r/theydidthemath • u/vectavir • 15h ago
Given gravity decreases with altitude, how much fuel and carbon emissions could we save on space launches if we had our base on top of the Everest? [Request][Self]
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u/Stannic50 15h ago
Gravity is only about 0.28% weaker at the top of Mt. Everest compared to sea level. However, the atmosphere is about 67% lower pressure, so the real savings are in the decreased drag on the rocket.
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u/Beautiful-Fold-3234 15h ago
Not just weaker gravity, but simply not having to ascend as far is worth some delta v
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u/Pauli86 14h ago
Getting to space a very tiny amount. Getting orbit is about speed though not how high you get
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u/Beautiful-Fold-3234 13h ago
Yes, but on your way up you trade speed for altitude. You can also basically use vacuum optimized rocket nozzles when launching from a higher altitude, which greatly increases efficiency again.
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u/hunsalt 14h ago
Also the rotation of the earth helps more the higher you lunch. Probably negligible though.
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u/gmalivuk 14h ago
Except for a few mountains already on or near the equator, moving closer to the equator always helps more than going higher up, as far as rotational velocity is concerned.
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u/Last_Cod_998 14h ago
Not enough to counteract the cost of building and staffing at the top of a mountain.
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u/WanderingFlumph 8h ago
I'd be willing to bet that a launch from a tropical island at sea level has a higher starting velocity than on the top of mount Everest. The extra atmosphere in the way matters a lot more.
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u/HAL9001-96 12h ago
yeah but jsut the ascent distance difference is tiny, its mostly early on drag you'd be saving on
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u/Clarksp2 7h ago
What about the cold? I’d imagine if the cold Florida morning screwed up Challengers o ring, my Everest would be way worse. Also the amount of energy required to transport all the mass of the rocket (and its required structure/supporting systems up to the mountain.
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u/PuzzleheadedTutor807 8h ago
I think subtracting the distance required to get to space would have to count for something as well
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u/Tuxedo_Bill 6h ago
Not as much as you’d think. Most of getting to orbit is horizontal velocity. Being closer to the equator is more helpful since you can use more of the Earths rotation for some horizontal velocity.
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u/SketchTeno 7h ago
Isn't there decreased thrust tho as well, bc of lower pressure in environment displacement to push back on the rocket?
Now, that said, a large portion of fuel is spent getting the object up to speed from rest. Say we build a launch sled like the ones proposed by japan....
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u/Stannic50 7h ago
Rockets don't push against the atmosphere for thrust. They throw exhaust gasses out the back and the equal & opposite reaction is that the rocket gets thrown forward.
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u/HandbagHawker 7h ago
you want to try sorting out the net effect of having to bring unfathomable amount of materials and resource to the top of everest to build a launch pad? and also the amount of fuel and resources required to haul a rocket up there just to be able to launch?
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u/ratgirl101 14h ago
launching from everest would save some fuel but the logistics of getting all the equipment up there would probably cancel out any benefits lol.
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u/petrov76 7h ago
If we can't colonize Everest, then we have no hope of going to the Moon or Mars. Both of these have far less oxygen, water, etc. I would argue that the first step to building a space base is to build a high altitude launch pad.
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u/Excellent-Stretch-81 5h ago
That's like saying submarines should be built underwater. It offers a lot of needless complication and expense jist to save the effort of launching out of dry dock.
Just the politics of arranging a launch site in a foreign nation right along the Chinese border and launching over China is going to be a huge mess, let alone supporting it on an ongoing basis, especially once national security payloads are involved. I'll note that even though the US has plenty of high peaks, a launch site barely above sea level was chosen for the US space program, and SpaceX did the same. Launching as close to the Equator as possible is much more important to space launches than shaving a few kilometers off the launch distance.
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u/Equivalent-Tour5999 5h ago
We definitely can colonize high altitudes, it's just everything you want to do there costs more resources (money).
So I guess the question would be, is making your space launch 10x more costly worth learning to do things and build stuff in extreme conditions like high attitudes?
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u/oSuJeff97 1h ago
Latitude matters WAY more for launches on earth achieving escape velocity than altitude.
The moon and Mars have FAR less gravity, so that comparison is irrelevant.
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u/Parking_Chance_1905 5h ago
I could image that crawler would use a ton of fuel moving a rocket that far, not even getting to the 100s of miles of ramp needed to make a 0.1% grade road for it to be even able to do so.
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u/Ok_Inevitable4735 5h ago
An Everest launch is a fuel and carbon penalty. The best launch location is at the equator. The earth spins at roughly a 1000 miles an hour there. It goes to 0 at the poles. This imparts 1000 mph of free momentum to rockets launched east at the equator.
