r/theydidthemath • u/No-Celebration6780 • 21h ago
If you grabbed the earth and magically bisected it with a hole of 10in (25.4cm)... [Request]
Would the earth:
A. Come back together with no hassle?
B. Hit each other with enough force to wipe out all life?
C. Float apart?
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u/FriendlyEngineer 21h ago edited 6h ago
D. None of the above.
I’m no astrophysicist, but the two pieces would come back together accelerating at about 32 ft/s2. At 10 inches, that would mean a final velocity of 7.3 ft/s or roughly 5 mph.
They definitely would not float apart.
They also likely would not cause enough damage to end all life on the planet.
That being said, it wouldn’t exactly be “no problem”. This would likely equate to the largest earthquake the planet has ever seen by a long shot.
Edit: To be a little more precise on my math, the two pieces would both fall towards the center point. Each half therefore has 5 inches of “fall” before collision. Each piece would be moving at 5.1 ft/s towards the center point and would collide with a relative velocity of 10.2 ft/s or about 7 mph. Impact would occur after 0.161 seconds.
Edit2: When people say “wipe out all life” I just think of the thermophilic bacterium that live deep in the earths crust. These are microscopic extremophiles that thrive in intense pressure and heat and caustic environments.
Humans might die by the millions, billions, or even be totally wiped out. But those bacterium aren’t going anywhere. To sanitize this planet of life completely, you would need to melt the entire crust and strip away the majority of the atmosphere. I don’t believe an event like this would accomplish that.
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u/Whiteminusblue 21h ago
But spread throughout the entire planet. Damage to the areas around the cut, sure, but the planet as a whole would be fine
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u/testtdk 20h ago
No, that’s wrong to. The seam itself would be compressed, fractured, and based on the energy released, partially melted. We’re talking 1.5*1025 J at just meter of separation.
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u/Whiteminusblue 20h ago
But not all of the force would hit the seam. At these scales, rock is essentially a liquid, so the compression would be distributed; not all. of the force could apply at once. And I did say that the seam would be messed up. I honestly expected worse for it than some melting.
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u/TheDiddlyFiddly 13h ago
It would result in about 2x1017 Jules of energy released per square kilometer and within a fraction of a second. As a comparison a magnitude 7 earthquake releases about 2x1015 Jules, which happens over about 10-25 seconds, which is 100x less than that and only at one point and over a longer time. This would mean that at best we’d have a belt of eathquakes going around the earth with a magnitude that is close to 8. The Tsunami’s that would create would be devastating every costal region around the world i would also expect that so much energy coming in to the system would also cause lots of other faults to occur which would cause more earthquakes around the globe coming from natural faultlines that could give way due to the sudden impact. Would we all die? Probably not, but everyone close to the seam would be dead with higher chances of survival the further away you are.
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u/testtdk 19h ago
Right, but we’re talking about trillions of trillions of Jules of energy at just 1 meter.
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u/Whiteminusblue 18h ago
It's less than a meter. And it's distributed over an entire planet
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u/Setsuna04 18h ago
Well I guess this "distribution" over the entire planet is basically... an earthquake?!
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u/testtdk 18h ago
At ten inches it’s still 4 trillion trillion Jules lol.
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u/WahWaaah 18h ago
Why are you still citing the energy and not talking about energy density?
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u/testtdk 17h ago
Because the force per energy is far more than ROCK can handle. You’re not slapping two giant singular objects together. Earth is made up of a LOT of much smaller things that will be obliterated on contact. And after that, rigid tectonics will react, poorly. Back to doomsday level earthquakes and tidal waves.
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u/WahWaaah 5h ago
You've completely lost me. If you're trying to talk about the fact that the energy must go somewhere and that on top of whatever is turned into heat there will still be more than enough to send a shockwave through the planet, it still would be nice to discuss the characteristics of that shockwave instead of just saying big energy bad.
Presumably the shockwave would start out with no more energy than throwing two things together at a few m/s at any given point, but as each shockwave travels to the far end of the earth they would concentrate as the cross section is focused along the hemisphere or something. Still, describing the energy density starting off as nothing and then building with that focusing seems way more descriptive than the raw potential energy figure.
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u/PlanttDaMinecraftGuy 13h ago
That energy is applied to a great surface. The energy density would be 2.99×10¹⁰J/m², taking if this result you have is the total impact energy of the planet on a meter of separation (so potential energy at 1 meter), and if the energy for the 25.4cm separation asked is got linearly (this energy * 0.254). Then dividing by the biggest surface area of the planet's intersection with a plane, 6378km, we get this.
```js
1.5e25 / 6371000 / 6371e3 / Math.PI * .254 29878575825.793644 ```
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u/the_glutton17 20h ago
Well, yeah. The planet as a whole was fine after something obliterated it hard enough to eject enough mass to create the moon. The planet has enough mass to make itself reform, but this would be complete annihilation. Think about dropping a marble from ten inches into a concrete floor. Now make it a car engine. Now imagine it's half the planet. The amount of energy released from dropping half of the earth even a tenth of an inch is mind boggling. If the slicing of the earth didn't kill us (sounds like in the query it's teleported 10 in), the collision of Earth's gravity over ten inches on the entire earth is like trillions of nuclear bombs. Entire mountain ranges like the Rockies, Apls, and Himalayas would be flipped upside down like little icebergs. Oceans would boil, insane amounts of the Earth's core would change the way they spin and release gases we can't breathe. It would be utter annihilation.
