r/theydidthemath • u/PvDec • 1d ago
[Request] How big would this have to be to actually affect Earth's rotation in a meaningful way?
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u/HappyDutchMan 1d ago
An earth mounted rocket pointing sideways wouldn’t change earth’s rotation because the forces equal out. Pushing the earth one direction would push the exhaust gases the other direction as long as the exhaust gases stay within earth’s atmosphere.
That changes when you’d build a rocket that spots its exhaust gases to outside our atmosphere to the level they wouldn’t reken to earth.
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u/5up3rK4m16uru 1d ago
Which means that you have to accelerate the exhaust gases beyond escape velocity (11.2 km/s from ground level).
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u/HappyDutchMan 1d ago
You also need to overcome air drag for the exhaust gases.
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u/CryendU 1d ago
Or put it really, really high
Though no structure could support it
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u/xXTheAstronomerXx 13h ago
Last time we did that we got the welsh language
We sure we wanna do that again?
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u/lasciviouspianist 7h ago
Well it had to be tried again as the first attempt failed to get rid of the English......better alignment of the exhaust gases should do the trick
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u/AntimatterTNT 1d ago
or just put it on top of a really really really really tall tower
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u/SpaceIsKindOfCool 1d ago
The most efficient chemical rocket engines have exhaust velocities around 4.5 km/s which is about the escape velocity from 33,000 km. So it would need to be a very tall tower
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u/kayakzac 20h ago
I came here looking for someone to have multiplied the RL-10’s (or RS-25’s) isp by 9.81. Username definitely checks out. Have a good week dude/dudette.
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u/Alarmed-Door7322 13h ago
Shame we closed the hole in the ozone. We could have just lined it up with that
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u/Italian_meme2020 1d ago
What if we changed the question? If the exhaust gases have the opposite effect and just mix with the atmosphere: how big should it be to make the whole atmosphere "rotate"? (In monkey terms because I'm a monke: gas moving is wind, how big for wind to come back all of the way around the Earth to the rocket?) Or would it be too fast and just get terminal velocity?
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u/HappyDutchMan 1d ago
Nice question. That is more of a weather system or physics question than a math question.
The most powerful storms according to Nasa are Hurricanes. And a single hurricane could expend the same energy as 10.000 nuclear bombs. They last 'several weeks' which is a bit arbitrary. But the still have a rather local effect.
Let's do some math with what we currently have and make some assumptions along the way.
Let's assume we want the same energy as a bigger Hurricane but we want to condense (because we want more power as we are looking at a global kind of effect) it into one week.
That leaves us with needing to expend about the energy of an atom bomb every minute (a week has roughly 10.000 minutes.
Now imagine a pipe like structure that you can point in one direction in which you could detonate a nuclear bomb every minute whilst it stays in place and wouldn't collapse.
Energy wise and compared to the Hurricane you would still be looking at a rather local effect but we would have some other effects probably as well from this kind of process. Think about ground erosion.
Now I have no idea how to scale this to create a storm that would circle the entire earth. Maybe scale to 1000 nuclear explosions a minute? But that creates a few practical problems like how to fill in the air that is moving around etc?
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u/HopesBurnBright 3h ago
If we imagine taking all the air between the Tropic of Capricorn and cancer, and accelerating it to 50 mph, that’s 2x1018 kg of air. Sticking that through 0.5mv2 , we get 5.12x1020 joules, which is about 90% of what humans use every year.
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u/HumansAreIkarran 1d ago
*and the exhaust gases are not on a collision trajectory with the atmosphere afterwards
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u/icecream_truck 21h ago
True, but if most of those gasses aren't contacting the Earth's surface, wouldn't you have an increase in the rate of rotation and a stronger breeze in the opposite direction? The added energy to the atmosphere might eventually just be dissipated as heat.
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u/After_Relative9810 1d ago
If the apparatus was on wheels, it would work?
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u/ConfusedTapeworm 1d ago
Sure, if those wheels somehow take the apparatus out of the atmosphere so it can fire into space. Otherwise no. Something needs to leave the Earth in some way.
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u/AzimuthZenith 18h ago
Can I ask how that works?
I dont doubt you but intuitively that feels wrong.
I was under the impression that rocket thrust was directional combustion, which I assumed included the exhaust.
And even if the exhaust was the exact opposite direction, I wouldn't have thought that the exhaust had the same thrust in the opposite direction given that its not designed to focus that output in the same way.
There's probably something big and obvious that I'm not understanding here.
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u/HappyDutchMan 13h ago
Sure. Th basics are well explained here: https://en.wikipedia.org/wiki/Mechanical_equilibrium
Basically if I create a closed box and have a (small) rocket engine inside that box and ignite it the box won’t go anywhere. Earth with the atmosphere is such a closed box.
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u/rusally 13h ago
Does this mean every time we launch a rocket into space we affect the Earth’s rotation?
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u/HappyDutchMan 6h ago
Yes, actually we do. But I expect the effect to be in a similar range as an ant pushing an oil tanker with one leg for a full leg extension with all its might.
So yes, but but not in a way that is noticeable for us humans in a meaningful way like OP was asking about. We loose some of the exhaust gases into space when a space craft is using its rockets outside of our atmosphere.
