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<h2>Eight-body problem</h2> This is an interactive model of an unrestricted two-dimensional eight-body gravitational problem, based on the general solution of an <I>n</I>-body gravitational problem. The theoretical background for this solution is set forth in the book:<br><a href="http://www.grevytpress.com" target="central"><I>Gravitation: master key to the universe: the greatest mystery of science is solved!</I></a> (ISBN 0-9689120-0-1) by Karel Havel.<br> The simulation is programmed to automatically stop either when one of the bodies flies out of the bounds or on a near collision between any two bodies (such collision could be simulated accurately if a much smaller time increment for the calculations was used).<br><br> Before you start experimenting with the model, please read the sections Technical Comments and Suggested Experiments.<br><br> <b>Your browser must be enabled for Java 2. To start the model, click on <i>Simulation</i> in the left panel. Allow several minutes, depending on your Internet connection, for the applet to load.</b> <br><hr width="100%" size="2"><br>  <h2>Operation</h2> <nl> <li>There are eight bodies: red, blue, green, magenta, cyan, yellow, gray, and orange, placed symmetrically along a circle. <li>There are three control buttons in the top of the left column: Play, Pause, and Reset, followed by a number of editable fields below. Click on Play button to run the simulation. Click on Pause to stop it. Click on Reset to restore the defaults. <li>The fields show the default values of the masses that can be changed. All values are in the metric system. The colors of the values respectively correspond to the colors of the bodies. When you hover the mouse cursor over the field, it displays its identifying label. The default masses of all bodies are 3.2e29. </nl> <br> <br><hr width="100%" size="2"><br>  <nl>Eight bodies are regularly positioned along a circle. All bodies have the same initial speed, but each velocity vector is a tangent of the circle. <br><br>This configuration is unstable. After one and a half perfect orbits the bodies go bananas. Observe how the irregularities of their orbits are perfectly symmetrical. </nl> <br><hr width="100%" size="2"><br>   <applet code="org.opensourcephysics.ejs.LauncherApplet.class" codebase="." archive="_library/_ejsLibrary.jar,unbody8c.jar" name="unbody8c" id="unbody8c" simulation="unbody8c.unbody8c" capture="mainFrame" width="397" height="320"> </applet>