The scientific community has made significant progress in understanding the three-body problem, one of the most difficult problems in theoretical physics and mathematics. University of Copenhagen researcher Alessandro Alberto Trani of the Niels Bohr Institute has made a discovery that could change the understanding of gravitational interactions and many other fundamental aspects of the universe.

The three-body problem, first described by Isaac Newton, concerns the motion of three-point masses interacting with each other through gravity. Contrary to the expected interaction between two objects, the emergence of a third large object makes the system chaotic and difficult to analyze. However, as recent research shows, this chaos has certain patterns.

“The three-body problem is one of the most famous unsolvable problems in mathematics and theoretical physics. The theory states that when three objects meet, their interaction develops chaotically, without any regularity and completely disconnected from the starting point,” explains Alessandro Alberto Trani. But his team discovered that “there are gaps in this chaos, ‘islets of order’ that depend directly on how three objects are positioned relative to each other at the moment of encounter, as well as their speed and angle of approach.”

To achieve this result, Trani developed a program called Tsunami, which allows the motion of astronomical objects to be calculated according to natural laws such as Newton’s gravity and Einstein’s theory of general relativity. The program is configured to perform millions of three-body collision simulations within certain parameters. The initial parameters of the simulation were the position of the two objects in the common orbit and the angle of approach of the third object.

The results of these simulations created a detailed map of all outcomes where “islets of regularity” emerged. Often, the object with the least mass was the one that was ejected from the system following the collision. “If the three-body problem were completely chaotic, we would see only a chaotic mixture of indistinguishable points, where all three outcomes are mixed with no discernible order. Instead, orderly ‘islands’ emerge from this chaotic sea where the system behaves predictably, resulting in uniform outcomes and hence leading to uniform colors,” Trani explained.

This discovery holds significant promise for a deeper understanding of the gravitational waves emitted by black holes and other massive objects. “The interaction of black holes as they meet and merge is crucial if we want to understand propagating gravitational waves. Particularly when three of them occur, enormous forces come into play. So our understanding of their encounters could be key to understanding phenomena such as gravitational waves, gravity itself, and many other fundamental mysteries of the universe.” added the researcher.

This discovery holds great promise but also presents a challenge for researchers. Pure chaos is something that can already be calculated using statistical methods, but when chaos is interrupted by patterns the calculations become even more difficult. “When some areas in this map of possible outcomes suddenly become regular, statistical probability calculations break down and lead to inaccurate predictions. “Our task now is to learn how to combine statistical methods, called numerical calculations, that provide high accuracy when the system behaves regularly,” Trani said.

Trani and his team’s research appears to have put the mission back on track, but it also offers hope for a whole new level of understanding in the long run.