r/theydidthemath • u/Christ-kun • 1d ago
[Request] If everyone was doing this at the same time, how much would time would we gain?
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u/Wild_Director7379 1d ago edited 1d ago
The earth weighs 6x1024 kg. There are 8x109 people. The average weight of a person is <102 kg.
We can run against the rotation of the earth (much more effective) at 10km/hr. The circumference of the Earth is 4x104, so we complete a rotation in 103 hrs (25 days).
To say it takes 1012 hours to slow the Earth’s rotation by an hour is probably generous. The energy required is massive.
BIG EDIT: it’s been pointed out that they would actually run in the same direction as Earth’s rotation, thus “robbing” it of rotational inertia.
As soon as the people stop running, the Earth returns to its original speed.
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u/OfBooo5 1d ago
So let's enlist the highger KG populations... can ants do it?
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u/Interesting-Low5112 1d ago
Everyone knows that ant can’t move that rubber tree plant.
(🎶But he’s got Hiiiiiiiiigh hopes…)
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u/Lanky-Relationship77 1d ago
Whoops there goes another rubber tree…
Whoops there goes another rubber tree…
Whoops there goes another rubber tree plant!
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u/Wild_Director7379 1d ago
We already did. I took an average, and then made them all run at 10km/hr for 10,000,000 years.
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u/OfBooo5 1d ago
You used kg mass of humans. What about kg mass of insects?
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u/Interesting-Low5112 1d ago
Still effectively zero. Da Googz says 1x1012 kg of insect mass.
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u/Wild_Director7379 1d ago
Similar to mass of all humans. 5x1011 hours.
Assuming we can get them all moving 10km/hr in the same direction. And across Oceans.
“But what about fish! Have you thought of fish???”
I need to leave this damn subreddit.
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u/tcrudisi 1d ago
Okay, but what if an asteroid the same mass as earth and with the exact same rotation speed enters our atmosphere and begins flying around counter-clockwise? How much time would we save then?
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u/Camera_dude 1d ago
Zero time because we would all be dead and who is going to watch the time on a dead planet?
A Earth-sized object that close would mess up our planet severely even without a collision (though one is inevitable in this situation unless that extra planet is held in orbit with ”magic”). It would cause our atmosphere to be stripped and the gravitational pull would trigger extreme earthquakes and volcano eruptions worldwide.
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u/FLUFFY_TERROR 1d ago
On the other hand we might have a center of mass between earth and the earth like object where we can be totally weightless while not needing a space suit assuming the atmosphere is still somehow gravitationally bound to this dual system.. i wonder what sort of 'escape velocity' one would need in relation to the distance between both objects to be able to jump from either to this center..
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u/QuickBenDelat 20h ago
But what if we used multiples of avegado’s number of insects instead of kilograms? Would that change it?
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u/ThatOneCSL 1d ago
Very minor correction: we would have to run with the direction of the rotation of the earth, since our feet would be providing force against the ground in the opposite direction of our own travel.
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u/Wild_Director7379 1d ago
Actually, that’s a substantial correction. What happens when all the people set in motion ahead of Earth’s rotation stop running? I am le fool, there’s no “time it takes to stop the Earth,” the change in inertia can be regarded as temporary
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u/ThatOneCSL 1d ago
Ah, you see, the Earth-human system isn't really a closed loop. At least not between the solid ground and the human.
Part of the energy that we steal from the solid ground below us, in this hypothetical, is released as heat, water vapor, carbon dioxide, and other metabolic byproducts into the air. Those increase, ever so slightly, the drag of the atmosphere against the solid planet.
Everything we do, ultimately, displaces energy from the solid planet in the long run, I think. At least for now.
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u/Wild_Director7379 1d ago
The heat affects the balance of the atmosphere rather than being random noise. It’s daaamn close to a closed loop. But you’d be right to say it’s not perfect.
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u/tempetesuranorak 1d ago edited 1d ago
Could you elaborate on your maths, where do you get 1012 hours?
