The Ultimate Engineered Solar System

Welcome to a new installment in the Building the Ultimate Solar System series. Be prepared: this is a far-reaching post with a big conclusion.

Sometimes it feels good to find out you were wrong. I had one of those moments a few weeks ago.

I was thinking about how to pack the orbits of planets as tightly as possible (who doesn’t spend their free time thinking about that?). I was thinking about more than one planet sitting on the same orbit.  This is a co-orbital setup. I always thought that co-orbital planets were just a neat trick. The Trojan points 60 degrees in front and behind a planet can be stable — and that is awesome. But there’s nowhere else to go.

Then I had my mind blown.

Let’s start at the beginning.  Imagine two planets orbiting a star.  The planets’ orbits can’t be too close together because it’s not stable. The planets feel the star’s gravity but also each other’s gravity. If the two planets’ orbits are too close together, the repeated gravitational kicks cause their orbits to slowly stretch out. Eventually their orbits cross.  Then the two planets can be in the same place at the same time. Then boom, the planets might collide or one might get ejected into interstellar space.  In any case, the planets’ orbital setup changes completely.

There is a simple limit for how far apart two planets’ orbits must be to be stable. The key ingredient is the Hill radius, a measure of the strength of a planet’s gravity. Concentric planetary orbits need to be spaced by a minimum number of Hill radii for their orbits to be stable. Let’s call that closest stable spacing N Hill radii. There are lots of studies to determine N for different situations. N must be larger than 5-10 for systems with many planets for the system to remain stable.

For a star like the Sun, 6 concentric orbits can fit within the habitable zone, that Goldilocks region where a planet can have liquid water on its surface.  It looks like this:

The orbits of six Earths within the habitable zone (shaded).  If the planets’ orbits were packed more tightly they would be unstable.

This might make you think that a star can have at most 6 possibly life-bearing planets. You would be wrong. If you’ve read other installments of this series you know that we can do better than thatMuch much better.

As a first step, we can imagine more than one planet on each orbit.  At a minimum, each orbit can hold two planets.  If the planets are separated by about 60 degrees along the orbit, the setup is stable.

This is the part where I had my mind blown. I re-read a paper from 2010 by Smith and Lissauer (the same researchers behind the idea for the retrograde setup from the Ultimate Retrograde Solar System).

It turns out there is a stability limit for the number of planets that can be spread along the same orbit. The planets must be evenly spaced and there must be at least 7 on one orbit (not a typo: at least 7!). The limit is simple: the planets sharing the same orbit must be separated by at least 12 Hill radii in distance along the orbit.  This is different from before, where we were looking at the distance between orbits.

Smith and Lissauer ran simulations with not 2 or 3 but 42 Earth-mass planets sharing the same orbit!  That is the maximum number of Earths that can fit along Earth’s present-day orbit. And guess what? It’s perfectly stable for billions of years. Over the last couple weeks I ran my own N-body simulations and they match perfectly.  By the hammer of Thor, it really works!

This crazy-looking orbital setup — with 42 Earth spaced evenly along Earth’s orbit — is stable for billions of years!  (For technical details see here or here).

Just this simple ring of planets eclipses our original Ultimate Solar Systems 1 and 2. They had 24 and 36 habitable worlds, and this one has 42.  And we’re not done yet.

Many rings of 42 planets can can be packed into the habitable zone.  The separation between rings depends on the individual planets’ masses, not the total mass on a given orbit.  That means that rings of planets can be packed pretty tightly.

Six rings of 42 Earths can fit within the Sun’s habitable zone and remain stable.

Six orbits — with 42 Earths each — packed into the Sun’s habitable zone (shaded), for a total of 252 possibly livable planets! This setup is stable for at least 10 million years and I have the N-body simulations to prove it!

That is 252 possibly life-bearing worlds orbiting a single star!  That’s almost as many as in the 16-star Ultimate Solar System.

There are two factors that determine the number of planets that can be packed in the habitable zone.  The first is the planet mass.  Lower-mass planets have smaller Hill radii. Compared with more massive planets, this means that more low-mass planets can share the same orbit.  It also means that each ring of planets can be closer to its neighbors.

Here is what it looks like for packed systems containing planets of 1/10th Earth’s mass (roughly Mars’ mass), Earth’s mass, and 10 times Earth’s mass (close to the mass of Neptune and Uranus).

Maximally-packed systems of  planets in orbit around a star like the Sun. Each panel is for a different planet mass: 1/10th, 1 and 10 times Earth’s mass (from left to right). The systems contain a total of 1157, 252, and 57 planets (left to right).

The Sun’s habitable zone can fit 57 mega-Earths (10 Earth-mass planets), 252 Earths, or a whopping 1157 Marses!  Holy banana pancakes Batman!

[Short note to skeptics. This may all just seem like too much. This is so far beyond what I thought was possible just a month ago. And as I’ve said, I was very skeptical. Luckily, this is physics that is easily testable. I ran a series of computer (N-body) simulations of a range of configurations (I run a lot of these for my day job after all).  I added some small random fluctuations into the system, and tested a bunch of different twists. And it works. I get the same answer as Smith and Lissauer. And extrapolating from there seems to work just fine.]