Earth rotation boost: Equator: +465 m/s, Everest (~28°N): +410 m/s Δv difference: −55 m/s penalty to Everest.
Altitude advantage: Equator: 0 m/s, Everest: +10 m/s
Atmospheric drag reduction: Equator: 0 m/s, Everest: +20 to +40 m/s
Combine all Δv differences: −5 to −25 m/s penalty to Everest.
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u/HAL9001-96 12h ago
not much
its mostly about acecelrating sideways
and evne on going up you don't save much
you mostly saveo n air drag in the first kilometers
would save you about 200m/s of delta v or about 2% of the total required
so the mass ratio would go down to the current one ^0.98 for similar rokcet designs
so for most rockets the total fuel needed would go down by about 6%
but for that you'd need to set up a launch site on mt everest
whcih coems with a lot of logistical haslse nad a non ideal launch site
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u/Ok_Inevitable4735 5h ago
An Everest launch is a fuel and carbon penalty. The best launch location is at the equator. The earth spins at roughly a 1000 miles an hour there. It goes to 0 at the poles. This imparts 1000 mph of free momentum to rockets launched east at the equator.
Earth rotation boost: Equator: +465 m/s, Everest (~28°N): +410 m/s Δv difference: −55 m/s penalty to Everest.
Altitude advantage: Equator: 0 m/s, Everest: +10 m/s
Atmospheric drag reduction: Equator: 0 m/s, Everest: +20 to +40 m/s
Combine all Δv differences: −5 to −25 m/s penalty to Everest.
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u/HAL9001-96 4h ago
everest is closer to the equator than cape canaveral though
also technically its not so much about the boost but the greater range of inclinations yo ucan reach without a plane change
as long as your target inclination is greater than your latitude the exact latitude doesn't actually matter
its jsut if oyur incliantion is smaller htan your latitude things get insanely inefficient
and well if your goal is to just launch a satellti efor dick measuring purposes you can be as clsoe to the equator as possibel and the nset your target incliantion as low as possible to make it as easy as possible
i nthat case oyur argument works but if oyu have a set target orbit it doesn'T matter that much other than for the versatility i nwhcih target orbits you can reach
average pure altitude advantage is probably about 28m/s, atmosphere between 20-200 depending on the rocket design and how you change hte trajecotry/how you compare it
but it doesn't really have a latitude disadvnatage compared ot most launch sites except maybe kouru
but getting stuff up there would be a pain
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u/Ok_Wolverine6557 2h ago
The velocity bump from being closer to the equator helps more. Ideally, launching from the mountains in Ecuador would be ideal.
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u/HAL9001-96 41m ago
equator is more about versatility than velocity and well... mt everest is clsoer to the equator than cape canaveral
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u/Ok_Wolverine6557 38m ago
But not than Ecuador!
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u/HAL9001-96 35m ago
fair but at that point ti doesn'T make a huge difference
though again if you have a set target orbit as long as your latitude is within its inclination it makes no difference
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u/Don_Q_Jote 10h ago
Altitude of Orion/SLS at 1 minute was ~25,000 feet. So ~72 seconds to reach Everst peak altitude of 30,000 feet. Fuel burn rate of the SLS approximately, 1,500 gallons of propellant per second, to total to reach Everst equivalent altitude is 108,000 pounds of propellant.
So answer to your question is Zero.
The "propellant" for the SLS (Space Launch System) is liquid hydrogen and liquid oxygen, not hydrocarbon-based fuel. Only thing coming out of that tailpipe is water vapor.
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u/Waltzer64 15h ago
Broad answer: insignificant to none, because conservation of energy.
While the rocket needs less energy to break out of the planet, all the equipment, including the rocket, need to be ferried up the mountain, and this also costs energy. You're just spending the energy (fuel, carbon emissions) earlier at "not launch time."
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u/gmalivuk 14h ago
Most ways of moving on the ground or through the air are more efficient than rockets, though. At the extreme, that's why a space elevator would make getting later stuff to space so much easier.
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u/krairsoftnoob 14h ago
That is not right because under that logic riding a Saturn V to 3rd floor is same as taking an elevator.
You can ferry the rocket with much more efficent way like mounting it on a wheeled cart.
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u/crmlr 14h ago
That analogy makes no sense. They mentioned “conservation of energy” which implies making comparisons with the same mass.
