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
Amd this does seem predictable, I saw this for almost a minute
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.
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.
Those are not stable solutions. Remember that Earth's moon only came into existence because of a collision with a protoplanet in the past, and if a large enough body passed close by in the future, we might lose our moon -- all because of the complexity of orbital systems with more than two members.
> (or any other planetary moon in the solar system)
There are any number of examples of planets gaining and/or losing moons because of multi-body orbital complexity.
Let me clarify something. A "three body problem" system is any orbital system with more than two bodies. The term "three-body problem" certainly doesn't mean systems with only three bodies.
> A tidally locked system with periodic resonance is permanently stable in the absence of external forces.
No. In an orbital system with more than two bodies, external forces are the name of the game. For such a system, the expression "permanently stable" cannot apply. Such a system is not open to a closed-form solution and all such systems must be modeled numerically.
Closed-form solutions are available for orbits with two bodies, and can sometimes approximate the behavior of systems with more than two, but the reliability of such a model degrades rapidly as time increases, until the predictions become meaningless.
From https://en.wikipedia.org/wiki/Orbit_of_the_Moon : "The properties of the orbit described in this section are approximations. The Moon's orbit around Earth has many variations (perturbations) due to the gravitational attraction of the Sun and planets, the study of which [ ... ] has a long history."
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.
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.
https://www.stochasticlifestyle.com/how-chaotic-is-chaos-how...
Computing the trajectory of a 3 body problem is a comparatively simple task.
The two grains of truth are that the solutions for most starting conditions are not analytic, roughly meaning that they can not be expressed in terms of functions. The other being that the numerical solution to an ODE diverges exponentially.