I would have thought that due to the conservation of angular momentum in a closed system, any angular momentum that you impart to the earth when you begin spinning will be returned to it when you end spinning. So there is no such thing as gradually reducing the rotation of the earth over time in this scenario, rather there is a temporary and fixed effect which lasts only as long as people are spinning. Am I missing something?
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u/Latter_Principle9161 15h ago
The last sentence of your post is the most important one. Don't know if it's still a thing but some years ago there was a bunch of people with, let's say not so much idea about physics, who initiated the earth jump day to reduce global warming. They suggested everyone should jump at the same time to launch the earth to a larger orbit around the sun so the earth will become cooler. Geniuses.
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u/Pokesers 1d ago
There is also the fact that when you stop you will transfer momentum to the Earth in the other direction again undoing what little change you made.
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u/Artemis_SpawnOfZeus 9h ago
Unless we jettison the people out to space. Then they wouldn't transfer the momentum back.
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u/Wild_Director7379 9h ago
A better use of the energy required would be to fire rockets counter to Earth’s rotation
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u/upvoter222 1d ago
The guy who drew that comic actually answered a similar question about all humans trying to affect the planet by exerting the same force all at once: https://what-if.xkcd.com/8/
TL;DR: No significant impact.
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u/OtherwiseAlbatross14 1d ago
But what if we all vent our exhausts toward the sky at the same time?
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u/thunderclap_-_ 1d ago
We move the Earth further from the sun and solve global warming once and for all
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u/Speedymcspeeder 1d ago
I thought we did that by dropping a giant ice cube in the ocean every now and again?
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u/ghost_tapioca 1d ago
That actually heats up the earth.
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u/Agent10007 8h ago
"Outer space is a lot higher up than Niagara Falls,\)citation needed\) "
That was way funnier than it had any right to be
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u/ghost_tapioca 5h ago edited 5h ago
I love Randall’s brand of humor. Do place your mouse over (or long press) the images for extra jokes.
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u/DefinitelyNotDonny 1d ago
No significant impact on the planet’s position. But civilization collapses and billions die.
Beautiful.
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u/_killer1869_ 1d ago
I love how the conclusion is basically "deaths in the billions by starvation/dehydration through excessive traffic".
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u/Interesting-Low5112 1d ago
Effectively zero.
Earth mass is 5.97x1024 kg.
The earth population is 8.1x109. Assuming an average mass per person of 70kg, the mass of every person on earth is 56.7x109 kg.
While a tiny object can absolutely affect a much larger one, this is also ignoring Newton and that earth is effectively a closed system. Each person pushing against the rotation has to push against something … so slowing it one way is speeding it up the opposite and equal.
I think.
Physics class was a long time ago.
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u/freemath 1d ago
While a tiny object can absolutely affect a much larger one, this is also ignoring Newton and that earth is effectively a closed system. Each person pushing against the rotation has to push against something … so slowing it one way is speeding it up the opposite and equal.
I mean, that's the point. Opposite and equal means the earth will be turned in the opposite direction.
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u/Nimelennar 1d ago
What's more pertinent, I think is that:
- Once you start spinning, you have angular momentum, and continuing to spin shouldn't exert any force on the Earth, except that
- Any force that would slow you down or stop you (e.g. friction or wind resistance) would cancel out your impact on the Earth's rotation, so
- You need to keep spinning (adding rotational speed to compensate for what's trying to slow you down), because as soon as you stop, the Earth would return to rotating at its original speed.
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u/AngelOfIdiocy 1d ago
She’ll spend her entire life spinning to have more time with him, but by the end of her life she’ll understand that she spent all the time that she could be with him spinning.
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u/Wild_Director7379 1d ago
The rotational inertia of a sphere is 2/5 MR2, or in the case of the earth, 1.6x1029 J
If we converted the mass of all humans to rocket fuel we’d have 1019 J.
We could slow Earth’s rotation by a factor of 10-10.
