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Supposing there is a system of several (four to twelve) celestial bodies which are orbiting a star. In this system of bodies, each body is similar enough in size that no single body has a dominant gravitational field. These objects lie in overlapping and fairly close orbits as well. Naturally, this system of planets would be very unstable and would inevitably collide together or sling each other out of the system. However, my main question is: How fast would this likely happen and could it happen slowly enough to be found in something other than a brand new solar system?

A few possible answers to this question that I can foresee would be for it to take several thousand years for these orbits to decay or perhaps several hundred thousand years, though I am unsure if these are accurate estimates. It would be interesting to perhaps even colonize one of those bodies and have the resulting society go through several iterations of civilization in the time it takes the system to fully collapses.

Now, to make sure that I'm being clear, I am NOT looking for a functional model of a multiple-body system with predictions of all possible futures. I am instead looking for a general estimate of the maximum time an unstable system might be able to exist without orbits collapsing.

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    $\begingroup$ You are asking a lot of questions at once. Please limit yourself to one question per post. $\endgroup$ – sphennings Sep 26 '17 at 14:31
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    $\begingroup$ play a bit with this and figure it out by yourself stefanom.org/spc/# . $\endgroup$ – L.Dutch Sep 26 '17 at 14:42
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    $\begingroup$ So, you're asking us to solve the Three-Body Problem (but harder since more than three), which is famously unsolvable and unpredictable. $\endgroup$ – Azuaron Sep 26 '17 at 15:07
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    $\begingroup$ Unstable planetary orbits are expected to get sorted out in millions to tens of millions of years, depending on a degree of unstability. At the end, some planets may collide, some get kicked out of system, and the rest would occupy orbits which are stable. $\endgroup$ – Alexander Sep 26 '17 at 18:04
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    $\begingroup$ Having run a simulation of our solar system with Jupiter's mass as 10% of the Sun's (i.e. a 100x increase), it took not even 300 years for a whole bunch of the other planets to get ejected. Granted, this was an extreme example, but in my experience, unstable orbit configurations sort themselves out fairly quickly. $\endgroup$ – IronWaffleMan Sep 27 '17 at 20:42
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As @Will said, if it has short term stability, it might be worth colonizing. Even if it is very short term, the planets might be mining prospects (though if you can reach that system, you can probably find better long term mining sites).

As for can such s system exist in the first place. Current theories say: yes.

We currently believe that all star systems start out unstable and that planets are constantly having close encounters which cause collisions, the planet being slowed to the point it drops into the sun or sped up to the point it leaves the system. Eventually, only the objects in stable orbits will be left. At least that's how they believe our system to have been generated.

They have also found gas giants in close orbits of their stars. Since they cannot form that close to the star, they must have drifted in from a farther orbit. They may still be drifting toward the star but we cannot tell that yet.

Just because our system has been mostly cleaned up (by Jupiter) doesn't meant that all (or most) other systems have been cleaned up. The main issue is that unstable systems won't last.

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Most N-body systems are chaotic, which means they are very sensitive to initial conditions. Start the planets moving just a fraction of a centimeter off from the "correct" placement, and they take a very different path. This makes it very difficult to answer a question of "maximum time" because the chaotic systems are, well, chaotic. It's hard to tell whether you're right next to an orbit that will last a hundred million years or one that decays rapidly.

Potentially of interest are the quasi-orbits that appear near unstable Lagrange points.

Although the L1, L2, and L3 points are nominally unstable, there are (unstable) periodic orbits called "halo" orbits around these points in a three-body system. A full n-body dynamical system such as the Solar System does not contain these periodic orbits, but does contain quasi-periodic (i.e. bounded but not precisely repeating) orbits following Lissajous-curve trajectories. These quasi-periodic Lissajous orbits are what most of Lagrangian-point space missions have used until now. Although they are not perfectly stable, a modest effort of station keeping keeps a spacecraft in a desired Lissajous orbit for a long time.

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We are talking about Mars colonies but the larger of the Martian moons, Phobos, is known to be in an unstable orbit.

from https://www.space.com/20346-phobos-moon.html

But Phobos won't zip around Mars forever. The doomed moon is spiraling inward at a rate of 1.8 centimeters (seven-tenths of an inch) per year, or 1.8 meters (about 6 feet) each century. Within 50 million years, the moon will either collide with its parent planet or be torn into rubble and scattered as a ring around Mars.

Having a moon land on you would be disruptive. But the predicted crash is far enough in the future that plans for the short to intermediate term seem feasible.

So with your system. An unstable system like those silly Universe Sandbox youtube videos (example) would be a bad place to colonize, because everything blows up. A system with instability over millions of years would be a better place.

But as regards a story this is a fine scheme: near term instability will infuse energy into the story, especially if the instability can be revisited in unexpected ways over the plot arc. The possibility of looming catastrophe injects energy. I am unenthusiastic about building a bunch of greenhouses and having babies on a planet with no assured short term future. I would definitely be up for frenzied prospecting for alien artifacts on a doomed planet. I'll get my hat and whip. You watch the tunnel mouth while I am down there - other people might have had the same idea.

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  • $\begingroup$ In contrast, our own moon is receding at (IIRC) a similar rate, which will cause its own set of problems with time. $\endgroup$ – a CVn Sep 26 '17 at 14:44
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This is an interesting question, and there are some subtleties in addressing it. There are 2 key timescales for your unstable system: the time until instability sets in, and the duration of the instability.

The time until instability can vary -- there are trends in N-body simulations (basically, the closer your planets' initial orbits the faster they go unstable) -- but no absolute law. Plus, those N-body simulations are quite idealized and it's easy to imagine systems in which planets go unstable only after a significant delay (e.g., top movie on this page). The time before instability is pretty boring. In technical terms, the planets' orbits are exploring available parameter space but most of this amounts to staying on roughly circular, well-behaved orbits.

Instabilities themselves can be pretty dramatic. Giant planets tend to eject each other into interstellar space, leaving behind eccentric orbits (see https://www.youtube.com/watch?v=dCRdEFU_lIo ) whereas terrestrial planets are more likely to end up colliding. There are other outcomes, which can range from disastrous (giant collision between planets, or one hits the star), arduous (being flung into insterstellar space to survive as a free-floating planet; see here), or not that bad (avoiding collisions and only having tidal stretching issues during close encounters and an eccentric orbit).

The time during the instability includes periods when the orbit is fixed punctuated by very dramatic close gravitational encounters between planets, which would tidally stretch them and impart strong gravitational kicks that suddenly change the planets' orbits. This would be a very exciting time to live on such a planet, even though you would be doomed...

For more on planets with oscillating orbits, see here: https://planetplanet.net/2014/10/08/real-life-sci-fi-worlds-3-the-oscillating-earth/. Your situation would be similar but with a very interesting chaotic element thrown in.

I forgot to mention that the duration of instability depends on the situation also. Gas giant instabilities tend to end quick (~100,000 years). For Neptunes it can be much longer (millions). For terrestrial planets it depends -- in some cases it can be very long.

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