Did watching Netflix’s 3 Body Problem make you think about chaos? The 2024 series, based on Cixin Liu’s novel of the same name, explores the unpredictable weather on a fictional planet orbiting within a three-body system of three stars.
I turned to my friend Deepayan Banik, a U of T PhD student researching extrasolar planets. Together, we realized that while the series masterfully introduces viewers to Trisolaris, the fictitious planet, it presents the three-body problem from a narrow perspective.
The three-body problem refers to the issue of predicting the path of three celestial bodies in a closed system. While Newton’s law of universal gravitation can predict the exact paths of two bodies, it becomes significantly more difficult when a third body is added to the mix.
It turns out that the presence of three stars in a system doesn’t automatically lead to unpredictable, chaotic conditions. Take the planet Proxima Centauri b: this exoplanet, as in from outside the solar system, and the closest one to Earth, is part of a three-star system — yet it maintains a stable orbit, seemingly contradicting the experiences of Trisolarans.
To explore this, we’ve examined why predicting the behaviour in a three-body system is difficult. U of T Computer Science Professor Steve Easterbrook’s book Computing the Climate profoundly shaped our understanding of the three-body problem’s impact on both celestial mechanics and climate science, inspiring the perspectives presented here. Easterbrook is a professor who aims to make computer science more accessible, whether it’s about the climate or the chaos all around us.
What makes the three-body problem so difficult to solve?
In 1889, to celebrate the birthday of King Oscar II of Norway and Sweden, astronomers proposed a prize for anyone who could provide a precise analytical solution to the three-body problem.
The prize was eventually awarded to Henri Poincaré, a mathematician and theoretical physicist, not for solving the problem but for demonstrating that a general analytical solution does not exist. Instead, an infinite number of solutions are possible.
Finding a specific solution to the problem requires effort, but it is not impossible. For example, the discovery of Neptune in 1846 — linked to a three-body solution involving the Sun and Uranus — predates the prize!
It requires a lot of math to solve even one specific three-body system. Thankfully, we have powerful computers today. Additional challenges arise from the imprecise knowledge of the system’s initial conditions.
In physics, chaos refers to systems that are governed by laws that apply at any moment in time and are also extremely sensitive to changes in conditions like temperature, pressure, and speed — tiny differences can lead to significantly divergent outcomes.
This concept parallels the distinction between weather and climate predictions. Short-term weather forecasts can be unreliable due to minor measurement errors that amplify over time, resulting in significant variations. However, when examining long-term patterns, these variations average out, allowing for more reliable climate predictions. This chaotic sensitivity to initial conditions is what makes the three-body problem both fascinating and formidable to solve.
From 1889 till now, a generalized solution to the three-body problem is still unknown.
Chaos in the real world
Chaos is everywhere — in human or insect populations, irregular heartbeats, financial markets, group dynamics, weather prediction, and space missions. Essentially, chaos appears in any system that can be mathematically modelled using nonlinear equations.
If you want to explore one of the most intuitive chaotic systems on a computer, our very own Physical and Environmental Sciences Professor Hanno Rein co-developed ReboundX, a library of code that simulates the physics of the three-body problem. It allows researchers to add new effects to planetary system models, which help scientists study planetary motion.
As for Trisolaris, whether such a planet could actually exist is a common question in astrophysics, especially given that over 5,000 exoplanets have been observed so far. Thanks to NASA’s space satellites — including Kepler, the Transiting Exoplanets Survey Satellite, and now the James Webb Space Telescope, which are in risky orbits around the Earth and the Sun — we can study these exoplanets from thousands of light years away. Understanding a planet like Trisolaris would require knowledge of how it orbits its star and its climate patterns, both of which independently exhibit chaos.
Like the climate-weather analogy, there are numerous other instances where we know the statistics, but not the exact law. We have a rough idea of how long we might live on average, but can we pinpoint exactly when the inevitable will occur? With the recent progress of artificial intelligence (AI), we often talk about AI taking over humanity — but what other paths could it take? Could such a model be chaotic? Perhaps! Or perhaps not!
