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Scientists find an effective solution for the three-body problem

phys.technion.ac.il

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

#31

Post by forgotpwd16 »

guerrilla wrote: post #10
reedf1 wrote: 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.

Not sure what the discussion is about, but the restricted approximation only works for "insignificant" masses (e.g. a moon if talking about two big planets and a star). And even then for "short" time periods (a few million years). In larger scales even that mass will (I assume you've heard of the butterfly effect) play role.

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

#32

Post by sasaf5 »

Aeolun wrote: post #19
ordu wrote: post #14

Earlier quoted context omitted.

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.

Better stated, the 2-body problem can be solved with a finite number of standard operations, i.e. a closed-form expression. This solution does not exist for the 3-body problem.

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

#33

Post by reedf1 »

thinkski wrote: post #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?

Chaos is the extreme dependence on initial conditions. The three body problem is significantly more chaotic than a two body problem. Welcome to chaos theory!

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

#35

Post by thomasz »

forgotpwd16 wrote: post #31
guerrilla wrote: post #10

Earlier quoted context omitted.

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.

Not sure what the discussion is about, but the restricted approximation only works for "insignificant" masses (e.g. a moon if talking about two big planets and a star). And even then for "short" time periods (a few million years). In larger scales even that mass will (I assume you've heard of the butterfly effect) play role.

https://en.wikipedia.org/wiki/The_Three-Body_Problem_(novel)

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

#36

Post by MaanuAir »

numpad0 wrote: post #6
bpodgursky wrote: post #5

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?

In The Redemption of Time, Baoshu offers his view.

It’s “only” a fan fiction, albeit approved by Liu Cixin.

It nonetheless gives a nice — and as expected — unexpected description of them.

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

#38

Post by guerrilla »

thomasz wrote: post #35
forgotpwd16 wrote: post #31

Earlier quoted context omitted.

Not sure what the discussion is about, but the restricted approximation only works for "insignificant" masses (e.g. a moon if talking about two big planets and a star). And even then for "short" time periods (a few million years). In larger scales even that mass will (I assume you've heard of the butterfly effect) play role.

https://en.wikipedia.org/wiki/The_Three-Body_Problem_(novel)

tl;dr three suns, one planet

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

#39

Post by extropy »

Grustaf wrote: post #29
alephu5 wrote: post #27

Earlier quoted context omitted.

For a two-body problem the discrepancies between your model and reality increase gradually with time, but it's still possible to predict eclipses decades in advance with a precise albeit imperfect measurement of initial conditions. With a three-body problem any slight shift causes a wildly different trajectory, bearing no resemblance to the original so your measurements of the initial condition have to be perfect.

No that's not it. The two body problem has a closed, analytical solution, the three body one doesn't, so you need to simulate it. It's a fundamentally different approach.

Both of you are correct.

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

#40

Post by bhay »

numpad0 wrote: post #6
bpodgursky wrote: post #5

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?

For me, I pictured them as the water aliens from Futurama's "My Three Suns".
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