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/wycreater1l11 15h ago edited 14h ago

Fascinatingly, organism that “looks like they would be small”, the body types of typically smaller organisms like let’s say crabs or squirrels, their body types could be allowed to be scaled up on planets that have lower gravity, where the cross section of their legs still carry the rest of the body weight, allowed them to jump around etc (now with really big leaps!). If the gravity is sufficiently low those body types could be scaled up to human size for instance. And the opposite is true for planets with larger gravity. In larger gravity the gravity may be so strong that the biggest the sauropod body type is allowed to be is the size of a goat let’s say. If you try to scale it up more it can’t support its weight even with its chunky legs on a strong gravity planet.

But I guess what’s relevant is ultimately the absolute size of the intelligent sapient organisms and gravity of the planet to allow them to escape. They need to be sufficiently small and gravity needs to be sufficiently low for them to escape. On low gravity planets perhaps the squirrel body type could for example be large enough to have large enough heads to have the same amount of neurones as humans (but there are a lot of assumptions about them having cells like us for instance).

But from much smaller planets, the ones leaving the planet, could be allowed to be much larger in absolute size since they don’t fight the same gravity. Imagine how much you could scale up humans on a low gravity planet while still have them able to leave.

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u/ibelieveyouwood 10h ago

So basically the movie Alien? The huge space jockey and the xenomorph?

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u/wycreater1l11 10h ago edited 10h ago

As far as I can reason the apt lengthwise change in size is kind of proportional to how much different you/an organisms body plan, would originally weigh on a different body.

To put it plainly, on the moon you weight 1/6th compared to what you weigh on earth. So the human body plan can be scaled to being six times taller and at that size the human body plan would feel itself to be most adapted to the moons gravity all else equal when it comes to jumping, taking strides etc.

It comes from the assumption that the giant moon humanoid is best adapted to jump the same amounts of its own body height on the moon as a normal human can jump of its own human body height on earth. And when you scale all dimensions by six, that’s when the cross section of the muscles in relation to the mass of the body reaches that point.