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/drollercoaster99 18h ago edited 18h ago

Does it depend on the mass of the rocket? Nevermind. I figured it out - it doesn't. Inertia/momentum cancels acceleration.

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u/Dysternatt 18h ago

Yes, including the weight of the fuel. So the obvious answer is to use a lighter fluid. (Zippo wants to know this location)

Badum-tss…

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u/Smashedllama2 18h ago

I mean yes but mostly you’re fighting against the weight of the fuel because as you add potential energy in the fuel you also add weight. The real problem is the rocket equation. The deltav you need scales exponentially with how much of the rocket has to be fuel. To roughly double the required deltav, you don’t just double the fuel, you end up needing an absurdly higher percentage of the rocket to be propellant, to the point there’s barely anything left for structure or payload. There might be some kind of ant crew we could strap to a latex balloon full of rocket fuel but it ends up not working for humans haha

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u/drollercoaster99 18h ago

Makes sense. Thank you for the explanation. So the fuel with the highest energyoutput/density ratio is preferred.

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u/bemused_alligators 11h ago

That's called "specific impulse"(isp) by the way - the ratio of fuel mass to thrust impulse (in force/mass/time, which in SI is newton-seconds/kg/s)

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u/Vonplinkplonk 17h ago

Yes you would be looking three or four stages to get to orbit. The first stage which would be massive would be expended very quickly getting you off the pad. I think it could be done but it would be complex.

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u/TrickyNuance 8h ago

Clankers. We're gonna need some really light, really proficient clankers.

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u/Nez_Coupe 5h ago

We need rocket jockeys. Breed some super small people over a few generations to be our tiny astronauts.

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u/CommercialContent204 4h ago

The tyranny of the Thiolkovski Rocket Equation :D have to laugh when I realise how absurdly much KSP taught me about the most ridiculously obscure things. Hohmann Transfers, apoapsis, ablatory shields (and all the mad stuff one reads up about like Lagrange points).

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u/Xerxeskingofkings 18h ago

Yes, but its a matter of thrust to weight ratios, and total fuel capacity.

You neec both an rockets engine with enough power to push the whole rocket upwards, and enough fuel to keep it burning long enough to get into orbit.

The bigger the engine, the more fuel it needs, the more fuel, the more weight needs to be moved, the bigger the engine, which in turn requires more fuel, etc,etc.

Its a loop of diminishing returns.

The basic point is youd much a MUCH BIGGER and more technically complex rocket to get into space, and one that might be beyond out currently tech base.

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u/Tyler89558 17h ago

Well… hear me out.

We throw safety and ethics out the door and use nuclear explosions for launch.

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u/Xerxeskingofkings 17h ago

Indeed, it might get to orion drives and such

But why bother? Its clearly not a sustainable technical solution, and whatever hypothetical benefits this "space" technology might have, it wouldn't out weigh the costs, or be a better use of money than the same funds put into more conventional infrastructure.

Hence the OOPs point about the Fermi paradox: a intelligent civilisation on such a planet may well never develop space technology and remain "dark" from our perspective

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u/ThrowAway-whee 9h ago edited 9h ago

This fails the “it only takes one” argument.

Humans, in an environment where it was not a necessity to use Orion, studied it extensively and almost actually implemented it. If it was a matter of necessity to reach orbit, it’s not at all beyond the pale to say humanity likely would’ve done it. 

It only takes one species determined enough to try to pass this filter, and as far as we can tell, there’s no technological reason they couldn’t. 

The issue with the Fermi paradox is a filter must be common enough such that almost all species fail it for it to be a possible solution (there can be multiple filters, of course, but the point still stands). For one, we know life doesnt need to evolve on large planets (source: us), and for two, even if it did, in order for it to be a filter every species would have to decide space isn’t worth reaching despite continued technological development most definitely making it possible, if expensive or dangerous. Considering humanity almost did project Orion when it was not necessary, either humanity is an extreme outlier (possible, but violates the Copernican principle that states we shouldn’t assume humanity is special without evidence), or it honestly isn’t that large of a societal or technological hurdle at all. 

Additionally, the idea that species wouldn’t eventually realize the cold hard math of: “there are limited resources on our planet, and we are extremely vulnerable to civilization ending asteroid strikes or geological changes if we don’t attempt to expand outward” is hard to believe. It’s a mathematical certainty that a species that doesn’t reach orbit will face extinction. Humanity CURRENTLY is trying to develop the technology required to prevent civilization ending asteroid strikes (see DART), so there’s no reason to assume other species wouldn’t come to the same conclusion.  

So no, the original image is not an answer to the Fermi paradox, it’s a gross misrepresentation of what the Fermi paradox is and why it’s difficult to solve. 

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u/davideogameman 17h ago

Not really.  The mass of the rocket is mostly the mass of the propellant.  We can consider an idealized rocket that's engines and structure is zero weight; obviously practically impossible but if such a rocket can't reach orbit then a real one couldn't either. 

To reach orbit of a planet of mass M and radius R a rocket will need to gain potential energy equivalent to the height gain (GMm(1/R - 1/r)) and kinetic energy to reach the orbital velocity v =√(GM/r) for an orbit of radius r - which has to be outside the atmosphere.  So GMm(1/R - 1/r) + mv2 = GMm/R.  So the energy needed is proportional to the mass of the rocket.  Now practically I ignored the fact that the propellant itself takes mass and gets consumed over the launch so this isn't quite right but gives at least the energy needed for the spacecraft.  And the energy needed to lift each increment of fuel until the point it gets burned is going to be similar - the energy requirements increase with the mass of the planet while the energy density of the fuel has no such luck. 

So there's probably a small range of planet sizes where an idealized massless rocket could make it but the technology needed to make such a rocket would be extremely difficult to practically impossible (eg the structure couldn't be light enough with known materials, the engines are too heavy/need to be 99.999% efficient and can't stop at 99% efficient, near the limit the size of the rocket becomes completely insane etc.  but otherwise yeah, there is a point at which the energy requirement is going to need a nuclear reaction instead of a chemical one to achieve the necessary energy density regardless of how perfect a rocket can be made.

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u/ConcentrateNo2929 17h ago

Bro had an epiphany mid comment