Mega Earths

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I’m occasionally asked if you can make a planet like Earth, only larger, bigger, and if so how much bigger? As we’ll see today, the answer is very big indeed. We often discuss building artificial habitats in space for humans to live on, today we will discuss building artificial planets. Not cylinders or rings for providing apparent gravity by rotation and centrifugal force, but rather the traditional sphere providing gravity by the traditional means of mass and genuine gravity. As we have begun finding exoplanets around distant stars, we developed the term Super-Earth, planets larger than our own, but not so big as a gas giant like Jupiter. You often hear these compared to Earth but realistically this is not the case. Even those not too close nor too far from their sun to have liquid water on their surface are not going to be much like Earth. The force of gravity strongly controls the makeup of the surface of a planet, its land, seas, and atmosphere. Most planets begin with a large amount of hydrogen on them, as well as helium, the two most common elements in nature but also the lightest. The colder a planet is and the stronger its surface gravity and magnetosphere, the easier it is for those elements to remain. Left to its own devices, a planet like Earth will leak away all its helium and most of its hydrogen, some hydrogen will remain bonded to oxygen to form water, but not much. When you consider that our planet is almost entirely covered in water kilometers deep, it’s worth remembering that is but a tiny remnant of the hydrogen we used to have. A planet would not need to be much more massive to potentially have a gravity well and magnetosphere strong enough to seriously diminish losses in hydrogen, so that a planet might be covered in water and a much thicker atmosphere. If it is much higher, it may have retained all its hydrogen and helium and be a gas giant instead. You spot a planet that is twice as wide as Earth and appears to be about the same density, and composition, and even has a 24 hour day, too. What’s different? First off, being twice as wide but having the same density, it has 8 times the mass and four times the surface area. That last sounds great, 4 times the living room, except if you landed on it you’d find the gravity was twice as strong as Earth. Mass rises with the cube of distance, if the object has no change in density, whereas gravity falls off as the square of distance. For such an object, the strength of gravity at the surface rises linearly with the distance of that surface to the center, the radius. Double the radius, double the gravity. I wouldn’t want to live in a place where I weighed twice as much and even a slip down the stairs could shatter bones, but there’s unlikely to be any land to live on anyway. Being bigger it also started with more hydrogen, and will have lost a smaller portion of it due to its increased magnetosphere and increased gravity, so odds are any land it has is buried under kilometers of ocean under even more kilometers of atmosphere. Needless to say we don’t want that, and of course this is a Megastructures episode so we are not interested in naturally occurring planets. We are interested in building our own. If you can build artificial planets and your goal is to make them as Earth-like as possible, just bigger or smaller, there’s a lot more to it than just dumping excess matter into some big heap. Since they are artificial, we can construct planets of different sizes that have the same surface gravity as Earth. The surface gravity increases linearly to radius, but that’s only true if the density remains the same. If we constructed a planet the same size as Earth but twice as dense, if it were made mostly of lead, it would have twice the mass, and so would generate twice the gravitational force, undiminished by a larger radius. So its surface gravity is the same as our example Super Earth a moment ago of 8 times Earth’s mass. Its escape velocity though is not double, but just the square root of 2 or 41% higher than Earth’s. If we went the other direction and lowered the density, to half, gravity at the surface would drop to half and escape velocity would drop to 71% of Earth’s. It might be too low to hold a thick atmosphere. But we can always find a specific density for a given planetary volume or radius that will give the exact same gravity as Earth on the Surface. And it’s easy to remember, as it is inverse to radius or diameter. If you want a planet that has the same gravity as earth but twice as wide, it simply needs to be half as dense. Ten times as wide, one-tenth as dense, one tenth as wide, tens times more dense. Earth has an average density of 5.51 grams per cubic centimeter, water is just one gram per cubic centimeter, and we use the term specific gravity to skip the mass per volume. Being 5.51 times as dense as water, we know a planet composed entirely of water would be 5.51 times wider to have the same density as Earth, and would have 30.4 times the surface area. Which is quite large. It would also contain 30.4 times as much mass. That’s a handy scaling factor when you are keeping to the same surface gravity, it