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

Mathematicians have been trying for more than 300 years to solve the almost insurmountable problem of how three objects can form a stable orbit around each other. Mathematically describe the motion of two bodies - simple enough, but the appearance of the third immediately spoils everything. At the same time, researchers have now discovered 12 thousand orbital arrangements corresponding to Isaac Newton's laws of motion.

This is stated in a study published on the arXiv preprints site. The results of the work of scientists have yet to be evaluated by the scientific community.

As New Scientist notes, it is relatively simple to describe the motion of two orbiting bodies and how the gravity of each of them affects the other. It is the appearance of the third that poses serious problems for the calculations.

In 2017, the scientists said they found 1,223 new solutions, doubling the number of solutions known at the time. But now Ivan Hristov of Sofia University in Bulgaria and his colleagues claim to have discovered more than 12,000 more working orbits.

Although the three-body problem is mathematical, it is of great interest to astronomers because it can describe how any three celestial objects - stars, planets or moons - can maintain a stable orbit.

The team of scientists was helped to solve the riddle by a supercomputer that was running an optimized version of the algorithm used in the 2017 paper. The updated algorithm was able to find 12,392 new solutions.

At the same time, Hristov believes that if the algorithm had run on a more powerful computer, the results would have been "five times more".

All the solutions found start with three bodies being stationary, and then gravity pulls them towards each other and they go into free fall.

In doing so, momentum prevents them from colliding and propels them past each other. Subsequently, all three objects slow down and return to rest until gravity sends them into free fall again.

Scientists say that in the absence of friction, this scenario would repeat indefinitely.

However, they recognize that it remains to be seen how stable the new solutions are when the tiny effects of additional, distant bodies and other real-world obstacles are taken into account.

"Their physical and astronomical significance will be better known after the stability study - this is very important. But nevertheless, stable or unstable, they are of great theoretical interest. They have a very beautiful spatio-temporal structure," Hristov stated.

In turn, Johan Frank from Louisiana State University (USA) noted that all these solutions are very interesting for mathematicians, but in reality their application will be very limited.

"Most, if not all (solutions. - Ed.), require such precise initial conditions that they will probably never be realized in nature," Frank explained.

According to him, in nature, the complex orbital interaction of three bodies eventually leads to the formation of a binary system and the ejection of the third body (usually less massive) outside of it.

Earlier OBOZREVATEL told about the fact that the mathematician of the 19th century found the planet Vulcan in the vicinity of the Sun.

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