File "newtons-law-of-gravitation.html"
Path: /StudyIB/physics/page/269/newtons-law-of-gravitationhtml
File size: 47.89 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>Newton's law of gravitation</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: Newton's law of gravitation"> <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="Newton´s universal law of gravity applies to the whole universe and, while on your data booklet, is certainly worth remembering."> <meta prefix="og: http://ogp.me/ns#" property="og:url" name="og:url" content="https://studyib.net/physics/page/269/newtons-law-of-gravitation"> <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="Newton´s universal law of gravity applies to the whole universe and, while on your data booklet, is certainly worth remembering."> <meta name="image" content="https://studyib.net/img/studyib-card-default.jpg"> <meta name="keywords" content="Circular motion, Gravity, IB, IBDP, InThinking, International Baccalaureate, Revision, Revision websites, Student Sites, Students, Learning, Guidance, Exam, Questions, Practice problems, Diagnose, Help, Notes"> <meta itemprop="name" content="StudyIB Physics: Newton's law of gravitation"> <meta itemprop="description" content="Newton´s universal law of gravity applies to the whole universe and, while on your data booklet, is certainly worth remembering."> <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: Newton's law of gravitation"> <meta name="twitter:description" content="Newton´s universal law of gravity applies to the whole universe and, while on your data booklet, is certainly worth remembering."> <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"><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="../443/circular-motion-and-gravity.html" class="dropdown-toggle toplevel-dropdown" data-toggle="dropdown"><i class="fa fa-ellipsis-v"></i></a> <a href="../443/circular-motion-and-gravity.html">Circular motion and gravity</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="../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="../823/astrophysics.html"><i class="fa fa-fw fa-caret-right"></i> Astrophysics</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"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../264/circular-motion.html">Circular motion</a></label><ul class="side-nav level-1"><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../265/centripetal-force.html">Centripetal force</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../266/examples-of-circular-motion.html">Examples of circular motion</a></label></li></ul></li><li class="expanded parent"><label style="padding-left: 0px"><a class="expander" href="#" style="font-size: .9em"><i class="fa fa-fw fa-caret-right"></i></a><a href="../268/gravitation.html">Gravitation</a></label><ul class="side-nav level-1"><li class="expanded parent selected"><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="newtons-law-of-gravitation.html">Newton's law of gravitation</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../270/uniform-fields.html">Uniform fields</a></label></li><li class=""><label style="padding-left: 14px"><i class="fa fa-fw"></i><a href="../271/orbits.html">Orbits</a></label></li></ul></li><li class=""><label style="padding-left: 0px"><i class="fa fa-fw"></i><a href="../1148/ahl-gravitational-fields.html">AHL Gravitational fields</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"> Newton's law of gravitation <a href="#" class="mark-page-favorite pull-right" data-pid="269" 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="../443/circular-motion-and-gravity.html">Circular motion and gravity</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><a href="../268/gravitation.html">Gravitation</a><i class="fa fa-fw fa-chevron-right divider"></i></li><li><span class="gray">Newton's law of gravitation</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 20 minutes"><i class="fa fa-clock-o"></i> 20'</span> </ol> <article id="main-article"> <p><img alt="" src="../../circular-motion/2-woolsthorpe.jpg" style="float: left; width: 250px; height: 166px;">The force between two 1 kg masses is very small. It was a big step for Newton to realise that it exists without being able to measure it.</p> <p>Newton´s universal law of gravity applies to the whole universe and, while on your data booklet, is certainly worth remembering.</p> <p>The field concepts here are also used in <a href="../180/electric-fields.html" title="Electric fields">Electric fields</a>. </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> <div class="panel panel-turquoise panel-has-colored-body panel-has-border"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Force between point masses</p> </div> </div> <div class="panel-body"> <div> <p>Gravitational forces form <a href="../239/newtons-third-law.html" title="Newton's third law">Newton's third law</a> pairs, with the forces in opposite directions, the same magnitude and acting on different bodies.</p> <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/164247815"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Inverse square law</p> </div> </div> <div class="panel-body"> <div> <p>The force experienced by a mass in the gravitational field of the earth is inversely proportional to its distance from the centre squared.