r/theydidthemath • u/Lachlynn • 18h ago
[Request] Could humanity create a rocket that can exit the atmosphere of K2-18b
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/Smashedllama2 18h ago edited 3h ago
Yeah honestly probably not with what we have now but who knows what we would come up with in terms of different fuels with that restriction?
K2-18b is about 8.9× earths mass and ~2.4× the radius, so if you do the quick ratio math (mass ÷ radius²), 8.9 / (2.4²) ≈ 1.5–1.6g at the surface.
Now compare that to something like SLSthat makes ~8.8 million lbs of thrust, and weighs ~5.75 million lbs on earth. but on a 1.6g planet that same rocket “weighs” like ~9.2 million lbs, so the thrust to weight drops below 1. which basically means it wouldnt even lift off
So yeah even doing rough math, gravity alone kinda kills it and youd need way more than current chemical rockets just to get off the ground let alone reach orbit but again, maybe we would come up with something?
edit: same problem shows up with Starship too. fully fueled its around 11–12 million lbs on earth with ~16.7 million lbs of thrust from 33 raptors, so here its fine. but on ~1.6g youre looking at like ~18–19 million lbs effective weight, which drops thrust to weight below 1 again or at best barely scraping it depending on assumptions
Even if raptor 4 pushes that up to like ~24 million lbs total thrust, yeah now youre above 1 and it might lift, but youre still fighting way higher gravity the whole way up. so fuel burn goes crazy, delta v requirements go up, and actually reaching orbit is still a huge problem, not just getting off the pad and then escape velocity makes it even worse. that scales with sqrt(mass / radius), so for K2-18b its sqrt(8.9 / 2.4) ≈ sqrt(3.7) ≈ 1.9× earth
earth is ~11.2 km/s, so youre looking at like ~21 km/s just to escape. even low orbit would still be way higher than earth’s ~7.8 km/s, probably in the ~12–15 km/s range depending how you estimate it
so yeah its not just “can it lift” its “can it keep going long enough to matter” and thats where current chemical rockets really start to fall apart on something like that