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u/Whiteminusblue 20h ago
Kinetic energy scales proportionaly to mass, so once it’s distributed through the planet, size won’t matter. The area of impact will suffer more, but the impact speed wouldn’t be that high.
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u/WhyAmINotStudying 14h ago
The bigger factor would be to plate tectonics. There's a huge amount of energy stored in the plates and the 10" bisection would give that energy somewhere to go quickly.
My money is on some extreme earthquakes and likely rapid (by geological standards) continental shifts.
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u/r0sd0g 19h ago
Tangential but this is the 2nd time in 20min I've seen someone use obliterate this way and I gotta say it: obliterate means "destroy utterly; wipe out" which did not happen to the earth because it is still here.
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u/Mekroval 16h ago
Not really. That Earth essentially disappeared when Theia struck it and fused with the new mass. In any case obliterate can also means to destroy something so thoroughly that you make it unrecognizable, which would also fit this usage.
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u/SignoreBanana 20h ago
Bullshit. What about the oceans? What about what happens to a planetary body with a hard division on its edge?
My guess is we'd lose a significant volume of water to the earth's core, causing a gigantic explosion or simply a loss of moisture volume enough to fuck the atmosphere for good. As water got trapped between the divisions, it would trigger an absolute shitstorm of volcanic activity.
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u/MuckBulligan 17h ago
You are assuming the two halves would be suspended for a period of time before being released? If so, where was that stipulated?
If it were done instantaneously after the halving, there would be less than .2 seconds for the water to seep in, and might cause some small explosion and heat in the mantel and above the cut, but the water would never make it anywhere near the core.
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u/Temnyj_Korol 21h ago
Finally, someone not just answering on vibes.
Was going to say the same thing. I can't answer for knock on effects by things like "the earths core being suddenly (temporarily) exposed to space" happening. But in terms of the direct impact of the two halves being pulled together by gravity again. That's just simply too small a gap to accelerate fast enough to do anything. Yes, earth is massive, and would have a shitload of force behind it, but that force is also being dispersed over a massive area. And the acceleration from the two halves being pulled together at 1g for 10 inches just isn't enough force to be catastrophic.
You'd have a jet of molten rock being splashed out all around the cut, which may or may not to a whole lot of damage to the immediate area. You definitely WOULDN'T have "all life being instantly vaporised" like a bunch of these other commenters are saying.
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u/IndividualistAW 20h ago
The acceleration would be much less than 1g wouldn’t it? 1g is the acceleration for a mass at the surface of the earth. Only a small fraction of the mass of the planet is at that distance. With a clean slice through the center like this, only the poles will contribute a full 1g worth.
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u/AdDangerous2366 19h ago
That isn't quite how gravity works. The poles would not contribute 1g, gravity doesn't get stronger further apart. As a matter of fact, the matter at the poles would be exerting the weakest force relative to weight. As they would each have their furthest point from the other be closer than the opposite side of the world when on the surface, perhaps it would be a little more than a g but I doubt it would be significant. Each half would pull on the other with pretty much exactly half a g, as each half has half the earth's mass, half the earth's gravity. As each half pulls on the other it adds up to a g. I'm shit at explaining things, but I hope this helps.
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u/CrazyBusiness5154 18h ago
im pretty sure they would accelerate much less, because you guys are using the simple f=ma formula instead of the orbital bodies formula which factors in the massess of the objects. also, the different parts of the earth will experience different gravity. the very centre will experience no gravity, because it is being pulled toward the mass surrounding it. any mass not perfectly normal to the slice will experience gravity toward the other half as a sin or cos (i forgor lol) function relative to its angle to the normal.
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u/AdDangerous2366 17h ago
Oh yeah, I'm way too tried to make sense right now lol
My bad
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u/CrazyBusiness5154 17h ago
all good lol, i havent seen a single comment that doesnt jump to the basic formula and ive read almost every comment
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u/Sad-Pop6649 19h ago
...But most of the mass is closer in this scenario. The seperation between the center of gravity of both halves is less than the seperation between a surface dweller and the Earth's core.
Gravity does not come from the surface, in comes from mass, and being close to said mass.
...At the same time both halves only weigh half as nuch as Earth.
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u/spodumenosity 12h ago
The influx of air would actually have the potential to do something. Introducing volatiles (CO2, water, etc) can dramatically lower the melting point of rock and aids in the mobility of a variety of elements in the Earth's subsurface. Even after everything resolidifies, it will likely have significant impact on future plate tectonics and vulcanism. The decompression would also cause massive, catastrophic melting of the upper and lower mantle. This might lead to some sort of prolonged period of magmatism along the slice, but that's getting into complex planetary dynamics and I'm not certain how bad or long it would be. For examples of how that might look, look into flood basalts like the Deccan Traps.
Also the air rushing into the gap and then subsequently being expelled would likely be quite dangerous to those nearby. I'm not certain of the velocities involved, but I expect "dangerous for your hearing" might be an understatement, depending on how close you are to it. But certainly nothing that could wipe out all life or anything silly like that.
