Megastructures E04: Rotating Habitats

## Transcript

Today’s topic, Rotating Habitats, is going to be a rather long one by the standards of this series thus far, so we’re going to jump right in. On the off chance this is the first of my videos you’ve ever seen though, you’re strongly encouraged to turn on the closed captions, my voice takes a bit of getting used to.

So our subject today is Rotating Habitats, and the first thing to understand about rotating habitats is that it is a huge zone of options, all linked by only one common denominator: Centrifugal Force. If you’re in a place that has no gravity, and you want some gravity, the only two ways we currently have to do that is to either pile a ton of mass together for its natural gravity or to fake it with ‘spin gravity’, essentially to use centrifugal force to mimic gravity.

Odds are if you’re watching this video you already know what centrifugal force is, we all encounter this force on a regular basis. You’ve probably heard it referred to as a fictional force as well, or more accurately as one which does not exist in an inertial reference frame, but for our purposes it’s real enough. It’s real enough because it lets us hold objects down against a surface like there was gravity even though there isn’t, and so long as the vessel you’re spinning is decently sized, basically bigger than a football field, the mimicry of gravity holds for most biological purposes.

So we can take a big ring, or cylinder, or torus, or anything else with radial symmetry like a sphere and spin it around and the sides become a floor you can walk around on. You can even jump up and down and land where you’re supposed to as the fake gravity keeps working even when your feet leave the floor. You won’t quite fall straight down due to Coriolis Effect but for any normal human leap on any decently sized rotating habitat you’d never be able to tell you missed your mark without highly precise equipment.

**Centrifugal Force**

# a

v
2

r

{\displaystyle a=\frac{v^2}{r}}

* a = acceleration
* v = velocity
* r = radius

**for Earth Gravity**

a = 9.8 m/s2 or 32 ft/s2

This gives us our first issue with using rotation to fake gravity though. That Coriolis effect can be a bit disorienting on humans as it acts on the inner ear to cause dizziness and nausea. As best as we can tell anything beneath 2 RPM, 2 rotations per minute, doesn’t affect anyone, and we expect people could adapt to rates of 20 RPM or higher. It’s basically akin to motion sickness though. Problem is, a slower rotation, or fewer RPM, results in weaker gravity. That’s fine for a space station, we can get away with picking astronauts who are less sensitive to the effect and go with less gravity. You could get away with having a metal can in space 30 feet in diameter spinning 10 times a minute and producing half gravity for astronauts.

That’s probably okay for some Mars Mission where they need to adjust to lower gravity anyway and you can pack a lot of Dramamine along for the motion sickness. But this video isn’t about space stations or ships, it’s about full blown habitats. Places that comfortably simulate what we’re used to. So we’re not interested in anything that doesn’t produce normal Earth gravity in a comfortable way. To get higher gravity at a slower rotation we need to make the rotating structure wider, and if you want Earth gravity provided under that 2 RPM threshold then your diameter is about 1500 feet or 450 meters. This is basically the minimal threshold for building mock environments since the idea is comfort, you can go wider, but you don’t really want to go skinnier.

You can’t go too much wider though because the wider these things get, without decreasing the simulated gravity, the more stress is put on them. For steel the usually assumed maximum is on an order of a diameter of several miles, for stuff like Kevlar or Carbon Nanotubes it’s much higher and is a lot like the problem we discussed way back in episode one regarding space elevators. Essentially the breaking length of a material in normal gravity tells you the maximum circumference of a rotating habitat made of that material simulating normal gravity because it’s the same thing. Since you’re operating in the vacuum of space besides the initial energy to get it spinning you don’t need to add much more to keep it spinning. That’s why mechanical flywheels in a vacuum are such an attractive option as batteries. No air drag to slow them down. Which means you can sack some of your gravity for emergency power too.

While their diameter is controlled by the strength of the building materials, and the amount of gravity you want, the length of the habitat is not, you can go anywhere from a thin ring to an arbitrarily skinny cylinder.

So that’s the basic intro, how the fake gravity works and what the control factors are. When we talk about rotating habitats in any long term sense, beyond just avoiding health ailments for astronauts, we’re talking about doing something that mankind has never truly done before, and that’s make more living space. Oh, we’ve built some fake islands, cut into mountainsides, or built vertically from time to time but as a whole, while we’ve made land and sea more livable to us, we’ve never added to it. Earth is our only world and its size does not change. If you want to add more people you can improve your farming technology and in the video on Fusion we discussed some of the ways you can use that, if you’ve got that, to really push out your maximum sustainable population, often called your carrying capacity, without wrecking your ecology or reducing everyone to a lower standard of living. There’s some other ways to push that even further we’ll look at in the future but ultimately you can just only pack so many people on a planet comfortably before you run out of space. Rotating Habitats give us a way to increase that space.

