None of the other orbits will be close enough to noticeably obscure the central star. The only eclipses worth considering would be from the binary planet's twin.
My assumption is that this simulation did for example not contian liquid planetary cores- who if repeatetly beeing subject to gravity fluctuations - would start to resonate- basically resulting in a sort of lava tide to shake the planets apart over time.
I believe you're underestimating the state-of-the-art. See [1], for example, which claims a method for saying that a sufficiently good numerical solution implies an exact periodic solution close by. (I doubt that the author of the original article did anything like this.)
Well, that's the question - is his 416-planet system chaotic? Do perturbtions get amplified or do they get pushed back to the stable configuration?
Of course, when you're talking about a civilization building 416 equal-mass planets equally spaced in 8 counter-rotating orbits, worrying about how stable they are is kind of silly; as long as they're "mostly" stable the maintenance of monitoring and tweaking their orbits for a billion years would presumably both be feasible and cheap compared to the initial construction.
Orbits on a N-body system are chaotic if N > 2. Always.
That said, the longer you simulate those orbits, the more certainty you have that they are stable. But you will never get a mathematical proof, because only symbolic math can ever prove things in a chaotic system, finite precision math can only deal with statistic degrees of certainty.
The point is, if you perturb it by a small enough epsilon will it go back to the initial configuration or fall apart?
Pencil standing on its tip kind of a deal.
I think the problem gets into some chaos theory, the kind you see in weather prediction.
When the forecast says "60% chance of showers tomorrow", what he really means is that they ran a few billion simulations of the environment with very tiny perturbations of the initial conditions and in 60% of those simulations, it rained. In 40%, it didn't.
Tiny little changes in any variable in a chaotic system will, in the long run, lead to huge variations in outcomes.
This system with it's 416 planets has one outcome- perfect orbits constantly. But if you add a single 1 kg asteroid to the system, that would perturb everything ever so slightly. That slight change could result in the entire system chaotically coming apart from stability.
"stable" always comes with conditions, even if implicit. there's no need to add any asteroids - if any of those planets has tectonic activity, that will already introduce perturbations into gravity fields and cause a collapse eventually.
going off on a tangent here, since you mentioned weather prediction, chance of rain % or probability of precipitation (pop) are computed not only for probability of rain in a given area but also for area of location that will receive the rain if any at all, ie 60% here expresses combination of degree of confidence that rain will occur in an area and geographic coverage of that rain.
more details on the wiki entry here - https://en.wikipedia.org/wiki/Probability_of_precipitation
Although obviously ridiculous in many ways, the ability to design large stable systems is relevant for when thinking about the question "How many O'Neil cylinders can we build in the habitable zone?".
If we mine the asteroids, Mars, and Mercury for materials we can build habitable surface areas that are in aggregate many times greater than Earth in size. Each carbon fiber Bishop Ring could have an internal surface area the size of India.
This simulation reminds us that space is really, really big, and really, really empty. If you can fit 416 planets, just think how many space stations you can fit.
With simple electromagnetic tethers! Drop a cable toward the sun, run a current through it and gain impulse from the ambient magnetic field. Or does this only work near a planet?
It would work (maybe) but the generated current would be about 50,000 times weaker than it would be using the Earth's magnetic field...at least at the distance of Earth from the Sun.
Yeah. The main problem with keeping a space station at a stable orbit above Earth is friction with the atmosphere.
There might be small adjustments that need to be made where Earth's atmosphere is almost completely negligible but there are fewer forces degrading the orbit and there's no immediate threat of crashing into a planet if the adjustments aren't made in time.
Im not sure biological organisms will ever stick around long enough to do such things. I think the benefits of inorganic organisms are too great. They'll be much more suited for life in space.
> the ability to design large stable systems is relevant for when thinking about the question "How many O'Neil cylinders can we build in the habitable zone?".
pretty sure the answer is "as many as we can figure out how to get the mass for".
absent dismantling the gas giants themselves, you're not going to do anything very interesting do the dynamics of the solar system, regardless of what you take apart, or how you reconstitute it.
and the man-made structures can include mechanisms for closed-loop control of their position. which they'd need anyways, as they'd accumulate positional error from vehicles coming and going.