takes an identical amount of mass to create the same living area at the same gravity. If you want a million times the living area, at normal gravity, you need a million times the mass. Such a giant sphere would also need to be a thousand times wider than Earth and a thousand times less dense. The air we breathe is actually less dense than the sphere itself, and an air-filled balloon or ball is reasonably sturdy. Nor does the density have to be constant. If you had a big thick shell around a point-like black hole, it wouldn’t matter that the intervening space was empty vacuum. Now there are some obvious downsides to building planets this way. Firstly, regardless of size you have to spend the same amount of mass for each amount of living area, which for earth gravity is 12 billion kilograms or 12 megatons per square meter of living space. You could build a very sturdy chunk of rotating habitat exterior shell for only a ton per square meter, and give yourself a nice thick layer of dirt and water for, say, 120 tons per square meter, maybe 50 meters deep, far deeper than we tend to dig, and use 1/100,000th the mass you would need to make the same living area with a classic spherical planet. The supermajority of the universe is hydrogen and helium, which aren’t too useful by themselves, but could be used to generate gravity just fine. And when we say supermajority, we are actually excluding dark matter, which - if you could ever collect and confine it - outweighs all the rest of the matter in the universe several times over. Just because your artificial planet needs a lot of mass, does not mean you need the rock and soil to go any deeper than our classic rotating habitat does. Our second issue is how you could possibly build something strong enough to act as a shell? You do not necessarily need one though. Saturn for instance, has almost the same surface gravity as Earth, and a shell built around it, like a balloon, could be kept up simply by balancing the internal pressure of the gas against the external pressure of the rocks and water sitting on the balloon shell. We have no material strong enough to act as a rigid shell. We have discussed doing that with active support in the past. I’ve talked about that enough this year, and indeed all the way back to the original Shellworld’s episode, that I won’t repeat that explanation again. See the Orbital Rings episode for a discussion of the mechanics involved. Such planets resemble a soccer ball. Underneath the exterior of rock and dirt is an immense series of windings around a bladder of gas, or even vacuum, and those windings are endless magnetic accelerators pushing materials around at orbital velocities inside themselves. Sounds fragile, but it is in fact is a lot sturdier than what we stand on already on Earth, floating atop a sea of hot magma. Artificial things make folks worry about failure, compared to the natural systems, but carefully designed, sturdy and well-maintained machines can easily survive a long time and, unlike natural systems, because you created them you know what to expect and how to fix them when tell-tale signs of things going wrong happen. Now there are limitations as to how big, or small, you can build these things, but it depends on type and some other factors. For type, you can define three: a rigid one held up by a network of orbital rings, the balloon kind held up by an equilibrium of internal and external pressure, and a raw dumping of matter, like is the case with Earth. Rocks, soil, and water are a good deal less dense than Earth’s average is, so you could build a bigger planet just by skipping on dense elements like iron and uranium in the planet’s core. This version is the one with the least variation, you can’t build much bigger than our Ocean planet, 5.5 times wider with 30 times the surface area, and presumably with floating islands for land. You can’t go much smaller either, your densest materials are stuff like Osmium, Tungsten, Gold, Platinum, Uranium, and Plutonium, none of which are particularly abundant and are only 3-4 times denser than Earth, thus allowing you to miniaturize only to about 3-4 times skinnier and about a tenth less land. The balloon type has size limitations too, you can’t really go smaller than Earth with one, but you can certainly go larger. Again, Saturn is practically ideal to be made one, however, you can’t go much larger, because these things begin to contract under their own mass, so that you’d have no pressure pushing back against the balloon at the Earth-gravity radius, and eventually they get massive enough to form their own sun, which you don’t want underneath you… usually. We’ll get to using exotic stars inside shell worlds like white dwarfs, or neutron stars another time. Now the episode is titled Mega-Earths, which by common prefix means millions, and if you want a planet a million times bigger than Earth you need to use the orbital ring shell approach. This is the type I usually mean when I say Shellworld, though you will also hear them referred to as Supramundane planets, but this indicates size, not what is keeping the thing from falling in on itself. Shellworlds have the greatest size range. They can be made either much