The classic version of this is called an O’Neill Cylinder, and it’s 20 miles long and 5 miles wide, about as wide as you’d comfortably want to make something like this out of steel. That means its internal surface area is 314 square miles. For comparison that’s about half again as big as Guam or a third the size of the State of Rhode Island or a quarter the size of Long Island New York, and almost identical in size to the island nation of Malta. So an O’neill Cylinder is not a small object. And you can go larger, titanium would roughly let you quadruple that, and stuff like Graphene could hypothetically let you make things on par with continents.

You can also connect the things together, like a string of sausages or in various other configurations. So that material strength issue isn’t all that strong a control factor on your true interior size since they can be linked to fairly seamlessly create one greater structure, even if it would be more like an island archipelago than a vast continuous plain. You can also go bigger by having multiple levels, the lower ones having slightly higher gravity than the higher ones, which is actually true on Earth too though much less noticeably. You can only go so many levels before even just the waste heat of lighting the place would make it uncomfortably warm even with an array of radiator fins on the cylinder. In space you can only get rid of heat by radiating it away, same as how our planet gets rid of its own heat.

In and of itself that’s the basic intro to what rotating habitats are and what the basic issues with them are. Now let’s get into some of the more fun aspects as well as some of the challenges. The first and most obviously big one is cost, which is way worse right now when we have to drag every ounce of building material up into space at phenomenal costs. We already talked about that in the prior videos though, and space is full of asteroids we can cannibalize too. If you feel like we’re going invent fusion one day, that we’re going to get way better at automated manufacturing and 3D printing, and you think we’ll get one or more of those cheaper launch systems built that we discussed in previous videos, then we can skip cost for now. Needless to say building new living area from scratch is a pretty major endeavor. But if you’ve got all three of those things you can do it.

Heck you don’t even need fusion but it saves the effort of screwing around with mirrors to bounce sunlight in to the habitat or transparent sections or needing to keep them fairly close to the sun, meaning you can use those asteroids out in the bet without having to either drag them close to the sun or creating giant parabolic mirrors to bouncing light in.

We should start this section then by discussing one common misconceptions about rotating habitats, and that’s the idea that you can see one spinning. Most of the images or videos of these I’ve put up so far, or that you can see elsewhere, always show them spinning. Usually when someone talks about building them inside hollowed out asteroids they will say they spun the asteroid. That last is especially wrong since only the largest asteroid have any really noticeable surface gravity and they’re all basically wads of gravel loosely held together. Spin one up to Earth gravity and it will fly apart.

But the notion of using hollowed out asteroids is on the right trail, because all that rock under your feet between you and space provides nice shielding from radiation and meteorites. Here’s the thing though. You don’t need your exterior shielding to spin any more than you need the casing for a centrifuge or washing machine to spin. In fact it’s pretty damn dumb to do that. Space ships with rotating sections won’t have some big hub you can see turning from outside, just some superstructure that doesn’t spin that it’s nested inside. That way your superstructure shielding isn’t under all sorts of strain from spinning when it’s taking hits, and what’s more everything that hits a rotating object is going to either add or subtract some of that spin speed to its relative strike speed, damage is pretty much synonymous with raw kinetic energy, which goes with the square of velocity, even though half as many objects are striking slower and half faster, you still take more damage. So you don’t see rotating habitats spin since inside you’re spinning with it and can’t tell and outside it’s surrounded by some non-rotating superstructure, or possibly one rotating considerably slower in the opposite direction.

This shielding material doesn’t necessarily need to be rock, or ice, or metal either. You could use the most common substances in the universe, hydrogen and helium, as your shielding. Hydrogen is also one of the best shields against cosmic radiation, pound for pound. So you could surround your rotating habitat with a non-rotating superstructure full of hydrogen tanks and other layers of shielding as seen appropriate. On a ship you can use that hydrogen as fuel, and you can also use your air and water reserves as more shielding. Radiation doesn’t really hurt them and better a micrometeor knock out a bit of your reserves than to knock out you. But in the context of asteroid mining, we would presumably use the slag.