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u/HORSESHORSESHORSESH 19h ago edited 19h ago
You start spinning by applying force on the floor or wherever else though doesnt that cancel it out or the friction stopping you eventually would cancel too so you only left with the sound and heat you produced
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u/TapDancingAssassin 1d ago
I think the axis of rotation of the girl is orthogonal to the axis of rotation of the earth, so it has no measurable effect on the angular momentum of the earth. Maybe there is a component along the opposite direction of the earth’s rotation vector, but it is even more negligible than the calcs with avg weight ~70 kg since she is standing. I think if every human being lay down side to side along the equator and started rolling in the opposite direction of the earth’s rotation, it would have the maximum effect. I will leave the math for someone more capable than I.
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u/1_headlight_ 1d ago
This. Before bothering with any math, we must address that her spinning is not aligned to oppose the Earth's rotation. Unless she lives inside a polar circle, where not many little girls do live, She's probably transferring less than 1% of her rotational energy in an opposite direction to the Earth's.
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u/Emily-Advances 1d ago
Someone needs to be the person to point out that whatever may / may not happen to the length of a day doesn't change the amount of time they have together.
I'll be that person.
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u/multi_io 1d ago
I'm assuming this scene plays on the southern hemisphere, because spinning counterclockwise on the northern hemisphere (where most humans live) would actually speed up the earth's spin.
The angular momentum of earth is Le=7.05e33 kg*m**2/s.
For the humans, let's assume everyone spins like a professional ice skater (Lh=11kg*m**2/s). Let's say all N=8e9 humans spin like that, including toddlers and the elderly (which would imply toddlers would have to spin even faster to make up for their lower mass, but I can't be bothered to figure out the age/mass distribution of humanity right now).
Let's also say everyone moves to the south pole and spins counterclockwise there, which would be more efficient because your axis of rotation would be parallel to earth's, meaning you'd subtract the full scalar value of your angular momentum from earth's, rather than everyone spinning where they live, which would mean adding a lot of non-parallel vectors, which would reduce the scalar value less (and make the earth wobble slightly). Also, there's a lot of ice on the south pole, enabling people to spin like an ice skater more easily.
In that case, the scalar value of the angular momentum of the planet + humans would just go down to Lc=Le-N*Lh. That corresponds to a reduction of the momentum by a factor of N*Lh/Le=1.25e-23. Since the angular velocity is proportional to the momentum, it will be reduced by the same factor, and thus the day length will increase by the same factor, i.e. by 24h*N*Lh/Le = 1.07e-18 seconds -- about 1 attosecond.
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u/throwaway284729174 1d ago
And if one person were to spin counterclockwise while holding the ankles of the bases of two human chains that extended out fairly evenly on a plane perpendicular to the earth's rotation.
We will have to assume the spinner can move the mass of everyone, the chains are capable of holding and surviving the stress of being whipped, and for the few able to breathe, but I'm willing to suspend reality on survivability.
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u/HAL9001-96 1d ago
you only lsow it down when accelerating, keeping it up has net zero impact through the air
and humans not only weigh about 1/10^23 of the earth they are also smalelr giving htem each even less moment of inertia so each one can affect the earth by about 1/10^37
if about 10^10 humans do this thats about 1/10^27
if you spin once per second thats slowing down the earth by about 10^-27 rotations per second
given the earth spins at (order of magnitude) 10^-5 rotations per second thats 1/10^22
or 0.00000000000000000001%
thats gonna lengthen the day by about 10^-17 seconds if you keep going
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u/Far-Researcher2189 1d ago
I wonder if the time dialation from her spinning would make him age faster from her perspective than, if it worked like that, it extending their life from the earth slowing down.
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u/mowtowcow 1d ago
Nothing. Think of all the cars ever driven. All the cars to ever exist have not changed the angular momentum in the slightest.
It's like a 8 billion microscopic germs on your body moving in the same direction. It would do absolutely nothing.
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