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<h2>Three-body problem</h2> This is an interactive model of an unrestricted three-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> Before you start experimenting with the model, please read the sections Technical Comments and Suggested Experiments. <br><hr width="100%" size="2"><br>  <h2>Operation</h2> <nl> <li>This model can be used to study the orbits of the planets in the Solar System. The size of the display is sufficient to accommodate the orbit of the Earth. <li>There are three bodies: red, blue, and green, placed in arbitrary positions. <li>You can drag the bodies to different positions. <li>You can change the masses of the bodies. <li>You can change the initial velocities of the bodies. An initial velocity is defined as the x and y components of a distance traveled in one second. <li>You can change the time increment of the calculations (which changes the resolution of the orbits). <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 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. <li>In the first three fields from the top are the default values of the masses of the bodies. The number in each window is internally multiplied by 1.0e20. By way of an example, the mass of the green body is 2.0e30 (approximately the same as the mass of the Sun). <li>In the next six fields are the values of the x and y components of the initial velocity for each body. By way of an example, the red value -15000.00 in the fourth field, labeled "Velx0", indicates the x component of the initial velocity of the red body. <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 these:</h2> 1. To view the orbits with the default values, click on Play and observe the shapes of the orbits of the two planets.<br><br> 2. The trajectories of the two planets are rather coarse, particularly near the perihelions. That is caused by the time increment of the calculations being rather large. However, we can fix it. Click on Pause and then Reset. Now hold your mouse pointer above the field in the left bottom corner. The label reads "Increment". The default value of the time increment is 1 hour (3600 seconds). Click into the field and change it to 1200.0. The field changes to yellow while you are editing the number. Hit Enter when finished. Now click on Play. The bodies move three times slower, but the resolution of their orbits is better.<br><br> 3. Now let's do something wild. Click on Pause and then on Reset. Hold the mouse cursor over the second field that displays the value 50000.0 in blue. The label reads "Mass1". This is the mass of the second (blue) body (20 zeroes are added internally, which makes it 5.0e24). Change the value to 50000000000.0, which, considering the additional internal 20 zeroes, makes the mass of the blue body 5.0e30, two and a half times larger than the mass of the green body. Click on Play and observe complex trajectories of the bodies.<br><br> 4. Click on Pause and on Reset. Drag with your mouse the bodies to different positions. Click on Play and observe different shapes of the orbits.<br><br> 5. Click on Pause and on Reset. Slightly change the values of the initial velocities for all bodies. Click on Play and observe the changed shapes of the orbits.<br><br> When making other experiments with the model, always remember to Pause before changing any defaults. <br><hr width="100%" size="2"><br>   Wait until the applet loads (it may take several minutes).<br> <applet code="org.opensourcephysics.ejs.LauncherApplet.class" codebase="." archive="_library/_ejsLibrary.jar,h3b_2d.jar" name="h3b_2d" id="h3b_2d" simulation="h3b_2d.h3b_2d" capture="mainFrame" width="397" height="320"> </applet>             Thank you for using <a href="http://fem.um.es/Ejs"><b>Easy Java Simulations</b></a></p>