Scientists Are Close to Finally Solving the Three-Body Problem

·4 min read
  • In new research, one scientist chips away at the three-body problem.

  • The three-body problem refers to astronomers' inability to track the collision course of three stars hurtling toward one another through space.

  • To better predict the fates of these celestial bodies, the secret is to treat space like a leaky balloon made of Swiss cheese.

Picture Earth and the moon careening together around the solar system. It's clear what will happen as the moon continues to circle our planet, completing its full orbit each month. Now picture—as in the 2011 film Melancholiaa rogue planet barreling toward Earth.

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With this third celestial body in the mix, all bets are off. Astronomers have spent centuries puzzling over this thorny and enduring "three-body problem" to no avail; even if scientists track the movements of each "body" from nanosecond to nanosecond, they still can't reliably predict how the three stars will affect one another.

But while scientists can't say what will happen in a specific case of the three-body problem, they've chipped away at the conundrum by creating statistical forecasts for many hypothetical scenarios, like the one mentioned above.

Now, one physicist is taking this probabilistic approach a step further, offering up a potentially revolutionary solution. His theory, published April 1 in the journal Celestial Mechanics and Dynamical Astronomy, makes use of a fairly abstract concept involving chaos between co-orbiting bodies.

What Exactly Is Chaos?

Photo credit: PM Images - Getty Images
Photo credit: PM Images - Getty Images

To break this down, let's unpack what physicists actually mean when they talk about "chaos." It's far more complicated than our Earthly conceptions of it: a teenager's bedroom with piles of clothing stacked to the ceiling, say, or a restaurant kitchen in the aftermath of dinner service.

Because the yawning emptiness of space is really filled with countless interacting forces at all times—from solar winds to the powerful gravity of distant stars—the result is true mathematical chaos. By definition, that's a truly unpredictable outcome. In popular culture, it's best known as the butterfly effect.

So, how do mathematicians and cosmologists cope with the three-body problem when it's based in chaos? They choose to study approximations of the probability of certain outcomes, rather than plainly trying to solve for each individual circumstance. And to help them study the problem abstractly, cosmologists have moved to "phase space," a customized, 21-dimensional arena for complex questions.

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In this realm, each spot represents one possible configuration of the three stars: That's a 3D position, a 3D velocity and a mass for each of the three bodies. A three-body event (such as one star flying toward a pair) starts at some point in phase space and traces out a path as it evolves from one configuration to another.

Once you add in physical limitations, like the law of conservation of energy, there are only eight remaining dimensions in phase space. From there, chaotic situations crawl out like tree branches through all of their possible outcomes, and that's where statisticians find their numerical values.

A Game of Chaos Kickball

Still, it's tricky to zero in on the chaotic region within that phase space. Scientists know when you have three co-orbiting celestial bodies, they can jump from chaotic motion to regular motion by kicking out one of those bodies, at least briefly, for a short period of time.

Physicist Barak Kol of the Hebrew University of Jerusalem may have changed the game within this eight-dimensional phase space. Rather than focus on a boundary between the chaotic region and the region of regular motion, Kol has proposed a theoretical hole in the chaotic system.

So, rather than viewing phase space as having some regularly distributed times where chaos switches on and off, Kol is saying these problems actually form holes like Swiss cheese. The holes represent places where chaos is most likely to switch on and off.

Over time, as the three bodies interact in the chaotic region, it becomes more and more likely that one of the bodies will find a hole and launch itself out of chaos. Kol wraps this complex theory up with a bow through a function he calls "chaotic absorptivity," or the likelihood a group of two celestial bodies will enter chaos when a third body enters the picture.

The next step is running many simulations of single stars colliding with paired stars. This will feel out the mathematical boundaries of Kol's Swiss cheese holes, one at a time. Hopefully, this distinction in chaos theory is a building block toward a fine-tuned mathematical model that could solve the three-body problem.

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