What is a Three Body Problem?

Question

What is a Three Body Problem?

In: Physics

Answer 1

So we’ve got this equation for gravity. And we’ve got this other equation for momentum. And we have enough other equations that if we have two things that are affecting each other out in space we know exactly where everything will end up at any given time.

For three things it all goes to hell.

So like if all there was was the sun and the earth we could run a simple equation and plot a perfect set of curves. That is we could plot an equation and depending on what we set time to we would get a place back out.

But because of the moon we can’t do that. We have to actually do a simulation instead. That is we have to advance time in little chunks and then look at the The position and direction of the earth the moon and the sun from scratch. And then we can move a little bit farther in time. But then we have to look at all the positions and start the math from scratch. And so on .

So the three body problem is the fact that we can build an equation for two things interacting in space because of gravity and just pick a date. But we can’t do like the entire solar system because there are too many things.

And it seems obvious that there are too many things.

But then we worked our way backwards and found out that three is too many things. So it’s called the three body problem.

This does not mean we can’t figure out where things are, where things were, or where things will be .

It means that we cannot easily figure out where things are, where things were, and where things will be.

So someone with pen and paper can do a good job of figuring out a theoretical solar system of one planet on a piece of paper.

But a solar system with two planets needs a computer in a simulation you can run forward and backward.

Note that this is also why you need a beefy GPU to play a lot of games. Particularly for ray tracing. But you can play those games in fact. For every frame it has to look at where the light is, where the thing is, and where the point of view is and calculate what color that pixel should be. And then each piece is moved individually according to its individual equations and inputs. And then the whole thing has to be done again for the next frame.

And lots of other things in the world have similar requirements for simulation rather than being expressed in a simple function over time.