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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>&nbsp;&nbsp;Feedback</button> </div> </div> <div class="col-md-9" id="main-column"> <h1 class="page_title"> Gravitation <a href="#" class="mark-page-favorite pull-right" data-pid="268" 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><span class="gray">Gravitation</span></li> <span class="pull-right" style="color: #555" title="Suggested study time: 15 minutes"><i class="fa fa-clock-o"></i> 15&apos;</span> </ol> <article id="main-article"> <p><img alt="" src="../../circular-motion/gravity-sma-1.jpg" style="width: 250px; height: 167px; float: left;">A&nbsp;field is a region of space where a&nbsp;force is experienced:</p> <ul> <li>Gravitational fields - objects with mass</li> <li>Electrostatic fields - objects with charge</li> <li>Magnetic fields - moving charges or permanent magnets</li> </ul> <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>Gravity is the phenomenon by which objects with mass are attracted to one another.</p> <p>To describe a region of space where a body experiences a force we use the term<em> field. </em>A gravitational field is a region where a mass experiences a force due to its mass. The force is also dependent on the mass of the body <span class="math-tex">\(F=mg\)</span>.</p> <p>Instead of using the term&nbsp;<em>gravity</em>:</p> <ul> <li><strong>Weight</strong> refers to the force acting downwards on objects close to the surface of the Earth</li> <li><strong>Gravitational force</strong> refers to the force acting between objects in radial fields</li> </ul> <p>NB: Take time to consider the Earth&#39;s gravitational field in each question, as our model varies depending on distance away. Is it uniform and parallel or radial from the centre?&nbsp;</p> <div class="panel panel-turquoise panel-has-border panel-has-colored-body"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field strength,&nbsp;<span class="math-tex">\(g\)</span></p> </div> </div> <div class="panel-body"> <div> <p>Gravitational field strength is the gravitational force per unit mass experienced by a small test mass* placed in the field:</p> <p style="text-align: center;"><span class="math-tex">\(g={F_G\over m}\)</span></p> <p>Gravitational field strength has units Nkg<sup>-1</sup>. While dimensionally equivalent to ms<sup>-2</sup>, avoid making this reference to acceleration here.</p> <p>*The reference to a small test mass means that the shape and magnitude of the field is not influenced by the introduction of another mass.</p> </div> </div> <div class="panel-footer"> <div> <p>&nbsp;</p> </div> </div> </div> <div class="panel panel-turquoise panel-has-border panel-has-colored-body panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Field lines</p> </div> </div> <div class="panel-body"> <div> <p>Field lines are drawn to show the direction and strength of the field. There are some features to note:</p> <ul> <li>The proximity&nbsp;of lines gives the strength of the field</li> <li>The&nbsp;direction of the arrows is the direction in which a test mass would move</li> <li>Field lines must not cross; they always show a resultant direction</li> <li>Field lines are perpendicular to&nbsp;<em>equipotentials</em>, lines of constant gravitational potential energy (literally like contours on a map)</li> </ul> <p style="text-align: center;"><img alt="" src="../../../ib/physics/activities/G1.png" style="width: 500px; height: 146px;"></p> <p><img class="sibico" src="../../../img/sibico/calc.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Calculator">&nbsp;Field strength is a vector quantity so must be added vectorially. Using <a href="http://www.thinkib.net/physics/page/18271/orbit-simulation-algodoo">this&nbsp;simulation</a>&nbsp;you can observe how the resultant field changes as you move around the field.</p> </div> </div> <div class="panel-footer"> <div> <p>&nbsp;</p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div>&nbsp;</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-border panel-has-colored-body panel-yellow"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Newton&#39;s universal law of gravitation</p> </div> </div> <div class="panel-body"> <div> <p>Newton wasn&#39;t able to go into space to measure the gravitational force but realised that the origin of the force causing an apple to fall to the earth was the same as the force holding the planets in orbit around the Sun. He was also convinced that this could be explained with a single mathematical equation.