What is a three body problem?

Q: What is a three body problem?

Krishna: I don't know about  science fiction or movies that are made based on the theme, but I will tell you what it is based on science. 

 Systems with two objects exerting gravitational force on one another, whether they're particles or stars and planets, are predictable. Scientists have been able to solve this two-body problem and predict the orbits of objects since the days of Isaac Newton.

But as soon as a third body enters the mix, the whole system gets thrown into chaos. The three-body problem is the statement that if you have three bodies gravitating toward each other under Newton's law of gravitation, there is no general closed-form solution for that situation. Little differences get amplified and can lead to wildly unpredictable behavior in the future.

I think the book based on it deals with aliens that live in a solar system with three suns. Since all three stars are exerting gravitational forces on each other, they end up throwing the solar system into chaos as they fling each other back and forth. For the Trisolarans ( people with three suns) , the name for these aliens, it means that when a sun is jettisoned far away, their planet freezes, and when a sun is thrown extremely close to their planet, it gets torched. Worse, because of the three-body problem, these movements are completely unpredictable.

Scientists have pondered the question of how to determine a stable starting point for three gravitational bodies that would result in predictable orbits for a long period. There is still no generalizable solution that can be taken out of theory and modeled in reality, although recently scientists have started to find some potentially creative solutions, including with models based on the movements of drunk people.

If you want to predict what the solar system's going to do, you can put all the planets and as many asteroids as you know into a computer code and basically say you're going to calculate the force between everything and move everything forward a little bit,"  say experts. This works, but to the extent that you're making some approximations … all of these things will eventually break down and your prediction is going to become inaccurate.

Three-body systems, and more than three-body systems, also show up throughout the universe, so the question is incredibly relevant. 

The relationship between the sun, Earth and our moon is a three-body system. But Blazek says since the sun exerts a stronger gravitational force on Earth and Earth does the same on the moon, it creates a pair of two-body systems with stable, predictable orbits, at least now.

Although our solar system appears stable, there's no guarantee that it will stay that way in the far future because there are still multi-body systems at play. Small changes like an asteroid hitting one of Jupiter's moons and altering its orbit ever so slightly could eventually spiral into larger changes.

That doesn't mean humanity will face a crisis like the one the Trisolarans face in "3 Body Problem." These changes happen extremely slowly, but  it's another reminder of why these concepts are interesting and important to think about in  science.

 Scientists think anything is going to happen on the time scale of our week or even probably our species—we have bigger problems than the instability of orbits in our solar system. If you think about billions of years, during that period we don't know that the orbits will stay as they currently are. There's a good chance there will be some instability that changes how things look in the solar system.

Source: https://news.northeastern.edu/2024/03/26/3-body-problem-netflix/