There is no need to stick with equal-mass planets. Within a given ring the planets must be evenly-spaced, so I believe the most stable setup is with equal-mass planets. However, there is no reason that all rings must have the same mass planets.  One could imagine a ring of Marses followed by a ring of Earths or super-Earths or whatever your heart desires (if your heart desires that sort of a thing…)

The second factor that influences how many planets can be packed into the habitable zone is the star, in particular its mass. For cooler the habitable zone is closer to the star than for the Sun.  And for hotter stars it is farther away. However, that turns out not to matter much in terms of how many planets can fit (see here). The star’s mass does affect the size of a planet’s Hill radius. Compared with an Earth orbiting the Sun, an Earth’s Hill sphere is twice as big around a star 1/8th as massive as the Sun. That means only half as many planets could fit on a given ring, and each ring would have to be twice as far apart. So only 1/4 as many planets would fit into the habitable zone.  This argues in favor of relatively massive stars. Let’s stick with a star like the Sun this time.

OK, now that we have a handle on things let’s get building.

Here are the ingredients for our mega-system. Our star: the Sun (or its twin).  Our planets: half of Earth’s mass (a lot of upside and little downside — see here). Our setup: a series of maximally-packed rings of planets in the habitable zone. Moons? No (I suspect they would mess up the system’s stability).

The smaller mass gives us 52 planets per orbital ring.

Let’s use the retrograde upgrade.  We can pack planets’ orbits more tightly if the neighboring planets orbit the star in the opposite direction.  For our purposes,  odd-numbered rings of planets (1, 3, 5, 7) will orbit in a prograde direction and even-numbered rings (2, 4, 6, 8) in a retrograde direction.  In case you are wondering, prograde is counter-clockwise when viewed from above the North pole.

Putting the pieces together, here is what we’ve got:

A stable system with 416 planets in the habitable zone. Planets on red orbits orbit the star in the opposite sense as planets on blue orbits. (See the Ultimate Retrograde Solar System for details)

The early Solar System may have had three habitable planets, before Venus and Mars went bad. The TRAPPIST-1 system has three Earth-sized planets in the habitable zone (four if you’re feeling generous). In our first two ultimate Solar Systems we fit 24 and 36 habitable worlds into the habitable zone. That was already pretty awesome.

Now we’ve got 416 planets in the habitable zone of a single star!  This is getting ridiculous!  That’s as many as the 16-star Ultimate Solar System!

I can only think of one way our 416-planet system could form. It must have been purposely engineered by a super-intelligent advanced civilization.  I’m calling it the Ultimate Engineered Solar System.


You might ask, if a civilization were advanced enough to create such a complicated planetary system, couldn’t they just give any planet the right conditions for life?  Well, I guess that makes sense (even though you are kind of raining on my parade here).

Let’s go with that and take it a step further. Assuming that this super-advanced civilization only inhabits one star, what is the most grandiose planetary system it could create?

I can think of one constraint that is hard to overcome. It’s the same one that sunk the Ultimate 16-star Solar System. No star exists in isolation. The region past about 1000 Astronomical Units (remember, 1 AU = the Earth-Sun distance) is affected by other parts of the Galaxy. Passing stars, spiral arms, and clouds of gas all give little gravitational kicks that add up and can destabilize things.  So, even advanced civilizations will want to keep their fancy system within 1000 AU.

This means many more rings of planets, so the spacing between rings will need to be a little wider to keep everything stable.  If we use Earth-sized planets (instead of half Earth-mass ones), here is what we’ve got.

A mega-system with 57 rings of orbiting planets from the inner edge of the habitable zone out to 1000 Astronomical Units.  Each ring contains 42 Earths equally-spaced along the orbit.  Planets on red orbits revolve around the star in the opposite direction from planets on blue orbits.

There are 57 rings of 42 planets each. That’s 2394 planets!  Ridiculous!  Most are colder than the habitable zone but hey, this advanced civilization might just throw a Dyson sphere up to warm them up!

I actually built this ridiculous system in a pretty conservative way.  I didn’t include any planets on orbits hotter than the inner edge of the habitable zone, and used larger planets that in our chosen system.

What if this civilization was able to maintain habitable conditions on slightly-smaller planets than Earth?  Let’s say, planets one-tenth as massive as Earth (about the size of Mars).  Well, in that case things get even crazier.

An even more spectacular/ridiculous system of 10,769 roughly Mars-mass planets (89 planets per ring and 121 rings).

With the smaller planet mass, 89 Marses can fit on each ring (instead of 42 for Earths). And 121 rings of Marses fit out to 1000 AU (instead of 57 for Earths). That makes a whopping total of 10769 planets in one system!

