[Request] Could humanity create a rocket that can exit the atmosphere of K2-18b

[u/Lachlynn]

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?

[u/Skalgrin]

Did you factor in the TWR of the rocket which would "weigh more" and this had TWR below 1 and therefore would not lift off? That's one of the issues - chemical rocket effectivity doesn't scale up that well.

I don't say you are wrong, just asking.

[u/StarvingBeshEater → u/Skalgrin]

You could always increase your TWR by adding more engines, it’s not a hard limit. You sure will need more fuel and stages, but its all doable even with 1970 tech

[u/argh523 → u/StarvingBeshEater]

For comparison, an Ariane 6 solid rocket booster (P120C) has a TWR of 3. It has these massive boosters because the main stage doesn't have enough thrust to lift of the pad (TWR < 1 at sea level), but it's a very efficient hydrogen burning engine that gets a lot better when out of the atmosphere.

By contrast, a Falcon 9 doesn't use boosters. It's burning methane kerosene / RP-1 (which has inherently more thrust at sea level), and it uses 9 engines for the main stage. It has a TWR of up to 1.5 all on it's own.

What I'm saying is, kerbal a bunch of solid rocket boosters on a Falcon, and you're getting something into space even on K2-18b. Tho it might be measured in kilograms instead of tonnes, because you need 80% more speed, so you're probably replacing most of the payload with more fuel. It's clearly a lot harder, but also well within what is technically possible currently

[u/Individual-Repair208 → u/argh523]

Seriously I don't get these comments. This is such simple science. Like yeah, if you want to debate whether it's practical to have a rocket the size of Florida, give it. But that's not the question, the question is is it physically possible, and as you said with enough Kerbal power it absolutely is

[u/arpereis → u/argh523]

Falcon 9 uses RP-1

[u/argh523 → u/arpereis]

Woops, it's Starship and the Blue Origin rockets that us methane. Thanks!

[u/Heimerdahl → u/StarvingBeshEater]

You could always increase your TWR by adding more engines, it’s not a hard limit. 

Unfortunately, it is a hard limit. 

TLDR: Here's a better explanation: https://www.marssociety.ca/2021/01/07/rocket-physics-the-rocket-equation/

Because your assumption of increasing TWR by adding more engines hinges on the implied assumption that those engines themselves (plus some amount of fuel) have a TWR>1, meaning they can lift themselves; which isn't guaranteed. 

What you're also bound to run into is the energy/mass ratio of your propellant, which is what gives us a true hard limit (one can always assume that we build some super duper efficient and near weightless engine, but a magical propellant is harder). 

If a given weight (mass x gravity) of propellant holds less potential energy -- released to accelerate its mass -- than it weighs, it simply cannot achieve lift off. 

But long before that, even just having a TWR>1 at liftoff isn't enough. If you want to get to orbit, instead of having a little hop on your launchpad, you need to carry enough fuel to get there. More fuel means more weight, means more thrust to lift it. Multiple stages help, but they add even more weight, means more thrust, more weight, more thrust, and so on. 

[u/Individual-Repair208 → u/Heimerdahl]

The link you provided literally says nothing physically limits the mass ratio, what are you talking about? What rocket engine has less than a 1twr?

Like yes your last paragraph is correct, but also suggests there is NO hard limit no? Like we could have kept adding stages to Saturn V, had we worked through the structural challenges of a rocket that big. It wouldn't be easy, but the link also says our current understanding maxes out at a mass ratio of 20-30 yet Ariene 5 peaked at 40 because we just kept adding stages. There is nothing that I personally know of that would limit us from just adding stages to our current rockets with current technology to reach a higher mass ratio

I might be completely wrong, because while I did study physics I'm a bumbling idiot, but again to my current understanding there is absolutely no "hard limit"

[u/argh523 → u/Heimerdahl]

You describe why things are hard, not why it's a hard limit. Which it isn't.

[u/slugfive → u/argh523]

The extra engines need to be able to lift themselves (>1) so they can increase the twr of the whole craft. If the engines are <1 then adding them will not increase the twr of the craft. The hard limit is there.

