precomposed" sizes="152x152" href="../../../img/favicon/apple-touch-icon-152x152.png"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-196x196.png" sizes="196x196"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-96x96.png" sizes="96x96"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-32x32.png" sizes="32x32"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-16x16.png" sizes="16x16"> <link rel="icon" type="image/png" href="../../../img/favicon/favicon-128.png" sizes="128x128"> <meta name="application-name" content="StudyIB: Your IB Learning Companion"> <meta name="msapplication-TileColor" content="#A5BED5"> <meta name="msapplication-TileImage" content="/img/favicon/mstile-144x144.png"> <meta name="msapplication-square70x70logo" content="/img/favicon/mstile-70x70.png"> <meta name="msapplication-square150x150logo" content="/img/favicon/mstile-150x150.png"> <meta name="msapplication-wide310x150logo" content="/img/favicon/mstile-310x150.png"> <meta name="msapplication-square310x310logo" content="/img/favicon/mstile-310x310.png"><script>var stdHash = "6da675cbcb3d25f050b05557349abc79", stdTicket = "082b9c9c4ae3624d";</script><script src="../../../js/user/local-stats.min.js?v=202205311700"></script><link href="../../../css/subjects-frontpage.min.css?v=202302031000" rel="stylesheet"></head><body class="public physics"> <noscript><iframe src="https://www.googletagmanager.com/ns.html?id=GTM-PZBWZ8J" height="0" width="0" style="display:none;visibility:hidden"></iframe></noscript> <div id="top-header"> <div class="wmap general hidden-sm hidden-xs subjects"> <div class="layout-wrapper"> <div class="container-fluid"> <a href=""> <img class="header-thinker" src="../../../img/header-thinker.svg"> </a> <h1> <a href="../../../physics.html"> IBDP Physics </a> <a href="https://inthinking.net" title="inthinking.net" class="inthinking-logo pull-right"> <img src="../../../img/header-logo.svg" style="height: 80px; width: auto;"> </a> </h1> <p class="slogan">InThinking Revision Sites for students</p> <p class="author">Website by <strong>Chris Hamper & Emma Mitchell</strong></p> <p class="updated">Updated 3 February 2023</p> </div> </div> </div> <nav id="public-topnav" class="navbar navbar-default"> <div class="container-fluid"> <div class="navbar-header"> <a class="navbar-brand hidden-md hidden-lg" href="../../../index.htm"> <img class="header-xs-thinker" src="../../../img/header-thinker.svg"> </a> <button type="button" class="collapsed navbar-toggle" data-toggle="collapse" data-target="#subject-navbar-collapse" aria-expanded="false"> <span class="sr-only">Toggle navigation</span> <i class="fa fa-fw fa-2x fa-user"></i> </button> <div class="brand hidden-lg hidden-md hidden-sm"> <a class="brand-xs" href="../../../physics.html"> <strong class="title" style="white-space: nowrap;font-size: 18px;">Physics</strong> </a> </div> </div> <div class="collapse navbar-collapse" id="subject-navbar-collapse"> <ul class="nav navbar-bar navbar-userbox hidden-md hidden-lg"><li class="dropdown"><a href="#" class="dropdown-toggle" data-toggle="dropdown"><i class="fa fa-fw fa-lg fa-user-circle" style="margin-right: 5px;"></i><span style="font-size: 16px;"></span></a><ul class="dropdown-menu"><li class="dropdown-submenu"><a class="dropdown-toggle" href="#" data-toggle="dropdown"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class=""><a href="../../../mathsanalysis.html">DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class="active"><a href="../../../physics.html"><i class="fa fa-caret-right"></i> DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="menu-item"><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li class="menu-item"><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li class="menu-item"><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li><li class="menu-item hidden-md hidden-lg mt-xs-3"><a href="../../../index.htm?logout=1" class="btn btn-primary btn-xs-block"><i class="fa fa-fw fa-lg fa-power-off text-danger"></i>Log out</a></li></ul></li></ul> <ul class="nav navbar-bar"><li class=""><a class="home" href="../../../physics.html"><i class="fa fa-fw fa-home"></i> Home</a></li><li class=""><a class="topics" href="#"><i class="fa fa-fw fa-th-large"></i> Topics</a></li><li class=""><a