smaller or larger than Earth, and the smallest you can make one is essentially the point at which its escape velocity is so low even room temperature gas will fly away into the void, for all that gravity feels the same. The largest size we will save for last, but happens to be when the escape velocity is the same as the speed of light. A shellworld does not rely on mass providing the gravity to keep it as a sphere rather than collapsing, so we can circumvent the maximum size issue at which something will ignite and turn into a star by using a black hole instead. In theory, those can be made of any size or mass. Our sun is not quite a million times more massive than Earth though, so if you want an actual MegaEarth, you either need to use a black hole or use a material that won’t undergo fusion at that mass. Helium might do the trick, dark matter should, and any element above helium will. Each will have a maximum total mass though, and if you build any bigger you will get a star, and probably a very short lived and explosive one at that. All this gravity and stuff though isn’t the only issue. Once you start building planets bigger than Saturn for instance, the rotation rate at the equator to produce normal 24-hour days starts exerting a rather noticeable centrifugal force acting in the opposite direction of gravity. You might not mind a little lower gravity at the equator, but it will get worse the bigger the planet gets. We can curb this by abandoning it being a pure sphere, indeed planets generally are not, being wider at the equator than the poles exactly because they spin, but in our case we do this backwards. We make equator more narrow, so when you are on it you are closer to the center of the planet’s stronger gravity, and moving slower, therefore having less centrifugal force. At some point, even this stops being viable though, even by the time you are getting to Jupiter size your planet is looking decidedly egg-shaped. Fortunately, at this size you are also getting near the maximum before something turns into a star anyway. Now, we say a day is 24 hours and how long the planet takes to spin around once, actually that only take 23 hours and 56 minutes, the sidereal day, 360 degrees of spin, but it needs to spin for another 4 minutes to get facing back toward the Sun since the planet moved. A day is not how long the Earth takes to spin once, but how long a day-night cycle takes to repeat. Now before you jump ahead and say “ah-ha, we’ll go geocentric and have a planet so big the Sun orbits it!”, let me head you off. To orbit something as massive as the Sun once a day means only being 3 million kilometers from it, Earth is 50 times further away, and an object at that distance would get 50-squared or 2500 times the sunlight per area, it would flash-fry you! That distance increases if the orbiting object is more massive, a pair of binary solar mass stars would orbit daily at 4 million kilometers. It also goes up if the central mass is much heavier, but a mass would need to be 100,000 times as massive as our sun to produce a daily orbital period 1 AU out, the distance Earth is, and if we want the same gravity on the surface, a Mega-Earth 100,000 times as massive as our Sun, or 30 billion times more massive than Earth. Meaning 30 billion times the surface area and 180,000 times the diameter of Earth, and would thus be over a billion kilometers wide, so you wouldn’t be scorched by the Sun if you were standing on the surface, but only because it would be deep inside the planet. If we took the very weakest of stars, those with a luminosity only one ten thousandth of our sun, we could be a 100 times closer to it and not get scorched, just 1.5 million kilometers away, and such a star could orbit once every 24 hours around a Mega-Earth just 20,000 times the mass of Earth. But that would be about a million kilometers wide itself. So even here you are getting pretty scorched, and the light coming in is almost entirely infrared and more like what an old incandescent bulb gives off. Now, we could spin such a planet backwards, letting us place the Sun a bit further out, giving it a longer sidereal day than sunset length, and contracting around the equator to deal with that fast spin issue, egg-shaping the planet. You also have a lot more distance to the poles so they are more habitable than on Earth. And you could get away with making the day a bit longer too, say 25 hours, so you could sleep in. Also, you can play with the albedo of the planet or even set up shades and mirrors around the Sun to block some of the light and redistribute some of that light to those poles. This lets you get your sun a bit bigger and whiter, but it’s hard to get above 100,000 times the size of Earth and that’s about it. Technically not a mega-Earth, as again that would be a million. This is pretty much our boundary even with an artificial sun, one that’s just a big light bulb of a brightness of our choosing, because once you get over a hundred thousand Earth’s worth of planetary mass, you can’t have an object spread out wide enough to only have normal Earth gravity on the surface that also have any orbits of 24 hours around it, rather than inside it. It does let you get just a