Here’s one final, completely bonkers system.  Imagine that 1) these aliens could maintain livable conditions on Moon-sized planets (~1% as massive as Earth), and 2) they could handle orbits as close to the star as 0.1 AU. [Maybe these advanced creatures could transfer energy from the too-hot planets out to the too-cold ones.]  In that case the numbers skyrocket to 341 rings with 193 planets each. It adds up to more than 65,000 planets orbiting a single star! It would be a titanic job to maintain habitable conditions on all of those planets, but hey, the engineers that built this thing must have been pretty smart already (right, Slartibartfast?).

This type of planetary system — with rings of co-orbital planets — would be an amazing setting for science fiction. The night sky would be dominated by arcs of bright stars, the different rings of co-orbital planets lining up on the sky because of their nearly coplanar orbits.  It would be a constant reminder of the existence and proximity of other worlds. Imagine the competition between species to develop interplanetary travel. Widespread colonization by the fastest-developing species. Only to ultimately discover that their whole Universe was created by a civilization so advanced they seemed like gods. And imagine a disillusioned terrorist who tries to take the whole system down. Any perturbation to one ring of planets would cause a cascade that would trickle down and destroy the whole system (like what happened to the 16-star Ultimate Solar System).  The good guys stop the terrorists at the last minute, only to meet the Creators, who had it under control the whole time….

So there you have it: the Ultimate Engineered Solar System.  Kind of nuts, isn’t it?


NEW: check out the visualizations of what it would be like to stand on a planet in the Ultimate Engineered Solar System by Lucas Bourneuf using the Space Engine software.

94 thoughts on “The Ultimate Engineered Solar System

  1. Wow!! You have truly out done yourself this time. 🙂 I wonder how small of a body passing through the orbits could destabilize the system. Watching transits would be a fun pastime, particularly on the outer planets. Thanks!

    1. Thanks! You are right — this setup is stable but a small perturbation could lead to chain reaction that would bring the whole thing down (kind of like here: I imagine a civilization advanced enough to build a system like this would have an outer ring of defenses, to zap any approaching space junk!

      And definitely — transits of inner planets would be an everyday thing!

      1. Planetary dominoes! Hmm, can you add rings of red dwarfs with planets to expand the system? 🙂

      2. you would have to strip several systems of everything to just make the 16 planet system. meaning there would be no little left overs to perturb the system. but, i think such a system would need constant
        maintenance, to keep running.

      3. A common misconception is that a 400-planet system would contain way too much mass to be plausible. But it’s not actually that much. That’s 200 Earth masses in solids (half an Earth-mass per planet). The disk that formed the Solar System may have had that much — it had at least about half. And there are plenty of disks around young stars with that much mass. It’s just a matter of getting all the mass in exactly the right place!

      4. Can you now imagine piloting the star of your 10K planet system? A localized warp in space can pull the star, acting like a rutter. The star may never go faster than the planets can handle, however you can steer the star into the desired direction.

      5. You could add a 3D aspect to this as well. A ring of planets outside the main ring. Like how Eris’s orbit is. Then double it up with binary planets for an insane star system.

    1. Years ago there was a DC Super-hero, Star Man, who came from an Empire based around a super-packed planetary system. All the planets had been moved there via ‘planetary engines’ and Star Man’s origin tale ends when they all depart en masse as the Empire had been enforced via a planet-busting weapon buried in the star. Now seems weirdly prescient…

  2. just a thought from a layman, I see you used Mars sized planets to pack the system. But what is the minimum sized planet that could maintain the inner core necessary to maintain the magnetic fields to protect water? (assuming water based life)

    1. The magnetic field thing is a furphy. Atmospheric erosion is negligible in present day solar wind conditions. It was significant during the Sun’s first aeon. Engineered systems presumably can pick and choose the star.

    1. I’m not sure how important tides would be in these systems. On Earth, tides from the Sun are ~2.5 times weaker than from the Moon. Take a raing of 42 Earths. Each of the other Earths is much farther away than the Moon (something like 50 times farther), so tides from other planets will be weak. I think in the end that tides will simply not matter all that much (unless I am missing something in this quick analysis).

      1. Very. Tidal friction from so many large bodies at once would cause them to get tidally locked rather quickly.

      2. Well, the importance of tides scales with the separation to a high power (5.5 to 6.5 depending on the tidal model) but much more weakly on the mass (about to the power of 2). Like I mentioned, the closest neighbors to each planet are ~50 times more distant than the Moon. Even accounting for the planets’ higher masses, I would estimate the importance of tides as about one millionth the strength of tides from our Moon. So, basically zero.

      3. Individually they would exert less than the moon, sure, but they’re working in unison. 3 to 4 immediate neighbors, and another 3 to 4 catty-corner with less, but still appreciable. You could use a moon to help counter those forces, but it would need to be moving fairly fast, and thus need to be closer to keep a stable orbit. But then waves and stresses on our core are an issue. Though, given the planets themselves are engineered that too can be overcome. Without moons the planets’ spin would decay to the point that days would be too long to be viable after a relatively short amount of time (on geological time scales, though. As a short term solution it would be fine, though)

  3. I just love it ! Also I was wondering if instead of a planet you could use a pair (or more) of them circling their mass centre. And then you could repeat it on those 🙂

    1. No one has studied the stability of moons or binary planets in this type of system. I don’t think that the system would be stable with binary planets in a setup like this, at least without making the inter-planetary spacing a bit wider. However, if the ring was made of ~Neptune-mass planets with a few relatively small (~Mars-mass) moons it might be stable. It’s actually quite hard to check that because the computer simulations are very slow

  4. Interesting idea. However, a Niven ring habitat you would need much less mass to construct. It would also have a much larger surface area for habitation.

