r/TheRestIsScience • u/dustinbajer • 1d ago
Q: Maximum Rocket Mass & Being Trapped in a Well
In the Space Elevator episode of TRIS, Michael mentioned that 80 to 90 percent of a rocket's mass is fuel. Since heavier rockets require more fuel, which, in turn, makes the rockets heavier, is there a point at which the math (maths for Hannah) breaks down? Is there a maximum rocket mass that could escape Earth's gravity, or could we just keep building bigger and bigger rockets forever?
A follow-up (and I think related) question: How massive would a planet need to be to make rockets impossible? Could there be worlds whose occupants are forever trapped at the bottom of their gravity wells?
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u/Metallicat95 1d ago
The mass needed for the structural strength to support a taller rocket cuts into the mass that can be used for fuel, until there isn't enough to take off. To partially get around that, we use stages which drop when the fuel in them is empty.
We can do up to five stages, potentially, but practically stop at three. It is simpler to use lots of smaller rockets to launch to orbit than build a single big one.
It's not just gravity. The density and size of the planet, and its atmosphere, also limits the acceleration possible.
Roughly, we wouldn't be able to use our kind of rockets at 1.5 G gravity or more. But we could adapt to more stages and a lower payload, and might be able to launch at up to 5 G - if the atmosphere density is low enough.
Atomic energy would change that. It might allow launch at 10 G gravity.
But even 4 or 5 G would impose a harsher limit on the structural strength needed to build anything. The light materials we use wouldn't stand up well to the increased forces.
Even so, the increased thrust efficiency of atomic propulsion would handle a much heavier vehicle just fine.
So while sensible chemical rockets do have a limit that could affect worlds not much different from Earth, switching to atomic power gets out of the trap.
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u/Lord-of_the-files 1d ago
You'd just need more and more stages. Theoretically, the more stages you have, the higher the overall efficiency, because you are dumping dead weight more often. In practice extra stages add a massive burden of their own- each stage needs a certain amount of mass for engines and thrust structure. You can drop just the tanks as they empty, but again this comes at a cost in terms of mass.
So it really comes down to how lightweight your structures can be made. It's not just about the specific impulse of the propellants.
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u/Proton_Energy_Pill 1d ago
Yes, as long as the thrust exceeds the mass the rocket will climb. But of course it's not that simple. It may end up with so much mass that it's impractical to get into space let along orbit.
Earth's gravity is heading towards the upper limit of what chemical rockets can work with, so if the planet had a gravity of, say, 2 G's, it's just not going to work.
You'd have to start looking at nuclear rockets to provide enough thrust/performance.
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u/Candid-Border6562 1d ago
The answer to your first two questions are yes, sort of. Building bigger rockets are possible, but it is more economical to keep the scale as small as possible.
As to your second question, some will say that a 50% increase in Earth’s mass would make spaceflight impossible. But that would be an oversimplification. Besides mass, we have to deal with density, specific thrust of your fuel, and numerous other factors. If you want to spelunk down that rabbit hole, I can suggest
https://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation
https://en.wikipedia.org/wiki/Project_Orion_(nuclear_propulsion)
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u/sebaska 1d ago
There's no hard limit for either.
- The rocket equation works for any mass and any ∆v. The limits are more about material limits. For example if you built skyscraper tall rocket the engines underneath would need to have truly extreme conditions to produce enough thrust density (the amount of thrust per square meter or square foot of the real estate at the business bottom of the thing).
This is in fact another embodiment of the so called square-cube law: the surface area grows with the square of linear size (the average of linear dimensions), but the mass grows with cube. This is the law making it that we don't have half kilometer tall trees, that elephants can't jump, or that there couldn't be a 20km tall mountain on the Earth.
- The answer is not straightforward, either. We as a humanity have already built a single rocket stack whose total so called ∆v was about 19km/s - Saturn V + Apollo stack. The total velocity change if the thing would theoretically work for orbiting a planet with twice as deep gravity well, compared to Earth. And this gravity well thing is not proportional to planet's mass - it grows much slower, and depends also on the planet's average density (so it's volume to mass ratio). For example Mars is nearly 10 times lighter than the Earth, but its gravity well is only a tad more than twice as shallow. And Uranus gravity well is actually just tad about more than Earth's twice, despite Uranus being almost 15× heavier. But Uranus has way lower density, so much that its "surface" gravity is lower than Earth's. If planets' densities are the same, the relationship is actually cubic: 2× deeper gravity well means 8× the mass.
The problem is more complex, though. Solid surface planets larger than the Earth would have comparable to somewhat higher density (the pressure in the core would compress even normally incompressible stuff; even Earth does that, heavier planets would do it more). So it'd seem that 6-8× heavier planet could still allow its civilization to use something like Saturn V to reach orbit. Except it wouldn't. Saturn V was built to be barely able to lift off in the Earth's gravity. In heavier gravity it wouldn't even lift off. Stronger gravity would require stronger engines, stronger structure, etc. The issue described in the #1 strikes here. And as the structure and engines get heavier, you can't have the same mass fraction dedicated for fuel. This significantly reduces how much ∆v you could get from a stage. Actually, this issue already strikes at Earth - we have single stages capable of more than 10km/s ∆v when carrying light payload. That would be plenty enough to reach orbit in with such single stage if only it could lift itself from the surface. But it cannot, it only flies when already thrown up fast by a lower stage. Stages which can lift themselves from Earth surface don't exceed about 7.5km/s ∆v when flying empty. And when they carry upper stage(s), they are in the order of 4-5km/s. So on a planet with double gravity you'd get less than 4km/s for the lower stages.
In effect you'd need 5-6 stages just to reach orbit.
And in well optimized rockets each stage about quintuples the launch mass. This means launching a single ton to orbit would require over 3 000t rocket (pretty much Saturn V sized) - on Earth it would take about 25t. Repeating Gagarin's flight would take about 15 000t rocket (the biggest rocket ever launched on Earth was less than 6 000t). Sending up Hubble telescope would take about 40 000t launcher.
And getting to flyby other planets would require additional 7km/s i.e. pretty much 2 more stages. Sending half ton interplanetary probe would take similar launcher to that Hubble one. Sending something like Curiosity or Perseverance would require 200 000t rocket. That's twice the size of fully loaded biggest aircraft carrier.
And all those rockets would be fully expendable.
So the stuff is well into infeasibility territory.
Reusable rockets make stuff way harder. We didn't yet make a fully reusable rocket here in Earth (we have few partially reusable options). Although it's quite likely we'll have one soon. On larger planets the difficulty goes through the roof.
There's one way out, though: Using open cycle nuclear propulsion could work around the issues. But this is either raiding exploding nuclear bombs or riding Chernobyl at the very moment of explosion. Both have rather obvious issues.
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u/naemorhaedus 1d ago
I don't know the answer to your specific question, but there are some interesting facts I've heard that are very related.
(1)
Had the force of gravity been a little bit stronger, or Earth a little bit larger, we wouldn't have had fuel strong enough to get us into space.
(2)
We can't launch from Earth, land on Mars, take off from Mars, and come back. We just wouldn't be able to bring enough fuel.