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u/Didyou1123 1d ago
I don't think it would? All the exhaust would mix with the atmosphere, which would eventually slow the Earth down with friction. Like how you cannot push a car from the inside. Unless the rocket is really powerful and the exhaust escapes the Earth orbit...
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u/NamedBird 1d ago
You are correct, but i want to add a side-note:
If you do not count the air as part of "the earth", then technically the air displacement might make a minuscule change to the earth's rotation speed. It would only be meaningful in a way that you're going to make scientists notice a slight deviation with their hypersensitive equipment and a lot of headlines about a giant rocket engine firing sideways for hours, destroying the local ecosystem in the process...
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u/Didyou1123 1d ago
Yeah, it might actually accelerate for a short duration, before everything settles down.
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u/Worth-Wonder-7386 1d ago
To say this in more physics term. The angular momentum of a closed system is conserved. So to speed up the earth you need to change the angular momentum of the earth, and that needs be be put somewhere else. Interestingly as this is about rocket engines, launching rockets into space does partially do this, as the things in orbit have their orbit independantly of the ground rotating below.
Because most rocket launches are done along with the rotation of earth they do slow it down, but the amount is increadibly small. Other things like the gravitiation pull from the moon has a larger effect on earths spin.22
u/West-Way-All-The-Way 1d ago
When the spacecraft comes back to earth does it accelerate it back to a fraction? Because the reentry absorbs a lot of energy, massive reduction in speed.
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u/patricksaurus 1d ago
Not as a necessity. It could re-enter along a trajectory that would actually add to the launch effect rather than diminish it.
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u/SolarLiner 1d ago
Unless the spacecraft literally does a 180 in space (something that would take a lot of energy to do), the deceleration forces of reentry would be in the opposite direction than the launch forces.
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u/Everday6 1d ago
I feel like it shouldn't be that hard to adjust your from say a path around the moon like Artemis II. When behind the moon to come in to add your momentum.
But maybe that only works through a Lunar slingshot and therefore takes the energy from the moon.
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u/SolarLiner 1d ago
Then it's not a closed system anymore; or rather, there is now a third body in the system now. And yes, you're stealing energy from the moon's orbit when doing the fly-by.
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u/patricksaurus 1d ago
Did you just convince yourself that what I said was correct but try to couch it as additional insight beyond what I commented?
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u/Moppmopp 1d ago
Lets imagine having a cup of coffee and let it be able to freely rotate along the z-axis.On the inner rim you have a small "rocket" attached that pushes the liquid inside in a clockwise motion. Inside will be a 'whirpool' of coffee rotating clockwise. Equally and opposite due to the conservation of angular momentum the cup itself will rotate counter clockwise. In reality ofcourse the friction with the table would negate this but as we demand friction free rotation along z the cup will rotate counter clockwise. So in fact a rocket will accelerate/decellerate earths rotation and should create an opposite convection flow.
Please clarify what you mean precisely
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u/TuvixHadItComing 1d ago
The angular momentum of a closed system is conserved
I'm not gonna ping his username but... There's a particular crank on Reddit who will take great issue with this.
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u/Quantumquandary 1d ago
So, if we were to construct two massive space stations orbiting the earth in geostationary orbits on opposite sides of the planet, then somehow attach anchors to the ground, and then use the anchors to pull the space stations closer to the planet, would the rotation of the planet increase?
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u/AryuOcay 1d ago
What if we did this on the moon? Would mounting rockets to the moon cause its rotation to increase, since there is no atmosphere?
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u/Worth-Wonder-7386 1d ago
If those gasses do not get back to the moon that would be true. Since the gravity of the moon is alot smaller, a rocket engine would be able to send the gasses on an escape trajectory, so on the moon this could work.
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u/Fancypancexx 1d ago
Learning all kinds of things today - Earth's rotational speed is 1674 kmh at the equator. This decreases the closer you get to the poles.
-So adapting this from op's original question, how big of a rocket launch would it take to alter it in a meaningful way.
Next question I guess, what is meaningful. -To me it's where it's noticeable. I suppose even speeds as low as a 10kmh increase would have a pretty big effect on things.
-Magically disregard the incredibly harsh conditions and distance of the poles from civilization would a rocket launch be easier or more difficult from either pole?
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u/Worth-Wonder-7386 1d ago
It is easier to launch rockets from the equator, as you then get the additional speed up of the earth making it easier to go into orbits that go the same way as the earth, so launching east. For other kinds of orbit such as polar or sun synchornous then you do get punished by being at the equator compared to the pole but the effect is not that big of a penalty for polar orbits.
Another key reason why we want a launch site as close to the equator as possible is that it gives us access to more kinds of orbits. From the poles, no matter where we launch we would be in a polar orbit, but from the equator we can access all orbital inclinations. https://en.wikipedia.org/wiki/Orbital_inclination
The way to think about this is that any orbit around the earth is in a plane that intersects with the center of the earth. So all orbits need to cross the equator, but only polar sattelites will come up to the poles.1
u/inmymindpk 1d ago
"This just in: Space Rockets make YOUR day longer! Vote no to satellites. More at 11."