      1. How about a ring in Lagrange 3 or 4 that’s 2.2 million miles in diameter (for 1g at 24 hours rotation) an impossible feat even for carbon nanotubes​ but presumably not for the planet engineers.

  5. my fav. part … You might ask, if a civilization were advanced enough to create such a complicated planetary system, couldn’t they just give any planet the right conditions for life? Well, I guess that makes sense (even though you are kind of raining on my parade here).

  6. According to the IAU definition of planets, these wouldn’t be planets!. They would be classed as dwarf planets since they wouldn’t have “cleared the neighbourhood” around their orbits.

    To be fair, if we did find a similar system out there it would probably be artificial so maybe they shouldn’t be called planets after all.

    1. Well, in the end it’s all a matter of arbitrary definition and semantics as Sean pointed out — I’d be comfortable calling them “worlds”

  7. What about ring worlds, would they have the largest surface area for earth like conditions? If multiple rings worlds they would need to be tilted so as not to block the light from the star. What would be the hill radius and could they be made to revolve in a stair step fashion. How long could these ring worlds be stable?

    1. How about mini-ringworlds in orbit around the star. Cf: the ‘orbitals’ in the Culture novels of Iain M. Banks. Put 7 or more of them in each orbit & you get a lot more livable area for the mass used.

      1. Before another person invokes a Niven Ringworld, aside from the stability issue (which is *fatal* by itself) and the non-existence of skrith (Ringworld structural material) there’s the slight problem of where all the orbital energy is going to come from. To create centrifugal gravity of 1 gee at 1 AU around a Solar Mass star means an orbital velocity of SQRT(g*AU) = 1200 km/s. Used quite effectively as a plot-point in the novels, but a significant impediment to would be builders. A one-Earth mass Ringworld ribbon would have the orbital energy equivalence of ~(40)^2 = 1600 Earths. Thus a Super-system full of Earths in the Habitable Zone beats the singular Ringworld for energy alone – let alone stability etc.

        Of course such an energy budget isn’t a total show-stopper if the Mega-Engineers are dismantling the star via star-lifting etc. Undoing the Sun requires the equivalent of ~50 megayears of Solar output, since most of the mass is close to the core. With a Z~0.02 there’s about 6,000 Earth-masses of heavier elements in the Sun, thus Star-lifting the lot would allow a civilization to make Mega-Systems or RIngworlds for each of the lower-mass stars formed out of the Sun. But rings of planets are seemingly more stable than Ringworlds.

      2. Jim. I think Adam Crowl has misunderstood your question.

        Adam, an Iain Banks “Culture” Orbital is *NOT* a Niven Ringworld. It’s basically a scaled-up O’Neill colony, so large that a 24-hour rotation rate results in one gee of simulated gravity. However, like a ringworld, it’s shaped like a big ring; depending on the design, it might or might not need a roof. It’s in orbit around the Sun, and its plane of rotation is inclined to the plane of its orbit, so there’s direct sunlight on every point of the interior for twelve out of twenty-four hours.


      3. Hi Herp
        I know Orbitals quite well. They do still suffer from the lack of materials strong enough to make them, and they’re still spinning at greater than orbital velocity to make 1 gee gravity. But they don’t suffer quite the same instability issues and are (only!) about 100 times smaller than a Ringworld 😉

      4. Say, as long as we’re going to use astounding super-science to give the star a pearl necklace of planets, why not go one step further toward making a ringworld? Why not link the co-orbital planets with physical bridges, essentially space elevators between them?

        Assuming 42 Earths in a 1 AU orbit, the bridges would be “only” 14 million miles in length, so they probably could be constructed of the same sort of handwavium as “conventional” space elevators. (That strength estimate might be off by an order of magnitude or two, but hey! Close enough! We’re talking astronomy here.)

        Unlike a ringworld, you wouldn’t need to rotate the entire multi-planet assembly at greater than orbital velocity to simulate gravity — assuming the bridges are made of really strong handwavium, the string between the pearls wouldn’t be massive enough to greatly affect each planet’s local gravity.

        The planets would need to be eyeball worlds in synchronous rotation, which would reduce their real estate value, but commuting between planets would be greatly facilitated. One of life’s tradeoffs, I guess.

        Sure, it’s an additional complication when you build the planetary system, but it shouldn’t add more than a few percent to the construction costs. ;^)

      5. This is an awesome idea! Like you say, the only downside is that it requires synchronous rotation. Unless the elevator linked with spacecraft at adjacent planets’ L1 or L2 points instead of connecting to the surface itself…

      6. Hmmm .. If you connect their L2 points instead of the planets themselves, then might be able to construct the bridge that links the L2 points from conventinal materials instead of handwavium! Alas, a space elevator from the planet to the L2 point 1.5 milion kilometers out would have to be made of handwavium.

