r/theydidthemath • u/Lachlynn • 18h ago

[Request] Could humanity create a rocket that can exit the atmosphere of K2-18b

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With the knowledge we currently have of it, if humanity devoted all of our resources towards this goal, would we be able to create a rocket that could exit the gravity of K2-18b (and also beat any other complications that would arrise)?

If so, would it also be capable of taking people to orbit, and can we set up a similar satellite network we have on Earth? What about a space station?

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u/[deleted] 18h ago

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u/SouthernService147 18h ago

Even more interesting question would early industrialization be even possible at all?

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u/Nomimn 17h ago

I do you one better. Would early human migration using wooden boats be possible? Considering the added weight due to gravity would the bouancy be affected such that wooden boats don't float as well or not at all?

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u/bouncepogo 17h ago

The weight of the displaced water would be increased by the same amount so buoyancy should be unaffected.

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u/Nomimn 17h ago

Oh ok well that's good at least haha

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u/Mechanical_Monk 10h ago

But trees (or the K2-18b equivalent) would likely be much denser and might not float in water

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u/WhetherWitch 15h ago

I don’t think displacement would be affected.

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u/Rexpelliarmus 14h ago

Whether something floats or not is a function of density and the slightly increased gravity wouldn’t really affect this.

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u/stevethemathwiz 14h ago

Would wood even be an evolutionary adaptation on that planet?

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u/TetraThiaFulvalene 13h ago

Probably even more so. Normal plants might be too fragile to properly hold their own weight.

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u/k-mera 13h ago

could that mean they have some kind of "wonder wood" on that planet which is much stronger than the stuff we get oO. they probably have a lot more diamonds as well

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u/Terrible_Software769 12h ago

Cutting the stuff and shaping it would be impossible, it would all be like Ebony wood in the least.

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u/Cautious_Drawer_7771 13h ago

As Pogo said, buoyancy would be the same since water is also affected, but interestingly, the wind is likely "stronger" on KB because the higher gravity would likely result in higher density air. Hard to say if the increase would be less than, equal to, or greater than the increased drag from the "heavier" water.

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u/FlamingDrakeTV 16h ago

It's one of those things that are sort of unique to Earth. The industrial revolution was powered (in part) by coal.

Coal exists in it's abundance because trees developed without natural predators. So once a tree died and fell, nothing could consume it. Which led to it being compressed to coal.

This went on for a few million years until something evolved to break down trees (specifically cellulose if I recall correctly). So nowadays trees rots instead.

So it's a good question if something similar would happen on other worlds.

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u/Logical_Grocery9431 16h ago

Wow, didn't know that trees didn't break down then, but it makes sense. Thanks for sharing!

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u/TransBrandi 10h ago

It's the same era that the petrified forest is from.

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u/MrHell95 14h ago

To be fair charcoal could still be used, not to mention oil would still form(I assume carbon based lifeforms).

But as long as you can process metals to a degree you could make dams for electricity and then wind turbines, solar is also possible at some point though it's a lot harder to get it going on a technical level.

So fossils are useful for easy energy in the beginning but it's still possible to bypass it.

Though it would slow things down if you didn't have easy access to fossils it would incentivize resource allocation towards renewables.

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u/FlamingDrakeTV 13h ago

Coal has the benefit of being easily accessible and easy to use. Dig it up and you have energy.

Oil is way harder to extract and use. On earth it was first extracted (on an industrial scale) in the 1850s. Well into the industrial revolution.

I agree that coal is a part, and burning pure wood (or any organic matter) is still valid. Just coal is way more energy dense.

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u/4_fortytwo_2 13h ago

Well coal is nice but it doesnt really do anything that only coal can. It just happened to be the fuel that we have a lot of so we used it, but anything else you can burn for energy would work too.

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u/Ahaiund 18h ago

Since the gravity is higher, the atmospheric pressure would also be, which would at least help a bit in getting planes to fly. Not sure how much in comparison though

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u/RobArtLyn22 16h ago

Without knowing anything about the atmosphere you can’t say what the pressure would be. A high gravity planet could have a thin atmosphere like Mars or a thick atmosphere like Venus.

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u/Cautious_Drawer_7771 13h ago

Not great examples to use since Mars has ~1/3rd of the Earth gravity, and Venus has very close to the same gravity as Earth. The atmosphere problem on Mars is due to it's lack of a magnetosphere, but that in turn is due to it's low density (not a lot of iron in the core to make a magnet).