little bigger than a dim red dwarf of a sun permits, and also lets you spread your light out better to not have a far wider spectrum of temperatures between equator and pole than Earth has, so it is better, but doesn’t let you get much bigger for size. This does not mean you have to stop. You just have to abandon lighting by a normal object you are orbiting or the reverse. For instance I could stick a huge mega-Earth around an actual sun and use all that power to light its surface by giant towers over it, streetlamps on an epic scale. Or I could build an orbital ring around the planet and have a fake sun race around that, rather than orbit, or forego that to just have light all over that ring that turned on and off, in each its own turn, so it looked like a sun was moving through the sky below even though it was series of massive light bulbs just turning on and off. There’s no size limit on this, but once you switch to an artificial source of lighting, you might want to start asking why you don’t just build more layers? After all a second thin shell a few hundred kilometers above the first is a whole new free planet, costing you very little extra mass. There’s not even much drop in gravity since you aren’t much further away, and indeed you can tweak the distance and mass of the next shell to add to the gravity at its own surface to keep it the same as the lower one. Successive concentric shellworld’s, what I usually label a Matrioshka Earth or Matrioshka Shellworld -- not to be confused with a Matrioshka Brain -- let you add each new layer for a mass cost parallel to rotating habitats, and indeed, I see this as one likely future scenario for Earth, as you could mine out lower layers of Earth to add new layers above and just add extra mass stolen from places like Jupiter. Your top layer is still entirely natural but your lower layers are artificially lit. Since you want your spacing between layers ideally bigger than the atmosphere is high, so you aren’t getting stupidly high air pressures on the lower levels, you could just slather the bottom of the next higher layer in black paint and some fake stars and an artificial sun ring and it will feel decently Earth-like. So in order to build a Mega-Earth, you have to be willing to go for artificial lighting, but once you accept that option you can jump even bigger by just adding more layers, though trying to do more than maybe ten is going to give you big issues getting rid of all the waste heat your artificial sunlight produces even if you are tweaking the spectrum to optimize for photosynthesis and human comfort. You could have almost countless dim twilight cavern layers full of mushroom forests or storage facilities though. Before we get to the biggest example, though, let’s go the other way and consider how small you can make them. There’s no limit as to how small a shell world could be made if you can use a black hole as the gravity source, but it eventually becomes more logical to use a traditional rotating habitat, because you need to start doming things under to keep your air in. Though you can build one just 100 meters in diameter whose Hawking Black Hole radiation would be enough to power a comfortable homestead on what would be about 7 acres, a bit over 3 hectares, of land. You’d need domes or force fields to keep the air in, but it lets you own your own planet. If you go much smaller, you have issues with gravity being noticeably different from head to toe and that black hole in the basement giving off too much energy for the planet to dissipate. Way back in the original episode on the channel at the end I mentioned that the largest megastructure I’d ever heard of was one of these artificial planets built around a galactic mass black hole, with multiple concentric layers. The notion was given to us by Paul Birch, who unsurprisingly also designed the original Orbital Ring concept, as well as the trick for cooling down Venus we discussed a couple months back in Colonizing Venus. An interesting feature of the original one is that being that close to that much mass seriously slows down time, so that the folks living on the lower levels have time pass much more slowly than on the higher levels. And you might be able to have a lot of levels since beyond being massive power sources, it is sometimes thought you can use black holes, especially bigger ones, as a place to dump waste heat. So you could potentially have folks from the top layer, level 1000, go visit levels 1 or 2 for an afternoon and come back to find out that your watch is quite off. Our own galaxy’s central black hole is 4.5 million times more massive than the Sun or 1.5 trillion times Earth’s Mass, which means that each layer has 1.5 trillion times the living room Earth has, and a thousand times what even a Full Kardashev 2 Dyson Sphere has. Even if you only had a dozen layers it would have about 20 trillion times the living room and you might be able to have hundreds or thousands of layers. Like I said though, we can go a bit bigger. That structure we just mentioned is so big it would occupy the entire volume out to Saturn, but the black hole itself would be much smaller, not even a hundredth as wide. The bigger a black hole