        A conventional space elevator to L2 would still need to be anchored to the cold backside of an eyeball planet. If the bottom of the space elevator didn’t touch the planet’s surface, but instead hung from a counterweight on the far side of L2 down to three or four hundred miles above the ground, then the planet could have a 24-hour rotation period. You’d use rockets (or some other technology based on free-flying vehicles) to commute between the ground and the bottom of the skyhook.

        “So why not just use rockets to fly directly from one planet to another?” you might ask. Well, even if you had to use rockets to commute between the planet and the bottom of the skyhook to L2, they wouldn’t need to be BIG rockets. A bridge would still be useful to provide life support and transportation infrastructure over the 14 million mile separation, just as Aldrin Cyclers would be useful for commuting between planets in our system.

        Once it’s built, the circumstellar bridge would be a cool thing to have. But building it could be … an non-trivial enterprise.

      7. I was commenting on the article on Centauri Dreams “Skyscraper in the Clouds” back in March of this year.
        The question was if a ring world or actually a ring moon could be built around the Earth at geosynchronous orbit? Here is the original concept:

        Michael Fidler March 30, 2017 at 19:48

        Has no one noticed that this would work as a tower crane with the pivot at the geosynchronous orbit point. Just put on the ion rockets at the asteroid and in the opposite direction below the pivot point and it will swing the lower end up to GSO! Now you have a nice crane to build a GSO ring-world. You could also bring asteroids into a factory on the counterweight asteroid and process the load for the main structure of the ring-world with the more advance materials and equipment being brought up from earth when the skyscraper is lowered. The whole process would be automated with AI and the ring-world would be laid out from the crane like you would lay a road out or a bridge, sections at a time, all being joined together. The question I’m wondering about, when you finish this ring-world would the centrifuge effect of this spinning mass moving at 6900 MPH create artificial gravity and at what G force. If it is a high G force it could tear the ring-world apart! Or would there be no centrifuge gravity at all???

      8. @Michael Fidler: Has no one noticed that this would work as a tower crane with the pivot at the geosynchronous orbit point. Just put on the ion rockets at the asteroid and in the opposite direction below the pivot point and it will swing the lower end up to GSO! Now you have a nice crane to build a GSO ring-world.

        There ain’t no free lunch. Either you use very powerful ion engines — powerful enough to supply the total energy to move the mass up to geosynchronous orbit from the surface — or you destabilize the space elevator. And you really don’t want to do that.

        The question I’m wondering about, when you finish this ring-world would the centrifuge effect of this spinning mass moving at 6900 MPH create artificial gravity and at what G force. If it is a high G force it could tear the ring-world apart! Or would there be no centrifuge gravity at all???

        The whole thing is in orbit. I don’t think there would be any centrifugal pseudo-gravity at all on a ring orbiting at geosynchronous distance. (I could be wrong, and if I am I’m sure I’ll be corrected.)

      9. How about a ring around each planet in geosynchronous position around the planet and space elevators going to the ring from the planet? Then you’d board a maglev and transfer to the interplanetary tether. This would allow the planet to rotate independently of the tether. 🙂

      10. That sounds like a winning idea! The trick for the space elevators/rings is to maintain the center of mass in the right place. I could imagine there being issues of that kind when connecting it with the co-orbital ring. (I think?)

      11. Herp McDerp but would not the asteroid balance it since is above the pivot point so all you would need is the give it enough inertia. It would be like a lopsided seesaw with a three hundred pound man on the asteroid end and a seven pound baby on the long earth-side end?

  8. What about the amount of sunlight reaching the planets? Wouldn’t there be constant solar eclipses beginning from ring 2 and thus reducing the habitable zone?

    1. Let me see… First, the angular size of the Sun is about half a degree. So the orbital inclination between rings of planets would have to be larger than that to systematically avoid having planets block some starlight. Not likely.

      Next, how much light would be blocked by each transit? Well, an Earth-sized planet blocks a little less than 1 part in 10,000 of the surface area of the Sun, so that is how much fainter the Sun would get each time. And how often would this happen? Well, take the case of a ring of 42 Earths along Earth’s orbit. They take 365 days to travel 360 degrees around the Sun, so about 1 degree per day. The planets are separated by 8.6 degrees along the orbit. So if you were sitting on a distant planet you would see a transit every 8.6 days. Each transit would last about an hour.

      Of course, there would be periodic transits from each ring interior to yours, so you would have to add all those up. But you could never drop the energy received from the star by more than a few hundredths of a percent at a time.

  9. Even if such planets would be stable IRL in the goldilocks zone, they will soon become UNinhabitable because of the quasi-permanent, planet-wide total solar eclipse which would occur on all but the most inner rings.

    Then again, if a civilization can perform such a feat, they could surely make ANY planet inhabitable, with or without atmosphere, in or out of the goldilocks zone. Even rogue planets lost to space would be easy peasy.