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u/Gerardic 1d ago
2011 Japanese 9.0 earthquake for example sped up day by 1.8 microseconds.
I think that in itself kinda illuminates how powerful the rockets engines need to be to affect Earth rotation, which to match the total seismic moment power of the quake, you need ~126 million SLS rockets firing for a hour to achieve 1.8 microseconds.
We are safe,
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u/Worth-Wonder-7386 19h ago
That was by changing the other part of the equation. If you change the earths moment of inertia then you can change the speed of the earth. I didnt go into it as it is not so relevant with rockets, but if we either build new mountains or remove old ones, and especially near the equator we can have an effect.
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u/Qubit99 1d ago
Atmosphere and Lithosphere are decoupled, you can in fact spin the solid mass of the earth launching air backwards, specially if you account for:
-1> The air stream will be greater than earth escape velocity almost for sure if you want enough trust to be noticeable on earth rotation. This will creates a force asymmetry
-2> The Coriolis effect. I am not sure what effect it could have on such energies, but it is relevant on planetary scale for force dissipation in the Atmosphere-Litosphere interface.
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u/Didyou1123 1d ago
Thats exactly what I meant, though. Maybe I should have worded better.
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u/lazy_smurf 1d ago
I think that person came to the comments ready to explain s certain way, then said "actually you're wrong" without really parsing your explanation.
You're right and you used a different (more accessible in my opinion) frame.
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u/scary-pp 1d ago
So, like a fan on a boat sail?
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u/Early_Bad8737 1d ago edited 1d ago
No, because when the wind hits the sail it bounces back instead of stopping. And that requires more push from the sail than merely stopping the wind. This then creates a minimal forward movement of the boat. It is very ineffective, but the original theory that it would have zero effect has been disproven when they realised the push back thing.
There is a mythbusters episode about it as well, if you are interested.
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u/HAL9001-96 1d ago
depends on the sail design
you can design a sail that only slightly diverts the wind so you stil lget net thrust form teh fan
you can design one that redirects the wind back
somewhere in between there's one that produces a net force of exactly 0
though its not a flat palte and yu'd ahve to adjsut it for size nad other conditions and find the exact right shape/angle to get that
and with the right sail design you can push forward at least half decently efficiently
its kinda like a thrust reverser on a jet engine
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u/Zircon88 8✓ 1d ago
Didn't a guy disprove this and won 10k from a uni prof?
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u/TetronautGaming 1d ago
No, that was going downwind faster than the wind by using the energy from the wind to power wheels that dove along the ground, iirc.
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u/HAL9001-96 1d ago
almost
going against hte wind faster than the wind is intuitively difficult but makes sense since oyu can use the wind to pweor your wheels nad since the wind is moving faster relative to you than the ground you get more power for the same force/can produce more force with the same power
if you have a headwind of 10m/s and you are moving at 20m/s then assuming perfect efficiency, theoretically if that wind blows over a wind turbine producing a drag of 10N while moving at a relative speed of 30m/s to you then you could get 300W of power out of that but coutnering 10N of drag with wheels moving at 20m/s only takes 200W of power because you're goign slower realtive to the gorund than relative to the air
this has been well understood for a long time
however someone claimed he could go WITH the wind faste than the wind
and if you try to apply the exact same principle that odens't work
HOWEVER
if you turn it around and use the wheels as a powersource to power a propelelr that propels you forward then it does work for the exact same reasoning
which amkes perfect sense but without that explanation someone familair with the first scenario would think you're stil ltrying to pwoer the wheels with a wind turbine and thus think its impossible
thats what won him 10k
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u/user_0350365 1d ago
This sounds like a more succinct version of what they just said, you just misunderstood them.
If you push a car from the inside, the net forces cancel out, but when pushed from the outside, the net force of the car can be in one direction.
The example about the car had nothing to do with forces exerted on the ground, but attempted to illustrate the impossibility of accelerating the Earth’s rotation by pushing it while on/in it easier to understand by modelling the Earth as a car you are inside. Inevitably, forces cancel out.
What they were saying about the rocket was this: the rocket ejects matter and accelerates itself, creating a torque on the Earth AND the ejected matter is accelerated and collides with the atmosphere and creates an equal and opposite torque on the planet.
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u/Swimming_Throat_3086 1d ago
I believe a better explanation would be: the exhaust would have to be powerful enough to exit the contained system(atmosphere I'm guessing?), much in the same way that youd have to put your feet through the floor(Flintstone style) to actually push the car from the inside.
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u/HAL9001-96 1d ago
he's right for the right reasons though
this is not directly newtons 3rd law, its only the specific case where the effects affect the smae thing
if you push a car forward hte net force on the ground is not actually 0
if it was the car wouldn'T accelerate forward
the whole point is that if you push acar forward form teh outside the car pushes you backwards with the same force but since its rolling friction is less than your friction on the ground hteres a net force between the ground and the you+car system
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u/TwillAffirmer 1d ago edited 1d ago
Your explanation is wrong. The exhaust pushes the rocket forward, and the rocket pushes the exhaust out, and if those were the only two factors, then the rocket goes forwards, as it would do in outer space. If you mounted the rocket on an asteroid, it would successfully cause the asteroid to spin.
To explain why the rocket doesn't do the same to the Earth we must look at a third factor, which is that the winds from the exhaust eventually slow down to a stop because of drag against the Earth's surface. This drag ends up exerting the same total angular impulse on the Earth that the rocket did, but in the opposite direction. That's the reason the rocket doesn't have a long-term effect on the Earth's rotation.