class="favorites" href="../../../physics.html"><i class="fa fa-fw fa-star"></i> My favorites</a></li><li class=""><a class="" href="../../flashcards.html"><i class="fa fa-fw fa-bolt"></i> Flashcards</a></li><li class=""><a class="qbank" href="../../test-your-knowledge.html"><i class="fa fa-fw fa-question"></i> Question bank</a></li><li class=""><a class="networks" href="../../networks.html"><i class="fa fa-fw fa-graduation-cap"></i> Virtual tutor</a></li><li class=""><a class="" href="../../blogs.html"><i class="fa fa-fw fa-paperclip"></i> Blog</a></li><li class=""><a class="sitemap" href="../../sitemap.html"><i class="fa fa-fw fa-sitemap"></i> Sitemap</a></li><li class=""><a class="activity" href="../../../physics.html"><i class="fa fa-fw fa-calendar-check-o"></i> My activity</a></li></ul> <ul class="nav navbar-bar navbar-right"> <li> <form class="navbar-form hidden-md hidden-lg" role="search" method="get" action="physics/search"> <div class="input-group"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search..."> <span class="input-group-btn"> <button type="submit" class="btn bg-blue"> <i class="fa fa-search"> </i> </button> </span> </div> </form> <a href="#" class="toggle-menu-search hidden-sm hidden-xs" data-toggle="dropdown"> <i class="fa fa-lg fa-search"></i> </a> </li></ul> </div> </div></nav><nav id="nav-menu-search" class="shadow-bottom hidden-sm hidden-xs" style="display: none;"> <div class="container-fluid"> <form class="" role="search" method="get" action="physics/search"> <input class="form-control nav-search" name="glob" type="search" placeholder="Search Physics..."> <button class="btn btn-sm btn-primary" type="submit"> Search </button> </form> </div></nav><div class="modal fade" tabindex="-1" role="dialog" id="modal-mini-login"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-body"> <button aria-hidden="true" data-dismiss="modal" class="close hidden-xs login-button-close" type="button">×</button> <form method="post"> <div class="form-group"> <input name="user-email" class="form-control" type="text" placeholder="Email"> </div> <div class="form-group"> <input name="user-password" class="form-control" type="password" placeholder="Password"> <input name="user-fp" class="fp" value="d8c893da5db7501669ffeeac46273ba6" type="hidden"> </div> <div class="form-group"> <a href="../../../reset-password.html" class="reset-password" style="font-weight: normal;"> Forgot your password? </a> </div> <div class="form-group"> <button type="submit" name="submit-login" value="1" class="btn btn-primary btn-block text-center"> <i class="fa fa-user fa-fw"></i> Log in </button> </div> </form> </div> </div> </div></div></div><div class="modal fade" id="show-topics" tabindex="-1" role="dialog"><div id="dialog-topics" class="modal-dialog modal-dialog-topics"><div class="modal-content"><div class="modal-body modal-body-topics"><div id="new-frontpage-toplevels-topics" class="frontpage-box"><div class="row"><div class="col-md-4 col-sm-4"><div class="item"><a href="../3015/free-access-weekend.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Free Access Weekend!</h3></div><div class="body"><div class="cropper" style="background-image: url('../../free.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../814/start-here.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Start here</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/getting-started/getting-started.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../819/revision-tips.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Revision tips</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/getting-started/exam-tips.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../2885/exam-questions.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Exam questions</h3></div><div class="body"><div class="cropper" style="background-image: url('../../practice-papers/flash-front.png'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../204/basics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Basics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/basics/basics.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../217/mechanics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Mechanics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/mechanics/mechanics.