September 21, 2023

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Mathematicians have found 12,000 solutions to the famous three-body problem

Mathematicians have found 12,000 solutions to the famous three-body problem

Until recently, it was nearly impossible to calculate how three objects could orbit each other in stable orbits. Mathematicians have now found a record number of new solutions.

Three celestial bodies can move around each other in stable orbits. Take, for example, the Sun, Earth, and Moon. The question of whether there are other ways to create three stable orbits has occupied mathematicians for more than three hundred years. Researchers have now found up to 12,000 possible configurations.

Big steps

The mathematical description of the mutual gravitational force and motion of two celestial bodies is relatively simple. But the problem immediately becomes more complex once a third object appears.

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In 2017, researchers found 1,223 new solutions to the three-body problem. That was twice the known number of possibilities.

Now computer scientist Ivan Hristov of Sofia University in Bulgaria and his colleagues are going one step further. they have 12,392 job opportunities were found Which works according to Newton’s laws.

free fall

The team used a supercomputer and an improved version of the algorithm from 2017. Hristov says that if he repeated the search using more powerful hardware, he would find “five times as much.”

To find the solutions, the researchers started by simulating three stationary objects. They then let the trio collapse in free fall. As they fall, the objects are pulled together by gravity. Their drive causes them to pass each other, slow down, stop, and then gravitate toward each other again. The team discovered that in the absence of friction, this pattern repeats indefinitely.

One of the new solutions to the three-body problem. Photo: Ivan Hristov, Radoslava Hristova, Veljko Dmitrasinović, Kiyotaka Tanikawa.

Solutions to the three-body problem are interesting to astronomers because they describe, for example, how stars, planets, or moons can find a stable orbit. But it remains to be seen whether new solutions actually exist in the universe. Small additional influences play a role, such as the gravity of distant celestial bodies.

“The importance of astronomy will become clear after we achieve stability [van de banen] “I studied – it’s very important,” says Hristov. However, whether they are stable or unstable, they are of great theoretical interest. They have a very beautiful structure in space and time.

The real world

Finding many solutions under these exact conditions is interesting for mathematicians, but has limited real-world application, says astronomer Johan Franke of Louisiana State University. “The majority, if not all [oplossingen]“It requires initial conditions so precise that they probably never occur in nature,” Frank says.

“After a complex but predictable orbital interaction, these three-body systems tend to split into a binary system and a runaway third body,” says Frank. This means that two celestial bodies stay together, while the third, usually less massive, body flies away.

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