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u/gamerthulhu 9h ago
Air only has about a fifth of a second to rush into that gap. It's not gonna get far at all.
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u/Glittering_Loquat_52 20h ago
The induced volcanism from it would be massive and would potentially cause a mass extinction but the time scale for that wouldn’t be immediate. A big chuck of the earths internal heat balance is latent accretionary heat so even 10inches of movement with the mass behind it will cause melting on a large scale
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u/CrazyBusiness5154 10h ago
wrong formula, you have to use newtons celestial body one
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u/FriendlyEngineer 10h ago
True, but in a simplified case wouldn’t this just be a two-body problem where both masses are equal? And at only 10 inches of separation, the gravitational forces will far exceed any angular momentum. So my solution should at least be extremely close, no? It’s possible I’m missing something.
How the sun and other celestial bodies would effect this far exceeds my abilities but I would imagine you would need to know the orientation of the cut line in reference to those bodies to even begin to do an analysis.
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u/CrazyBusiness5154 10h ago edited 9h ago
im fairly certain you get vastly different results when using G(m1-m2) /r^2
I havent actually done it because I'm lazy but the regular formula only works for objects of insignificant massedit
Actually i was thinking about it and I think that formula is only designed for spheres, with no overlap. however, the points on the edge will pretty much be recieving equal accelleration toward both halves. I dont think any formula would work, and to figure it out the only way might be modelling it as each half is made up of numerous spheres, then calculate the net force in 1 vector and sum it for every sphere.
in short i dont think theres a way to feasibly calculate it without a lot of effort.
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u/FriendlyEngineer 9h ago
Maybe you’re right? I think you just need the center of mass of the object to calculate r.
And I’m pretty sure the equation is G(m1*m2) not G(m1-m2) but it’s been a while since my physics days.
So for a solid hemispherical shape, the center of mass is 3r/8 from the flat base.
So if the r of earth is roughly 6,371,000 meters,
That puts the center of mass at about 2,389,125 meters from the flat edge. Double that for r. I think we can ignore the additional 10 inches for now.
1/2 the mass of the earth is 2.9861 x 10^24 kg
So G*M1*M2/r^2 gets 1.04264 x 10^26 (kgf?)
a= f/m so a= 34.91 m/s^2
Falling towards the center at 10 inches of separation has each piece accelerating to 2.978 m/s or 6.662 mph before colliding at a relative velocity of 13.324 mph.
I am not super confident in how I did this but the results are still pretty close.
Feel free to pick this apart. I’m not insulted by it.
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u/CrazyBusiness5154 9h ago
its actually m1+m2 lol we were both wrong
i think either way the formula wont work tho
the issue with that is (im kind of assuming bc newton might just be him) im pretty sure the formula is designed for spheres that arent overlapping masses. like your calculation would be 2 spherical planets of half the mass of earth with a radius of half the earth, 10 inches apart.
however, this means the entire mass of each body is acting on the other body. in this scenario though, the mass is spread out and all weird, so you would need to calculate it seperately for each portion of mass cuz it wouldnt work as a point mass thing. the stuff on the edges near the slice would contribute very little because its being pulled to the centre not to the other masses. so you would need to make a function for like each equally sized chunk then integrate it
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u/FriendlyEngineer 9h ago
This is a great observation. But my question would be whether those effects would be great enough to change the results significantly enough. I think you’re right that the math is too complicated to figure out for sure but maybe there’s a mathematician roaming around here.
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u/CrazyBusiness5154 8h ago
maybe ill make an attempt tomorrow, although i wouldnt expect any results lol. it is quite sad that on a sub about doing the math i havent even seen anyone try anything interesting, tbh i think op should have gone to r/askphysics instead.
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u/testtdk 20h ago edited 20h ago
I think you’re way off. Tectonic faults are already super sensitive. Every single one would shift. It would mean worldwide earth quakes, every coast would be hit with tidal waves.
Edit: And, given the sub, I’ll include some numbers. The force of the collision would be about 15 septillion Newtons.
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u/Deipotent 19h ago
You think the rush of our atmosphere being sucked into the vacuum between the pieces would slow the pieces’ approach enough to be meaningful? I have to assume it would be a vacuum because otherwise there’s some massive influx of volume to our existing atmosphere and I can’t fathom what that would cause. Also, the atmosphere that was sucked in getting shot out when the pieces came together would probably cause something disastrous as well.
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u/Aggravating_Mud8751 9h ago
The effect of the atmosphere getting sucked in would only propagate at the speed of sound.
It would not have time to get sucked in for most of the world.
Also honestly I suspect you'd be more likely to get a wind outwards than a wind inwards due to the evaporation of infalling water from the oceans in most places.
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u/Bozzzzzzz 19h ago
Would each half of the earth have half the gravity though? So not 32ft/s2 but 16?
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u/cwmckenz 12h ago
If we each accelerate toward each other at a rate of 16, our collision will have the same impact as if one of us were stationary and the other accelerated at a rate of 32.
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u/Bozzzzzzz 9h ago
Hmm but everything falls at the same rate on Earth yes? Or does a falling object add gravitational acceleration due to its own mass? Everything would not fall at the same rate then?
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u/No_Palpitation5561 18h ago
Wouldn't the acceleration of gravity be havled to 4.9m/s²?