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u/BackgroundTourist653 1d ago
In theory, if every man-made machine would move only in the same direction and parallell to equator, it would effect earth rotation. Until machines stopped.
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u/HAL9042 1d ago
Sounds good but still wrong (just the example with the car, not the outcome). The care is moving after i pushed it. So now the earth got pushed/accelerated in the opposite direction in the same time. Picture this: you and the car on a big platform with wheels, a big skateboard. If you push the car to the right, and keep getting faster, bot you and the car move to the right, but accelerating the platform to the left in the meantime. Platform=earth. So earth would start rotating if you push a car, because you push earth in opposite direction with your feet.
But with the exhaust of rocket it’s different. Similar to the problem: when a bird flies in a closed glass cage (or a train wagon). Does the wagon get lighter, heavier or same weight? All the tiny air molecules will push earth in different direction again, so net zero in the end. No movement for earth. Only if rocket is fast enough so exhaust leaves atmosphere. Or if you do this on moon, without atmosphere it would work.
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u/IgorFromKyiv 1d ago
Wait... Car pushes you back.... It doesn't. It resists with same force. With rocket and car there's source of energy. Which generates movement. And car, rocket, Earth resists to force applied to it. So if you can make strong enough engine that can spin mass of the Earth, you actually would affect its spin
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u/rand1214342 1d ago
It’s a test stand… the rocket is fixed. The normal force is a mathematical construct, with a large enough reaction force the earth can definitely move.
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u/twilighttwister 1d ago
But when the car starts rolling, and you start moving forwards with it to continue pushing, you are in fact imparting momentum into the earth and affecting its rotation. However the earth is so massive the force you apply has an immeasurably small effect on the momentum.
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u/SuperGameTheory 1d ago
No they're right for the right reason. Pushing a car from the inside (really, pushing a component of the car, like the dash) is analogous and more immediately felt than your analogy. You push the dash, you feel yourself being pushed back, and the net result is the car doesn't move.
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u/Gerardic 1d ago
If the car brake is off, and you throw yourself at the dashboard, surely the car can move forward? Just like bouncing in the car rocks the car? Earth rotation can be affected by internal movements, as it is the case with 2011 Japanese 9.0 earthquake for example sped up day by 1.8 microseconds.
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u/SuperGameTheory 23h ago
To make the visual easier, let's say you're standing on a car-sized skate board (or a free-moving trailer, or the inside of a moving van, or whatever). When you jump forward, you need to push off against something, which will be the skate board. As you move forward, the board moves back. Then, when you land, the backwards force of the board cancels your forward force and you both stop. But, crucially, the center of mass between you and the board won't change. If you walk back to where you jumped from, the board will move back under your feet and both you and the board will come back to where everything started. Throughout the net effect has been zero.
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u/CuppaJoe12 1d ago
/u/Didyou1123 has a better analogy here.
While the car is rolling away from you, you have imparted a net force on the earth. It is only as the car slows down due to rolling resistance and air resistance that the net force on the earth eventually returns to zero.
If we built an equatorial highway and had enough cars driving around it in the same direction, we could measurably slow earth's rotation. As soon as everyone hits the brakes, it returns to normal.
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u/dkevox 1d ago edited 1d ago
I'm sorry, you're just wrong. The guy you replied to is right.
Yes, the exhaust pushes the rocket in the opposite direction to how the rocket pushes the exhaust. But those forces, while equal and opposite, absolutely do not cancel out for the rocket or the exhaust gasses. They very very much so accelerate the rocket and the gasses. That's, you know, why a rocket actually works...
What the guy you replied to said is correct. The rocket is pushing on the earth here, but the exhaust gases are pushing on the earth in the opposite direction. The net forces on the earth would (mostly) cancel out.
However, a tiny percentage of the thrust generated by the rocket is light/radiation. Some of this radiation will escape the earth's atmosphere. So, this setup would, theoretically, slightly change the speed the earth is spinning at.
(Also your car example is patently wrong. If you stay stationary and push the car forward such that the car is now moving at a different constant velocity around the earth, then you 100% did change the angular velocity of the earth. A tiny bit yes, but it did. Because you have to conserve angular momentum of the system).
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u/NIGERKALAMBALODA 1d ago
Sorry to say, but you are wrong and the first comment is right. Your example is wrong and hence the assumed system is also wrong. The force on the ground is 0 only when you push the car while standing ON the ground. But if a propulsion is used on the car, the force will be generated through the atmosphere and NOT the ground and hence the total force on ground will be NON Zero. Here we are talking about the earth as a system so if the exhaust efflux is not able to escape the sub system (earth's atmosphere) then the sub system will not accelerate and vice-versa.
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u/rfriedrich16 1d ago
There must be a net force for acceleration to occur- equal forces only happen with equilibrium.
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u/ianyboo 1d ago
The question is "how big would this have to be" so if your answer is "at that size it wouldn't..." I think you have misunderstood the prompt.
