The infamous three-body problem – the mathematical puzzle of how three objects can orbit one another according to Newton’s laws – now has hundreds of new solutions.
Last year, at Shanghai Jiaotong University in China and his colleagues used a supercomputer to calculate more than a thousand new solutions, nearly doubling the known number of answers to the three-body problem. Now, they’ve added 231 more ways that three bodies bound together by gravity can orbit one another without colliding.
As before, the new solutions all hinge on periodic orbits, meaning each object begins and ends its path at the same point. These new solutions have a slight twist – each object starts at a standstill, instead of beginning with a bit of speed, and free-falls towards the others.
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Liao and his colleagues began by assigning the three bodies a ratio of masses – they found solutions for scenarios where all the masses are equal to one another, as well as those where they differ. Liao says they didn’t select the mass ratios for any special reason because, in theory, periodic orbits can be found for objects of any mass. “There should exist an infinite number of periodic orbits of the three-body system,” he says.
Their results are sometimes extremely simple – and more often mind-boggingly complex – dances in which the three objects skirt around one another, narrowly missing head-on collisions.
Although these three objects don’t necessarily represent planets, many of the orbits are stable so it’s theoretically possible, if incredibly unlikely, that we could find sets of worlds in configurations like this.
Imagine, for example, living on the blue world in this scenario:
Or riding the terrifying rollercoaster that is this three-body system:
Chaos theory, the study of systems in which tiny initial variations can cascade into outsized effects, is seen at work in the messes of loops and swirls:
Some of the solutions result in something that looks like a simple line-drawing. This one, for example, resembles a dragonfly:
Another is reminiscent of Picasso’s cubist portraits:
“Frankly speaking, I was deeply moved and captivated by their beauty,” Liao says.
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