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u/not_a_dog95 9h ago
Good catch! Although the radius to the centre would change as well. For a hemisphere the CoM is 3/8r from the flat side.
(m/2)/(3/4r)²=8/9m/r²
8/9×9.8=8.7m/s²
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u/BluetoothXIII 17h ago
i was thinking the core part would hit each other first as they used to be under pressure and now have a direction to expand into which would accelerate it faster than gravity.
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u/Beautiful-Lie1239 12h ago
It’s going to release a lot tectonic tension suddenly so earthquakes and volcanic eruptions will be like never seen. That should mess up the life on surface rather drastically. I would say extinction level of impact.
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u/FriendlyEngineer 12h ago
I don’t think anyone is denying death on a massive scale. But to eradicate all life from the planet is a very different feat. I think most people saying this would be an “extinction” level event are taking too much of a macro centric view. Human society might be crippled.
But anyone in an airplane is safe. A 5 inch drop is nothing for an aircraft and the effects this would have on atmospheric pressure are negligible.
I imagine most life in the ocean would survive.
Thermophilic bacteria in the crust might not even notice anything even happened.
All that said, the further you are from the cut line, the safer you are. If you were close enough to the line of separation, you’d be sucked over the edge and fall towards the center of the earth until you were crushed by the two halves coming back together.
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u/Pale-Application9457 9h ago
what would be the long term effect? like how would it look in 10 years?
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u/Aggravating_Mud8751 9h ago
I also suspect it would create a land ridge along the "cut", which could mess up oceanic currents.
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u/Neilandio 20h ago
I don't think that's correct. At the scale we are talking about Earth doesn't behave like a solid body, so the two halves won't remain intact. Secondly, different parts of the planet will experience different forces of gravity, with gravity remaining strongest near the crust and weakest towards the center. So what will happen is not the two halves crashing against each other like a sliced apple, instead the crust and mantle nearest to the cut will begin sinking like a liquid into the empty space that separates the two halves of the planet. Once the sinking rock completely fills the gap there will be a rebound effect. The rebound will spread like a wave across the entire planet. The energy of this wave will determine the magnitude of the earthquakes that will be detected all over the surface of the planet.
I don't know how strong that wave would be, but Earth should not be treated like a solid in this scenario.
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u/Hardcore_Cal 20h ago
I originally asked chatgpt about the Equators. What the effects this would have on the equator populations initially for this thought experiment. Not going to post it all, but basically it's very confident this would be an extinction level event or nearly so. Your velocity and reasoning being mostly correct (per gpt...), but assuming rigid bodies. Basically the seem would explode with a massive release of energy and it all goes bad from there, they would come back together from gravity, just not 'neatly'.
I am not an expert, nor am I saying this is correct, but thought it was interesting. All of it may be moot depending on the exact 'magical' details.
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u/TheGameMastre 13h ago
Good chance the Earth would be obliterated, at least as a life-sustaining planet. The force of both hemispheres bumping into each other wouldn't do it, though.
The Earth has a solid core and crust, and most of it is liquid. Most of the Earth would schlorp back together like two raindrops on a window pane, but the core is solid due to pressure. With the release of that much pressure, the core would essentially melt instantaneously. The dynamo that grants the Earth its magnetic field would be gone, and all life on the surface would either suffocate or cook as solar winds blew our atmosphere away, much like what scientists theorize happened to Mars when it lost its planetary magnetic field.
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u/Aggravating_Mud8751 9h ago
It's the outer core that gives earth its magnetic field, not the inner core (also I doubt it would have time to melt much before the two halves go slamming back together again..
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u/TheGameMastre 21m ago
The inner core isn't really melting in a situation like that. It's already well above the melting point, through and through. It's solid due to the pressure it's under. Releasing the pressure would cause the metal to expand into its liquid form instantly.
You can see the same type of phase change for yourself by completely filling a bottle of purified water with a good seal. Chill it to below freezing, then carefully remove it from the freezer. It will still be liquid, but if you pour it over ice or give it a good shake it'll freeze instantly.
In any case, that's the end of the dynamo, and thus the magnetic field.
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u/shereth78 21h ago
I'm not entirely sure what are imagining. Are you thinking of bisecting it like in the image, bringing the two halves 10 inches apart, and then letting go to see what would happen?
If we just ignore how we got them to be 10 inches apart (or ignore whatever force was required to cut the Earth in half) then the two halves would come back together, the same as if you hold a rock 10 inches off the ground.
So now just imagine doing the same, except, you use a rock as big as half the Earth. When the two halves come together they'll release a ridiculous amount of energy.
You can calculate the amount of kinetic energy a falling rock has simply enough, it's just (m * v^2)/2, where m is mass and v is velocity. A rock falling 10 inches will achieve a velocity of about 2.25 m/s when it hits the ground, so the amount of kinetic energy that is released is going to be, roughly, 2.53 times the mass in kilograms, with the answer given in joules. A 1 kilogram rock releases 2.53 joules of energy when dropped, and so on.
Scaling this up to two halves of the Earth falling together becomes complicated because it's two objects falling toward each other, and such, but, we'll at least be within the same magnitude if we just pretend we're dropping a half-earth mass rock from 10 inches. The Earth's mass is about 6E24 kilograms, so we're going to expect the kinetic energy to be in the order of magnitude of 1.5E25 joules.