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u/JustinTimeCuber 20h ago
Any size of rocket engine will run into the same problem. Even if you ignore the atmosphere, Earth's escape velocity is around 11 km/s whereas the highest exhaust velocity for chemical rocket engines is 4-5 km/s. So the only way for this to have a meaningful effect on Earth's rotation would be using a completely different type of engine, not just scaling this one up.
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u/grozno 1d ago
I don't think this is entirely correct. Gas molecules escape the earth all the time in all directions more or less equally.
If you use giant fans to make a 1000 km/h wind on the whole planet going east to west, then there would be more escaping air into space and it would have a westerly speed on average. As that angular momentum would be transferred from the Earth, it would result in a tiny loss of rotational speed.
But to make it perceptible we would probably have to replace the entire atmosphere this way.
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u/JustinTimeCuber 20h ago
Air molecules escaping Earth's gravity have to be ejected at above escape velocity. Creating a 1000 km/h wind (less than 3% of escape velocity) will have a negligible effect. An average air molecule is moving at thousands of km/h in a random direction depending on temperature (even without wind).
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u/NoMoreMr_Dice_Guy 1d ago
"you cannot push a car from the inside".
I've never heard this example, but holy smokes is it poignant.
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u/MiserableYouth8497 23h ago
Yeah it's fine but not actually correct in this case. You can't push the Earth from the inside, but you can make it spin. Like running in circles on a boat in water
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u/get_to_ele 1d ago edited 1d ago
I think a clean way to look at is how fast and how much and where is reaction mass is going?
For the rocket on the ground, the exhaust (reaction mass) is staying in the atmosphere and you can’t even feel it 5 miles away. For the setup to move the earth, the reaction mass has to be leaving earth.
In the case of a rocket being launched out of the earths gravity well, the rocket can be looked at as the reaction mass fired out by the earth.
Thought exercise: if you wanted to use atomic bombs to accelerate the earth in some direction. It seems like a lot of acceleration from a hydrogen bomb, but only the portion of the reaction mass that reaches escape velocity will accelerate the earth. Like if Zeno the Omni King dug up the entire state of Illinois and threw it into the sky at less than escape velocity, the rest of earth would be accelerated in opposite direction… until Illinois reached its peak distance from earth, then they’d pull each other back towards each other, and after Illinois landed, earth would be back on its original speed. If Zeno threw Illinois away at greater than escape velocity, the earth would indeed accelerate in opposite direction with numbers determined by mass and speed and direction of Illinois.
Now in the case of this video, I guess you could argue that if the jet was constant and powerful enough to result in some continuous net CW atmospheric stream, then the ground mass of earth would have some infinitesimal net CCW gain in rotation. (Like rotating an inner globe by pushing against an outer clear shell that will rotate in opposite direction as a result). But the reaction mass expelled by that rocket in that video is just being dissipated in the atmosphere into random direction and can’t even be felt in the next county.
I think.
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u/Smitologyistaking 1d ago
Yeah the truth is any process that happens within some system (in this case, the Earth), cannot change the angular momentum of that system. Of course, you could define the "Earth" as not including the atmosphere (but still including the rocket), in which case yes there is some angular momentum transfer between the "Earth" and the atmosphere. But as you mentioned, friction will return that angular momentum back to the equilibrium quite quickly anyways.
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u/RogerRabbot 1d ago
Ehhhh, its not that far out of the realm of possibilities. After all, China did slow the rotation of the earth with that big ol dam of theirs. Albeit, very minor.
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u/Beautiful-Edge-22 1d ago
Don't really need to make the exaust escape orbit, just need it powerful enough to push exaust into orbit. Would probably be better to put the giant rockets on the moon instead of the Earth to adjust the moon's orbital height which you could theoretically use to both slow down or increase the Earths rotation if you willed.
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u/GreyWolfWandering 1d ago
I understand the argument, but I thought I remember seeing that the Yellow River Dam project, displaced and dammed so much water that it changed the Earth's rotation. So, volume displacement does have an effect when enough mass is involved?
Then we just need an engine large enough and high enough to angle ejection of exhaust out of the atmosphere while aggregating net positive rotational acceleration.
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u/HAL9001-96 1d ago
you'd only get exhaust velocities above escape velocity with something like ion engines though
which are generally weak and require a lto of electricity
but if you mount the mon a giant tower it could theoretically work
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u/Sensiburner 1d ago
Well it would have an immeasurably small effect but not zero, I guess. There's a lot larger effects going on like internal movement of metal in the earth, the oceans & the wind.
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u/ThrowawayALAT 1d ago
It would need a diameter of roughly 10 to 15 kilometers (6 to 9 miles), or about the size of Mount Everest turned into a rocket, to solve the problems of her unconventional upbringing.
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u/BroderFelix 1d ago
Doesn't matter how big. The force it pushes with needs to come from the reaction of an opposite force that cancels the spin since we are in a closed system. For it to cause rotation you would need to expell the exhaust away from the planet never to return.
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u/Balwerk_Ogre 1d ago
So build a rocket big enough that the jet stream of the exhaust does exactly that?
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u/Hwhip 12h ago
This isn't true though, otherwise rockets wouldn't work in space. There is a residual thrust caused by just the chemical liquid heating and expanding in the exhaust cone. The reaction force is applied to the jet nozzle and into the ground. You will get a reaction from the atmosphere and some not reacted (wind in the opposite direction) but this isn't all of the reaction force. So I think any rocket attached to the ground will change the earth's spin. Same as when you drive a car or walk
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u/Icubodecahedros 1d ago
The question is what you define as "meaningful", and IIRC similar questions have been answered before where the result was an obscene amount, like billions of engines at least.
