‘Islands of regularity’ detected in chaotic three-body problem

Scientists can easily predict the movement of two massive objects that are in space under the influence of gravity.

However, when three objects interact in space, it leads to complex and often unpredictable paths, making it difficult to determine their future positions. This phenomenon is called the three-body problem.

“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 evolves in a chaotic way, without regularity and completely disconnected from the starting point”, said Alessandro Alberto Trani, astrophysicist at the Niels Bohr Institute at the University of Copenhagen.

A new study by Trani and his team suggests that the three-body problem is not as chaotic as previously believed and actually follows some regular patterns. Researchers refer to these patterns as islands of regularity.

“Our millions of simulations demonstrate that there are gaps in this chaos – ‘islands of regularity’ – that depend directly on how the three objects are positioned relative to each other when they meet, as well as their speed and angle of approach,” Trani said. . added.

Exploring millions of possibilities

To understand the three-body problem in detail, Trani developed Tsunami, a software that runs simulations of three-body interactions in space. Tsunami takes into account all fundamental principles such as gravity, general relativity, etc. when making calculations.

Using the software, the study authors ran millions of simulations exploring the results of all types of three-body encounters. They calculated the movement and positions of interacting objects in different situations. This experiment revealed some interesting findings.

For example, the study authors noted that “the object that is eventually ejected from the system after encounter. In most cases, this is the object with the lowest mass.” However, a completely chaotic phenomenon should not lead to such uniform results.

Tsunami simulations also resulted in a map that describes all possible outcomes of three-body interactions in space. When the study authors examined this map in detail, they discovered several regions highlighting regular patterns.

“Our analysis reveals that regular trajectories occupy a significant fraction of phase space, ranging from 28% to 84% depending on the initial configuration,” the study authors added.

These islands of regularity could help scientists better understand the science behind three-body interactions in space. Furthermore, it could also unravel several mysteries associated with gravitational waves and gravity, according to the researchers.

Islands of regularity require new theories

While the discovery of regular patterns would give scientists the opportunity to unfold the three-body problem from a new angle, the findings could also raise questions about the relevance of existing theories.

Even if some theories remain relevant, the emergence of regular patterns could further complicate the calculations needed to predict the behavior of objects during a three-body interaction.

“When some regions on this map of possible outcomes suddenly become regular, it confuses statistical probability calculations, leading to inaccurate predictions,” Trani said.

Our challenge now is to learn how to merge statistical methods with so-called numerical calculations, which offer high precision when the system behaves regularly”, he added.

The study is published in the journal Astronomy and Astrophysics.