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../252/thermal.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Thermal</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/thermal/thermal.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../444/oscillations-and-waves.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Oscillations & waves</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/waves/waves.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../445/electricity-and-magnetism.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Electricity & magnetism</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/electricity/electricity.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../443/circular-motion-and-gravity.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Circular motion & gravity</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/circular-motion/circular.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../354/atomic-nuclear-and-particles.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Atomic, nuclear & particles</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/atomic/atomic.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../446/energy-production.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Energy production</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/energy-production/energy.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../848/options.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Options</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/astro/options.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../823/astrophysics.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Astrophysics</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/astro/black-hole.jpg'); height: 10vw;"></div></div></a></div></div><div class="col-md-4 col-sm-4"><div class="item"><a href="../849/engineering.html"><div class="header" style="height: 35px;"><h3 class="title special" style="margin-top: 0;">Engineering</h3></div><div class="body"><div class="cropper" style="background-image: url('/media/physics/engineering/lift-off.jpg'); height: 10vw;"></div></div></a></div></div></div></div></div></div></div></div><div class="container-fluid shadow-ith"><div class="row frontpage"> <div class="col-md-3" id="left-column"> <p class="visible-xs-block"></p><div class="dropdown user-menu hidden-xs" style="margin-bottom: 20px;"> <button type="button" class="btn btn-default dropdown-toggle" data-toggle="dropdown" style="border-radius: 0; padding: 6px 18px;"> <i class="fa fa-fw fa-user-circle"></i> <small><i class="fa fa-caret-down"></i></small> </button> <ul class="dropdown-menu"> <li class="dropdown-submenu"><a href="#"><i class="fa fa-fw fa-globe"></i> Subjects</a><ul id="user-subjects-menu" class="dropdown-menu"><li></li><li class=""><a href="../../../biology.html">DP Biology</a></li><li class=""><a href="../../../chemistry.html">DP Chemistry</a></li><li class=""><a href="../../../englishalanglit.html">DP English A: Language & Literature</a></li><li class=""><a href="../../../mathsanalysis.html">DP Maths: Analysis & Approaches</a></li><li class=""><a href="../../../mathsapplications.html">DP Maths: Applications & Interpretations SL</a></li><li class="active"><a href="../../../physics.html"><i class="fa fa-caret-right"></i> DP Physics</a></li><li class=""><a href="../../../spanishb.html">DP Spanish B</a></li></ul></li><li class="divider"></li><li><a href="../../../user.html"><i class="fa fa-fw fa-dashboard"></i> Dashboard</a></li><li><a href="../../../user/profile.html"><i class="fa fa-fw fa-cog"></i> My profile</a></li><li><a href="../../../user/messages.html"><i class="fa fa-fw fa-envelope"></i> Messages</a></li> <li class="divider"></li> <li> <a href="../../../index.htm?logout=1"> <i class="fa fa-fw fa-power-off"></i> Log out </a> </li> </ul></div> <div id="side-nav"><h4 class="side-nav-title dropdown"><a href="../823/astrophysics.html" class="dropdown-toggle toplevel-dropdown" data-toggle="dropdown"><i class="fa fa-ellipsis-v"></i></a> <a href="../823/astrophysics.html">Astrophysics</a><ul class="dropdown-menu"><li><a href="../../../physics.html" style="padding-left: 5px; border-bottom: solid 1px #ddd"><i class="fa fa-fw fa-home"></i> Home</a></li><li><a href="../3015/free-access-weekend.html"><i class="fa fa-fw fa-caret-right"></i> Free Access Weekend!