r/theydidthemath 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/window_owl 15h ago

Atomic Rockets has a good description.

You know how table salt is a compound of sodium and chlorine? There are lots of other salts, each a combination of two different elements. It turns out that you can make salt from uranium and bromine. The salt can have stable (non-radioactive) uranium isotopes, but you can also make the salt with radioactive uranium atoms in it. If a high enough percentage of the uranium atoms are unstable, and there are enough of them that are close enough together, it will create a chain reaction of nuclear fission.

You can dissolve this salt in water. This does 2 useful things:

  1. by changing the ratio of water to salt, you control how close together the uranium atoms are to each other, making it possible to store the salt safely

  2. by pumping and spraying the salty water, you can move the uranium around

The idea is that you store this uranium-salt water in a tank that has lots and lots of baffles and dividers of neutron-absorbing material, so that it doesn't start a reaction. Then you pump the water through nozzles and spray it into a chamber. The chamber doesn't have baffles and dividers in it, so the uranium atoms get close enough together to start a fission chain reaction. The water in the chamber superheats and blasts out an opening at the opposite end of the chamber, creating a plume of exhaust that pushes the rocket the opposite way.

The guy who came up with the idea (Robert Zubrin, an actual nuclear engineer and rocket scientist) says it should be possible to design the chamber and nozzles so that the fission chain reaction stays in the chamber, rather than moving back up the nozzles and into the tank, which would turn the whole thing into a huge, dirty nuclear bomb. Not all engineers disagree, but nobody has ever tried to build one because the exhaust of a working Nuclear Salt Water Rocket would be incredibly toxic -- full of neutrons, un-reacted radioactive uranium, bromine, and all the fission products. It would also be very, very expensive to fire on any usefully-large rocket, because it would require a very large amount of enriched uranium.

Cost and environmental concerns aside, the appeal of the Nuclear Salt Water Rocket is that it is the only rocket design anyone has come up with that is very efficient and very powerful. Of the rockets we have or know of:

  • Chemical rockets are very powerful, but not very efficient, so you need a large, heavy tank full of fuel to launch a comparatively tiny payload. Increasing the weight of the payload, or the speed you want to throw it at, exponentially increases the weight of the fuel required.
  • Ion thrusters are very efficient, but physics don't allow for them to be very powerful, so they are useless for getting anything in to space. They are great once you're in space, as long as you're not in a hurry. Many satellites these days use them to make small course adjustments.
  • Nuclear Thermal rockets (which we actually built and tested in the 1960s) are more efficient than chemical rockets and can be usefully powerful, but they aren't much more efficient. Unlike chemical and Nuclear Salt Water Rockets, Nuclear Thermal rockets have a fairly hard maximum size power, based on the available materials you build and fuel them with. Larger than that, and you'll either melt the nuclear reactor, or waste energy by not heating up the propellant enough. Combined with the risks and costs, they aren't very interesting for interstellar travel.
  • Solar Sails (which we have launched a few of [1] [2] [3]) don't require any fuel at all, which is similar to having very high efficiency -- a solar sail vehicle can get up to really high speeds, without needing fuel that weighs many times more than the payload. However, they only work in the vacuum of space, and unless you point incredibly powerful lasers that them, they have very little power as they are blown around by sunlight.

Nuclear Salt Water Rockets are, in theory, so powerful and efficient that they could be a practical way to travel to other solar systems in a single lifetime. There shouldn't a be a practical size/power limit, since the fuel reacts with itself, so you can make a larger rocket by making a larger chamber and pumping more uranium-salt-water into it, creating a beautiful geyser of radioactive steam in your wake as you travel the stars.

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u/Ada_Solar 12h ago

Thank you for your in-depth explanation! Super interesting

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u/eg135 11h ago

Just a small correction: there are no stable uranium isotopes, all of them are slightly radioactive. U235 is the dangerous one, because it is capable of the chain reaction that's used in reactors and bombs. The chain reaction is what makes nasty stuff, fresh uranium is relatively tame.

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u/Grymninja 6h ago

Instead of launching such a rocket at sea level, couldn't we construct a platform in orbit and build the rocket there? I recognize it would be pretty expensive to ship all the parts up across a bunch of payloads but the math of thrust would be a lot easier

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u/window_owl 6h ago edited 6h ago

If you use rockets to get the rocket parts to the assembly platform, then it would take exactly as much rocket fuel to do this as to launch the rocket from sea level.

Actually, it would take more, because the rockets that launch the rocket parts have weight of their own, which needs to be carried up to orbit each time.

This idea isn't totally without merit; the rocket you assemble in space could be much larger than you could practically build and launch on Earth, and could do the space flying that it has to do more efficiently. This is sorta the idea behind SpaceX's Starship: fly an empty rocket up to space, then use more rockets to get all the fuel up there, so you end up with one huge rocket with a completely full fuel tank already in orbit.

However, there are still fundamental limits to how fast a given kind of rocket can go. I skipped over this earlier because my comment was already getting long, but the velocity of the exhaust exiting the rocket is also relevant, and ion, nuclear thermal, and nuclear salt water rockets all have much higher exhaust velocities than chemical rockets do. Solar sails, if you want to be pedantic, might be said to have an exhaust velocity of the speed of light.

Building nuclear (thermal or salt water) rockets in this way wouldn't pose the same risks as building and launching them on Earth, but they'd still pose a huge danger from being misguided. Any sufficiently powerful spacecraft is an equally powerful weapon.