The thing is, you don’t really need to hollow out an asteroid. If you come across any of the roughly million or so asteroids in our solar system that are around a mile wide that’s really not a good approach. It’s not hard, shoveling rock on even a big asteroid with decent gravity is like shoveling packing peanuts, and even on the largest, Ceres, generally considered a dwarf planet now, not an asteroid, you could bench press a truck without breaking a sweat. One of these smaller ones, the mile across kind that outnumber the big named ones thousands to one, you could kick around boulders the size of your house and your big problem mining is you’d need to erect a dome over you to keep the debris flying off into space. Asteroids generally don’t tend to be one solid chunk of rock you’d need to cut either, many are basically wads of gravel. Nothing you build inside needs to be terribly sturdy either, your typical asteroid is so small and with such weak gravity that even under hundreds of feet of material the pressure isn’t strong enough to crush an empty beer can, so you don’t really need to shore your tunnels up like you do when mining on earth.

So why wouldn’t you hollow one out then? Well in a nutshell because it’s intensely wasteful of material. Let’s say you come across some conveniently spherical rocky asteroid a mile across and want to use rock as your shielding. Fact of the matter is anything much beyond a dozen or so feet is going to stop micrometeors with ease and drop cosmic radiation to near nothing. Here, on Earth, over your head, is about 14 pounds per square inch of air or 10 tons per square meter. That’s roughly comparable in mass to being under 10 meters of water or 3 to 5 meters of typical rock, so you’ve got as much raw mass between you and space with thirty feet of rock as you do down here on Earth. But let’s say you want a hundred feet of protection of rock, way more than is needed to protect you from anything but a direct nuclear strike. You’d still have only used about 3 or 4% of that mile wide asteroid, and a much smaller percentage on a bigger asteroid. And the rest, all hollowed out, it just air surrounded by a thin layer of dirt, water, and steel.

What do you do with the rest of that raw material? Well you could ship it all off elsewhere but rock is really only valuable for making habitats once you’ve stripped out the valuable stuff like platinum, gold, iridium, and so forth. After that, it doesn’t have much export value. Truth be told with asteroids in this size range it’s probably easier to mine it if you spread it out anyway so you might want to just make the whole asteroid into one much bigger hollow sphere 5 or 6 times wider and then just slowly replace what you mine over the year with hydrogen tanks. In the long run, in a fusion economy, you’d want to trade away excess minerals for larger quantities of hydrogen stored in exterior tanks that slowly replaced that rock as shielding. As discussed in the fusion video you could light up and power a rotating habitat for billions of years with less hydrogen then you’d use just normally shielding it from cosmic radiation. So you can take that tiny asteroid and turn into a nice big sphere with a rotating habitat inside it and lots of zero-gravity storage or industrial spaces or smaller additional cylinders, maybe to used for hydroponics. When dealing with a bigger asteroid you can either break it up into multiple spheres or if you don’t want bigger cylinders you can arrange your cylinders into various geometric shapes touching each other at the tips.

This brings up another point. These things don’t have to be the same radius the entire length, you can taper them at the edges and the gravity will fall off as it gets more slender. You can also put in dips and rises in the shell to let you get away with taller hills and deeper lakes without needing to put tons and tons of dirt and water inside. Similarly new materials like aerogel, that are incredibly light weight and sturdy, could be used below the topsoil to help. We don’t generally dig much more than a few meters deep on Earth nor do most roots go much deeper, so there’s now real need to have hundreds of meters of dirt and rock in these things.

Lighting for the inside would either be provided by mirrors coming in through the cylinder caps or preferably by fusion powered lamps putting out their light only in those frequencies we can see or that plants use, that helps cut down on waste heat letting you do multiple layers without sacrificing the aesthetics. And the upward curving horizon can be dealt with in part by just disrupting the flatness with hills and valleys, though on very large rings you wouldn’t even see that. Big difference, and the hardest one to deal with, is that the sky isn’t blue and cloudy, it’s your neighbors, and the stars in the night sky are their porch lights. You can get some of that blue with lots of lakes as opposed to grass and forest since water really is blue, but if people really wanted that blue sky effect you’d probably want to nest another smaller thinner cylinder inside to fake a sky, preferably a bit more elaborately than just painting it but that would presumably work. When you’re building land many meters deep over a thick steel shell building a giant LCD TV overhead isn’t really that much of a stretch either.

