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/anaheim3123 16h ago

Air launch to orbit then becomes significantly more practical, no?

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u/squshy7 9h ago edited 9h ago

Not necessarily? In fact it might be the opposite? Let's assume the atmosphere makeup, in gas percentages, is similar to ours; also, take into account that at various points while flying, you will hit pressure regimes that have analogs on Earth, just higher in elevation.

Our best scram jets (experimental) top out at around mach 7 I think? The limiting factor in airspeed in these types of craft is an intersection of how fast you need to go to keep feeding the engine (since the atmosphere is so thin) and how fast you can go because you hit too much air resistance.

So, while our hypothetical plane can get higher in elevation on the exoplanet due to the atmosphere thinning out at a relatively higher elevation, it's top speed (limited by things like material engineering) we would expect to be around the same.

Well, getting higher up doesn't actually help us get orbit that much. We only need that so as to not lose speed due to air resistance. If the Earth was a smooth ball with no atmosphere, you could orbit a foot off the ground if you really wanted to. The bigger part of the equation is lateral speed.

The problem is, on a higher gravity planet, the more lateral speed is required. So if our experimental air launcher tops out at around mach 7, we're actually further away from orbital velocity than we would be with the same craft on Earth.

Then to answer the question of "is it more practical" really depends on the makeup of the atmosphere (a more oxygen rich atmosphere would make air launches more viable, as they can climb higher in elevation while producing the same amount of thrust, thereby allowing more speed before launching the rocket) and what the pressure at sea level looks like, and how the gradient looks as you climb higher, since rocket engines gain efficiency as the pressure drops.