</p> <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/164290319"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-turquoise panel-has-colored-body panel-has-border panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Newton's universal law of gravitation</p> </div> </div> <div class="panel-body"> <div> <p>Every particle of mass attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to their separation squared.</p> <p style="text-align: center;"><span class="math-tex">\(F=G{Mm\over r^2}\)</span></p> <p>The constant of proportionality is very small so the force between two 1 kg masses 1 m apart is only 6.67 x 10<sup>-11</sup> N.</p> <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/164375476"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </p> </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> <div class="panel panel-has-colored-body panel-has-border panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field strength (g)</p> </div> </div> <div class="panel-body"> <div> <p>The field strength tells us how much force would be experienced per kg if a body was placed at that point. So the force experienced by an body of mass m would be mg.</p> <p>For a radial field:</p> <p style="text-align: center;"><span class="math-tex">\(g=G{Mm\over r^2} \div m\)</span></p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow g=G{M\over r^2}\)</span></p> </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/164377639"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <div class="panel panel-has-colored-body panel-has-border panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field lines around a spherical mass</p> </div> </div> <div class="panel-body"> <div> <p>Field lines are drawn to show the direction and strength of the field. The field lines around the Earth are radial, this shows that the field gets weaker the further away we go, as is indicated by the <span class="math-tex">\(1\over r^2\)</span> term in the equation.</p> <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/164381021"></iframe></div> </div> </div> <div class="panel-footer"> <div> <p> </p> </div> </div> </div> <p> </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 quizzes to practise application of theory.</i> </p> <br><a class="btn btn-primary btn-block text-center" data-toggle="modal" href="#b5b91b8e"><i class="fa fa-play"></i> START QUIZ!</a><div class="modal fade modal-slide-quiz" id="b5b91b8e"> <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%;"> Newton's gravitational law <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="6-69-269" style="opacity: 0"> <div class="exercise shadow-bottom"><div class="q-question"><p>Fill in the gaps in this statement of newton's universal law of gravity.</p><p>Word list: directly, indirectly, inversely, point, square, product, sum.</p></div><div class="q-answer"><p>The force between two <input type="text" style="height: auto;" data-c=" point "> <span class="review"></span> masses is <input type="text" style="height: auto;" data-c=" directly "> <span class="review"></span> proportional to the <input type="text" style="height: auto;" data-c=" product "> <span class="review"></span> of their mass and <input type="text" style="height: auto;" data-c=" inversely "> <span class="review"></span> proportional to the <input type="text" style="height: auto;" data-c=" square "> <span class="review"></span> of their separation.</p></div><div class="q-explanation"></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 units of G can be expressed as Nm<sup>2</sup>kg<sup>-2</sup></p><p>This is the same as.</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> m<sup>2</sup>kgs<sup>-2</sup></label></p><p><label class="radio"><input type="radio"> m<sup>2</sup>kg<sup>-1</sup> s<sup>-2</sup></label></p><p><label class="radio"><input class="c" type="radio"> m<sup>3</sup>kg<sup>-1</sup>s<sup>-2</sup></label></p><p><label class="radio"><input type="radio"> m<sup>3</sup>kg<sup>-1</sup>s<sup>-1</sup></label></p></div><div class="q-explanation"><p>from F = ma we know that N is the same as kgms<sup>-2</sup></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>Calculate the force between a 4 kg sphere and a 2 kg sphere place 2 m apart.</p><p>Take G = 7 x 10<sup>-11</sup> Nm<sup>2</sup>kg<sup>-2</sup></p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 4.2 pN</label></p><p><label class="radio"><input type="radio"> 0.42 μN</label></p><p><label class="radio"><input class="c" type="radio"> 1.4 pN</label></p><p><label class="radio"><input type="radio"> 0.14 μN</label></p></div><div class="q-explanation"><p>F = GMm/r<sup>2</sup> = 7 x 10<sup>-11</sup> x 4 x 2/2<sup>2 </sup>= 2 x 7 x 10<sup>-11</sup> N p is 10<sup>-12</sup></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 spheres of equal mass but different density are placed as shown</p><p style="text-align: center;"><img alt="" src="../../images/nugq1.png" style="width: 314px; height: 109px;"></p><p>At which point will the two gravitational fields cancel out?</p></div><div class="q-answer"><p><label class="radio" style=" float: left; margin-right: 40px; "><input class="c" type="radio"> B</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> A</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> C</label></p><p><label class="radio" style=" float: left; margin-right: 40px; "><input type="radio"> D</label></p></div><div class="q-explanation"><p>B is equidistant from the centres.