And again if you’ve got fusion to power these things you can build them anywhere. Around planets from the smaller moons or rings, out in Oort Cloud, out in interstellar space. They’re fairly mobile too though not ideal as spaceships since they’ve got so much superfluous mass in the name of comfort. As we discussed in the Rogue Planets video, interstellar space is littered with junk, there might be more planets and asteroids between two stars than around either in their solar systems. Maybe a lot more. These things are more than big enough to support sufficient gene pools even if technology didn’t give us a lot of easy workarounds to genetic bottlenecking. So just as example if some ideological or religious group here on Earth decided they wanted their own sealed off place, they could grab any of the millions of asteroids or comets kicking around our solar system and turn it into a habitat able to support a million or so people indefinitely, or even several thousand if they were of a bit of techno-primitivist bent. These being effectively low-grade space ships you could set your course for deep space and leave other people behind if you found the core civilization too undesirable to share space with.

Nor do you have to build it all at once. You start with a small cylinder and either make it longer with time or just add more cylinders. You could even drag in mostly empty prefabricated ones and arrange them outside the asteroid then just build a thin shell around the whole thing and disassemble the asteroid for exterior shielding and fill dirt for the habs.

In terms of how many of these we can make in our solar system that all just depends on how thick you want your dirt, since again you can use hydrogen as your real exterior shielding. If you disassembled all the rocky planets in the solar system to make habs with about 10 meters thick of dirt and hull you could get away with fabricating an amount of these equivalent to a few million Earth’s worth of living area. Less dirt, more living area, more dirt, less living area. If you’re using that dirt as your main source of food, rather than mostly hydroponics, a population a few million times our own, if not, if it’s really more for gardens and lawns and some dedicated habitats as wildlife preserves, than maybe a hundred times as dense.

Okay, we’ve looked at the more plausible ones. Let’s close out by reviewing some of the bigger and often more famous designs. As I mentioned earlier if you’re working with metals like steel, or even titanium, you can just only make these things so wide. Once we discovered carbon nanotubes and graphene we set our sights a lot higher and came up with two called the Bishop Ring and the McKendree Cylinder. These are things with circumferences on the order of a thousand miles, not just ten or so and they are big enough to nearly be considered planets of their own. Same concept as before, just bigger.

But even before we discovered carbon nanotubes we already had two rather well known fictional examples. The smaller, more recent, and less well known of those first appeared in the late Ian M. Banks 1987 novel Consider Phlebas and we call it the Banks Orbital. What’s noteworthy about this ring is the rather specific spin rate. It rotates once every 24 hours. Meaning that if you turn it on its side facing the sun it will replicate our normal 24 hour day night cycle without needing artificial lighting or mirrors. You can even give it a little tilt to simulate seasons. Of course you need what we call an airwall many miles high to keep the air spill out of the thing but the object is so huge you’d barely even see those and you’d probably sculpt them as fake mountains. You get the same sky, day and night, as on a planet, and the horizon is so far off all the air in between would probably hide it so you just saw a thin bridge over head.

In order to achieve that 24 hour spin rate and produce earth-like gravity the Banks Orbital has to be a very specific size. For any given planetary gravity and day length there is only one unique diameter that will work. An Earth Banks Orbital would be roughly 2 million miles in diameter, and it can be as wide as you want but the wider you make it the brighter your night sky since the sunlit side will glow. Even one just a thousand kilometers wide is going to make the nights brighter than a full moon. One that wide would have a couple hundred Earth’s worth of surface area though. Again you can make them wider but at the cost of brighter night time skies and since the nice thing about these is how closely they replicate Earth, since it’s already got a couple hundred time more living area than Earth, you might as well just build a second neighboring skinny one rather than make it wider.

The obvious issue with building ones of these is the material stress. Nothing, not even Graphene, comes close to being strong enough not to be ripped to shreds. Nor could any type of molecule ever do it. In theory some sort of material like Neutronium, the loose concept for some material held together by the strong nuclear force that binds atomic nuclei together, could maybe pull it off but the usual method in science fiction is a handwave to force fields.

The next and better known, and also older and larger design, is Larry Niven’s Ringworld. These are just under a hundred times wider in diameter than a Banks Orbital and wrap a star entirely. They require an even stronger material than a Banks Orbital does and since they always face the sun you have to put up shades to block the light that orbit at some spacing and rate to produce a 24-hour day. And that just has you go from high noon to midnight in short order, though you could get around that by making the edges of the shades translucent especially to red light, to mimic twilight. Banks Orbitals don’t have that issue, they have a natural day and night with regular old twilight and dawn. That’s one of the reasons why the concept is pretty popular even though it’s newer and smaller than the idea of a Ringworld.