I think the point of building habitats is that spherical planets are a very inefficient use of matter from a surface-area-to-mass ratio point of view. We could create a lot more surface area (i.e. usable land) with less material if it were arranged in a more useful configuration.
> absent dismantling the gas giants themselves, you're not going to do anything very interesting do the dynamics of the solar system, regardless of what you take apart, or how you reconstitute it.
I would consider reconfiguring available materials to achieve more usable surface area to be interesting (not to mention potentially useful if we manage to accomplish it someday).
However, what's "interesting" is highly subjective and dependent on context. Perhaps you meant something different by "you're not going to do anything very interesting" than the way some of us are interpreting it?
"you're not going to do anything very interesting..." to the dynamics of the solar system.
the orbital dynamics of the solar system. (the thing you'd be worried about if you thought you needed to learn how to make 416-body systems stable.)
certainly packing the habitable zone full of new places to live is interesting, on all sorts of social and technological levels. it just doesn't raise any questions about the stability/dynamics of the n-body system that is the solar system (until you maybe start taking apart the gas giants).
And I agree; it turns out that planets are really heavy and have an incredible amount of inertia; moving some asteroids around isn't going to cause the Earth to slip on a banana peel and fall into the sun.
The original article about placing 416 Earth-sized planets in a stable orbit does involve a quantity of mass greater than Jupiter (at 317.8 Earth masses), but building habitats out of what we have available in and inside the asteroid belt is a much more modest scope.
I love how turning the entirety of the asteroid belt, and maybe Mercury, into livable space stations "is a much more modest scope". :-D
Not that I disagree! We also have the Hilda, Trojan, and Greek asteroids (in Jupiter's Lagrange points) to work with. The Jovian and Saturnian moons too. It'll be a long, long time before we need to worry about dismantling the gas giants themselves.
On our path towards maximizing the livable land area in the Solar System, I wonder what we will run out of first. It looks like water, iron, carbon, etc. are all pretty abundant. We'll run out of* some rarer element (like Phosphorous or something) before we ever approach maximum constructed land area.
*And by "run out of", I mean even with perfect recycling, the spot market demand for the material maintains a price level where it's uneconomical to develop further, barring discovery of new supplies or more efficient usage.
This assumes that we don't create such elements as a by-product of fusion or other processes that we develop in parallel with the technology advances required to bring significant industry outside earth's gravity well.
Space is really, really big. Also, 3 dimensions are really "big." If you take feasible theoretical material strengths into account, space stays a lot bigger than practical habitats that have gravity.
A planet cannonballing through the plane is generally very disruptive, giving anything they pass near an impulse normal to their orbit and eventually making the whole thing wobble like a plate on a circus clowns finger
Reading the article, I imagined what the people (?) on those planets must think when they discover they're not alone.
Let's say we discover we are not alone. We know those aliens must not be from our galaxy, so do we push for development of faster-than-light travel? If so, why? Intelectual curiousity, defense, offense, trade, habitation?
As for the hypothetical galaxy with two planets of life: Are they developing the same? If not, do they, and if so why, expand to the other? If they are, are they afraid of each other? Do they have a "cold war"? The possibilities are endless.
Like Firefly, there are many posibilities for great sci-fi.
I got to the bit about 2 earths circling each other and instantly thought of the Fire/water planets that exist on the opposite side of the sun to earth which is why we didn't know they exist, from the TV show Lexx (season 4, worst season ever)
Except for binarity of planets, I don't thing sky renderings would be particularly cool.
If we have habitable zone of 50 millions kilometers wide - just a rough number - then planet ring to planet ring distance would be 6 million kilometers, 20 times Earth-Moon distance. With 52 planets along the single orbit and orbital radius 150 millions kilometers (~billion kilometers circumference) the distance between planets on the same ring would be 20 millions kilometers. So I don't think planets would appear too big on the sky.
What I'm not sure about is how we'd deal with sea tides caused by binary planets. Even Moon causes significant tides; an Earth-sized planet would have to be much farther away than the Moon so it woudn't cause ever bigger tides...