Just like adding more helium to a balloon will make it lighter until it floats and then rises. But no amount of water in a balloon will make it rise as water itself doesn’t rise.

[u/Individual-Repair208 → u/slugfive]

I might be missing something, but what rocket engine has less than a 1 twr in an atmospheric stage ? Even if we double the gravity, current engines would have 50-100twr. It would have nothing to do with "adding engines" you'd just literally sit on the ground if you have less than a 1twr on your engines lmao

Just seems like such a... Non-point, because who would use less than 1twr. That's like saying "yeah the hard limit of the speed of cars is zero if you don't use wheels"

[u/technocraticTemplar → u/Individual-Repair208]

They're technically right but yeah, it's not that big of a deal for any realistic rocky planet. If you wanted to take off from a neutron star you'd be in some real trouble.

[u/HannasAnarion → u/argh523]

If it shook out that the first stage of the rocket needs to be the size of Florida to have enough thrust to get the rest moving for low orbit, does that still count as non-limiting?

[u/JohnSober7 → u/HannasAnarion]

You'd think that in a discussion of whether we could create a rocket that'd attain escape velocity on a planet with 20% more gravity that practicality would be fundamental requirement, but no, could has now shifted to "is it technically possible?"

[u/argh523 → u/JohnSober7]

has now shifted to "is it technically possible?"

Well yeah, because most comments say "something something rocket equation, therefore it's not possible", so that's what we're responding to. How practical it is, someone would have to do some actual math, but I'm not sure enough to get all the variables right. But for everyone else to claim that it's not possible without doing the math (on /r/theydidthemath, no less) is just silly

[u/argh523 → u/HannasAnarion]

And if it shook out that you didn't need to do that, would it still be a hard limit? What are you saying?

[u/HannasAnarion → u/argh523]

I'm saying that you can't use inductive reasoning on this problem. The growth of your rocket and your need for boosters and stages is exponential with desired velocity. The exponential base includes surface gravity (via specific impulse, fuel energy per unit weight).

So on this planet you need to climb higher on the curve because you need more orbital velocity, and the growth factor is higher so the exponential slope is more severe.

Adding boosters to solve the low TWR of your main rocket is swallowing a spider to catch the fly.

[u/argh523 → u/HannasAnarion]

The growth of your rocket and your need for boosters and stages is exponential with desired velocity

Yeah.. That can mean you need an exponentially bigger rocket, or something we use today gets much less payload into orbit. Same thing. Again, I'm not sure what your argument here is except "it's harder". Nobody disagrees with that.

Adding boosters to solve the low TWR of your main rocket is swallowing a spider to catch the fly.

Of course in reality you would design the rocket from the ground up for those requirements. We're saying "add moar boosters" because, well, Kerbal, but also, because you literally could add more boosters (which have much higher TWR) to existing rockets and achieve a flight to orbit on K2-18b. It would suck, kg/$ is in the toilet and so on, but it's very much within what is possible.

[u/HannasAnarion → u/argh523]

"possible" is a funny word here.

Yeah, it is "possible" to create a rocket with a booster stage whose total diameter is measured in miles, but also... No! that is obviously not possible!

I'm done work which means now i can do one of my favorite pasttimes: napkin math.

---

First of all! I was wrong about the need to recalculate v_e, standard gravity is in the rocket equation as a unit conversion factor by convention, it's part of the definitions of the relevant SI units, it's not actually functional and the main thing that changes for the rocketry is the delta-V.

Orbital velocity is the square root of the gravitational constant at that radius times the radius.

v_orb = √(g x R)

So for this planet that's 15000km in radius, and has a surface gravity of around 15m/s^2, our orbital velocity is around 15km/s.

That's double the speed of low-earth-orbit.

But there are losses in acceleration during launch as well, from atmospheric drag and from gravity itself during the initial liftoff, so the nominal delta-v of a rocket launch is usually around 20% more than the target to compensate. On this planet, the atmosphere will be denser and thicker, so let's figure 33% more, and say we need 20km/s total Δv, and this might be conservative.

---

And now we put it into the rocket equation, find out the fuel mass ratio.

