Click on the button for “Download Test Tube Games Gravity Simulator” at the bottom of this page.  This simulator uses imaginary adapted units, but it is good enough for qualitative work just to test out various forms of gravity laws, and general ideas. But there is a problem in that the free version does not allow you to change the gravity law. In order to run the simulation with my adjustments, you will have to download and install the full version.  The good news about this, is that the full version only costs $7.

Once you have the full version installed, try running it.  When you’re sure that it is installed properly on your computer, you can press the escape key twice to close it.  After it is closed, highlight and copy the following text:

//Gravity fun at TestTubeGames
_settings(gravity: 2.3*sin(1.2*sqrt(r))*(1/(r+.1)^2)+(1/(r+.1)^2), name: square rings, x: 0, y: 0, zoom: 0.005);
_add(m: 0.0025, d: 1, col: 1, lcol: 1, pic: 0, x: 9900, y: 0, vy: .31, t: 0);
_add(m: 947.218, d: 0.2810409, col: 2, lcol: 2, pic: 0, noGrav, x: 0, y: 0, t: 0);
_add(m: 0.0025, d: 1, col: 1, lcol: 1, pic: 0, x: 2300, y: 0, vy: .4471, t: 0);
_add(m: 0.0025, d: 1, col: 1, lcol: 1, pic: 0, x: 22800, y: 0, vy: .242, t: 0);
_add(m: 0.0025, d: 1, col: 1, lcol: 1, pic: 0, x: 40750, y: 0, vy: .195, t: 0);

After it is copied, follow these steps to run my simulation that produces square orbits using a CGC-type sinusoidal gravity force law:

1.  Run the simulation program.  Press the “Build” button.
2. Once it loads, immediately press the “pause” button in the upper left.  Then press the “clear” button on the top left to clear out whatever is in there.
3.  Click on the “Save” button and then select on the top right the “Current” option.
4. On the left side, highlight and delete everything in there.
5.  Paste the simulation settings that you copied earlier into the box on the left, where you just deleted all the existing settings.
6.  Click “Load”, then click “OK” on save changes.
7.  Once you’re back in the simulation screen, in the lower right make sure the settings are all expanded so that you can see them.
8.  Click on “trails” and then check “trails on.”  Now close the trails dialogue box.
9.  Click on the clock to set the time.  Set it to 10,000, then close the time dialogue box.
10.  Over on the left click on “quick save”.  This is done so that you can start over with all the same settings once you’ve run the simulation a bit.  If you don’t do this, then you will have to do the settings from scratch each time. 
11.  Now press “play” and let the simulation run for as long as you want.  When you are finished, then press “pause”.
12. When you are ready to run it again, press “quick load.”

If you want to try other scenarios, press the save button and then select one to try, and then load it.  Notice that with the full version you can also try out whatever gravity force law that you can imagine — just click on the “Physics” icon over in the settings.  The f(r) that my “square orbits” simulation uses is: 

2.3*sin(1.2*sqrt(r))*(1/(r+.1)^2)+(1/(r+.1)^2)

Also please see all of the helpful links on the download page to get an idea of the things that this simulator can do.