    Also, assuming the universe is actually infinite, this kind a planetary setup has already been put in place around stars… an infinity of times.
    I’m beginning to get unimpressed.

    1. See my other comment about this. Each time a planet in an inner ring “eclipses” the star, it’s really a transit, not an eclipse, because the planet only blocks a small part of the star, about 1 part in 10,000. So the star gets fainter by the same amount (1 in 10,000, or 0.01%). Each transit lasts about an hour and happens once every 8.6 days (for a ring on Earth’s orbit). There would be transits from each ring interior to your orbit, but even adding up a bunch of them, the star’s brightness would never drop by more than a few parts in ten thousand.

      1. Not that it matters to the habitability, but could the rings be slightly inclined to one another so as to minimize transits? Cheers!

      2. I was quick to comment 😀
        You are right, the sheer scale of the whole setup would render eclipses insignificant.

  10. In the simulations I tried, inclinations between rings larger than a degree or so were unstable. However, smaller inclinations were okay. So, my feeling is that the system need not be absolutely coplanar but it must be close, at least with this level of compactness.

  11. Have you tried simulations of rings with different mass planets? Does that cut the stability?
    BTW I played with super planet crash & put in multiple earth size planets on the same orbit. 6 didn’t work, 8 did, but I had no way to run the simulation for more that a few (simulated) centuries. It’s interesting to see that more can be put in.

    1. No, I haven’t tried that. In principle it should work fine, as long as the planets on a given ring are equally-spaced along the orbit.

      And that is awesome that you tested this with super planet crash! Studies say that you need at least 7 planets per orbit for this to work, so it seems like your experiment agrees!

      1. I’ve been playing with Super Planet Crash for a few weeks. You can put 9 Jupiters in the same orbit at the outer edge of the habitable zone, an Earth-mass planet in a circular orbit at the inner edge of the HZ, *AND* a 30,000 Earth-mass *dwarf star* in a very tight orbit around the Sun … and it’ll be stable over 500 years! (This can be real bitch to set up, though.)

        I’ve noticed that as long as the orbital radii are close to identical, the planets seem to have a shepherding effect on one another — if you start out with mildly irregular spacing between the Jupiters, their spacing smooths out over time.

  12. After reading this article and the comments I was curious as to how much living space this would afford our advanced system engineers. So I did a little hunting on the internet and found an estimate of about 25 million sq. mi. habitable land on Earth, which accounts for mountains, deserts, and oceans. So using that value I decided to take a look at the systems you created.

    First I calculated the system with 252 Earth sized planets in 6 rings of 42 and found this system to have 6.2 billion sq. mi. which is impressive. Second I looked at the system with 1157 planets 1/10 Earth size in 13 rings of 89 and found this to be only 2.9 billion sq. mi., still impressive just confusing. Next I looked at the system with 57 planets ten times the size of the Earth in 3 rings of 19 and found this system to have a little over 14 billion sq. mi. of habitable space. As this confused me further I did a little digging and noticed that even though the planet size changed by a factor of ten the number of planets only increased by a factor of 4.5.

    Now I do realize that the factor 10 planets are either too big or too small, so let’s look at the planets half the size of the Earth. This is 416 planets in 8 rings of 52 which gives us a system habitable area of 5.1 billion sq. mi. and that is smaller than the Earth sized planets above. Yet again even though the size of the planet goes down by 2 the number of planets goes up by only 1.6. So, what if we double the size of the planets? Based on my calculations above the number of planets increased and decreased by comparable amounts. Therefore, I estimate that if we were to double the size of the planets the number of planets would drop by about 1.4 for 180 planets, keep in mind I’m purely estimating, so 5 rings of 36 for 8.9 billion sq. mi.

    As I’m certain that all of these planets would be completely engineered to maximize the habitable space, I am completely certain my estimated habitable space is not even close to accurate. By the same token I am certain that each planet would be specialized to fill specific niches within the needs of their society. This being said, other than my estimate above, what would you estimate the largest land area of a stable system possible based on your simulations?

  13. I like the most picture describing a stable system with maximum of 416 planets in the habitable zone (some call it the Goldilocks zone), orbiting a star like Sun. It’s hard to expect some advanced printing technique to achieve pictured imagination, but one never knows. From my present point of view something like that would seem too invasive. On the other hand, there are so many beautiful UN countries and thinking of the constant growth of the population, giving a planet to each nation does not seem like a bad idea. Such project would remind me of a “One Laptop per Child” initiative, witch has, from my perspective, turned out to be a “One Smartphone per Kid”.
    Deep looking at the picture I think of engagements in planet’s core.

  14. Nicely done! Though you don’t need a dyson to warm them, and it would offer a lot more living room per unit of mass anyway. But we can use the same trick we do for an Alderson disc, and float thin mirrors over the sun’s poles as statites and angle them to give those more light.

  15. Can you improve this by reducing the hill radii?

    Make the sun analogue a binary pair with another sun-analogue/nuetron star/quark star/black hole and you can have the nice properties of the sun analogue + a lot more mass.