</a></li><li><a href="../814/start-here.html"><i class="fa fa-fw fa-caret-right"></i> Start here</a></li><li><a href="../819/revision-tips.html"><i class="fa fa-fw fa-caret-right"></i> Revision tips</a></li><li><a href="../2885/exam-questions.html"><i class="fa fa-fw fa-caret-right"></i> Exam questions</a></li><li><a href="../204/basics.html"><i class="fa fa-fw fa-caret-right"></i> Basics</a></li><li><a href="../217/mechanics.html"><i class="fa fa-fw fa-caret-right"></i> Mechanics</a></li><li><a href="../252/thermal.html"><i class="fa fa-fw fa-caret-right"></i> Thermal</a></li><li><a href="../444/oscillations-and-waves.html"><i class="fa fa-fw fa-caret-right"></i> Oscillations and waves</a></li><li><a href="../445/electricity-and-magnetism.html"><i class="fa fa-fw fa-caret-right"></i> Electricity and magnetism</a></li><li><a href="../443/circular-motion-and-gravity.html"><i class="fa fa-fw fa-caret-right"></i> Circular motion and gravity</a></li><li><a href="../354/atomic-nuclear-and-particles.html"><i class="fa fa-fw fa-caret-right"></i> Atomic, nuclear and particles</a></li><li><a href="../446/energy-production.html"><i class="fa fa-fw fa-caret-right"></i> Energy production</a></li><li><a href="../848/options.html"><i class="fa fa-fw fa-caret-right"></i> Options</a></li><li><a href="../849/engineering.html"><i class="fa fa-fw fa-caret-right"></i> Engineering</a></li></ul><div class="pull-right"><a class="sidenav-expand" title="Expand all" href="#"><i class="fa fa-plus-circle"></i></a> <a class="sidenav-compress" title="Compress all" href="#"><i class="fa fa-minus-circle"></i></a></div></h4><ul class="side-nav level-0"><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../830/objects-in-the-universe.html">Objects in the universe</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../825/stellar-quantities.html">Stellar quantities</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../826/spectra.html">Spectra</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../831/stellar-characteristics.html">Stellar characteristics</a></label></li><li class="expanded parent selected"><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="cepheid-variable-stars.html">Cepheid variable stars</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../832/stellar-evolution.html">Stellar evolution</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../827/cosmology.html">Cosmology</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../834/age-of-the-universe.html">Age of the universe</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../1153/ahl-stellar-processes.html">AHL Stellar processes</a></label></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../1154/ahl-further-cosmology.html">AHL Further cosmology</a></label></li></ul></div> <div class="hidden-xs hidden-sm"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Cepheid variable stars <a href="#" class="mark-page-favorite pull-right" data-pid="833" 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">Cepheid variable stars</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/cepheid-1.jpg" style="float: left; width: 153px; height: 150px;">Some stars act as <em>standard candles</em>. Like a standard solution of known concentration in Chemistry, a standard candle is a star of known luminosity. Cepheid variable stars, a pulsing star following the red giant stage, act as standard candles.</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>Observations of cepheid variable stars have provided astrophysicists with data that shows a relationship between the period over which the cepheid variable star pulses and its luminosity. This is useful, as cepheid variable stars are bright enough to be observed over great distances, acting as a reference for determining the distance of other stars from us.</p> <p><img alt="" class="gifffer" data-gifffer="/media/physics/astro/cepheid_trend.gif" style="float: right; width: 240px; height: 150px;">The pulsation of cepheid variable stars can be explained by their expansion and contraction:</p> <ul> <li>The core of the star produces heat, which is absorbed by the outer layer.