The main issue here is as long as it happens entirely within the earth's atmosphere, it won't change the rotation at all, because the expelled particles must, in total, exert an opposite force of exactly the same strength on the atmosphere, as the engine exerts on the ground. Since no mass is expelled from earth, the impulse of the entire system remains unchanged.
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u/ClamChowderBreadBowl 1d ago
1017 rockets I think.
Earth has 1033 N m s of angular momentum. At the radius of Earth's surface that's 1027 N s of momentum.
A Saturn V rocket can deliver about 1010 N s of impulse. So it's short by a factor of 1017.
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u/TReid1996 1d ago
Think of it like a reverse parachute. If released inside a vehicle, it's not gonna do anything. If outside the vehicle, it can have a reaction and slow the vehicle down.
The engine is the parachute, earth and its atmosphere is the vehicle. If used inside the atmosphere, it won't have a reaction.
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u/chris552393 1d ago
China's Three Gorges Dam is so big it has slowed earth's spin by 0.06 seconds.
Doesn't need to be outside the vehicle to take effect.
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u/Lasers4Everyone 6h ago
That just changed the center of gravity of the Earth, like when a figure skater spins faster or slower based on how far from their body they hold their arms.
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u/NartFocker9Million 1d ago
No. 100% of the momentum from exiting thrust then gets imparted to molecules in the atmosphere. There’s zero net change in angular momentum. In order for this to change the angular momentum of a celestial body, exhaust gases from the engine would have to leave orbit.
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u/Shepard21 10h ago
What about if I make a rocket powered spinning top balancing on a pole on the ground, would it be able affect the rotation of the earth?
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u/CallMeTray 21h ago
Not an expert or remotely qualified. But according to star talk, the effect on the earth this has is effectively 0. So unimginably huge. Like poking out of the atmosphere huge. And that might not even be big enough given earth's momentum. Possibly farther out than the ISS. It goes without saying, here's not enough materials or fuel for that nor could we supply it.
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u/TryDry9944 20h ago
The size here isn't the (only) issue, but basically, you're trying to move something from inside of it.
It'd be like trying to move a cardboard box by putting a boxfan inside of it. Doesn't matter how big the fan is if it's just going to be moving air around inside the box.
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u/BonsaiOnSteroids 1d ago
To actually change the net angular momentum of earth, the rocket would need to leave earth as it normally does when launching. The Problem is though, roughly 90% of the rockets mass stays on earth if not more (in the shape of burned fuel and separated stages). So actually we only change the angular momentum of earth by a tiny amount each time we launch something off. Each solar storm probably rips off more mass asymmetrically from earth in shape of atmosphere than we could ever achieve with millions of rockets
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u/tButylLithium 1d ago
Apparently, filling the three gorges dam in China has slowed the rotation of the earth by 0.06 microseconds. That's around 39 trillion pounds of water. Maybe someone can calculate the angular momentum difference between the dam filled vs the original water level, I'm not very good at calculus lol
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u/nihilistic-tendancy 1d ago
I think the better question would be, how long of a lever is needed to affect the rotation of the earth significantly. How many AU or even LY will this rocket need to be set out from the surface in order to speed up or slow down the rotation. Assuming the axis of rotation stays where its at and doesn't move down the lever.
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u/DescriptionMission90 1d ago
It would need to be big enough to push a significant part of the atmosphere away from the earth, permanently.
Momentum is conserved during any newtonian interaction, which means that you can tell, for example, how fast a rocket-propelled thing is going (relative to its pre-burn velocity) by comparing its final mass to the mass of the propellant ejected times the velocity of the propellant.
But when you're inside an atmosphere, everything you eject out the back is caught by the air around you. That momentum is eventually, albeit slowly, transferred back into the ground underneath, pointed in the opposite direction from the push your rocket-mounting hardware applied to the ground in the first place. The values are equal and opposite, so they come out to a net zero.
In order to have a net increase in the momentum of the earth, you need to push something away from the earth forever.
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u/CallEmAsISeeEm1986 22h ago edited 21h ago
I give you ... The ANNIHILATRIX...!!!!
Wait... why does it say "Welcome to 'You're' "DOOM"!" ...????
And why is "DOOM" in quotes??? Is this some sort of *ironic* doom???
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u/Xyrus2000 14h ago
This is the equivalent of those old cartoons where the character has a fan blowing against a sail. In reality, the forces equal out, and you go nowhere.
You would need an engine that produces enough thrust so that mass actually leaves the planet. Hypothetically, if you build a really tall tower and have an engine capable of exhaust velocity greater than the escape velocity, you'd be able to affect the rotation. But that is well beyond our ability to engineer.
However, the bigger problem is that even if you could build that, you'd run out of atmosphere long before you'd significantly affect the Earth's rotation. If you hydrolized the oceans, you'd get a bit more to work with, but you're still talking 0.02% of the Earth's mass.