Otherwise they’re much alike, and much akin to the Bishop Ring. You have airwalls to keep your atmosphere in. Ringworlds can be arbitrarily wide too but usually we put the number at around a million earth’s worth of surface area or more. They have stability issue, and they’re spinning at nearly half a percent of light speed meaning you’ve really got to worry about debris hitting them, but realistically if you can build the thing in the first place those kinds of problems are pretty insignificant. Kinda like worrying about if you’ve got enough power outlets in the kitchen on an aircraft carrier, it matters but it’s just not that big a hurdle compared to floating a hundred thousand tons of steel on water. About the only thing the Banks Orbital has to worry about that a Ringworld doesn’t is tidal forces, the thing is big enough that the part near the sun gets yanked on more than the part farther from the sun but that’s not necessarily a bad thing since if gives you tides, another thing rotating habitats wouldn’t have unless you brute forced it by having attached cisterns that pumped some water in and out of the habitat on appropriate times.

Both of these are very popular designs but not really in the realm of currently plausible science. Amusingly it is typically in the realm of doable in most space operas and scifi like Star Trek which is one of the reasons why it often seems a bit strange the dudes are always squabbling over planets when they could just build these things instead.

Back in the realm of plausible science, but similar immense in size, is another object popularized by Larry Niven that also showed up in one of Bank’s novels called a Topopolis. You might recall earlier I mentioned you could connect rotating habitats together at their ends like sausage links, this one goes one better and avoids some of the problems with that by just having one insanely long habitat that doesn’t resemble a ring, or cylinder, or even a skinny pencil but is more like a giant spool of wire. And you just wrap it around a star as many times as you want, or if it isn’t solar powered, around whatever you want like some gas giant you’re mining for the hydrogen to fuel the fusion reactors to light the giant thing.

It could be steel, some miles in diameter, or graphene, some hundreds of miles in diameter, and arbitrarily long until you ran out of raw materials to build it anyway. There’s literally no difference between them and the shorter O’Neill or McKendree Cylinders. No tricky engineering or anything like that. They’ve not show up much in fiction though, which has always surprised me. Personally I always like to think of them having some super long river running down the whole length for millions or billions of miles. Even though all these things can only be built by high tech, often clarketech, civilizations they always seem to make people think of them as inhabited by lower tech civilizations of more of a fantasy than science fiction bent. Medieval not high-tech, and I’m not really an exception, the Topopolis is rather neat for the option of being one giant coastline of port cities.

The Topopolis is as big as it gets for rotating habitats that are a single piece and don’t require inventing new science, but they’re not the end of the story. Earlier I showed a couple ways of linking these things together in groups and it might have occurred to you at the time that a direct connection like that has some problems. The most obvious being if you connect a spinning cylinder to a sphere that isn’t spinning with it you’re going to start leaking air or have gears grinding on each other or both. That’s a serious issue with the classic rotating habitat exposed to void but there’s two work arounds. The first is a plasma window or similar technology, that I discussed in the last video as way to keep air from leaking into evacuated tunnels at the end of launch loops. It can work the opposite way too, keeping air from leaving pressurized tunnels. The second we’ll touch on in a moment.

First let me hit on one point, if you’re connecting multiple cylinders at the same junction then that junction really can’t be spinning to produce gravity itself, another reason you’d probably taper these cylinders near the end so that gravity ebbed off slowly for those entering the spheres. You could however fill them with air just fine so birds could fly through. In theory land critters could learn to maneuver in zero gravity and you could line the edge with easily gripped, or clawed, materials and arrange a constant outward air pressure to blow things back against the sides of the sphere.

That doesn’t help sea life if you want fish to be able to migrate between habs though and we do often think about using rotating habs as a way of making truly protected wildlife reserves so overcoming that is worth consideration. You’d almost have to have two big pipes running out of each hab with pressure pushing water in through the one and out though the other so things could swim between, but it could be done and could also work in tandem with faking some tides and currents. Rotating habitats aren’t really ideal for deeps seas either but you also really don’t need much gravity for marine life, just enough to make sure stuff goes the right way so slower spinning habs mostly full of salt water and much deeper is an option, with the lower apparent gravity the pressure rises slower too and so they can be much deeper. If you saw the rogue planets video and remember me mentioning the idea of vertical reefs this would be another applicable cases. You’re always going to want a nice supply of reserve water and water is very plentiful in this universe, so you might prefer to put it to use as an ecological niche rather than just as a protective ice sheath for habitats.