</li> <li>This increases the temperature of the outer layer, which in turn expands.</li> <li>The outer layer now absorbs less radiation, so the net brightness observed increases.</li> <li>As this radiation is now escaping, the outer layer cools and contracts under gravity.</li> <li>The collapse of the outer layer causes the cycle to repeat.</li> </ul> </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>Knowing the luminosity of a cepheid variable star from its period enables us to calculate its distance from Earth:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(b={L\over{4\pi d^2}}\)</span></p> <p>Rearranging: <span class="math-tex">\(d=\sqrt{L\over {4 \pi b}} \)</span></p> <ul> <li><span class="math-tex">\(d\)</span> is the distance of the cepheid variable star from Earth</li> <li><span class="math-tex">\(L\)</span> is the luminosity of the cepheid variable star, determined using knowledge of the star's time period</li> <li><span class="math-tex">\(b\)</span> is the brightness of the cepheid variable star, measureable at Earth</li> </ul> </div> <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/358639861"></iframe></div> <p><img alt="" src="../../astro/instability-strip.png" style="float: left; width: 263px; height: 300px;">Cepheid variable stars appear on the HR diagram in the <em>instability strip</em><em> </em>along with other types of pulsating star.</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="836" data-subject-id="6" data-n-flashcards="5" 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="#7db06566"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="7db06566"> <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%;"> Cepheids <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="6-310-833" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>A cepheid variable star is brightest when...</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>the core gets hot</span></label> </p><p><label class="radio"> <input type="radio"> <span>the outer layers are most dense</span></label> </p><p><label class="radio"> <input type="radio"> <span>the outer layers absorb most radiation</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>the outer layers expand</span></label> </p></div><div class="q-explanation"><p>When the outer layers of gas expand, they become less dense and absorb less radiation. Therefore, more radiation is emitted and can be observed beyond the star.</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>A cepheid is measured to be 100 pc from the Earth. A second cepheid with the same time period is half as bright. How far from the Earth is this star?</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>400 pc</span></label> </p><p><label class="radio"> <input type="radio"> <span>1000 pc</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>140 pc</span></label> </p><p><label class="radio"> <input type="radio"> <span>200 pc</span></label> </p></div><div class="q-explanation"><p>The same time period implies that the star has the same luminosity as the original cepheid.</p><p><span class="math-tex">\(b = {L\over 4}πd^2 \Rightarrow d \propto \sqrt{1\over b}\)</span></p><p><span class="math-tex">\(b\)</span> has halved, so <span class="math-tex">\(d\)</span> increases by a factor <span class="math-tex">\(\sqrt2\)</span></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>Two cepheids are 100 pc from the Earth. A has time period 1 day and B 10 days.</p><p style="text-align: center;"><img alt="" height="188" class="gifffer" data-gifffer="/media/physics/astro/cepheid_trend.gif" width="301"></p><p>What is the ratio <span class="math-tex">\(\text{brightness}_\text{A}\over \text{brightness}_\text{B}\)</span>? </p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>2</span></label> </p><p><label class="radio"> <input type="radio"> <span>0.01</span></label> </p><p><label class="radio"> <input type="radio"> <span>10</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>0.1</span></label> </p></div><div class="q-explanation"><p>Using the graph, B has luminosity x10 that of A. Since they are the same distance away, brightness is proportional to luminosity, which will also be x10 that of A.