gets, the weaker the gravity near its surface gets, which is why you get torn to ribbons approaching a normal one but can get a lot closer to the bigger ones before tidal forces rip you apart. Is there a black hole size so large that the gravity at its surface is the same as Earth’s Surface? Yes, a black hole with 1.5 trillion times the mass of our sun, or 500 quadrillion times the mass of Earth, has a diameter of nearly one-light year and a gravity at its event horizon equal to Earth’s own. This is the absolute largest any structure of this type can be built since any bigger and you would be inside the black hole. A single layer of such a shellworld would be almost a billion times the living area of a dyson sphere, and given a modest number of layers it would match in living area an entire Kardashev 3, galaxy spanning empire. Not one where every system has an inhabited planet, but where each one was its own Dyson Sphere. You can also build one with approximately the mass of a galaxy too. Needless to say, time runs very slowly on the lowest layers and even the higher ones, but that makes it a nice place to hide to pass the time and since you would harvested your entire galaxy and maybe a bit more to build it, you don’t have any reason to care what is going on elsewhere. It’s basically the most massive structure you can build since firstly, anything bigger will be inside the black hole and secondly, anything bigger requires harvesting material from outside the area of the Universe gravitationally bound to you, rather than destined to fly off over the cosmological event horizon one day. Since Paul Birch is far less well-known than he deserves, and since this channel is big enough I can coin names and expect them to stick, I am going to name this a Birch Planet. The largest possible Earth-like megastructure you can build under known physics. I will go ahead and include the smaller original version around a galactic center black hole as a Birch Planet too, TeraEarth not sounding right compared to a mega-Earth or Giga-Earth. Okay, why would you build these? Any of these? They use a ton of matter, and too much to really justify that they are more Earth-like than a rotating habitat. However, as I’ve mentioned before any galactic scale civilization, or even just a decently long-lived interstellar one, needs to think on timelines of more than one classic human lifespan to continue to exist or even come to be in the first place. So the amount of mass one person needs for one lifetime stops being a good path for determining the stockpiles of resources you need to keep around. When you engage in starlifting and other stellar engine creation, you often will have a ton of useless mass leftover, hydrogen and helium for instance, which has little value except for its mass or mass-energy for fusion or matter to energy conversion. You still want to store that stuff so you can use it later, and you might want to take advantage of the gravity it produces. If you’ve got some big fuel bunker in space shaped like a sphere, as it presumably would be, you might want to just dump some dirt, water, and air on it and build some houses too. In the long term you want to harvest the entire galaxy, and even further if you can, because the raw materials of the Universe are not stored well. A solar system you leave sitting around untouched for a million years instead of harvesting is losing value that whole time, burning hydrogen, having solar wind escape, having valuable rocky asteroids and comets crash into their sun, and so on. If you are harvesting and storing all that for eventual use, you might as well make use of its gravity now. And if you are thinking on those timelines, you aren’t interested in how many centuries or even millions of years some rotating habitat could run its fusion reactors off its tanks of hydrogen fusion fuel, but how many trillions or quadrillions of years a hollow planet stuffed full of hydrogen can run its lighting off that hydrogen, slowly lowering gravity or even contracting the planet as the fuel gets used. We will talk about some of those scenarios more when we do our next installment in the Civilizations at the End of Time series. Another big advantage of a Birch Planet relates to the scale of Kardashev 3 or K3 civilization. A K3 civilization makes use of all of the energy put out by its galaxy. I’ve mentioned in other episodes that divergence will inevitably occur due to the timelines involved in setting up and communicating in a K3 civilization that has no faster than light travel or communications. It takes potentially a million years to travel across the galaxy even when approaching relativistic speeds. Colonizing a galaxy takes millions of years and, even without technological tinkering, folks on the other side of the galaxy might be as genetically different as we are to the dinosaurs. The consequence is that members of the K3 civilization across the galaxy are going to be very alien to one another, even if they originally came from the same species. If a K3 civilization wanted to make itself cohesive, then the Birch Planet is a solution to the divergence problem. A K3 civilization can install itself into a Birch Planet and will be able to