Our solar system has millions of objects in orbit. How come it isnt chaotic?
I dont remember some small letter clause that it isnt a real 3 body system unless they are all the same size

>>16729132 (OP)
solar system is chaotic n-body system.

>>16729132 (OP)
The divisor is wrong.

>>16729132 (OP)
Its in the name. The sun has enough mass to provide order on a certain scale. Its still technically chaotic but I don't think that's what you're asking.

>>16729162
>. Its still technically chaotic but I don't think that's what you're asking.
It is what im asking and i dont know why you would think it isnt. Order at a certain scale is weasel language.
Whe certain scale? I dont remember the 3 body problem requiing some "scale".
Im aware that two starts orbiting each other and then some grain of sand also orbiting them is a 3 body problem but you can ignore the effects of the grain of sand. However in the solar system jupite has 0.1% of the mass of the sun, this is small but a measurable effect, and i dont see how it doesnt cause small effects in all the orbits. Would you think its ok for the earth orbit to drift "only" 0.1% every century?

>>16729132 (OP)
3 body problem is fake to a certain extent. Their inability to calculate it without their simulations evolving into a chaotic system is a problem with the math used, not with the natural world.

>>16729172
Its seen experimentally like in these double pendulums

>>16729169
The solar system is chaotic. So your question is flawed.

>>16729172
Indeed. People forget that probability works with likelihood and confidence intervals given a certain time frame. You are computing "close enough". The "chaos" becomes a problem when you try to predict the distant future- the less precise your initial observations, the more chaotic the outcomes will be, or the more sensitive the system becomes to changes to the initial state. Of course this is all at the scale of classical physics. You aren't predicting the path of every electron within a planet. You're simplifying the system to fit inside a computer program.

It used to be more chaotic, but after 4 billion years it fell into a more stable configuration. Also having most of the mass be in the central star keeps things simple so its inherently far less chaotic than if we had 2 suns.

>>16729132 (OP)
It is chaotic though.
But of course the sun is, relatively speaking, so fat that it dominates the orbital center of most of the objects.

>>16729132 (OP)
Nonlinear doesn't necessarily mean chaotic, and even chaos itself is a matter of degrees.

The solar system is a large N-body problem, which is nonlinear, but because of the extremely different scales of bodies in the system (sun vs planets, planets vs moons, moons vs asteroids, etc.) most of this nonlinear behavior is merely perturbatory rather than acutely chaotic.

>>16729585
>he solar system is a large N-body problem, which is nonlinear, but because of the extremely different scales of bodies in the system (sun vs planets, planets vs moons, moons vs asteroids, etc.) most of this nonlinear behavior is merely perturbatory rather than acutely chaotic.
At what scale does the alleged chaotic behavior begin?

>>16729684
Lightyears and eons.

>>16729684
As a general rule of thumb, you see chaotic behavior in the regimes where the dominant interactions are 'collisions' between similarly-massed objects.

For example, you don't see chaotic interactions between most of the planets in our solar system, because their interactions between one another are perturbatory compared to the interactions between all of those planets and the sun, but you do see chaotic interactions between some groups of moons in some planets where the interactions between the moons with each other becomes significant compared to the interactions between the moons and the planet they're orbiting - Hyperion, Titan, and Saturn, as I recall, behave as a nonperturbative three-body system (at least for the moons), and I think the moons of Pluto are believed to be a chaotic system as well. With stars, you don't really see much chaotic behavior between stars in lower density regions the way you do closer to the centers of galaxies.

It's just like turbulence in fluids - all fluids are subject to the same kinds of nonlinear interactions that lead to turbulence, but that doesn't mean that all fluid behaviors result in turbulence. The study of what conditions a nonlinear system needs to meet to become chaotic, or how to measure 'chaoticity' is a whole subfield in mathematics and physics.

>>16729132 (OP)
It is chaotic. You're just extrapolating from the most simplified models and shortest time spans.

>>16729132 (OP)
What gave you the impression that it isn't chaotic?

>>16729132 (OP)
Why didn't you do any review before asking your question?

>>16729132 (OP)
>How come it isnt chaotic?
it very much is. it's just the lyapunov exponent for a lot of dynamics in the solar system are long enough for us to plan ahead and make midcourse corrections based on updated observations

>>16729132 (OP)
Answer me.

>>16729187
>>16729769
You can quantify the tendency of a system towards chaotic behavior in terms of Lyapunov exponents or times, the shorter the time, the more quickly trajectories in phase space for the system are to diverge.

I recall reading a paper that did some simulation work and estimated the Lyapunov times for various bodies in the solar system. For something like Hyperion it works out to be about a month, whereas the average for solar system is like 5M years. There's exceptions, of course, particularly bodies that are likely to pass in regions of overlapping gravitational influence like when a near-Earth body passes between us and the Moon and its trajectory gets radically altered, but those are expectations, not the rule; we can pretty reliably predict where shit is going to be for a few centuries.

>>16729132 (OP)
The gravitational pull among planets onto each other is negligible next to the gravitational pull of the sun onto those objects. That's why all of them can approximately be treated like two-body systems.

As for constellations like the earth and the moon, which are of a comparable mass, those can be treated as one object in relation to the sun, because they're very close to each other.

>>16732874
>The gravitational pull among planets onto each other is negligible next to the gravitational pull of the sun onto those objects.
Doesnt matter, the effect is not that small and it acumulates over time. Consider the influence of a planet like Jupiter on Saturn and viceversa, they might change each other's orbit a bit and with enough orbits the effect will pile up. If the effect was 1 in a thousand, you could expect some serious changes after 1 thousand orbits.
Jupiter has 1/1000th of the mass of the sun, thats not insignificant.

>>16729132 (OP)
no jews in space

>>16732814
/thread.

>>16732915
>Jupiter has 1/1000th of the mass of the sun, thats not insignificant
It's a thousandth of the mass and, on average, about five times farther from us.

That's 1/25,000th of the force. That literally is insignificant over the space of a few millennia.