Scientists spot silent ‘islands of regularity’ in chaotic three-body problem

Scientists can easily predict the motion of two massive objects meeting in space under the influence of gravity.

However, when three objects interact in space, it leads to complex and often unpredictable paths, making it challenging 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 chaotically, without regularity, and completely detached from the starting point,” Alessandro Alberto Trani, an astrophysicist at the University of Copenhagen’s Niels Bohr Institute, said .

A new study from Trani and his team suggests that the three-body problem is not as chaotic as it is believed, and in fact, follows some regular patterns. The researchers refer to these patterns as the isles of regularity.

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

Exploring millions of possibilities

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

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

For instance, the study authors noticed that “the object that is eventually ejected from the system after the encounter. In most cases, this is the object with the lowest mass.” However, a completely chaotic phenomenon shouldn’t lead to such uniform outcomes.

The simulations from Tsunami also resulted in a map depicting 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 the phase space, ranging from 28% to 84% depending on the initial setup,” the study authors added .

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

Isles of regularity demand new theories

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

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

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

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

The study is published in the journal Astronomy & Astrophysics .