Have Researchers Solved Newton's Three-Body Problem?

Our solar system contains far more than just three bodies, which makes the three-body problem particularly embarrassing. NASA

If you thought that Issac Newton made physics simple, think again. The laws of motion might themselves be simple equations, but the actual motions of objects according to these laws can get complicated fast.

For instance, imagine a universe with just two objects in it: say, two stars. Newton's laws are reasonably sufficient for helping us to understand how these gravitationally bound objects will interact with each other. But add a third object — a third star, perhaps — and our calculations become dicey.

This problem is known as the three-body problem. When you have three or more bodies interacting according to any inverse square force (like gravity), their interactions conflict in a chaotic way that makes their behavior impossible to predict precisely. This is a problem because, well ... there are a lot more than three bodies in the universe. Even if you just narrow the universe down to our own solar system, it's a mess. If you can't even account for three bodies, how are you supposed to predict the motions of a sun, eight planets, dozens of moons, and the countless other objects that make up our solar system?

Because you only need three bodies to make it a problem, even if you just try to analyze the motions of the Earth, sun and moon, you can't do it.

The two-body answer

Physicists get around this problem by instead treating all systems like two-body systems. For instance, we analyze the interactions of the Earth and the moon alone; we don't factor in the rest of the solar system. This works well enough because the Earth's gravitational influence on the moon is way stronger than anything else, but this cheat can never truly get us 100 percent there. There's still a mystery at the heart of how our complicated solar system all factors in.

Needless to say, it's an embarrassing conundrum for physicists to have, especially if our goal is to make perfect predictions.

But now, an international team of researchers, led by astrophysicist Dr. Nicholas Stone of Hebrew University of Jerusalem's Racah Institute of Physics, think they might finally have made progress on a solution, reports Phys.org.

In formulating their solution, the team looked at one guiding principle that seems to apply across certain types of three-body systems. Namely, centuries of research has revealed that unstable three-body systems all eventually expel one of the trio, and inevitably form a stable binary relationship between the two remaining bodies. This principle provided a crucial clue for how this problem might be solved in a more general way.

So, Stone and his colleagues crunched the math and came up with some predictive models that could be compared against computer modeling algorithms of these systems.

"When we compared our predictions to computer-generated models of their actual movements, we found a high degree of accuracy," shared Stone.

He added: "Take three black holes that are orbiting one another. Their orbits will necessarily become unstable and even after one of them gets kicked out, we're still very interested in the relationship between the surviving black holes."

While the team's success represents progress, it's still not a solution. They've only shown that their model lines up against computer simulations in special case scenarios. But it's something to build on, and when it comes something as chaotic as three-body systems, that scaffolding goes a long way in helping us to understand how our theories might be used to more accurately construct models of reality.

It's a critical step toward a fuller understanding of how our universe operates.