That's ambitious! But I could definitely see being able to produce a few preset configurations. That would be easy enough (relatively speaking) to put together in Unity—maybe even with a bit of interactivity (eg. day/night cycle). Even without VR the game is a lot of fun:
On steam there is Universe Sandbox^2 that has a VR version included. I don't think you can simulate the surface of planets, though. (I have it, but I haven't tried the VR version yet due to some persistent glitches with Oculus on many Steam apps).
It's real question how dark these planets would ever get. With 416 planets reflecting light, the closest ones would be pretty bright all the time. Maybe even visible discs from the surface, although I'm not sure. Brighter than Venus is on Earth though, and lots of them.
You'd have to take that into account when doing your global warming models too.
Venius is a long way from impacting earths climate. The scale is 2.512^(x-y).
Sun −26.74, Moon −12.74 (average full moon), Venus -4.89 to −3.82. So sun is around 400,000 times as bright as the moon, and the moon is ~1500 times as bright as the Venus which is bright largely because it's so close to the sun.
Mars is −2.91 at it's brightest. So 1/2 as much light as Venus because it's further from the sun even if it's closer. These might be closer than Mars, but not closer than the moon.
Venus all by itself is minimal. These planets would be closer and there'd be a lot more of them. If they're supposed to be Earth-like they'd also have clouds, making them reflect more like than airless worlds like the Moon does. I bet there would be a measurable effect.
The moon is about one light second away from Earth. The sun is about 600 (10 light minutes)).
52 evenly spaced planets in an Earth-like orbit would be about (2pi600)/52 light seconds apart, which comes out to about 72 and a half light seconds. So, the closest neighbor planets would appear a lot smaller than the moon, but a lot bigger than, say, Venus.
I'm not sure how widely the adjacent rings would be spaced, so you might sometimes have neighbors that are closer than 72.5 light seconds as they zip by in the opposite direction.
The article also talks about arranging the planets as binary pairs, in which each planet might be very close to its neighbor, possibly appearing bigger and brighter than the moon from Earth.
its worth noting, that they were not orbiting a star (I don't know if that would be a positive or negative issue, for stability .. they moved away from the star to cool off)
If I recall correctly, they were attempting to move away from the galactic core, so that they could escape some ultimate cataclysm faster than the destruction could catch up to them. Their major technological problem was rejection of waste heat.
Well, these are beasts of a different feather. These 416 aren't orbiting around each-other like in a Klemperer Rosette, they're just equally spaced out alone the same orbit around the sun. So it's a lot easier to get higher numbers.
I mean, our own solar system has more planets than "Pierson's Puppeteers".
Makes you wonder whether the remarkable density of terrestrial planets in the TRAPPIST-1 system is the result of engineering. Maybe somebody is planning far ahead and counting on the tiny star's long lifetime (which is in the trillions of years) to keep their civilization going?
On the other hand, the intense star flares and tidal locking seem very inconvenient.
Is it always such a big lifetime for small stars? White dwarfs have a long lifetime, but they have interesting stories behind them; what about other types of small stars?
If I'm not mistaken, the smaller stars don't have as high a gravitational gradient and are fully convective so the helium ash and hydrogen fuel mix closer to uniformly, allowing them to burn through all of it. Stars on the scale of sol slowly build up helium until it chokes out, compresses and starts burning helium at higher temperatures, causing the rest of it to expand.
Becoming a Type II civilization on the Kardashev scale might involve construction of a Dyson swarm. This is a thought experiment in which each of the swarm elements is Earth sized, presumably providing near-ideal additional habitat for a larger human population.
Is a complete Dyson sphere even possible? Given the mineral resources available in a solar system.
Say you are an advanced alien civilization. And you reach the point where you haven't nuked yourself to death, so now you can expand into space. The first thing you do is to mine all the asteroids, that hadn't coalesced into a planet. So you spend all this energy to capture them, to smelt them, and then you build out your Dyson sphere.
You can achieve some coverage of the star, but is it even possible to cover the entire star with solar collecting panels, to capture all the energy output of the star?