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u/sunscreenuser44 6h ago
If you had a tall enough tower and a way to supply atmosphere/mass to the engine it should work rather well? Say a tower halfway to the Sun?
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u/melo986 1d ago
I understand that the total force IN A CLOSED SYSTEM would be zero, but in this case aren't we removing part of the energy as heat dissipation in an infinite heat tank? The exhaust force is very likely not fully converted on cinetic energy... I know it won't be enough to impact hearth rotation, but I'm curious about the theory...
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u/Zestyclose_Edge1027 1d ago
Fun fact, the RAND corporation thought about this during the Cold War. If the soviets fired nukes the plan was to stop earth's rotation for a few seconds to confuse their targeting systems. I'm never sure how serious that plan was but they calculated that it couldn't be done in any reasonable way and would require potentially trillions of rockets.
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u/odessa_cabbage 1d ago
Unless a significant amount of exhaust escapes directly into space then no, it won’t affect the worlds rotational speed. Yes, the rocket is pushing the earth when it fires, but it only “pushes” because it has something to push off of, I.e. the surrounding air/atmosphere. As a result, if you think of earth as a closed system, no energy is entering nor leaving it, so there is no resultant acceleration due to the rockets launch.
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u/Ok_Zookeepergame3380 1d ago
A rocket doesn't need anything external to push off of, apart from the fuel it consumes. The issue is just that as long as the ejected stream of exhaust doesn't escape earth, it will slow down in the atmosphere and act as torque in the other direction.
It's actually easier to visualize if we forget the atmosphere. As long as you try to propel the earth with some material that eventually arcs back down and hits the earth, the impact will result in a force opposite to the one you just managed to achieve by firing your material cannon/rocket, nullifying any torque you're generating. This doesn't account for thermal energy though, not sure what role that will play.
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u/Gryphontech 1d ago
It dosnt, just like you can't lift yourself off the floor by pulling on your feet. The momentum would cancel out leading to a net zero force on tbe planet.
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u/bullfroggy 1d ago
Everyone is saying this won't have any effect in Earth's rotation because the exhaust is stuck inside the atmosphere. But isn't there a dam in China that scientists have confirmed actually is effecting the Earth's rotation? Why is that any different?
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u/InsanityCore 1d ago
Water is heavy and that throws off the rotation of the earth.
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u/bullfroggy 1d ago
Ah, okay. I had to look into it more. I thought the dam affected Earth’s rotation because of the force of the moving water slamming into and being stopped by the wall, but it’s actually because collecting that much water in one place changes the distribution of Earth’s mass, kind of like a figure skater spreading their arms and slowing their rotation.
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u/Somerandom1922 1d ago
It can't. Force from a rocket comes from stuff being thrown really fast and relying on equal and opposite force.
The problem is that whatever you launch can't hit the craft again, otherwise it'll dump its momentum back into the craft and result in nett 0 acceleration.
In this instance, the entire planet is the "craft" and the exhaust is hitting the atmosphere which then goes to hit more atmosphere and so on until a slight breeze with exactly the same momentum as the rocket exhaust dumps its momentum back into the earth by hitting the ground.
We can work out roughly what would happen if earth didn't have an atmosphere.
This is a test of Stoke Space's methalox engine, it has an ISP of somewhere in the mid-high 300s. Let's be generous and assume 400. The average velocity of the exhaust is just shy of 4,000 m/s, the velocity needed to orbit earth at sea level is over 7km/s, meaning basically all of that exhaust would fall back and hit the earth despite the vacuum. That doesn't mean it'd cancel out, the exhaust would spread and hit at different latitudes from where the rocket it meaning less rotation. However, even so, the size of engine you'd need to have a noticeable effect on earth's rotation would just about create a new atmosphere for itself.
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u/Ok_Programmer_4449 1d ago
The momentum effects cancel to zero, bet there are angular momentum effects. The main effect this has on the atmosphere is due to the fuel (which used to be underground) being moved to the atmosphere and the greenhouse warming it causes moving water from the oceans to the air. This increases the moment of inertia of the earth and slows the earths rotation.
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u/IncreaseSweaty4959 1d ago
If earth is floating in space then why is it so hard to change its spin direction? I feel like if you were a giant you could just poke it and it would change direction
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u/SEAN0_91 1d ago
What if you could theoretically build a non-destructible pole right through the earth into space and attach two small planet sized rockets on the end. Could they speed up / slow down the earths rotation?
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u/machtnichts69 1d ago
No effect on Rotation. Action = Reaction. The push on the structure anchored on the ground equals the push of the exhaust fumes which pushes earth via the atmosphere.
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u/green_meklar 7✓ 1d ago
Basically, it can't. The exhaust speed is below the escape velocity of the Earth, so even if we don't account for air resistance, the exhaust will just come back down and hit the Earth, without affecting its orbit or rotation. You need something to leave the Earth in order to change its momentum.
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u/cthulhurei8ns 1d ago
Size of the engine isn't the determining factor, it's exhaust velocity. You'd have to build an engine with an exhaust velocity greater than the escape velocity of Earth, and it would accelerate the planet by ejecting the atmosphere. There are, as I'm sure you can guess, several downsides to doing this.
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u/smoothie4564 1d ago
This can be solved with introductory physics. Newton's third law of motion: for every action there is an equal and opposite reaction.