</p><p>HINT: Check the order of the ratio!</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>Cepheid C has time period 1 day. Cepheid D is half as bright with time period 10 days.</p><p style="text-align: center;"><img alt="" height="188" class="gifffer" data-gifffer="/media/physics/astro/cepheid_trend.gif" width="301"></p><p>If C is 100 Mpc from the Earth, the distance to D is:</p></div><div class="q-answer"><p><label class="radio"> <input type="radio"> <span>500 Mpc</span></label> </p><p><label class="radio"> <input type="radio"> <span>10 Mpc</span></label> </p><p><label class="radio"> <input type="radio"> <span>2000 Mpc</span></label> </p><p><label class="radio"> <input class="c" type="radio"> <span>450 Mpc</span></label> </p></div><div class="q-explanation"><p><span class="math-tex">\(d_C = {\sqrt{L \over 4\pi b}}\)</span></p><p> <span class="math-tex">\(d_D = {\sqrt{10L \over 4\pi {b\over 2}}}\)</span></p><p><span class="math-tex">\(d_D=\sqrt{20}d_C\)</span></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="833"> <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>Cepheid variable stars</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/833/cepheid-variable-stars"> <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; justify-content: space-between; align-items: center;"><p id="fc-viewer-info" style="width: 80%;"></p><button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button></div></div></div></div><div id="flashcard-body" class="modal-body"><div class="row" style="margin: 0;"><div class="col-md-8 fc-viewer-main"><div class="fc-viewer-inner"><div id="fc-viewer-main-front"><div class="fc-viewer-content"></div><span class="mark-favorite" style="position: absolute; top: 10px; right: 10px; font-size: 22px;"><i class="fa fa-lg fa-star-o"></i></span><span id="issue-report" class="issue-report hidden-xs hidden-sm" title="Report a problem"><i class="fa fa-fw fa-lg fa-exclamation-circle" style="font-size: 1.5em;"></i> </span> </div><div id="fc-viewer-main-back" class="reverse-flashcard green-bg"><div class="fc-viewer-content"></div><span class="mark-favorite" style="position: absolute; top: 10px; right: 10px; font-size: 22px;"><i class="fa fa-lg fa-star-o"></i></span></div></div></div><div class="col-md-4 fc-viewer-controls"><div class="fc-viewer-controls-middle"> <div class="fc-viewer-controls-middle-inner fc-back"><div class="fc-viewer-controls-answers mt-xs-0 mx-xs-0"><button id="right-answer" class="btn btn-success text-center btn-block" title="Mark this flashcard as CORRECT"><i class="fa fa-check"></i> Correct</button><button id="wrong-answer" class="btn text-center bg-red btn-block" title="Mark this flashcard as INCORRECT"><i class="fa fa-remove"></i> Incorrect</button></div><table class="table stats"><tr><td>Times flipped</td><td id="fc-viewer-tflipped" class="text-right">0</td></tr><tr><td>Marked as <em>correct</em></td><td id="fc-viewer-right" class="text-right">0</td></tr><tr><td>Marked as <em>incorrect</em></td><td id="fc-viewer-wrong" class="text-right">0</td></tr></table><a href="#" class="btn btn-default btn-sm btn-block text-center reset-stats hidden-xs hidden-sm" title="Reset stats for this flashcard" style="margin: 10px 0;"><i class="fa fa-undo"></i> Reset</a> <div class="fc-notes-container hidden-xs hidden-sm"><textarea class="form-control notes fc-back card-notes" rows="4" placeholder="Write your own notes here..." style="resize: none;">
</textarea><a href="#" class="btn btn-default btn-sm btn-block text-center save-notes" title="Save personal notes for this flashcard" style="margin-bottom: 10px;"><i class="fa fa-pencil"></i> Save notes</a> </div><div class="fc-viewer-actions-sm hidden-md hidden-lg"><button type="button" class="btn btn-sm btn-xs-block reset-stats"><i class="fa fa-fw fa-undo"></i>Reset</button> <button type="button" class="btn btn-sm btn-xs-block" data-toggle="modal" data-target="#card-notes-sm-modal"><i class="fa fa-fw fa-pencil"></i>Notes</button><button type="button" class="btn btn-sm btn-xs-block" data-toggle="modal" data-target="#report-problem-sm-modal"><i class="fa fa-fw fa-exclamation-circle"></i>Report error</button></div> </div></div><div class="fc-viewer-controls-bottom hidden-xs hidden-sm"><div