At best, I think you might be able to get a ring around the star. But even this, is dubious.
and possibly large scale transmutation. Disassembling the gas giants might be enough for some designs.
My understanding is that it isn't physically possible to construct rigid spheres or rings in that orbit, so it would be an orbital swarm of some kind, with the elements able to actively correct for the inevitable perturbations.
To be fair, where did the 400+ planets come from? One must surely be able to import some material as well.
Most of the mass in a generic system should be in the planets, if I remember correctly from an old article here in Sol if we scrapped all the planets we could create a 3m thick Dyson shell. But a ring should be a lot easier to construct.
The 416-planet solar system is the equivalent of the large explosion that ends most Mythbusters episodes.
The interesting part of the article is the explanation of the different ways that the number of planets in the habitable zone of a star can be greater than one, and how it's possible that most stars have more than one habitable planet each. This has direct consequences for the Drake Equation and the likelihood of contemporary alien life in the galaxy.
It's hard to imagine natural formation of such a complex structure in real universe. It needs a lot of precision (interplanetary engineering?) or luck to put 416 bodies in the exact positions and velocity for the model to be stable.
Another unnatural thing about this model is that adjacent orbits rotate in opposite directions: according to existing theories of formation of planetary systems, it seems impossible for the gas disk to go into different directions in layers.
Anyway, this model is definitely cool (416 bodies in stable orbits!) and might be a useful blueprint for interplanetary engineering of the future.
> This system is completely stable—I double-checked with computer simulations. But nature would have a tough time forming this system. If it exists, it could only have been built by a super-advanced civilization. That’s why I call it the Ultimate Engineered Solar System.
The fact that it would never occur naturally makes it even more interesting. Imagine interplanetary civilizations rearranging star systems to send the unambiguous signal "1. intelligent life lives here, and 2. they are powerful enough to arrange planets, so a peaceful posture is probably advisable.".
Probably if you're capable of capturing and moving 400+ planets into a new sun's orbit in a decent enough amount of time, then no one is going to be bothering you.
This points to a fundamental problem in the understanding of planetary systems. Planets do not come to being out of nothing; enourmous amounts of matter have to come together to make up a planet. Great example of experts ignoring "details" outside their expertise.
This is really nice read! I remember I visited a local Planetarium few weeks ago. They had a game where you will need to pick like 5 planets and design the solar system. It had the asteroid belt. Big planets and small ones. The game will end if the EARTH collides with any other planet and if the other planet collides you lose points. The simulation was just amazing.
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[ 2.9 ms ] story [ 195 ms ] threadI would think that's a hilarious joke if the author didn't seem so serious.
https://en.wikipedia.org/wiki/N-body_problem
And yes, that the N-body problem is chaotic.
[1] http://ww2.ii.uj.edu.pl/~kapela/papers/nosym.pdf
Of course, when you're talking about a civilization building 416 equal-mass planets equally spaced in 8 counter-rotating orbits, worrying about how stable they are is kind of silly; as long as they're "mostly" stable the maintenance of monitoring and tweaking their orbits for a billion years would presumably both be feasible and cheap compared to the initial construction.
That said, the longer you simulate those orbits, the more certainty you have that they are stable. But you will never get a mathematical proof, because only symbolic math can ever prove things in a chaotic system, finite precision math can only deal with statistic degrees of certainty.
https://en.wikipedia.org/wiki/N-body_problem#n-body_choreogr...
https://news.ycombinator.com/item?id=14767295
obviously if another star smashes into planetary system - it won't survive, at least not in original form.
When the forecast says "60% chance of showers tomorrow", what he really means is that they ran a few billion simulations of the environment with very tiny perturbations of the initial conditions and in 60% of those simulations, it rained. In 40%, it didn't.
Tiny little changes in any variable in a chaotic system will, in the long run, lead to huge variations in outcomes.
This system with it's 416 planets has one outcome- perfect orbits constantly. But if you add a single 1 kg asteroid to the system, that would perturb everything ever so slightly. That slight change could result in the entire system chaotically coming apart from stability.