    Also does all that planetary mass have any significant contribution to the system’s centre of mass?

    Also if you could stably put an ultimate engineered solar system of moons around each planet you could increase the number by orders of magnitude.

    1. Good question! You are right that, all else equal, it would be great for this experiment to shrink the planets’ Hill radii down as much as possible, and one way to do that is to crank up the mass of the “Sun”. The trick is, I’m not sure whether this would compromise the stability of the system. Close binary stars introduce additional frequencies into the system in a non-trivial way, which can shake things up. No one has looked at this question so the answer is: I’m not sure whether this would remain stable (but I like the concept).

      For your second question: each ring of planets has a center of mass at the center of the star so there is no shift

      Third question — also very clever! And I also don’t know the answer. Let’s see — the moons would have to have to have small enough Hill radii (with respect to the planet) to fit ~100 (>7 moons x spacing of 12 Hill radii) on a given orbit. For the Earth/Moon system, the Moon’s Hill radius is too small: only 39 Hill radii fit along the orbit. To crank the Hill radius down by a factor of 2.5-3 would require shrinking the Moon’s mass by that factor cubed, or its size by that same factor (assuming constant density). So this is doable with a ring of Ceres-sized moons around an Earth. There are still tidal issues that could destabilize the system, and the moons are too small to avoid cooling off very fast, but in principle this is possible!

  16. Ok, Here is my brainstorm 🙂

    If a black hole of about 350 to 400 solar masses is used as the primary, it should have a much larger hill sphere galactically speaking. One could then setup about a dozen orbits separated by 15+ AUs full of orange dwarf stars of about 64% the mass of Sol. I chose this number as these stars would burn juuusst hot enough to have a habitable zone far enough away that the planets would not be tidally locked. With say 11 red dwarfs per orbit and a minimum spacing that allows stability for planets to share several orbits . That should allow around 132 red dwarfs or so. Each with dozens of planets orbiting them. I dunno of any simlators that could handle so many objects! Maybe it would be better to simulate ‘just’ the black hole and one ring of stars, with a few rings of planets each.

    As long as the whole arrangement is less than a several hundred AU across, galactic gravitational disturbances should not have enough influence to destabilize it for the ~30 billion of years the low mass stars would take to burn out.

    Wouldn’t this make Tabby’s star look tame if we spotted one!

  17. I actually have a question relating to the formation of rocky planets. We’ve discovered thousands of super-Earths with thick H/He envelops which indicates a quite fast formation process before gas disk dispersed, but what made the formation of Earth/Venus so slow and late that majority of mass was accreted after gas dissipation and didn’t become a super-Earth?

    1. That is a good question. It seems to be a matter of mass. We think that the building blocks of the terresrtial planets were about the mass of Mars or so (give or take a factor of 2). That is just a little below the mass needed for migration to kick in and push those planets much closer to the Sun.

      The next question is: why? We think that Jupiter is the reason that the terrestrials never got too big. If Jupiter formed relatively early, it would have blocked the inward drift of both small particles and large ones, effectively protecting our rocky planets from invaders. See here for one idea on that:

  18. hey, since you have explored all the possibilities of solar systems that can have live, how much to increase it to try to create the solar system more massive possible, with the planets more near and more distant of a star and things like that

  19. Super-cool! Awesome!

    I think we want the sun to be a little smaller than ours. Smaller stars burn a lot longer. But they don’t burn as bright, so we’ll have to pack the planets in close to the star.

    Have you thought about adding orbits off the plane of the solar system? I’m thinking about building a sphere of earth-like planets orbiting the star.

    If you know of a neat tool or script that someone has written to model a system like this, I’d love to hear about it.

    I think it would be better to use artificial shell worlds rather than actual rocky planets. With a shell world you can choose size and gravity, and you don’t waste so much material under the surface. Half earth size is probably doable. Probably easier to build than full earth size too.

    Pump the middle full of hydrogen gas which we slowly convert to helium and provide power through fusion. Electrify the metal shell to create a magnetosphere. Set the density of the filler and the spin of the planet to get full earth gravity. Add maybe a mile of rock, soil, and water on top of the shell. And bang! A tremendous amount of living space with near-Earth conditions.

    If you don’t watch Isaac Arthur’s youtube channel, you ought to.

    1. With orbits at different angles you still have enough gravitational interference that you need to keep the space between the orbits large enough to prevent that.

      As for the size of a star, I fount that one a bit over 56% the mass of our star will do nicely for planets. The reasons are 1) and smaller and the habitable zone is so close to the star that the planet becomes tidally locked, and 2) when you’re too close to a star you also get a lot more radiation from flares that might make the planet uninhabitable. The radiation problem would also apply to the outer layers of a shell world too.

      As building a shell world would probably be better around a gas giant, as gravity is a lot more effective at holding helium, which leaks though other materials over time. Helium is stored in nickel plated tanks as that is the least leaky, but over just a few decades significant amounts would leak away. Even a large gas giant would work, as the inner layers of a shell world could just be a series of orbital rings hundreds of km wide, spun up to some percentage of orbital speed to reduce their surface gravity to something bearable.