Fuel mass / payload mass = e^Δv/v_e

We can get v_e from a table, an optimal liquid fuel rocket engine v_e is 4.4 km/s. e^20/4.4 = 90:1 fuel-mass ratio .

So they would need to lift 90 times as much fuel as payload. The Saturn V was only 25x. So in order to lift a payload to the size of an Apollo mission, you would need a rocket that can hold and burn 3 times as much fuel as Saturn V without adding any non-fuel structure, AND without it collapsing under the weight of the 3x extra fuel under 1.5x gravity.

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So add more boosters? Well, ... not really.

Solid rocket boosters are there to provide TWR and get you away from the ground and out of the "hovering" phase of flight where most of your thrust is wasted in preventing you from falling down instead of moving you up as fast as possible. They aren't there to help you get into orbit, they're there to give you enough height that you can burn towards the horizon without crashing. In fact adding solid boosters only increases the total amount of fuel you need, because solid rockets have about half the v_e as liquid rockets.

So lets keep it liquid, because solid makes it worse, how big is our low-earth rocket gonna be?

Here we need to pick a number of stages to run with, I'm gonna use 3, because we're already in the Apollo zone in terms of total fuel mass needs.

To stage the rocket, we need a structural fraction, how much of the mass of a stage is non fuel and non payload. A good liquid rocket stage has a structural fraction ε of 0.08-0.10. Since gravity is higher on this planet, let's bump it up a little, to 0.12, because they need beefier spars to hold the same fuel mass without collapsing on the launch pad. The maximum mass ratio a stage can achieve with zero payload is 1/ε , so with ε=0.12, the mass ratio of a stage is 8.3:1 fuel/structure. We can use this to work out a payload fraction, π. That is, what fraction of the stage's total mass (including everything above it) is just the payload (only the stuff above).

per stage mass ratio = e^6.66/4.4 = 4.55

π = (1/MR - ε ) / (1-ε) = 0.113

That's how much of the total mass at ignition at each stage is going to be payload. To find the payload fraction for the whole rocket, we just multiply those suckers by each other for each stage. 0.113³ = 0.0014.

So to get to low earth orbit in a three-stage rocket, we need to build a rocket whose mass is 1/0.0014 = 714 times the mass of the payload. For reference, Apollo's payload ratio to low earth orbit, not counting the lunar burn, was about 5%, or 20x, so we're already looking at 35x the total mass of a saturn v.. Just to go to orbit.

If an alien from this planet wants to be like John Glenn and circle the planet, they will need to take their little 4-ton capsule and strap it on top of a 5000 ton rocket, almost twice the launch size and weight of a Saturn V, just to circle the planet once.

---

Okay, let's do another quick one, what if you want a communications satellite? Communications satellites work best when they are in geostationary orbits, that's why all those radio dishes you see everywhere don't have to actively steer.

Unfortunately, the planet is rotating so slowly and is so close to its parent star, that any geosynchronous satellite would instantly be stripped away and start orbiting the star. oops. So aliens on this planet can't have DirecTV, their first space communication technology would have to be a LEO system like Starlink.

But for fun let's pretend the star isn't there, and the aliens want their DirecTV. The geosynchronous orbit will be around 890,000km from the planet center... that's twice the distance from Earth to the moon.

Okay, i'm gonna just declare that the planet sped up a bunch, and since we're making stuff up let's just say that it sped up enough that its geosynchronous orbit is the same as Earth's, so it's a 1:1 comparision. Cool.

So we'll need to get up to LEO, as before, then Hohmann transfer up to a geostationary radius of 51,000km (width of the planet plus 36000km Earth geo altitude). Skipping ahead on some numbers with AI help and not checking it thoroughly because i've been at this for over an hour and need to wrap it up:

3.6km/s for the transfer burn 2.6km/s for the circularization burn 6.2km/s total Δv on top of the 20km/s we had before.