</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 point mass M is placed 2m from a second point mass 10M. The force on M is 2 μN.</p><p>The force on the 10M mass is:</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 20 μN</label></p><p><label class="radio"><input class="c" type="radio"> 2 μN</label></p><p><label class="radio"><input type="radio"> 5 μN</label></p><p><label class="radio"><input type="radio"> 10 μN</label></p></div><div class="q-explanation"><p>Newt 3</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 large spherical asteroid has a radius of 5000m.</p><p>If a 100 kg mass experiences a force of 0.004 N on the surface what force will it experience when 5000m above the surface?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 0.003 N</label></p><p><label class="radio"><input class="c" type="radio"> 0.001 N</label></p><p><label class="radio"><input type="radio"> 0.0005 N</label></p><p><label class="radio"><input type="radio"> 0.002 N</label></p></div><div class="q-explanation"><p>The distance from the centre is increased by a factor 2. F is proportional to 1/r<sup>2</sup> so F will be 1/4</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 field strength on the surface of a spherical asteroid is 1 x 10<sup>-4</sup> Nkg<sup>-1</sup></p><p>A 5 kg mass is released 0.5 m above the surface, how long will it take to hit the ground?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 10 s</label></p><p><label class="radio"><input type="radio"> 0.1 s</label></p><p><label class="radio"><input type="radio"> 1 s</label></p><p><label class="radio"><input class="c" type="radio"> 100 s</label></p></div><div class="q-explanation"><p>The acceleration = field strength<br>Using s = ut + 1/2 at<sup>2</sup></p><p>t = √(2s/a) = √(10<sup>4</sup>) = 100</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>In Algodoo the value of G can be set to 1 Nm<sup>2</sup>kg<sup>-2</sup></p><p>What is the field strength 10 cm from a 2 kg mass in this universe?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 0.02 Nkg<sup>-1</sup></label></p><p><label class="radio"><input type="radio"> 0.2 Nkg<sup>-1</sup></label></p><p><label class="radio"><input type="radio"> 2 Nkg<sup>-1</sup></label></p><p><label class="radio"><input class="c" type="radio"> 200 Nkg<sup>-1</sup></label></p></div><div class="q-explanation"><p>F/m = GM/r<sup>2</sup> = 2/0.1<sup>2</sup> = 200 Nkg<sup>-1</sup></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>In Algodoo the value of G can be set to 1 Nm<sup>2</sup>kg<sup>-2</sup></p><p>What is the force between two 100 g masses placed so that there is 10 cm between their centres.</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 10 N</label></p><p><label class="radio"><input type="radio"> 1000 N</label></p><p><label class="radio"><input class="c" type="radio"> 1 N</label></p><p><label class="radio"><input type="radio"> 100 N</label></p></div><div class="q-explanation"><p>F = GMm/r<sup>2</sup> = 1 x 0.1 x 0.1 /0.1 x 0.1 = 1 N</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>In Algodoo the value of G can be set to 1 Nm<sup>2</sup>kg<sup>-2</sup> The diagram shows two masses in that universe.</p><p style="text-align: center;"><br><img alt="" src="../../images/nugq2.png" style="width: 329px; height: 228px;"></p><p>What is the force on the blue mass?</p></div><div class="q-answer"><p><label class="radio"><input type="radio"> 33 N</label></p><p><label class="radio"><input class="c" type="radio"> 12 N</label></p><p><label class="radio"><input type="radio"> 100 N</label></p><p><label class="radio"><input type="radio"> 10 N</label></p></div><div class="q-explanation"><p>F = GMm/r<sup>2</sup> = 1 x 30 x 10/52 =300/25 = 12 N (r is distance between centres)</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="panel panel-has-colored-body panel-default"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Exam-style Questions</p> </div> </div> <div class="panel-body"> <div> <p><em>Online tutorials to help you solve original problems</em></p> <iframe src="../../../pages/subjects/page-networks/index-73.htm?ticket=082b9c9c4ae3624d&network-id=45&sitename=physics&subject-id=6&fullscreen=false&node=start" style="width: 100%; height: 640px; max-height: 80vh" id="network-45" class="network-viewer"></iframe> </div> </div> <div class="panel-footer"> <div> </div> </div> </div> <div class="page-container panel-self-assessment" data-id="269"> <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>Newton's law of gravitation</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/269/newtons-law-of-gravitation"> <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> </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 = 269;</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/std-networks.min.js?v=202201261522"></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=269&s=6&x=22511';var sData='k4iA6GSB03BgPm14amgRPHpsE3KeSVBAEzP5PHpsE39FIxiA6GSB0bfjSYyBPm1FUnKbSYv2ibOlWYcbPYvnPYS460EjSYcrZGv2PFAF7YcHEKvr6GSDPmjn6GyDEzAFWGcrE0ij6GyDPmjn6GyDEzAF7bKFEYv86GB2Pm1FPFAF7YcrZxP5PBAh7Ysq73Bm7LAh7YcHEKAhOm6q0xv2E0SrW3qDIGysS4LhEFLH7nc3Z0fsSYBhWFiv';var loopSecs = 30;var minSecsLog = 60;var lsKey = '6-83610-269';</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>