That protective sheath brings us back to our other fix for leaking air and water. Remember that our spinning cylinders are not exposed to outer space directly. They have a non-rotating exterior layer around them. That can be welded right onto the junction sphere, nice and air tight. If it isn’t rotating then you can just let a bit of leakage occur where the rotating section meets the connecting junction sphere because you can pump that back to near vacuum. Running a vacuum pump in gap between the rotating section and the stationary sheath, and adding a bit more spin to the cylinder to make up for a bit of loss to air drag in the near vacuum, is fairly energy intensive but it doesn’t even get into the ballpark of the kinds of power needed to light and heat these things normally, and all that drag and pumping would end as heat anyway. So with those exterior sheaths we don’t need to worry much about leaks where moving parts connect and that increases our options.

We can do more than long sausage chains or even fairly two dimensional layouts and go for 3D. So long as you taper the cylinders down before jamming them into a junction sphere you can cram them together fairly tightly and these junctions spheres with no gravity of their own don’t need to be very large and they can also have exterior access to actual space through the usual airlock mechanisms. You can, from the 2D angle, lay yourself out wide mesh grids like ribbons and fill the gap in between with solar panels if you either don’t have fusion or want to take advantage of the free supply in a sun.

This is one of the ways you can go about creating a Dyson Sphere, or Partial Dyson Sphere if your raw materials run out, by just wrapping these ribbons all the way around a star then doing another ribbon cocked at a different angle and so on, until you have a sphere. Unlike the Ringworld they only need to be moving at normal solar orbital speeds because they get their entire gravity from spinning locally, rather than around the entire star. Such combined structures, possessing thousands if not millions of times as much living room as a planet, let you get away with devoting whole planets worth of space to things like natural habitats for all the flora and fauna we have here on Earth while still devoting the super majority of it to human-centric interests. It’s also a lot easier to protect a rotating habitat from invasive species or careless campers.

Taken as a whole, as we close out for the day, rotating habitats offer us the advantage of millions of times more space than we’d ever get just terraforming planets and are doable inside the laws of known science. Plus as we’ve seen they can be made very comfortable to mankind and quite safe and secure, arguably a lot more than planets are. Unlike planets you can choose your own day length and temperature and climate and gravity, and while as we saw in the terraforming video there are ways to do that with other worlds too it’s a heck of a lot easier with these sorts of constructs. This is, fundamentally, why many of think that vast swaths of rotating habitats are more likely in mankind’s future than endless terraformed worlds.

So this concludes all the prepwork we needed to finally get to the video on interstellar colonization. Once we finish that up we’ll be returning to the megastructures series to look at another type of artificial world, this time with real gravity, in Shell Worlds, and from there probably move on to the slightly more fantastic Discworlds. Our next stop on the habitable planets series is going to be a look at Double Planets. If you want alerts when those videos come out, click the subscribe button, and if you enjoyed this video, hit the like or share buttons and try out some of the other videos. Questions and comments are welcome down below, and as always, thanks for watching and have a great day!

1. ↑ The Coriolis Effect is present in any rotating system, planet or habitat.
2. ↑ The Kinetic energy of a 200 kg meteor moving 1000 m/s is 100,000,000 Joules or 100 MJ. So 2 meteors would be 200 MJ. But if they hit a rotating station, their speed would add or subtract the station’s spin rate. If that spin were 200 m/s and one subtracted and the other added, then one is going 800 m/s and the other 1200 m/s.

K

=

1
2

m

v
2

K

=

1
2

×
200
(

800
2

1200
2

)

K

=
64
M
J
144
M
J

=
208
M
J
>
200
M
J

{\displaystyle \begin{alignat}{4} K &= \frac{1}{2}mv^2 \\ K &= \frac{1}{2} \times 200(800^2+1200^2) \\ K &= 64 MJ + 144 MJ \\ &= 208 MJ > 200 MJ \\ \end{alignat}}
3. ↑ Ceres -- Diameter 1200 mi.
4. ↑ 14 PSI is Literal. There is a lot of weight on your shoulders.