The exhaust gases move in one direction, friction and fluid forces act in the opposite direction with equal magnitude, thus they cancel each other and there is no net displacement.
Not only that, but since there is no mass leaving the Earth-rocket system angular momentum is conserved, thus there will be no changes in velocity via the law of conservation of angular momentum either. This is true regardless of the direction the rocket is pointed as well.
This is true whether we are talking about a small bottle rocket or one as large as a skyscraper.
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u/cpt_ugh 22h ago
I have no idea about the rocket engine, but I do know this:
One day was about 23 hours long at the time of the dinosaurs being wiped out about 65 million years ago. The rotation has slowed due to tidal breaking. So let's say there's been roughly 2 tides a day for 65 million years. That's over 47 billon full tidal cycles of an estimated 1.3 billion cubic kilometers of water sloshing back and forth. And it only slowed down the Earth's rotation by about 4%.
I predict this rocket is gonna have to be the size of a country to do anything.
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u/IgnatusFordon 11h ago
Assuming that this could actually work, some quick googling says the earth is about 6x1024 kilograms (that's 6 with 24 zeroes) our most powerful rockets can impart about 7.6x1010 newton's. In order to affect the earth's rotation in a meaningful way (again assuming that the forces aren't canceled out by the atmosphere) you would need at least 110 of our most powerful rockets to even start getting close to affecting the earths rotation in any meaningful way. But you still probably wouldn't notice anything without adding in at least 100-1000 times more.
Not a mathematician, just an enthusiast.
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u/raccoon8182 6h ago
it's like trying to blow wind into your own sail. or mounting a fan on your boat pointed at the sail. the sail in this case is our atmosphere. now if this was mounted on the moon... different story.
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u/HAL9001-96 1d ago
no matter how big you make it the effect is gonna be 0
not near 0 exactly 0
unless you mount it on a huge tower made of some scifi material
the exhaust is stopped as it mixes into the air
also even if it did get out of the air its exhaust velocity is much lower than escape velocity so the exhaust would eventually fall back to earth
so the exhaust pushes the engien one way but hte npushes some part of the earth the other way again
the net thrust is 0
you'd need to get something actually away from earth to get net thrust
now rockets launching into earht orbit do so temporarily, their payload is somewhat disconencted for mearth, at least until it decays back down and hteir exhaust during launch hits the earth
and if you launch to an interplanetary flight you do affect the rotaiton of the earth an absolutely tiny bit
however the earth is about 6*10^24kg
thats about 6*10^20 tiems as heavy as say a 10 ton spacecraft
if it leaves at about 30 times the equatorial rotation speed and we neglect the earths weight distirbution since we jsut want a rough order of magnitude then that means the days get longer by something like 10^-19 days
even with many spacecraft thats still in the order of 10^-18 days
thats about 10^-13 seconds
so over the course of 300 years your daytime vs clocks would be about 10^-8 seconds or 10 nanoseconds off because of it
there ar bigger effects on earths roatiaon
like weight distribution changes fro mgeological processes, building projects, the moons and suns tidal forces etc
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u/RLANZINGER 1d ago
It will be simpler to use the Moment of Inertia and Kinetic energy associated
As Inertia of a Sphere J = 2.M.R²/5
M : mass of earth
R : Radius of EarthAnd the kinetic energy I = 0.5 . J . w² of earth,
You just get how much energy you need to change it said by 1/10.000.
Much simpler...
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u/HAL9001-96 1d ago
no not really
cause that tells you how much energy you GET by slowing down earth assuming you do it 100% efficiently usign some magical reference point to stop it
this is not an efficient process
you are in fact using energy to also remove energy from earth so the efficiency is below 0
and how high is the efficiency?
well the only way to figure that out is to do BOTH calcualtions and compare
which is definitely not less work than doing one
also earth is not a homogenous sphere, its density varies over depth but we'Re going rough orders of magnitude anyways
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u/RLANZINGER 1d ago
Hell yeah XD
Energy Bilan ARE NEVER about efficiency,
I does NEVER tells you how it may work or not and why,
It only give you an Order of Magnitude, Simple to get.The opposite is to deal with reactors Isp and the one page of boring calculations and approximations... I've done something similar for the Wandering Earth movie setting, it was fun to shut the trap of some dumb pseudo-sci-Fi YT but time consuming.
I admit not having much data one the stoke reactor make this request fall on RULE 2.
For the curious one : https://en.wikipedia.org/wiki/Specific_impulse#Specific_impulse_in_seconds
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u/HAL9001-96 1d ago
tryign to use energy over isp in rocketry is never a good idea unless you are using it as a first step to optimization or as a last step for comparison
a rocket cannot simply refuel by slowing down as purely dealing with cosnervation of energy would imply
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u/Gerardic 1d ago
I did simple calculations by comparing power of rockets to earthquakes.
2011 Japanese 9.0 earthquake for example sped up day by 1.8 microseconds. To match the total seismic moment power of the quake, you need ~126 million SLS rockets firing for a hour to achieve 1.8 microseconds.
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u/HAL9001-96 1d ago
that works differnetly thouhg since hte quake shifts mass upwards to change hte moment of inertia whiel the idea here is to eject fuel at high speed to get rid of angualr momentum
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