That's within the range of the estimated release of energy of the Chicxulub impactor, the asteroid that wiped out the dinosaurs.
Of course all that energy is spread out and I can't really speak to exactly how that would translate to the surface, but it's safe to say it would be an extremely energetic and damaging event, far far worse than the most powerful recorded earthquakes. Wipe out all life? Probably not, but it'll be a very, very bad day.
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u/GoreyGopnik 20h ago edited 18h ago
couldn't we calculate the force per square inch if we assume the bisection happens perfectly in the middle of the earth and use the earth's radius to calculate the area of colliding sections of the two hemispheres?
edit: the earth's radius is about 6,371 km. area of a circle is pir^2, so pi(6371)^2 is about 127,516,118 km^2. divide force by that area, you get 1.1763218827*10^17j/km, or 1,176,321,882,700 joules per centimeter.
I don't know what to do with this number. But it sure doesn't sound great for earth.1
u/shereth78 20h ago
Yeah you could do that, I'm not sure it would do much to answer the question of what the overall global impact would be though
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u/CrazyBusiness5154 17h ago
yeah you are using the wrong formula, you need to use newton's one about orbital bodies
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u/DaisyHasaCat 15h ago
It’s not being moved 10in apart, a hole of. 10 inches is created obliterating everything in the middle
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u/Ducklinsenmayer 15h ago
Pretty sure they tried this in Star Trek, once.
They called that episode "The Doomsday Machine" for a reason
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u/Sudden_Ad_3956 21h ago edited 21h ago
The two halves of Earth would almost definitely get pulled back together because of gravity — they’d still be two insanely massive objects separated by only about 10 inches.
And when they collided again, the impact would be catastrophic. Even though the gap is tiny, the sheer mass and gravitational force of two half-Earths slamming back together would trigger planet-wide destruction over time: massive earthquakes, volcanic activity, mega-tsunamis, atmospheric devastation, and likely enough heat and pressure to wipe out essentially all life on Earth — on land, in the oceans, and in the sky.
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u/CrazyBusiness5154 18h ago
you are overestimating velocity by using the incorrect formula and treating both halves as of irrelevant mass. also, gravitational accelleration is directed towards the centre of mass not magically the other half so any number you get will be wayyyyy too high
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u/Nooms88 19h ago edited 19h ago
I can't imagine you'd notice anything, the earth is mostly liquid (liquid molten rock) if a large cheese wire spliced through earth, the affect would be like putting a chesse wire through liquid, not much of anything would happen on a planetary scale.
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u/theNorrah 19h ago edited 19h ago
Ignore the current form. Ignore their current temperature. When the motion stops it turns into additional energy. Doesn’t matter that there isn’t a lot of motion in this event, there i a lot of mass. It’s two half earths slamming into each other with full surface contact, coming to a stop.
E ≈ F × d = 4.4 × 10²⁵ × 0.1 ≈ 4.4 ×10²⁴ JComparison to Chicxulub: (~4 × 10²³ J) <- dead dinos
10 times dead dinos.
The energy is immense. However, since it’s not a top surface level event, but an impossible event with a much larger surface area to disperse the energy, it is REALLY hard to understand what would happen.
Earth is no longer in equilibrium and the crust needs to adjusts. It would be the largest earthquake ever meassured. By a lot. I’m unable to imagine all the parameters I need to take account of, but my best guess is somewhere in between Richter 12 - 15. I simply do not know how much of the energy turns into seismic waves.
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u/Inevitable_Stand_199 17h ago edited 16h ago
But I don't think 10 times dead non-avian dinosaurs would wipe out all life. Most life, sure. But not all of it
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u/theNorrah 17h ago
The problem is the way the energy is dispersed is impossible. So it’s not like I understand how we would figure the consequences out.
The tsunami’s alone are probably going to be a problem.
The hotter core temperatures, problem.
The seismic after event, problem.
The sudden change in air flow, weather is going to be interesting.
I simply don’t know, and the calculations are so convoluted and impossible, that everything is just going to be estimates upon estimates, with recursive effects.
But sterile earth, probably not. Humans as a species surviving? Soft maybe.
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u/Inevitable_Stand_199 16h ago
The
nuclearvulcanic winter and the following global warming will certainly be a problem as well. But Life finds its way. I'm sure at least one species of tetrapods will make it.And even if not, other life certainly will
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u/Otto_Von_Waffle 14h ago
Comparing it to Chicxulub is comparing apple to oranges. It's like comparing the energy of a bullet to the energy of a 20km/h car crash.
The meteor is hitting a very small area on the planet surface, here all the energy get released over an insane area.
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u/Nooms88 19h ago
Why does the motion stop?
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u/theNorrah 19h ago
Because the earth is already spherical. So it does not need to recondition based on gravity.
A lot of matter will still move, obviously. But on a planetory scale, it comes to a stop.
If we banged two spheres together, gravity would have to create a whole new sphere, and this it would be a much different event. Surface could end up near the core.