      Also about 2/3 the way through your comment I was thinking you’d like Isaac Arthur’s youtube channel 🙂

      Universe Sandbox2 would be a good program you can simulate a lot of this stuff in, I’m not sure about shell worlds and orbital rings though.

  20. I saw this article and the one where a black hole is used to have colossal numbers of planets in orbit, and both are impressive with consideration of the number of planets involved, but I wonder whether you could do the same thing with rings of equal mass stars that then separately have planets around them in their own unique orbits and with their own unique masses. In the black hole solar system, rings of stars were used for illumination quite close in, both inner and outer, but if they were spaced much further out, they could be given big enough hill spheres to have their own planetary orbits in turn. So we’re going for numbers of unique star systems in the same orbit rather than the highest number of orbiting planets (though in theory, you could nestle rings of 42 Earths around each star, but I don’t think you’d get anywhere near one million Earths!)

    So your article inspired me to look into it.

    I’m not sure if my maths are right, but I started with the assumption of a 1/5th hill reduction factor for planetary orbits rather than ½ or 1/3, since a star that is effectively librating around a more or less similar point not too far away is going to exert a more constant tug. With two stars on each side, if they are too close, not only is the system as a whole unstable, but planetary orbits might become eccentric.

    I also chose a star of 0.75 solar masses, which should have about 31.64% the luminosity of the sun via (mass of star/mass of sun)^4, which I think is the right equation, so (by the square root) that means the equal solar isolation point to the Earth is 56.25% of Earth’s semi-major axis (?). An extra safety margin, but the stars are not so small that the planets will definitely be tidally locked billions of years in (there was a paper recently on this dealing with atmospheric drag and planet rotation).

    Each star must be exactly the same, and I assume they can’t be too active as solar activity may push them out of the resonance(?).

    The inner boundary for the rings is the point where the hill sphere of a star is greater than 5AU, and the outer boundary is 1000AU.

    I chose a 100,000 solar mass black hole. With a bit of rounding up, the hill sphere of chosen stars is greater than 5 at 370AU semi-major axis for a black hole of this mass. The number of stars per ring must be around 38 for a separation of 12 times the hill radius.

    For the separation between rings, with the MUTUAL hill radius at 12, the orbits of rings pop out like this (rounded to whole numbers):
    370 AU
    455 AU
    559 AU
    686 AU
    843 AU
    1036 AU

    Depending on whether you allow going over the boundary condition by 36AU, that’s 5 or 6 rings of 38 stars, for 190-228 stars in total. If you omitted every second ring for long term stability reasons, that’s still 114 stars to have unique systems around. At 370 AU semi-major axis stars are circularly separated by 60AU, and by 170AU at 1036AU semi-major axis.

    Did I go wrong anywhere? If this is in a spiral arm and other systems are on average 4 light years away at whatever relative velocity is expected, would a 100,000 solar mass black hole draw them into dangerous close encounters rapidly in the system lifetime? I also looked at the case of a 10,000 solar mass black hole and got 68-85 stars over 4-5 rings. How small a black hole before it’s safe from dragging random stars into its influence from light years away?

    1. Nice job on the calculation! Your reasoning is generally sound. Let me try to answer some of the questions you’ve asked.

      Should stellar activity play a role in orbital stability/resonance? In principle: activity should not affect gravity and so the answer is no.

      And the reduction factor for the Hill sphere depends on relative masses of objects, so 1/3rd should be about right.

      Finally — given that very massive black holes are thought to grow by gobbling up nearby stars and gas, it stands to reason that a lot of stuff would continue falling down. So there is a bit of a logical leap in imagining a massive BH+star+planets system that is isolated from other stars. I invoked cosmic art by very advanced civilizations to create such systems, and I’m sure you can come up with something interesting…

      1. Thanks. I assumed there would be a larger hill reduction for more closely packed objects in general, since I know that analyses of the potential for moons around the TRAPPIST-1 planets assumes a greater reduction factor.

        I think in principle whether or not the engineered system could be in the galaxy or outside of it would depend on whether the relative velocities of stars a few light years away are likely to keep being greater than the escape velocity of that black hole over the system lifetime, which I did not calculate. For a rough estimate: if the average relative velocities remain the same, then the average distance needs to be increased by the square root of the mass increase (?), and sqrt of 100,000 is approx 316, the sqrt of 10,000 is 100. Multiply by an average star separation of 4 light years for our sun’s local neighborhood, and the blackhole systems need to be transplanted to regions where that separation is 100 to 316 times greater, so far far less dense. I’m going to assume that’s well outside of even the most tenuous regions of the galactic arms, considering the sun is already in a low density region. Possibly it could orbit the Milky Way like the magellanic clouds do.

  21. Ultimate Engineered Solar System
    With out any out side bodies entering the system in less then 6g years shoes signs of orbit shifting. The inner and outer orbits are destabilizing the fastest with no pro-grade or retrograde adjacent to stabilize their orbits.

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