Netflix's '3 Body Problem' Highlights An Astronomical Mystery That Stumped Isaac Newton

Take a glance at our solar system and beyond, and outer space seems pretty orderly. Our eight planets travel around the Sun with apparent predictability and even the stars themselves appear to march in orbit around the supermassive black hole at the galaxy’s heart. That’s why hundreds of years ago, astronomers and natural philosophers understandably referred to the cosmos as a kind of “Clockwork Universe,” one that was wound at creation and has been ticking along in complete perfection ever since.

A beautiful idea that’s also completely wrong.

In reality, the universe is filled with chaos, and nothing quite encapsulates that idea as perfectly as the Three-Body Problem. While enjoying some (long overdue) attention thanks Netflix’s new adaptation of a 2008 Chinese sci-fi novel of the same name, the Three-Body Problem is much more than some inventive sci-fi plotline — it’s a real-world astronomical conundrum that’s beguiled some of history’s greatest mathematical minds.

The problem itself is deceptively simple: Accurately predict the trajectory of three bodies (planets, suns, black holes, etc.), mutually attracted by gravity, when given their initial position and velocity. But despite the problem’s elegant simplicity, for centuries scientists have tried — and failed — to generate a solution, for the most part.

As is often the case with chaos mathematics, it’s complicated.

An Impossible Problem

To understand why determining the trajectories of three orbital bodies is such an impenetrable mess of physics, it’s best to go back — way back — to the beginning of the problem (and to most things gravitational) as first posed by Sir Isaac Newton in his masterwork, Principia. In this treatise, the English polymath laid out his laws of motion and universal gravitation, and with these new discoveries, he worked out the details of Earth’s orbit around the Sun (a classic hierarchical two-body problem). But then Newton stumbled across a problem he couldn’t quite solve: What happens when you add a third body?

“So the thing about the two-body problem…is that if you start with some initial conditions — like a position for planet A and a position for planet B and they’re orbiting each other — you can write down with simple formulas their orbit for the rest of time,” Nicholas Stone, an astrophysicist and senior lecturer at the Hebrew University of Jerusalem, tells Inverse. Stone’s recent research leverages the mathematical chaos found in three-body problems to create statistical probabilities of solutions. “But for the three-body problem, you can’t do that, and people looked for a very long time.”

For two hundred years, many astronomers tried to tackle this tricky question, including Italian mathematician Joseph Louis Lagrange who discovered his eponymous Lagrange Points while wrestling with the problem in 1772. Things came to a head in 1890 when, participating in an international prize hosted by the King of Sweden and Norway Oscar II, French mathematician and theoretical physicist Henri Poincaré found that the general three-body problem simply had no solution.

While he didn’t use the term at the time, Poincaré had essentially discovered the principle of mathematical chaos, a system that is simply too complex with too many variables to ever be solved by a single analytical equation.

But not all kinds of three-body problems are unsolvable.

For example, if two objects have significantly greater mass than a third body — like a planet orbiting a binary star system — then the mass of that third object can be largely ignored, which makes an analytical solution possible. This is what’s known as a restricted three-body problem, and the Earth-Moon system on its orbit around the Sun is another example (albeit with two low-mass objects and one big one). Then, there’s the three-body problem that can instead have a “hierarchy of separation” rather than size.

“You have two objects that are really close to each other and a third object that’s always really far away,” Stone says, “then you can write down a sort of pen-and-paper solution that takes the initial conditions and tells you what's happening in the future.”

While these can’t make perfect deterministic solutions, they’re good enough and extremely useful when NASA or other space agencies are planning deep space missions.

But when it comes to three-body problems that don’t exhibit any of these hierarchies (that is, all the bodies are relatively the same mass and are mutually attracted by gravity) then all bets are off. The arrival of artificial computers in the mid-20th century made approximations of these problems possible using a method known as “numerical integration,” but to this day, it’s impossible to create a deterministic solution to a general three-body problem.

Life in a Three-Body Problem

In Liu Cixin’s Three-Body Problem, the Trisolarans — called the San-Ti in Netflix’s adaptation — live on a planet caught in the cosmic unpredictability of a three-body problem, meaning Trisolaris (their homeworld) located in Alpha Centauri is continually subjected to the unpredictable nature of its three suns. This has led the alien race to adapt an extremophile survival strategy as the planet transitions between Chaotic Eras and Stable Eras.

“That description of periods of chaos and periods of stability is actually a really good description of the general, non-hierarchical three-body problem,” Stone says. “There are periods of intense chaos [until] one star gets shot out into a wide orbit and it’s sort of well-behaved — and it splits into two, two-body problems.”

But eventually, that far-flung star returns and the Chaotic Era resumes.

While this experience of punctuated equilibria on Trisolaris works scientifically, the very existence of the alien race on this world raises a few questions. Earth, for example, took 4.6 billion years for intelligent life to take form on its surface, but Stone says that the long-term survival of Trisolaris is likely impossible. That’s because most general three-body problems share an interesting characteristic: Eventually one of the three bodies gets ejected from the system, which usually creates a tightly bound, stable binary system in its wake. So three-body problems usually only stay in these chaotic states for a very short time (at least on universal timescales).

“Given enough time, [three-body problems] uniformly explore every possible state…and one state that is available is ejecting a star to infinity,” Stone says. “So eventually, after enough chaotic interactions, the system will stumble into a state where a star gets ejected.”

This doesn’t necessarily mean that it’s impossible for Trisolaris — and by extension their conquest-friendly inhabitants — to exist, but it requires a bit more science fiction to make it happen.

“Astrophysically, no — you couldn’t have that situation, but it is mathematically possible,” Stone says. “There is a way to arrange the three-body problem that’s infinitely fine-tuned, so you can get a stable orbit…but it would never happen in the universe. Theoretically, if the Trisolarans had very advanced technology, maybe they could put their stars into this super, fine-tuned orbit.”

Of course, if Trisolarans could pull off such an amazing feat of stellar engineering, they probably wouldn’t need to take over Earth in the first place. Sci-fi tends to enjoy its stories of interstellar conquests (see Dune, Star Wars, Star Trek, Battlestar Galactica, etc.), but if the past three centuries on Earth are any indication, a deep space epic about an advanced alien race actually solving the three-body problem…well, that would be quite the page-turner.