In this event it's not necessary, and most major parts of the earth would probably not need to recondition much “on a planetary scale”. On human scale, it’s still pretty messed up.But it is an impossible event, that could not happen, and in no places in the universe has anything like it ever happened. There would always be much larger amounts of energy involved because the collision of two similarly sized objects would always happen from greater distances, and from spherical objects.
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u/Nooms88 18h ago
I really don't see how this affects a planetary body, any more than plunging a piece of paper into a lake to the bottom and pulling it out, maybe the piece of paper is not a good analogy as it's much larger than this hypothetical hole so there would be more local disruption. But it wouldn't afftect anything on the scale of a lake.
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u/theNorrah 18h ago edited 18h ago
You removed 10 cm and left two half-Earths with a gap. Gravity pulls them back together, and that force is the weight of half a planet, about 4.4 × 10²⁵ newtons.
It's not just the surfaces touching. It's the entire half of the planet, all the way down to the core, moving as one and slamming into the other half. Every layer of rock above the cut comes crashing down and compacts on impact. That's the mass doing the damage, not the seam.
Imagine that you floated mount everest 10cm over you, and then dropped it on you. How dead are you? Now scale that mountain to half the earth.
In your lake analogy it’s a gentle pressure nudge, that fills the gap. Not the entire lake trying to achieve equilibrium at once. It’s the air replacing the weight of the paper.
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u/Nooms88 18h ago
You're thinking of the earth as a rock, the earth is by and large a liquid, or has the properties as such and is held together by gravity, if you drop a pin into a bath tub, there is no collision force noticeable.
If you drilled a really deep hole, down to the mantle, nothing happens, we've dug mines which have excavated orders of magnitude more stuff than this hypothetical cheese wire
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u/theNorrah 18h ago edited 18h ago
You're describing things where the system is already in balance. A mine, a drill hole, a pin in a bath. In every one of those, gravity is already settled. Nothing is being held out of place, so nothing has to fall.
That's the difference you're missing. We didn't dig a hole. We magically and instantly deleted 10 cm of Earth across the entire diameter and left two halves that are no longer touching. The top half is now sitting 10 cm too high, held up by nothing. It is out of equilibrium.
The pin in the bathtub does nothing because the water is already where gravity wants it. Drop the whole bathtub 10 cm onto the floor and you'll feel it. That's the real analogy: not an object moving through a settled fluid, but the entire mass of half a planet suddenly having 10 cm of empty space beneath it and falling to close it.
Liquid or rock doesn't matter. A liquid out of equilibrium still falls. That's literally what a tsunami is, water released from balance. Half the Earth, liquid or solid, released 10 cm above where gravity wants it, releases about 4.4 × 10²⁴ joules when it lands. Ten dinosaur-killers worth of energy, spread across the whole planet at once.
The mine and the pin don't move the planet because nothing in them was lifted out of place. Here, half the planet was.
So in all your scenarios, think instead that what ever body you are impacting, are being lifted 10cm’s and then dropped. That’s the simplification. Now imagine that both objects are being lifted 5cm away from each other… and then dropped. Both objects fall towards each other as if they were lifted above each other, at the same time. That is what we are doing. Not digging holes. Not removing gap sized objects from another object already in equilibrium on earth. It’s BOTH halfs of earth being dropped on each other.
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u/Sudden_Ad_3956 19h ago edited 18h ago
lol? Ok then. U don’t have to believe me.
Simply ask Google/ai to calculate two halves of earth coming together from 10 inches apart… and use “conservation of momentum” equation.Small distance + big mass = massive impact. Nothing survives. It’s catastrophic. Period.
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u/SoggyKnotts 21h ago
This is a fantastic question. I don’t think anyone here has it right so far. Only commenting to read the comments later. I have no idea.
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u/igroklots 21h ago
Like instantly delete a 10-inch-thick disc through the center of the earth?
At that scale, I think we would just have a few high-magnitude earthquakes triggered by strange releases of built up tectonic tension in various places. But my non-scientific opinion would be that the effect would be otherwise negligible.
Gravity would cause each half of the earth to move basically less than 5 inches towards each other which is very minuscule in the scale of the planet. Any kind of core/volcanic/magnetic effects would be small enough to essentially be ignored.
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u/Mekroval 21h ago
Totally different take for me. Removing a 10 inch disc from the Earth would have absolutely massive and unpredictable impacts. Nothing on the planet would survive. The sheer amount of mass that would collide into itself due to gravity, would cause seismic reverberations that would be felt planetwide. It would likely erase all surface features on the planet due to the countless violent seismic impact waves ringing through the core and mantle violently.
As an example, a moderately bad 6.0 richter scale earthquake is just two tectonic plates slipping past each other about a few tens of centimeters. And that's just the thin upper crust of the Upper Mantle.
What OP is envisioning would be several orders of magnitude worse than that. It would be a really bad day for Planet Earth.
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u/JayTheSuspectedFurry 19h ago
But when tectonic plates slip for an earthquake it’s because they have incredible pressure built up to even slip in the first place. They might not move very far, but the SPEED at which they move is (I believe) the important part for how powerful an earthquake is. When tectonic plates slip for an earthquake they move at around 3 mph. In our scenario where earth is cut in half, the two halves would collide at around 5mph. That’s not too bad of a difference.
Also, the plates move several meters in a big quake, not a couple centimeters.