class="fc-move"> <button class="btn bg-turquoise text-center disabled" rel="prev" title="Previous flashcard"><i class="fa fa-fw fa-chevron-left"></i>Prev</button><button class="btn bg-turquoise text-center disabled" rel="next" title="Next flashcard">Next<i class="fa fa-fw fa-chevron-right"></i></button></div><div class="fc-actions"><button class="btn btn-default btn-block text-center shuffle"><i class="fa fa-random"></i> Shuffle</button><div class="fc-progress"><div class="progress"><div class="progress-bar"></div></div><div class="text-right"><span class="fc-viewer-results-counter"></span></div></div></div></div><div class="fc-close-sm hidden-md hidden-lg"><button id="fc-xs-close" type="button" class="btn btn-default btn-block text-center" data-dismiss="modal" aria-label="Close">Close</button> <hr class="thin"> <div class="fc-actions" style="width: 100%;"> <button class="btn btn-default btn-block text-center shuffle"> <i class="fa fa-random"></i> Shuffle </button><div class="fc-progress"><div class="progress"><div class="progress-bar"></div></div><div class="text-right"><span class="fc-viewer-results-counter hidden-md hidden-lg"></span></div></div> </div></div></div></div></div><div class="modal-footer"><div id="report-error-container" class="report-problem"><div class="row"><div class="col-md-8"><div class="msg"></div><div class="form-group"><label>Report a problem for flashcard <span class="fc-viewer-id"></span></label><textarea class="form-control issue-description" cols="4"></textarea></div><button type="button" class="btn btn-primary pull-right send-report disabled"><i class="fa fa-paper-plane"></i>Send</button><button id="close-send-report" type="button" class="btn btn-default" style="margin-left: 0;">Close</button></div></div></div></div></div></div></div><div id="card-notes-sm-modal" class="modal fade overlay-modal" 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">Notes</h4></div><div class="modal-body p-xs-3"><textarea class="form-control notes fc-back card-notes p-xs-3" rows="8" style="resize: none;">
</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 aria-hidden="true">×</span> </button> </div> </div> </div> </div> <div id="fcgame-body" class=" modal-body modal-body-fcgame"> <div class="row-fluid"> <div class="col-lg-12 col-md-12 col-sm-12 fc-content" id="fc-content" style="padding: 15px;"></div> </div> </div> <div id="end-game" style="display: none;"> <div class="col-lg-10 col-lg-offset-1 col-md-10 col-md-offset-1 col-sm-10 col-sm-offset-1 result shadow-bottom"> <div id="end-game-dismiss"></div> <div id="end-game-results"></div> <div id="show-percent" style="margin-bottom: 30px;font-size: 16px;"></div> </div> <div id="end-game-fc" class="col-lg-12"></div> </div> <div id="start-game" class="col-lg-12 col-md-12 col-sm-12 centered"> <div style="width: 200px;"> <button class="btn btn-success btn-xs-block" id="play-game" style="display: block; width: 100%; margin: 10px 0;">Start</button> <button class="btn btn-default btn-xs-block" id="cancel-game" style="display: block; width: 100%; margin: 10px 0;">Cancel</button> </div> </div> <div class="modal-footer"></div> </div> </div></div><div id="fcgame-modal-issue-report" class="modal fade" tabindex="-1" role="dialog"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title">Report error</h4> </div> <div class="modal-body"> <textarea id="issue-description-fcgame" class="form-control"></textarea> </div> <div class="modal-footer"> <button id="send-report-fcgame" type="button" class="btn btn-primary">Send Report</button> </div> </div> </div></div> </article> <hr class="hidden-md hidden-lg"> <div class="hidden-md hidden-lg mt-xs-3"> <button class="btn btn-default btn-block text-xs-center" data-toggle="modal" data-target="#modal-feedback" style="margin-bottom: 10px"><i class="fa fa-send"></i> Feedback</button> </div> </div> <input type="hidden" id="user-id" value="38342"></div><input id="ticket" type="hidden" value="082b9c9c4ae3624d"><input id="tzoffset" type="hidden" value="new"><input id="fp" class="fp" type="hidden" value=""></div><div id="std-footer"> <div class="wmap"> <div class="layout-wrapper"> <p> <a href="https://www.inthinking.net"> © <span id="footer-year"></span> <em>InThinking</em> <script>document.getElementById("footer-year").innerHTML = new Date().getFullYear();</script> </a> | <a target="_self" href="../../../about.html"> About us </a> | <a target="_self" href="../../../terms-and-conditions.html"> Legal </a> | <a target="_self" href="../../../contact.html"> Contact </a> </p> <p> <a class="social" target="_blank" href="https://twitter.com/#!