I was in physics and had a brief conversation on chaos theory and we started talking about space and he briefly mentioned about the 3 body problem.
Thing is, everything interacts with other things for a reason right? I understand it’s complicated, but if you know all the necessary data, why can’t we do it?
In: Planetary Science
So the problem is in how you solve it, mathematically.
With only two bodies, you can have an “analytical” solution, that is you can simplify the system of equations into a single equation with a smoothly varying time, to the point where if you give some initial configuration, you can then get a solution for any past or future time. Like an animation where you have time on a slider.
This is not the case if you introduce even one more interacting body. At that moment you have too many variables to simplify the equations into a nice “analytical” package.
What is instead done in that situation, is you kind of solve it by brute force with an approximation. It’s called a numerical solution. You just give it some initial best guess values, run the calculation over and over until the result converges on a stable value within a tolerance you decided.
That’s only your first time step. You then move on to the next time step. You decide how big of a step, the smaller, the better the precision, but the more calculations you do overall. And precision matters, because the error compounds with each time step. At some point the solutions will be just plain wrong, and it’s up to you to know when.
As you can hopefully see, you go from “basically can get a highschooler to calculate by hand” to “will make a computer sweat” in one simple move.
The other issue is, the 3 body problem is very sensitive to the initial configuration, so I’m not surprised it came up in the context of chaos. Small initial changes mean big difference down the line. And that’s fundamental , even without the compounding error of the numerical solution.
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