</p> <div class="box"> <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>In this equation, <span class="math-tex">\(G\)</span> is the universal gravitational constant,&nbsp;6.67&nbsp;&times; 10<sup>-11</sup>&nbsp;m<sup>3</sup>kg<sup>-1</sup>s<sup>-2</sup>.</p> </div> </div> </div> <div class="panel-footer"> <div> <p>&nbsp;</p> </div> </div> </div> <div class="panel panel-has-border panel-has-colored-body panel-yellow panel-expandable"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Orbits</p> </div> </div> <div class="panel-body"> <div> <p>The gravitational force can provide the centripetal force required to cause a body to move in a circle.</p> <p>In the absence of other forces (a very reasonable assumption in space), we can equate the gravitational force to the centripetal force to derive Kepler&#39;s Third Law:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(F_G={GMm\over r^2}={mv^2 \over r}\)</span></p> <p style="text-align: center;"><span class="math-tex">\({GM\over r}=v^2={(2\pi r)^2\over T^2}\)</span></p> <p style="text-align: center;"><span class="math-tex">\(\Rightarrow {T^2 \over r^3}={4\pi ^2\over GM}\)</span></p> </div> <p>Kepler&#39;s Third Law tells us that the ratio of T<sup>2</sup> to r<sup>3</sup> is constant for&nbsp;<em>any</em>&nbsp;body orbitting a common centre. This means that, for example, we could work out the distance from any planet to the Sun if we knew its length of year.</p> <p><img alt="" src="../../../ib/physics/activities/G5.png" style="width: 272px; height: 285px; float: left;"></p> <p>Since everything on the right hand side is constant, we can also say that:</p> <div class="box"> <p style="text-align: center;"><span class="math-tex">\(({T_1\over T_2})^2=({r_1\over r_2})^3\)</span></p> </div> <hr class="hidden-separator"> <p><img class="sibico" src="../../../img/sibico/quiz.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Quiz">&nbsp;Why don&acute;t satellites fall down?</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden">Provided that a satellite&nbsp;does not collide with anything, the only force acting is perpendicular. Therefore, its speed will not change. It will have a constant time period and radius.</section> <p><img class="sibico" src="../../../img/sibico/quiz.svg" style="height:1.25em;width: auto;vertical-align:text-bottom" title="Quiz">&nbsp;Is it possible to have a satellite above the same point on the Earth at all times?</p> <button class="btn btn-xs bg-turquoise showhider"><i class="fa fa-fw fa-plus"></i></button><section class="hiddenbox hidden">Only directly above the equator, where the time period will be exactly the same as the length of an Earth day (24 hours). This is referred to as a <em>geostationary</em> orbit and is used in GPS.</section> </div> </div> <div class="panel-footer"> <div> <p>&nbsp;</p> </div> </div> </div> </div> </div> <div class="panel-footer"> <div>&nbsp;</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><em>Use&nbsp;flashcards&nbsp;to practise your recall.</em></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="520" data-subject-id="6" data-n-flashcards="6" style="text-align:center">Show flashcards</a></div><hr> </div> </div> <div class="panel-footer"> <div>&nbsp;</div> </div> </div> <div class="panel panel-has-colored-body panel-red"> <div class="panel-heading"><a class="expander" href="#"><span class="fa fa-plus"></span></a> <div> <p>Just for Fun</p> </div> </div> <div class="panel-body"> <div> <p><em>Check out this&nbsp;&pi;g physics summary.</em></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/389470634"></iframe></div> </div> </div> <div class="panel-footer"> <div>&nbsp;</div> </div> </div> <div class="page-container panel-self-assessment" data-id="268"> <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>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">&times;</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/268/gravity"> <input type="hidden" name="feedback-subject" value="6"> <input type="hidden" name="feedback-subject-name" value="Physics"> <div class="pull-left"> </div> </form> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary btn-xs-block feedback-submit mb-xs-3 pull-right"> <i class="fa fa-send"></i> Send </button> <button type="button" class="btn btn-default btn-xs-block m-xs-0 pull-left" data-dismiss="modal"> Close </button> </div> </div> </div></div> <div id="fc-viewer" class="modal fade modal-flashcard" tabindex="-1" role="dialog"><div class="modal-dialog" role="document"><div class="modal-content"><div class="modal-header" style="background-color: #fafafa;"><div class="row" style="width: 100%;"><div class="col-md-12 tags-heading"><div style="display: flex; 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