## 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.)

 Just the orbit. Click to start or stop. Pretty repetitive, huh. Can we put a planet around it? Sure. You can drag the mouse to rotate about the center of gravity, or shift and drag to zoom or rotate clockwise. 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. Can we make the figure-eight out of planets orbiting a star? Sure, we can do that too. Here's an example. The 8 likes to lay with its major axis perpendicular to the sun. You change the viewpoint by dragging with the mouse. The center object has been given a position error of +.05x. It slowly rotates. The center object has been given a position error of +.05y. It starts rotating and gradually falls apart. (The shooting off at high speeds after collisions is due to the simulation failing to cope with very close passes, it's not real.) The center object has been given a position error of +.1z. It oscillates back and forth. 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 +.1x. I can't tell any difference. The center object has been given a velocity error of +.05y. It quickly falls apart. The center object has been given a velocity error of +.2z. 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.