What's the rarest figure eight in the universe?

As many of you have noticed, the planet Earth has not been hurled into space or fallen into the sun. It just keeps orbiting in the solar system. It seems pretty simple, but this fact has baffled minds like Newton. That's because when you have more than two bodies in an orbiting system, they are inherently unstable. Unless they're orbiting in a very specific, very cool way.

One of the oldest problems ever calculated, once the laws of motion and the theory of gravitation were set down, was how different objects (or bodies) orbited each other. The issue arose naturally enough. People began studying the movement of the planets in the solar system ā€” and that made them question the physical laws of the universe. The fact that those laws also applied to objects on the surface of the Earth was an epiphany. It seemed as though, with a few simple calculations, we could find out how literally everything moved, or would move. Mathematicians and physicists started out simple, with two bodies in a stable orbit. No problem. Sometimes the bodies drifted apart, and sometimes they collapsed, and sometimes they stayed in orbit ā€” at least for an unimaginably long length of time. The different outcomes of a two-body system were easy to calculate.

The theorists took a single step up, adding another body, and got stuck. And, to a certain extent, they have remained stuck. Three bodies interacting with each other in space change velocity, position, and proximity constantly. As these values change, they affect each other in ways that alter the values still further. It was impossible to predict in Newton's day, and despite the advent of computers, which can calculate the different factors at a speed that no human could, it remains difficult to predict what a three-body system will do. They're unstable.


And so the hunt for answers turned to different ways that the three-body system could be made stable. A few work-arounds have been found, but in the 1980s and 1990s, an entirely new three-body solution was conceived. Instead of a traditional orbit, like the kind the Earth takes around the sun, the three bodies would move in a perfect figure-eight pattern. They'd all trace the same path along a perfect plane, but always be at different points. The objects would have to be the right mass and speed, and the orbit just the right size, but it could happen.

The more mathematicians and physicists look at it, the more they agree it can exist. But does it? In a universe this size, it certainly has a chance, but few are hopeful of finding it. Neil deGrasse Tyson says, in his book Death By Black Hole, that it's doubtful that any such system exists in the Milky Way galaxy, and probably only a handful of them exist in the universe. It would be amazing to see one, though. Who knows? Maybe someday we can even construct one.

Image: Samer Abdallah

Via UIUC, Wolfram Research, AMS, and Science Direct.