Figure Eight Orbits

This is a stable figure-8 orbit formed by three bodies of equal mass discovered by Richard Montgomery and Alain Chenciner and located numerically by Carles Simo. (It was previously discovered empirically, in 1993, by Cristopher Moore.)

Click on images to start them moving, or to stop them. Dragging changes viewpoint. It helps your CPU if you only have one running at a time.

Just the orbit. Pretty repetitive, huh.
Can we put a planet around it? Sure. (I couldn't find any center to this class of orbits. All of them wobble left and right, in and out, and pay no attention to simple fractions of the periods of the three stars. Very strange.)

You change the viewpoint by dragging with the mouse.

Can we make the figure-eight out of planets orbiting a star? Sure, we can do that too. Here's an example.

You change the viewpoint by dragging with the mouse.

The center object has been given a position error of +.05x
The center object has been given a position error of +.05y
The center object has been given a position error of +.1z. No, I didn't tune the error. Any z error in any of the objects causes the same thing.
The center object has been given a velocity error of +.05x.
The center object has been given a velocity error of +.05y.
The center object has been given a velocity error of +.5z. That's huge. If you rotate the image so you look at it edge on, you will see that the objects are still coplanar. Go figure.
The center object has been extra mass of +.01
The center object has been extra mass of -.01
A Stellar Juggling Routine! This is the current champion at mesmerizing my baby. The right mix of predictability, unpredictability, and flash.

Even stranger orbits
Ye Olde Catalogue of Boy Scout Skits
Formulas for simulating orbits
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