He said he came across that particular problem in a system which handled rounding numbers in a very suspect manner.
https://en.wikipedia.org/wiki/Stability_of_the_Solar_System
https://www.ias.edu/ideas/2011/tremaine-solar-system
5-6 billion years is probably just fine.
Previous discussion: https://news.ycombinator.com/item?id=14764125
It even links to the same site and the blog was posted by the same guy. I wonder why he's recycling content.
[0]: https://nautil.us/blog/a-letter-from-the-publisher-of-nautil...
If we mine the asteroids, Mars, and Mercury for materials we can build habitable surface areas that are in aggregate many times greater than Earth in size. Each carbon fiber Bishop Ring could have an internal surface area the size of India.
This simulation reminds us that space is really, really big, and really, really empty. If you can fit 416 planets, just think how many space stations you can fit.
There might be small adjustments that need to be made where Earth's atmosphere is almost completely negligible but there are fewer forces degrading the orbit and there's no immediate threat of crashing into a planet if the adjustments aren't made in time.
pretty sure the answer is "as many as we can figure out how to get the mass for".
absent dismantling the gas giants themselves, you're not going to do anything very interesting do the dynamics of the solar system, regardless of what you take apart, or how you reconstitute it.
and the man-made structures can include mechanisms for closed-loop control of their position. which they'd need anyways, as they'd accumulate positional error from vehicles coming and going.
> absent dismantling the gas giants themselves, you're not going to do anything very interesting do the dynamics of the solar system, regardless of what you take apart, or how you reconstitute it.
I would consider reconfiguring available materials to achieve more usable surface area to be interesting (not to mention potentially useful if we manage to accomplish it someday).
However, what's "interesting" is highly subjective and dependent on context. Perhaps you meant something different by "you're not going to do anything very interesting" than the way some of us are interpreting it?
the orbital dynamics of the solar system. (the thing you'd be worried about if you thought you needed to learn how to make 416-body systems stable.)
certainly packing the habitable zone full of new places to live is interesting, on all sorts of social and technological levels. it just doesn't raise any questions about the stability/dynamics of the n-body system that is the solar system (until you maybe start taking apart the gas giants).
hopefully that clears that up?
And I agree; it turns out that planets are really heavy and have an incredible amount of inertia; moving some asteroids around isn't going to cause the Earth to slip on a banana peel and fall into the sun.
The original article about placing 416 Earth-sized planets in a stable orbit does involve a quantity of mass greater than Jupiter (at 317.8 Earth masses), but building habitats out of what we have available in and inside the asteroid belt is a much more modest scope.
Not that I disagree! We also have the Hilda, Trojan, and Greek asteroids (in Jupiter's Lagrange points) to work with. The Jovian and Saturnian moons too. It'll be a long, long time before we need to worry about dismantling the gas giants themselves.
On our path towards maximizing the livable land area in the Solar System, I wonder what we will run out of first. It looks like water, iron, carbon, etc. are all pretty abundant. We'll run out of* some rarer element (like Phosphorous or something) before we ever approach maximum constructed land area.
*And by "run out of", I mean even with perfect recycling, the spot market demand for the material maintains a price level where it's uneconomical to develop further, barring discovery of new supplies or more efficient usage.
https://www.youtube.com/watch?v=HlmKejRSVd8
Let's say we discover we are not alone. We know those aliens must not be from our galaxy, so do we push for development of faster-than-light travel? If so, why? Intelectual curiousity, defense, offense, trade, habitation?
As for the hypothetical galaxy with two planets of life: Are they developing the same? If not, do they, and if so why, expand to the other? If they are, are they afraid of each other? Do they have a "cold war"? The possibilities are endless.
Like Firefly, there are many posibilities for great sci-fi.
Then it would just be a huge asteroid belt which would eventually form a normalized amount of planets.
Someone should make a VR app that lets you simulate the surface of any kind of planet and any kind of sky based on a solar system configuration.
Like the simulations of what will be seen from Earth when the Milky Way and Andromeda merge (https://en.wikipedia.org/wiki/Andromeda%E2%80%93Milky_Way_co...) but with hundreds of planets !