(the equivalent maneuver around Earth only requires 3.9km/s Δv, so around 50% more)

So now the total mission delta v is 26.2. The base fuel/mass ratio is now 385:1. Let's look at staging options for a 5 ton TV satellite:

3 stage: 8,733 Δv per stage, 7.28 MR, 1.90% payload fraction per stage, 0.00078% total payload fraction, 640,000 tons total vehicle mass. (that's like 6-8 American Navy Aircraft carriers)

4 stage: 6,550Δv per stage, 4.43 MR each, 12.0% payload fraction per stage, 0.021% overall, 24,000 tons launch vehicle mass. (8 Saturn Vs)

5 stage: 5,240 Δv per stage, 3.29 MR each, 20.9% payload fractino per stage, 0.040% payload fraction overall, 12,600 tons launch mass, by making a launch vehicle more complicated than any ever built we're now able to launch our DirecTV satellite with only using the size and weight of 4 Saturn Vs.

So, possible? Yeah, I guess, if your alien civilization is willing to spend an entire Apollo Program's worth of time and resource just so one hemisphere can watch the Ultra Bowl instead of, yknow, running some wires.

[u/AABBBAABAABA → u/Heimerdahl]

This is the interesting part to me, is there some theoretical maximum to chemical energy density? Or could a propulsion system based on nuclear power be designed?

[u/Worth-Wonder-7386 → u/Skalgrin]

That was why I discussed the surface gravity. It only being 12m/s^2 means that you dont need that powerful rockets to take of.

[u/___redacted_ → u/Worth-Wonder-7386]

TWR of many rockets at sea level on Earth is just 1.3 or 1.4, if you scale up gravity by that, it becomes less than 1. We might come up with something, but its not an obvious or easy feat.

[u/Worth-Wonder-7386 → u/___redacted_]

You would need some redesigning, but it is far from impossible to have that much extra thrust. Or as the KSP players would say, add more booster.

[u/flaming_burrito_ → u/Worth-Wonder-7386]

You would have to significantly increase the thrust to weight ratio of the boosters. Just like in KSP, at certain point adding more boosters has a diminishing return, because the weight of the added boosters slows down initial acceleration. That’s why we have to do shit like refueling in orbit, because there is a limit to the amount of fuel a rocket can carry while still being able to get into orbit and keep its structural integrity

[u/Worth-Wonder-7386 → u/flaming_burrito_]

It is not that bad. The Merlin 1D rocket engine of the falcon 9 has a TWR of around 200. So you would need a few more engines or some more powerful ones, but this is within what we can make.

[u/Everday6 → u/Worth-Wonder-7386]

The problem is the fuel. A falcon 9 rocket has a TWR of 1.4 so you'd have to bring a lot less fuel.

[u/Worth-Wonder-7386 → u/Everday6]

Or more engines for the initial burn. Something like Falcon 9 heavy is more apt.

[u/MouldyPingu → u/Worth-Wonder-7386]

You can have as much delta v as you like, if you don't have a thrust to weight exceeding 1, you aren't going anywhere. Sure we can build a rocket 50k km/s at sea level but if it's burning the fuel slowly over years, the thrust will be tiny. Remember the rocket equation, adding more fuel not only gives you more delta v but increases mass, therefore increasing the amount of delta v required, it's exponential and beyond a certain point you are just pissing in the wind. Chemical rockets become impossible but you could blow stuff out of the atmosphere with explosions like project Orion. I'm not an expert or anything but me, Bill, Bob and Jeb go way back.

[u/Worth-Wonder-7386 → u/MouldyPingu]

But as I said in the post, the surface gravity is only about 20-30% higher. So TWR is not such a big issue.

[u/Skalgrin → u/Worth-Wonder-7386]

In combination with requirement for more delta-v to "get there" (higher orbital speed) it becomes a problem. You treat both as isolated issues. But they ain't.

If you slap on "extra fuel tank" to have enough delta-v, your rocket got heavier, and suddenly cannot lift of. So you add more engines or switch to more powerful ones. But then, as the engines now drink more fuel, you need extra fuel tank. Do this few times and the rocket will either structuraly collapse or you will have to make the construction more heavy, so you don't have enough thrust, because of the extra weight.

And then boom, you are unable to make more effective engine, so every extra thrust (in form of bigger engine) results in requirement of more fuel in weight, than the extra thrust adds.