communicate to its entire population, a billion, billion times as many individuals as Earth holds, in timelines of about a year. Many an old empire from our own history existed within similar constraints and still remained relatively cohesive. You can also start building one and just keep making it bigger as more mass becomes available, you don’t have to build a Birch Planet all at once. This also leads onto a possible solution to the Fermi Paradox I speak so much about on this channel, which at its simplest is an apparent contradiction that despite a seemingly high probability for the existence of space-faring aliens that there is no evidence that such aliens actually exist. Now, we’ve been actively looking for sentient alien life in our galaxy for decades, but we’ve also been looking for signs of it in other galaxies. If there were a K3 civilization, we would usually expect to be able to see it from the tell-tale waste infrared heat that it would output, but possibly not if that K3 civilization was on a Birch Planet. Even if a Birch Planet put out the ferocious amount of heat that such a vast civilization would produce, we wouldn’t necessarily notice it since it would be concentrated. The construction of one uses up an entire galaxy, and while it should be very visible if you are looking at that spot, the odds of looking at that spot aren’t very high. What’s more, a maximum sized one is hanging out just over the event horizon of a black hole, so the light leaving it is going to be massively red-shifted, you won’t spot one of these, even the smaller ones, if you are just looking for the infrared signature of an Earth temperature Dyson Sphere. But moreover, as mentioned earlier, it is thought that you might be able to dump waste heat into black holes, which you would want to do if that trick works, so a Birch Planet might be incredibly hard to see since it is very far away from any other civilization, very tiny compared to a galaxy, has all it’s light red-shifted, and might be able to use that black hole as a heat sink. Now, construction of such a thing is not even vaguely covert, so the civilization that made it isn’t going be hiding, but they’d be hard to see and a Birch Planet, once constructed, would be the perfect place for a K3 civilization to hide from us. Perhaps this is the reason we have not seen a K3 Civilization, they build inwards, not expand outwards, just dragging in matter to add to their single immense planet. We had to do a lot of math today to discuss our topic, as usual, I did try to keep it to the minimum and supplementary, so that folks who wanted to design artificial planets of their own had the available tools. I left out a lot of the math in this video… but to start doing your own research into distant worlds you’re going to need a toolbox… a perfect place for that is Brilliant. It's a great place to improve your skill and comfort level with math and science so that you can think like a physicist. In Brilliant's Astronomy course, starting from simple beginnings, you can also learn how to model the habitable zone around different stars, look for observational signatures of distant worlds and analyze the logistics of sending probes to explore them. With these basic skills, you can go on to explore places like we discussed today, or even dream up new ones. To support the channel and learn more about Brilliant, go to brilliant.org/IsaacArthur and sign up for free. As a bonus, the first 200 subscribers will get 20% off the annual Premium membership. Next week, we return to the Outward Bound series for Colonizing Jupiter, and we will look at the concept of a mini-solar system of gas giant moons along with oceanic colonies on places like Europa, and how to colonize an actual gas giant itself. The week after that we’ll continue our look at Artificial Intelligence, and follow that up with a look at the concept of Hive Minds. For alerts when those and other episodes come out, make sure to subscribe to the channel and if you enjoyed this episode, hit the like button and share it with others. Until next time, thanks for watching, and have a great week!
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Channel: Isaac Arthur
Views: 240,568
Rating: 4.9325261 out of 5
Keywords: megastructure, construct, space station, futurism, physics, planet, artificial world, habitat, colony, worldbuilding
Id: ioKidcpkZN0
Channel Id: undefined
Length: 32min 4sec (1924 seconds)
Published: Thu Nov 16 2017
Reddit Comments

This made me realize the Death Star must be a Dyson sphere, right? Way better explanation than fictional "crystals."

👍︎︎ 2 👤︎︎ u/boredserf 📅︎︎ Nov 17 2017 🗫︎ replies

What about the opposite? Something with earth gravity, but much smaller. Like the little prince or mario galaxy. (Not that small. I'm thinking closer to a medium sized asteroid)

👍︎︎ 2 👤︎︎ u/Doobly_Baggo 📅︎︎ Nov 17 2017 🗫︎ replies

So Isaac Arthur is now doing those smooth ad transitions too. :D

👍︎︎ 1 👤︎︎ u/taulover 📅︎︎ Nov 18 2017 🗫︎ replies

If gravity is Earth-level, but the event horizon is right below the ground level, what does that mean, practically speaking?

👍︎︎ 1 👤︎︎ u/Nulono 📅︎︎ Nov 24 2017 🗫︎ replies
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