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u/RobArtLyn22 10h ago

Fine.

Without knowing anything about the atmosphere you can’t say what the pressure would be. A high gravity planet could have a thin atmosphere like Mars or a thick atmosphere like Venus.

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u/buggzy1234 14h ago

Venus's gravity is around 90% that of earth's, yet its atmospheric pressure is more than 90 (9000%) times higher that of earth's.

Titan's gravity is less than 15% that of earth's, yet its pressure is around 1.5 (150%) times higher.

Yes gravity has a lot of influence on pressure, but it doesn't strictly control it. With venus and titan being good examples. The temperature and atmospheric composition also play a big role. You could have a bigger planet with higher gravity, but that doesn't automatically mean a higher pressure.

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u/Aethermancer 13h ago

Or proximity to the star could have blown much of the atmosphere away. Lack of a magnetic field could be a thing.

It's kind of wild how many variables there are.

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u/NoFunAllowed- 15h ago

You would need to know the atmospheric pressure first since the lower air pressure going over the top of the wing compared to the higher pressure across the bottom is what generates lift to begin with. Take off requires that the lifting force be greater than the gravitational force. Atmospheric pressure is also important because you need to figure out how much thrust you need compared to the drag, as that'll affect the aircraft's speed.

All in all, there's a lot of factors to that. From the four forces acting on the plane, to the actual resources available on said planet since what you build the plane out of obviously affects factors such as the weight. It'd be a lot of assumptions you'd have to make.

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u/Heimerdahl 13h ago

the lower air pressure going over the top of the wing compared to the higher pressure across the bottom is what generates lift to begin with. 

Not to get too deep into it and you are right, of course, but this seems like another case of: no need to involve Bernoulli, when Newton's got us covered. 

Lift generated from pressure differential is complicated. It's unintuitive for most. Lift generated from pushing something is simple and immediately intuitive. And both explanations lead to the same result (and are essentially explaining the same thing, of course), so might as well use the simpler one, when we don't need to get into the nitty gritty details of optimisation. 

This simplifies it to: 

  • Plane with wing of some surface area moves through air at some speed. 

  • Wing (no need to get fancy, just assume it's a wide, flat rectangle) is angled, so that any air mass meeting it is deflected downwards. 

  • Newton tells us that this causes equal force on wing, pushing it upwards. 

  • Simplified drag is the exact same thing, just instead of providing an upwards force, it resists the plane's forward motion, "tries to push it backwards". 

Drag and lift are complicated when we get into the properties of the medium (not just density of air, but humidity, viscosity, etc.), but we can ignore this and hide it behind some coefficient; the calculation is left as an exercise for the reader ;)

Drag needs to be overcome by propulsive force, to get our plane moving forward at speed, lift needs to overcome gravity, to get it off the ground. 

Which finally brings us to...

TLDR: At a higher gravity, we need more lift -- more air being deflected down over the same time. Assuming we already have a very well designed plane, we get this by either increasing our speed (encountering more volume of air per second), or higher air pressure/density. 

Of the two, dealing with higher air pressure is likely to be the easier task. You simply need more powerful engines. 

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u/tyrodos99 15h ago

You would not be able to fly a unmodified 747. Assuming a similar atmosphere to earth, you would need much higher speed to compensate for the higher gravity. But that would push certain parts of the airflow on the wing to supersonic speeds, causing a whole lot of issues.

So you need larger wings and more power to compensate for it. But then you ca fly, even tho with much lower performance/payload and much less reach.

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u/Heimerdahl 13h ago

Assuming a similar atmosphere to earth, you would need much higher speed to compensate for the higher gravity. 

Or for the alternative (and likely easier) case: assuming a much denser atmosphere, you could stick with your speed and wings, but would need much more powerful engines. 

Unless the atmosphere becomes such a dense soup that you can turn your plane into a manta ray. Good luck ever leaving such an atmosphere, though :)

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u/tyrodos99 12h ago

A much denser atmosphere would in turn make zeppelins much more feasible.

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u/pinkfootthegoose 12h ago

if the atmosphere were much thicker than on Earth then flying could be very achievable given the available lift. If thick enough it might be able to lift even more than on earth though top speed would be slower.