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Scientists find an effective solution for the three-body problem

phys.technion.ac.il

11–20 of 264 posts

Re: Scientists find an effective solution for the three-body problem

#11
post #4

Earlier quoted context omitted.

Much to my pedantic horror upon reading, they don't need the solution to a three body problem, but a four body problem!

You sure about that? The fourth body, being so small, can't really effect the motion of the other three; however if you have the evolution of the first three then you can determine the motion of the fourth.

Because three-body systems are chaotic, the fourth body can affect the motion of the other three, however small it is.

Re: Scientists find an effective solution for the three-body problem

#13
When they say motions of three bodies are random and unpredictable, I assume they mean not able to be modeled with a closed form equation? Seems like the motions would still be entirely deterministic — could still predict the locations of the bodies computationally, given your computer computes faster than reality (at least for a reality with only 3 bodies), no?

Re: Scientists find an effective solution for the three-body problem

#14

When they say motions of three bodies are random and unpredictable, I assume they mean not able to be modeled with a closed form equation? Seems like the motions would still be entirely deterministic — could still predict the locations of the bodies computationally, given your computer computes faster than reality (at least for a reality with only 3 bodies), no?

They would be deterministic. But they are unpredictable. Minuscule fluctuations (coming from influence of some much smaller bodies, that are not in the model, or approximations in calculations) can lead to dramatic differences in the outcome.

So theoretically speaking, they are deterministic, but practically they are unpredictable.

Re: Scientists find an effective solution for the three-body problem

#15

When they say motions of three bodies are random and unpredictable, I assume they mean not able to be modeled with a closed form equation? Seems like the motions would still be entirely deterministic — could still predict the locations of the bodies computationally, given your computer computes faster than reality (at least for a reality with only 3 bodies), no?

While we can simulate three (or more) bodies' gravitational interaction, the chaoticness means that any error in initial state, no matter how small, will be hugely amplified. This makes long-term predictions untractable

Re: Scientists find an effective solution for the three-body problem

#18

When they say motions of three bodies are random and unpredictable, I assume they mean not able to be modeled with a closed form equation? Seems like the motions would still be entirely deterministic — could still predict the locations of the bodies computationally, given your computer computes faster than reality (at least for a reality with only 3 bodies), no?

The initial conditions are usually known up to a small epsilon in practice. I guess this initial error grows exponentially with time, hence "unpredictability".

Re: Scientists find an effective solution for the three-body problem

#19
post #14

When they say motions of three bodies are random and unpredictable, I assume they mean not able to be modeled with a closed form equation? Seems like the motions would still be entirely deterministic — could still predict the locations of the bodies computationally, given your computer computes faster than reality (at least for a reality with only 3 bodies), no?

They would be deterministic. But they are unpredictable. Minuscule fluctuations (coming from influence of some much smaller bodies, that are not in the model, or approximations in calculations) can lead to dramatic differences in the outcome. So theoretically speaking, they are deterministic, but practically they are unpredictable.

Huh? If this is the case, wouldn’t a 2 body problem also be practically impossible to calculate?

I mean, you can certainly still predict to a certain (probably high) level of accuracy, but ultimately that motion is also influenced by factors outside your model.

Re: Scientists find an effective solution for the three-body problem

#20
post #6

Earlier quoted context omitted.

Yes, they are throwing a party in Australia. Everyone is invited.

Does that mean we finally get to know how they look like?

I always imagined them as some kind of "plants", given how they're described to replicate/combine and how they're dried up and stored and later rehydrated...
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