We just got 12,000 new solutions to the infamous three-body problem

In 1687, Isaac Newton formulated his laws of universal motion and gravitation, shedding light on the motion of stars, moons, and distant planets.

With the stroke of a feather, Newton’s pioneering work also sparked a centuries-long search for mathematical solutions to rein in chaotic triadic systems, such as the Sun, Moon, and Earth, which researchers still puzzle over to this day.

Ivan Hristov of Sofia University in Bulgaria and his colleagues are the latest in a long line of astronomers and mathematicians who, since Newton’s days, have been trying to find solutions to explain how three celestial bodies remain locked in a stable dance, tossing each other under mutual gravitational forces without colliding or launching into space. .

The dilemma is called Three-body problemIt extends to any trio of gravitationally entangled bodies. The solution will allow astronomers to plot the expected movements of these objects given their initial positions and velocities.

It may seem simple, but throwing a third body into a two-body system makes predicting those movements much more difficult. Supercomputers Neural networks have certainly helped.

Now, Hristov and his colleagues have reported 12,409 orbital patterns for three-body systems that operate within the limits of Newton’s laws and have three equal masses. It’s a surprising number of solutions that have not yet been peer-reviewed, but should nonetheless generate some healthy debate.

No comprehensive and comprehensive solution to the three-body problem has been found; Most systems result in chaotic motion that is difficult to predict.

But, like this latest study, a set of solutions have been discovered for special cases, when the system works under certain conditions. However, some are more relevant to practical astronomy than others.

This latest batch of solutions is for systems in which the three objects are initially stationary, before “falling into” each other’s gravitational clutches. So, while the solutions may satisfy curious mathematicians, they probably have few real-world applications.

“Most, if not all, require such precise initial conditions that they are probably never achieved in nature,” said Louisiana State University physicist Johann Frank. Tell Journalist Matthew Sparks new world.

However, Hristov and his colleagues used a supercomputer to build on previous work, It was published in 2019which found more than 300 new families of periodic orbits for the free-falling three-body problem, specifically.

According to Kristof and colleagues“This work left much to be desired” and so they sought to resolve the mathematical point of contention, namely that objects in free-fall systems do not fall into closed, warping orbits but oscillate along open paths. However, Hristov and colleagues’ work is different, because it takes into account three objects of equal mass, rather than random ones.

Free-fall orbits “may be of astronomical interest,” say Hristov and his colleagues He writes. Although it depends on how stable the new solutions are when the influence of distant objects or solar wind is taken into account.

Three-body systems tend to collapse, Frank says, where two objects combine into a binary system and spew out a third mass.

For now, at least Hristov is fair Celebration In the beauty of expected orbits. “Stable or unstable – it is of great theoretical interest.” Tell Sparks. “They have a very beautiful spatial and temporal structure.”

It was the study Published on arXiv Before peer review.