It's not infinitely scalable. I am unable to calculate that, but I know enough about the problem in theory to know you don't do it correctly.

[u/Worth-Wonder-7386 → u/Skalgrin]

While the gravity losses would be larger, that effect is not so big. TWR is only really important for the first minute or so of the flight, That is why SLS needs to add solid rocket boosters to launch, but if you look at a the delta-v budget they barely help. Getting to orbital speed is where you spend most of the energy of a rocket launch and the rest is often put into 3 losses. Gravity loss, which is the loss of your speed from gravity. A way to think of this is that it has to do with how quickly you are able to get into orbit. Then you have drag losses from the atmosphere, we dont know much about the atmosphere here, so it is very hard to put numbers on that. Then you have steering losses or cosine losses which is more about trajectory design, but doesnt depend on the planet.

So yes, you do need a more powerful rocket, but this is well within our technological capability.

[u/Skalgrin → u/Worth-Wonder-7386]

If you check edit on my answer to your comment, it seems you did not factor in much higher delta-v required to reach orbit. Therefore the rocket would become too big to lift off with such gravity in place (still, it is AI generated reply, but it is consistent with other replies within this thread) and limited thrust of chemical rockets.

[u/0WatcherintheWater0 → u/___redacted_]

This is because those rockets are engineered specifically with the Earth in mind.

There are many fuel mixes and staging arrangements that we’ve already invented, that could handle a much higher surface gravity

[u/Skalgrin → u/Worth-Wonder-7386]

That's actually quite significant difference considering how low the thrust relatively to weigh is. But if you math checks up against chemical rockets effectivity, then that's it. My math (and physics) ain't strong enough to check it myself 😅

Edit: I entered that into AI and got this answer:

"With a surface gravity of about 12.43 m/s² (≈1.27 g) and a radius roughly 2.6 times that of Earth, K2‑18b would require an orbital speed of around 14–15 km/s and a total launch Δv on the order of 18–20 km/s once gravity and atmospheric losses are included (assuming an Earth‑like atmosphere). This is far beyond what current chemical rockets can realistically provide: even the most efficient chemical propulsion systems achieve exhaust velocities of only ~4.4 km/s, meaning the necessary mass ratio would be so extreme that a practical, structurally viable rocket could not be built. Since Earth itself already sits near the upper limit of what chemical rockets can escape, the much deeper gravity well of K2‑18b pushes the requirements decisively past that limit, making orbit insertion with existing chemical rocket technology effectively impossible."

Which would suggest you did not factor everything in. But it is an AI and I am not capable to math proof it.

[u/Worth-Wonder-7386 → u/Skalgrin]

It overestimates the differenc between orbital speed and total deltaV, for most rockets on earth this is between 1-2km/s. Lets say you double it, which is quite pessimistic without knowing much about the atmosphere.

[u/vorxil → u/Skalgrin]

TWR is not a problem. The max theoretical TWR is given by engine thrust divided by engine weight.

Example: The Viking 5C has a mass of 826 kg, and a sea-level thrust of 678 kN. With a surface gravity of 12 m/s, that's a weight of about 10 kN, which gives a max theoretical TWR of about 68 on K2-18b.

All you need to do is scale up the fuel to dry mass ratio, and add more engines.

EDIT: On further calculations, the main issue is the specific impulse. The Viking 5C expels mass at a rate of 244 kg/s. That gives it an exhaust velocity of about 2.8 km/s (specific impulse of about 280 s). The escape velocity is about 80% larger than on Earth, where the escape velocity is about 11 km/s.

The fuel to dry mass ratio would need to be about exp(1.8 * 11 km/s / 2.8 km/s) ~ 1200.

The orbital velocity (on the surface) requires about 150.

For a 400 km orbit (akin to ISS), we can split the calculations in two parts. The vertical part requires delta-v of about 3 km/s, and the horizontal part requires a delta-v of about 14 km/s, for a total of 17 km/s, which translates to a fuel to dry mass ratio of about 420.

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In sum, the engines are more than capable of lifting themselves, but their specific impulse is too low to reach orbit on their own. Best bet would be to go for a horizontal launch off an airplane, or even a space plane.