/inthinker"> <img src="../../../img/social/twitter-square.svg"> Twitter </a> <a class="social" target="_blank" href="https://www.facebook.com/inthinking.net"> <img src="../../../img/social/facebook-square.svg"> Facebook </a> <a class="social" target="_blank" href="https://www.linkedin.com/profile/view?id=139741989"> <img src="../../../img/social/linkedin-square.svg"> LinkedIn </a> </p> </div> </div></div><script src="../../../js/jquery-1.11.3.min.js"></script><script src="../../../js/bootstrap.min.js"></script><script src="../../../js/jquery-fancybox/jquery.fancybox.min.js"></script><script>var pageId = 833;</script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui-custom.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.js"></script><script type="text/javascript" src="../../../js/std-quizzes-helpers.min.js?v=20220406"></script><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script type="text/javascript" src="../../../js/slick-carousel/slick.min.js"></script><script type="text/javascript" src="../../../js/std-slide-quizzes.min.js?v=20220406"></script><script type="text/javascript" src="../../../js/jq-boxfit/jquery.boxfit.min.js"></script><script src="../../../ajax/libs/mathjax/2.7.0/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script><script type="text/javascript" src="../../../js/flashcards/flashcards-utils.min.js?v=202211221200"></script><script type="text/javascript" src="../../../js/flashcards/std-flashcards.min.js?v=202211221000"></script><script type="text/javascript" src="../../../js/hammerjs/hammerjs.min-1.js?v=20220414"></script><script src="../../../js/gifffer/gifffer.min.js"></script><script src="../../../js/gifffer/gifffer-player.min.js?v=20201126"></script><script type="text/javascript" src="../../../js/jqueryui/jquery-ui.min.js"></script><script type="text/javascript" src="../../../js/jqueryui/jquery.ui.touch-punch.min.js"></script><script src="../../../js/user/page-my-progress.min.js?v=202211221000"></script><script>var sAJAX='/pages/subjects/activity/user-stats-page.php?t=082b9c9c4ae3624d&p=833&s=6&x=20144';var sData='k4iA6GSB03BgPm1NODORPHpsE3KeSVBAEzP5PHpsE39FIxiA6GSB0bfjSYyBPm1FC3KAZYKjExp360ij6GiREzpDSYc474PRPHpsE3KeSYcH74P5EncR739RPnLsSYK4ZGcR74P5EncR739RPHaL6nfhWGcjWFP5PFPRPHpsSYlFwFi7Ibp1k0aj6ba7IbpsE3K7IDlDOLAh63KAZYKjExL360ij6GiREzLDSYc474iv';var loopSecs = 30;var minSecsLog = 60;var lsKey = '6-83610-833';</script><script src="../../../js/subjects/activity/user-stats-page.min.js?v=202205311700"></script><script src="../../../js/subjects/activity/my-favorites.min.js?v=20220610"></script><script src="../../../js/subjects/feedback.min.js?v=202211221000"></script><script>var sessionUpdateSecs = 300;</script><script type="text/javascript" src="../../../js/session-updater.js"></script><script>(function(i,s,o,g,r,a,m){i['GoogleAnalyticsObject']=r;i[r]=i[r]||function(){(i[r].q=i[r].q||[]).push(arguments)},i[r].l=1*new Date();a=s.createElement(o),m=s.getElementsByTagName(o)[0];a.async=1;a.src=g;m.parentNode.insertBefore(a,m)})(window,document,'script','https://www.google-analytics.com/analytics.js','ga');ga('create', 'UA-98480796-3', 'auto');ga('send', 'pageview');</script><script src="../../../js/devicefp/devicefp.min.js"></script><script src="../../../js/jq-quickfit/jq-quickfit.min.js?v=20220201"></script><script src="../../../js/frontpage-subjects.min.js?v=202211161300"></script><script type="text/javascript" src="../../../js/studyib-jq.min.js?v=202211241300"></script><script type="text/javascript">$(document).ready(function(){ $('#trigger-modal-video-overview').click(function() { if( $('#modal-video-overview .modal-body iframe').attr('src').length == 0 ) { $('#modal-video-overview .modal-body iframe').attr('src', 'https://www.youtube.com/embed/hxxtdiLdTFk?rel=0'); } }); $('#modal-video-overview').on('hidden.bs.modal', function() { $('#modal-video-overview .modal-body iframe').attr('src', ''); }); });</script></body></html>