No physics expert but isn't this unpredictable (based on what I saw in series) ?

Amd this does seem predictable, I saw this for almost a minute

adastra22 2 hours ago | parent | next [-]

No, and please don’t try to learn anything from that science-free series. The author doesn't even have a Wikipedia-level understanding of what he is writing about.

N-body problems for N>3 do not have exact, closed form solutions. For N=2 the solution is an ellipse. For N=3+ there is no equation you can write down that you can just plug in t and get any future value for the state of the system.

But that is NOT the same as saying it is unpredictable. It is perfectly predictable. You just have to use one of the many numerical solutions for integrating ODEs.

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jgchaos 7 hours ago | parent | prev | next [-]

The link points to one of the stable solutions, and there are actually quite a few of those. The problem is that there’s no general closed form that tells us exactly where the bodies will be in the future, so we rely on numerical methods to approximate the motion. If you hit Reset All a few times or add more bodies, you’ll start to see the chaos

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Pulcinella 7 hours ago | parent | next [-]

There actually is an analytical solution using a power series that actually converges (Karl Sundman's work). Unfortunately, the universe still mocks our attempts. Though the series converges, it does so incredibly slowly. From Wikipedia:

The corresponding series converges extremely slowly. That is, obtaining a value of meaningful precision requires so many terms that this solution is of little practical use. Indeed, in 1930, David Beloriszky calculated that if Sundman's series were to be used for astronomical observations, then the computations would involve at least 10^8000000 terms.

	▲	Nevermark 4 hours ago \| parent [-]
		> the computations would involve at least 10^8000000 terms. Well we could speed up that simulation pretty easily, just arrange the actual masses and velocities somewhere... Then I thought, is there a way to scale the distances, masses and velocities to create a system with the same, but proportionally faster behavior? One guess as to perhaps why not: As distances get small, normal matter bodies will get close enough to actually collide. Perhaps some tiny primordial black holes would be useful.

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taneq 5 hours ago | parent | prev [-]

When you say 'stable' here, do you mean 'periodic' or are these solutions actually stable in the face of small perturbations (as opposed to the sensitive dependence on initial conditions that we'd expect from a chaotic system)?

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lutusp 6 hours ago | parent | prev [-]

> No physics expert but isn't this unpredictable (based on what I saw in series) ?

A three-body orbital problem is an example of a chaotic system, meaning a system extraordinarily sensitive to initial conditions. So no, not unpredictable in the classical sense, because you can always get the same result for the same initial conditions, but it's a system very sensitive to initial settings.

> Amd this does seem predictable, I saw this for almost a minute

The fact that it remains calculable indefinitely isn't evidence that it's predictable in advance -- consider the solar system, which technically is also a chaotic system (as is any orbital system with more than two bodies).

For example, when we spot a new asteroid, we can make calculations about its future path, but those are just estimates of future behavior. Such estimates have a time horizon, after which we can no longer offer reliable assurances about its future path.

You mentioned the TV series. The story is pretty realistic about what a civilization would face if trapped in a three-solar-body system, because the system would have a time horizon past which predictions would become less and less reliable.

I especially like the Three Body Problem series because, unlike most sci-fi, it includes accurate science -- at least in places.

	▲	adastra22 2 hours ago \| parent [-]
		There are stable solutions. See: Earth’s Moon (or any other planetary moon in the solar system).