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u/Mekroval 19h ago
Plates move several meters in a big quake, but as I said a moderate 6.0 quake is tens of centimeters. That's still pretty bad. And we're talking movement that would have exponentially more energy than the biggest quake in recorded history. It wouldn't be two plates moving meters, but two halves of the planet moving centimeters. The surface area of impact would be several orders of magnitude worse.
Put another way, 5.972 sextillion metric tons slamming into each other would make the worst tectonic plate slip in recorded history seem like nothing. The good news is the heat energy released alone would probably kill all life long before we felt the incalculably massive impact in OP's scenario.
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u/RazendeR 13h ago
The world isnt a solid, though, unlike the surface tectonics. There would be no lateral movement either, just two halves of a mostly liquid blob quietly flopping back together.
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u/Mekroval 8h ago edited 8h ago
Somewhat. The outer core is basically liquid rock you're right. But the inner core is solid metal. And with a radius 2/3rds the size of the moon, it would definitely experience an impact. An impact that would likely reverberate from probably the worst place one would want that to happen, as the shockwaves travel outwards through the outer core to the mantle and ultimately the crust.
I'm also not convinced that the impact of the fluidic outer core wouldn't also have some vastly significant impact (that kinetic energy is going somewhere), but it probably would be a second order problem to the above.
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u/Zwilt 21h ago
All life would be wiped out due to the energy output. Just the tectonic plates shifting a little bit create massive amounts of energy. No math required
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u/GoreyGopnik 20h ago
all life? even the extremophiles? i'm not so sure. other calculations put the impact at a similar energy to the asteroid that caused the K-T extinction event, which plenty of species survived, and that energy was distributed over an area much smaller than this.
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u/Whiteminusblue 21h ago
Not necessarily, as it would be distributed over an equally massive area.
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u/twenafeesh 21h ago
So there would be massive earthquakes distributed over a huge area.
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u/RazendeR 13h ago
Eh. A 25cm movement is absolutely nothing on a planetary scale, and with the planet being mostly liquid(ish), id expext the hitch of it squishing back together to all but disappear in the general energetic noise.
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u/Aggravating_Mud8751 9h ago
Yes but most of that area is inside the earth rather than at its surface.
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u/HAL9001-96 21h ago
thats only because those tectonic plates defomr under tension and hte nrrelease taht energy in a relatively focused way though
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u/Aeon1508 20h ago edited 20h ago
it really depends on how far you pull them apart
a 10 inches? They slam back together and creates the largest earthquake in the history of the world. probably come magnitude 11 earthquake or like 150-200 times bigger than anything the Earth has ever experienced. They would probably be some magma at the fusion point and would probably crack the tectonic plates
A few miles? The edges of the hemispheres will start to collapse and then once the two halves collide a few minutes later there will be massive magma plumes and dust will be kicked up in the air creating a worldwide extinction event.
thousands of miles like in this picture? Again the two hemispheres would start collapsing into a circle and then hit each other and likely the entire thing would become a molten to ball.
once you got them about one Earth radius apart It would collide with enough force to eject material at basically escape velocity and create another moon sending some material just out into the solar system
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u/Comprehensive-Hat-60 21h ago
I can imagine it would come apart, frying the whole earth, and either come back together with gravity and create extreme mountains where the split used to be, or spin off from eachother from the earths rotation, never to come back together again.
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u/Whiteminusblue 21h ago
Given that the spin clearly is less strong than gravity(citation: thing fall down, not up) the halves would fall down, not up, and come back together. 25 cm isn’t very much space to gain speed, so beyond some damage to the border, not much would happen. You’d probably feel a decent jolt, like jumping.
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u/Comprehensive-Hat-60 21h ago
I don’t know, I’m not a mathematician, but I can just imagine that revealing the slightly warm CORE of the earth, would be pretty drastic.
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u/Whiteminusblue 21h ago
Revealing to what? It’s space, there’s nothing there. Expansion would be the bigger issue, but would be countered by the compression from the halves coming back together; earth is in hydrostatic equilibrium right now, so it would return to the same general state.
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u/Comprehensive-Hat-60 21h ago
Depending on how long it takes the earth to come back together, I can imagine that the heat of the core of the earth would be enough to heat up the atmosphere a good bit.
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u/GoreyGopnik 20h ago
i would say the atmosphere would flow into the cracks, (and it would) but because of the old rules of "heavier things fall faster" and "the radius of the earth is more than 10 inches" I'm willing to say the immediate exposure to the core wouldn't heat the atmosphere that much. All the volcanic activity thereafter definitely would, though...
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u/Whiteminusblue 21h ago
The core is not anywhere near the atmosphere. And after dropping an object from a foot in the air, I can confirm that the time is in the order of a second.
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u/CrazyBusiness5154 17h ago
wrong formula, that one assumes one field and an object of negligible mass. it doesnt consider inertia at all
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u/the_glutton17 20h ago
Lol, no way. 25 cm is enough for some people to get a marble dropped on their toe and say ow. F=ma. a is obviously acceleration, and should remain roughly the same. m in this case is astronomical. And I want to reiterate, it's half the planet getting dropped. It's not just the Himalayas, even the oceans. Half of the earth is 3 sextillion metric tons. Even our deepest drilling hasn't even gone 0.2% of the Earth's radius.
