The complex three-body problem has tens of thousands of solutions?

Science and Technology Daily, Beijing, September 11 (Reporter Liu Xia) According to a report on the British "New Scientist" website on the 9th, for more than 300 years, the question of how three objects orbit each other in a stable orbit has been puzzling mathematicians. In the latest research, Bulgarian mathematicians have found more than 12,000 solutions to this complex three-body problem. The relevant paper has been submitted to the preprint website.

While it's relatively simple to mathematically describe the motion of two objects orbiting each other and how the gravity of each affects the other, the problem becomes much more complicated once a third object is added. At the same time, astronomers are interested in solutions to the three-body problem because these solutions can describe any three celestial bodies - whether they are stars, planets or moons.

The simplest example of the three-body problem is the motion of the sun, earth, and moon in the solar system. In the vast universe, the size of the planets can be ignored and they can be regarded as particles. If the influence of other planets in the solar system is ignored, their motion is only caused by gravity, and their motion can be regarded as a three-body problem.

In 2017, researchers found 1,223 new solutions to the three-body problem. Now, Ivan Hristov of Sofia University and his colleagues have used supercomputers to run an optimized version of the algorithm used previously and found 12,392 new solutions. If repeated with more powerful hardware, the team could find "five times more solutions."

The team found that all of these new solutions follow a similar pattern: three stationary objects fall freely under the influence of gravity, then the momentum of the objects causes them to "pass by" each other, then slow down, stop, and be attracted together again. Assuming there is no friction, this pattern will repeat infinitely.

The stability of these solutions remains to be seen, given the possibility of other objects joining in, as well as the influence of "noise". Juan Frank of Louisiana State University in the United States pointed out that so many solutions are interesting to mathematicians, but most of the solutions require such precise initial conditions that they may not be achieved in nature.