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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, orbiting 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. <li>The field at the bottom, labeled "Increment", is the value in seconds of the time increment used in the calculations. </nl> <br> <br><hr width="100%" size="2"><br>  <h2>Before you start your own experiments, perhaps you should try this:</h2> To view the orbits with the default values, click on Play and observe how the eight bodies chase one another along a circle. By changing the masses of the bodies, you can control the shapes of their orbits.<br>This is how you change the default values. Click on Pause and then on Reset. By way of an example, to change the mass of the red body, hold the mouse cursor over the first field that displays the value 3.2E29 in red. The label reads "Mass0". This is the mass of the red body in the scientific notation. Click into the field and change it to 3.2E30 (ten times more). The background color of the field changes to yellow while you are editing the number. Hit Enter when finished. The background color changes back to white to indicate that the edit is finished. Click on Play and observe drastically different orbits of all bodies. You can change any of the remaining default values of the masses by the same technique.<br><br> When making other experiments with the model, always remember to Pause and Reset before changing any defaults. <br><hr width="100%" size="2"><br>   <applet code="org.opensourcephysics.ejs.LauncherApplet.class" codebase="." archive="_library/_ejsLibrary.jar,unbody8a.jar" name="unbody8a" id="unbody8a" simulation="unbody8a.unbody8a" capture="mainFrame" width="397" height="320"> </applet>