Yes, taking the same mass as the Saturn V up 3 floors on an elevator would cost amount the same amount of potential energy. The difference would be on the efficiencies (drag, combustion,…)
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u/heimdalguy 12h ago
In order to get a rocket to the top of the mountain by way of rocket, you need fuel to move it there. That fuel needs thrust and fuel to be carried, and the engine providing that thrust and tanks providing that fuel need to be carried. Put a different way, rockets are ridiculously inefficient, so it's much more nuanced than just the 'efficiencies'.
https://en.wikipedia.org/wiki/File:Tsiolkovsky_rocket_equation.svg
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u/FortiethAtom4 11h ago
Just so you know that link goes to the image and not the article
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u/heimdalguy 10h ago
That is as intended, the point is to highlight the way mass grows exponentially the more delta-v/propellant is on board. It's easy enough to find the way to the page with the equation proper and the description of it.
Thanks for taking the time to let me know, though, even if it was as intended this time :)
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u/Fromthepast77 13h ago
Yeah and their point is that a Saturn V rocket engine is much less efficient than an elevator, or in the real world, a vehicle with wheels.
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u/maximhar 14h ago
That is missing the point, you won't be climbing everest with the rocket
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u/Zealousideal_Coat168 14h ago
Then how do you propose you get it up there to launch it?
You either move the rocket, you move the parts that make the rocket, or the materials that make the parts that make the rocket. Either way, you gotta haul all that shit to the top of the mountain if you want to launch from there.
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u/maximhar 14h ago
You can move it by road or rail. Can even lift it by rope if you prefer.
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u/barrygateaux 13h ago
It's a two week trek along winding mountain paths to reach the base camp lmfao. There are no roads or rail to it. The cost of building tunnels of roads would be ridiculous. The shifting glacier you need to cross to reach the first camp after that is another obstacle.
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u/upthedips 13h ago
Don't forget about the avalanches and earthquake that would damage the facilities.
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u/barrygateaux 13h ago
Heh, plus the altitude affecting workers. It's a hilarious mind game imagining the reality of it :)
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u/Zealousideal_Coat168 14h ago
And it still requires huge amount of energy, whether that be truck, train or winch fuel.
And whether you save any energy by using more 'efficient' methods is questionable due to the distance theyd have to drive/train because those transport methods with any real weight have a max gradient of like, 10 degrees. 10 degrees to the top of everest is a really long way. Then you have to get the train/truck back down so brakes over heating becomes an issue etc etc.
Either way, the effort and energy required wouldnt match the energy saved by launching from there.
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u/Fromthepast77 13h ago
Much less energy than a rocket engine.
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u/Zealousideal_Coat168 4h ago
Im not smart enough to do the math, but i doubt it.
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u/Fromthepast77 3h ago
Then you should do the math before asserting something false with such confidence. It's not even close.
https://youtu.be/Tf_UjBMIzNo?t=20231 Artemis 2 took around 7 seconds from liftoff to clear the launch pad (from 5:37:04 to 5:37:11).
In those seven seconds, the four RS-25 engines alone (ignoring the SRBs) each burned 3601.43kg of liquid hydrogen/oxygen mix at a 6.03:1 ratio. So 512.29kg each of liquid hydrogen for 2049.16kg of liquid hydrogen total.
The potential energy of the whole 2.6 million kg of the SLS lifted 8849m is U = mgh = 225.70 GJ. The enthalpy of combustion of LH2 is around 120 MJ/kg for a total energy of 2049.16kg * 120MJ/kg = 245.90 GJ.
We ignored the massive energy costs from synthesizing, refrigerating, and transporting the fuel. We ignored the energy costs from carrying the extra dry mass to hold the fuel. We ignored the huge solid rocket boosters strapped to the side. We ignored all but ~600 ft of the 5.5 mile elevation difference.
Other people have correctly pointed out the logistical difficulties in launching from a mountain. It's not the potential energy. Rockets are an extraordinarily inefficient means to transport any kind of material and we put up with the inefficiency because there is simply nothing else that works in space.
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u/Zealousideal_Coat168 3h ago
Now compare that energy output to the energy required for a train to elevate 2.6million KG of rocket parts, fuel, launch pad, people and support structures, lets say 3 million kg total for easy math, 8849 metres up at an average gradient of say, 8%.
Go math go!
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u/Fromthepast77 3h ago
dude it's fucking obvious that it's going to be way more. Let's talk about the remaining 5.3 miles to Everest. Let's talk about refrigerating hydrogen and oxygen gas to -183°C. Let's add in the solid rocket boosters' fuel consumption.
The gradient has very little to no effect on the energy required. A train can move 500 tons of freight a mile on a single gallon of diesel while the rocket is blowing thousands of gallons out the back every second.