Even a render of the "binary earth" would be cool.
If we have habitable zone of 50 millions kilometers wide - just a rough number - then planet ring to planet ring distance would be 6 million kilometers, 20 times Earth-Moon distance. With 52 planets along the single orbit and orbital radius 150 millions kilometers (~billion kilometers circumference) the distance between planets on the same ring would be 20 millions kilometers. So I don't think planets would appear too big on the sky.
What I'm not sure about is how we'd deal with sea tides caused by binary planets. Even Moon causes significant tides; an Earth-sized planet would have to be much farther away than the Moon so it woudn't cause ever bigger tides...
http://store.steampowered.com/app/230290/Universe_Sandbox/
On steam there is Universe Sandbox^2 that has a VR version included. I don't think you can simulate the surface of planets, though. (I have it, but I haven't tried the VR version yet due to some persistent glitches with Oculus on many Steam apps).
You'd have to take that into account when doing your global warming models too.
Sun −26.74, Moon −12.74 (average full moon), Venus -4.89 to −3.82. So sun is around 400,000 times as bright as the moon, and the moon is ~1500 times as bright as the Venus which is bright largely because it's so close to the sun.
Mars is −2.91 at it's brightest. So 1/2 as much light as Venus because it's further from the sun even if it's closer. These might be closer than Mars, but not closer than the moon.
52 evenly spaced planets in an Earth-like orbit would be about (2pi600)/52 light seconds apart, which comes out to about 72 and a half light seconds. So, the closest neighbor planets would appear a lot smaller than the moon, but a lot bigger than, say, Venus.
I'm not sure how widely the adjacent rings would be spaced, so you might sometimes have neighbors that are closer than 72.5 light seconds as they zip by in the opposite direction.
The article also talks about arranging the planets as binary pairs, in which each planet might be very close to its neighbor, possibly appearing bigger and brighter than the moon from Earth.
Also, I'm wondering about tidal forces ...
1: https://en.wikipedia.org/wiki/Pierson's_Puppeteers#Homeworld...
I mean, our own solar system has more planets than "Pierson's Puppeteers".
On the other hand, the intense star flares and tidal locking seem very inconvenient.
Is it always such a big lifetime for small stars? White dwarfs have a long lifetime, but they have interesting stories behind them; what about other types of small stars?
Say you are an advanced alien civilization. And you reach the point where you haven't nuked yourself to death, so now you can expand into space. The first thing you do is to mine all the asteroids, that hadn't coalesced into a planet. So you spend all this energy to capture them, to smelt them, and then you build out your Dyson sphere.
You can achieve some coverage of the star, but is it even possible to cover the entire star with solar collecting panels, to capture all the energy output of the star?
At best, I think you might be able to get a ring around the star. But even this, is dubious.
https://en.wikipedia.org/wiki/Star_lifting
and possibly large scale transmutation. Disassembling the gas giants might be enough for some designs.
My understanding is that it isn't physically possible to construct rigid spheres or rings in that orbit, so it would be an orbital swarm of some kind, with the elements able to actively correct for the inevitable perturbations.
Most of the mass in a generic system should be in the planets, if I remember correctly from an old article here in Sol if we scrapped all the planets we could create a 3m thick Dyson shell. But a ring should be a lot easier to construct.
The interesting part of the article is the explanation of the different ways that the number of planets in the habitable zone of a star can be greater than one, and how it's possible that most stars have more than one habitable planet each. This has direct consequences for the Drake Equation and the likelihood of contemporary alien life in the galaxy.
Another unnatural thing about this model is that adjacent orbits rotate in opposite directions: according to existing theories of formation of planetary systems, it seems impossible for the gas disk to go into different directions in layers.
Anyway, this model is definitely cool (416 bodies in stable orbits!) and might be a useful blueprint for interplanetary engineering of the future.
> This system is completely stable—I double-checked with computer simulations. But nature would have a tough time forming this system. If it exists, it could only have been built by a super-advanced civilization. That’s why I call it the Ultimate Engineered Solar System.
But it'll send a pretty impressive message.