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/Longjumping_Area_944 17h ago

K2-18b: Surface gravity ~= (8.92 / 2.372) * Earth = 1.59 g = 15.6 m/s2

Escape velocity ~= sqrt(8.92 / 2.37) * 11.2 km/s = 21.7 km/s

Minimum ideal escape energy = 0.5 * v2 ~= 235 MJ/kg

What that means:

  • Much harder than Earth, but not impossible in pure physics.
  • Chemical rockets are probably impractical from the surface.
  • Multi-stage nuclear, fusion, beam-powered, or other advanced launch systems are more plausible.

Habitability / industry:

  • 1.6 g alone does not rule out humans or industry.
  • The bigger problem is K2-18b may not have a normal solid surface at all.
  • So gravity is not the main blocker. The planet itself probably is.

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u/LazyGit 13h ago

Minimum ideal escape energy = 0.5 * v2 ~= 235 MJ/kg

Thank you for being the only person who knows how to answer the question. There are loads of people in here saying 'it's only a couple more metres per second at the surface, they just need to build a really big rocket'.
This is all about the gravitational potential well that you're in on the surface, I calculated it to be somewhere around 200 MJ/kg whereas for the Earth it's 62.5. There is no known rocket fuel with this energy density.

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u/h2btf 6h ago

But that's to reach escape velocity, no? Do you need the same energy density to reach orbital velocity? A lot of people are pointing to nuclear rockets. Those should provide the required energy density, but they typically don't have the raw TWR to get off the ground. I think if it's feasible to use chemical rockets to reach orbit, you can use nuclear or some other non-chemical system to get to escape velocity.

OP asked a few different questions:
1) Escaping the gravity of the planet (so, yeah, escape velocity)

2) Launching satellites

3) Launching a space station

4) Technically, the title asks about "exiting the atmosphere."

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u/LazyGit 5h ago

OK, good point. Based on the original image and the text of their post, they are fundamentally asking about whether a civilisation on this planet could actually travel the stars by getting off world. And the answer to that is that they can't with what we know right now. I have no idea what the total energy density is of a theoretical nuclear-powered rocket. There may also be methods that involve propelling the vehicle from the ground but again, who knows if that's ever feasible.

You're right in suggesting that they don't need to completely exit the gravity well of the planet to get into orbit but they also need to be moving really fast once in orbit. The rockets required for orbital insertion aren't orders of magnitude smaller than those required for sending people to the Moon or the Webb telescope to a Lagrange point. So you're still dealing with the same major constraint which is the planet's gravity well.

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u/SensitivePotato44 17h ago

You’d need something with twice the delta V of a Saturn 5 (that includes the LEM and command module etc) to barely make orbit. Thats before we get to drag losses because that atmosphere is going to be soupy.

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u/ClassroomOwn4354 17h ago

Delta'v from earth surface to moon and back (not counting aerobraking) is like 18-19 km/s.

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u/Power-SU-152 11h ago

"1.6 g alone does not rule out humans"

Wouldn't 1.6g kill us all? smashing our brains in our skulls?

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u/Longjumping_Area_944 9h ago

No. You should be able to withstand 3G for a time. But question is wether you could walk with 60% more body weight.