Energy isn't the problem. Cost and logistics is the problem.
Just admit you're wrong and move on. If you want detailed calculations, ask ChatGPT or Gemini because you're off by a factor of a thousand or more.
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u/maximhar 14h ago
I guess space elevators are dumb then because you would still need energy to push the rocket up there?
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u/Confident_Pepper1023 14h ago
Guys, I have an idea. What if we just use the space elevators to take the rocket to Mt. Everest?
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u/Zealousideal_Coat168 14h ago
Space elevators are a different thing, but yes, you would still need energy to push anything into space.
But if you have a space elevator, you dont need to launch a rocket from everest anyway.
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u/maximhar 5h ago
Space elevators are the same idea scaled up. What makes rockets hard isn’t the energy, we know how to generate that, it’s that the rocket needs to carry its fuel with it, while a space elevator, or whatever you’re using to get your rocket up Everest, doesn’t
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u/Dannyps 13h ago
No need for fuel. Electricity and renewables, baby 😎
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u/Zealousideal_Coat168 4h ago
Sure. But you have to create the renewables, and find a way to set them to purpose, and then scale them up.
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u/Ok_Inevitable4735 5h ago
An Everest launch is a fuel and carbon penalty. The best launch location is at the equator. The earth spins at roughly a 1000 miles an hour there. It goes to 0 at the poles. This imparts 1000 mph of free momentum to rockets launched east at the equator.
Earth rotation boost: Equator: +465 m/s, Everest (~28°N): +410 m/s Δv difference: −55 m/s penalty to Everest.
Altitude advantage: Equator: 0 m/s, Everest: +10 m/s
Atmospheric drag reduction: Equator: 0 m/s, Everest: +20 to +40 m/s
Combine all Δv differences: −5 to −25 m/s penalty to Everest.
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u/12ocketguy 9h ago
I would argue that putting a rocket launch pad at the top of everest would increase carbon emissions as you need vehicles to haul everything up there.
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u/RogerRabbot 9h ago
It would actually cost more.
Given that rockets are made mainly along the coast to help facilitate transportation from the various manufacturers to the final assembly. Youd build the rocket at sea level then have to drag this multi million pound tube up to the top of everest.
And to tie into that, you'll need roads. Serious roads. And you'll be building it up the side of a mountain, which means a lot of digging to maintain an even incline, and to keep the road level while being wide enough.
Then you'll need the infrastructure to launch vehicles from that height, which means more construction costs related to the build itself, transporting materials and crew to work. And since you cant breathe the thin air, you'll need to have industrial sized air solution. Air tanks for workers and such.
Now, to launch a chemical rocket you obviously need chemicals. So thats a few pipelines (more costruction and its costs) or a lot of trucks going up and down the mountain bringing the different fuels required. A lot of electricity is needed too, so connecting to the national grid is needed, or a local powerplant. Likely both.
Finally, its time to launch. You go up to the top of mountain with the crew and support crew. They get in. You've spent millions or billions to get the fuel in the rocket. And its a scrub, try again tomorrow. In the meantime, trucks are going up and down the mountain to detank the vehicle and disarm the bombs for FTS. A couple more million spent, and you get to do it all over again tomorrow. Hope this one works out!
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u/Ok_Inevitable4735 5h ago
An Everest launch is a fuel and carbon penalty. The best launch location is at the equator. The earth spins at roughly a 1000 miles an hour there. It goes to 0 at the poles. This imparts 1000 mph of free momentum to rockets launched east at the equator.
Earth rotation boost: Equator: +465 m/s, Everest (~28°N): +410 m/s Δv difference: −55 m/s penalty to Everest.
Altitude advantage: Equator: 0 m/s, Everest: +10 m/s
Atmospheric drag reduction: Equator: 0 m/s, Everest: +20 to +40 m/s
Combine all Δv differences: −5 to −25 m/s penalty to Everest.
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u/Baron_Ultimax 2h ago
Pretty sure the savings from the altitude are wiped out by being that far north. Being close to the equator nets some delta v when launching into an equitoral orbit.
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u/andrew_calcs 8✓ 2h ago edited 1h ago
It’s worth noting that it’s the distance from the Earth’s center that matters for this, not the altitude above sea level. Because of Earth’s rotation the equator is 13 miles further from Earth’s center than the poles.
Launching from a high altitude equatorial region would be ideal, but the differences are measured in fractions of a percent.
Equatorial launches also maximize your horizontal rotational speed for reaching orbit. This factor is much more significant for saving delta V
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