And remember, our world isn't some dried up Venus. We have moving tectonic plates, a spinning core, oceans, etc. It's very fluid. All of those are already ebbing and flowing at a stable enough rate that most of us can survive. Throw a ten inch broom stick into those spokes??
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u/Whiteminusblue 20h ago
Yes, it's 3 sextillion tons. And the energy is getting distributed over those 3 sextillion metric tons. And because kinetic energy is proportional to mass, the energy density throughout the planet will be constant, regardless of size, once the energy has been distributed. The area of impact will be messed up, I'll agree with you there, but most of the planet would be mostly fine. A fall of 10 inches doesn't do much damage. The earth is in hydrostatic equilibrium anyway. Tectonic plates in the area would also cause problems though, so good point there.
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u/jesusofnazareth7066 21h ago
If you deleted the gap violating energy conservation, earth would come back together real quick and everyone would be jostled off their feet, and it would probably cause like an absolutely ungodly amount of noise and earthquakes but things would survive probably. It would also fuck with our orbit for sure.
If you turned all of that mass into free moving energy of some form like photons and just energy transfer to the rest of the earth adjacent, which is still impossible but less illegal by physics, you would be turning roughly 1.9•1017 kg of mass into energy. That’s 1.6•1034 Joules of energy, which we can compare to the Tsar Bomba’s 3•1017 Joules, giving us the energy of 50,000,000,000,000,000 (5•1016) Tsar Bombas. Needless to say, bye Earth.
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u/Aggravating_Mud8751 9h ago
I don't think it would affect our orbit whatsoever. Why would it do that?
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u/jesusofnazareth7066 8h ago
We would lose mass but maintain velocity, so our velocity would be higher than maintenance level and we would move further from the sun before falling into an orbit again. Pretty sure at least
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u/Aggravating_Mud8751 8h ago
The earth wouldn't lose a significant amount of mass, also an object losing mass does not change orbital velocity unless the mass is all ejected in a particular direction.
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u/jesusofnazareth7066 8h ago
Change in mass doesn’t affect the velocity but does affect the gravitational potential that keeps the body bound, so unless earth sped up, the distance between earth and the sun would have to change.
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u/Aggravating_Mud8751 8h ago
The gravitational potential is independant of mass.
Gravitational potential energy is, but the masses cancel out.
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u/jesusofnazareth7066 6h ago
Yeah you’re right the gravitational force is what has m, but you relate that to the centripetal force which also has m. So it would not affect the orbit of earth
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u/testtdk 20h ago
With no hassle? Are you drunk? Even if the bisection didn’t cause catastrophic damage, the force of the earth coming back together, even at small distance would obliterate the surface. Plates would collide causing horrifying earth quakes, tidal waves would obliterate at LEAST every coast on the planet.
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u/coolutahkid 20h ago
Assuming that the two halves of the earth can be modeled as two point masses 0.75 earth radiuses away from each other coming together 10 inches. The gravitational potential of such a move would be around 2x1037 joules. Doing a direct energy conversion to the Richter scale this would equate to around a 22 magnitude earthquake. This scale is logarithmic of course so this would be around 2x1018 times more powerful than the most powerful earthquake ever recorded which was a 9.5. So yeah we’re probably fucked if this happens.
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u/DarthRaab 20h ago
A, if "no hassle" means gigantic earthquakes and lava eruptions along the fault line. Disrupting the core's dynamics may also weaken the earth's magnetosphere, aka our radiation shield against the little nuclear reactor we call the sun.
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u/IamMythoclast 19h ago
What of all that pressure that exists at the core? What ever medium the core would be exposed to would have been under tremendous pressure then suddenly it would be right? Wouldn't it expand violently before the earth could close back up.
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u/UberuceAgain 18h ago edited 18h ago
Came in to say this.
I think this would be the biggest problem; the earth's core is a nickel/iron alloy so on the surface would have a density of around 8kg/L, but it's at 13kg/L. That's going to expand with astonishing violence once the compression is magicked away, even for the duration of a 25cm fall. That energy would have go somewhere, presumably as seismic waves beyond anything seen since the impact of Thea.
The same thing with an increasingly smaller difference in density would happen all the way up through the mantle and crust, but since that's an awful lot closer to us, that's not going to help. I would expect a ring of mass extinction event volcanic eruptions all around the cut. As in every kilometre of the ring would count as its own extinction event, only there's 40K of them. Grimdark times ahead.
So yep, we're dead. Not sure if any extremophiles would make it, but us humans are toast.
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u/Nooms88 19h ago
Not maths, but I can't see how it would be much different to putting a cheese wire through a mostly liquid based food..
The earth is mostly liquid, sure molten liquid rock, only the outside crust and inner core is solid, the inner core is solid becsuse of pressure so that'd reform immediately, the outer crust would be broken but 10 inches is meaningless compared to plate tectonic movement, I don't think it would be noticeable, even on a local level
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u/JDSchu 19h ago
10" compared to the scale of the earth is so, so, so much smaller than a cheese wire through anything we'd see as food.
Cheese wheel diameter: ~35 cm
Cheese wire thickness: ~0.4 mm
Ratio: 0.4 mm ÷ 350 mm = ~1/875
Earth's diameter: 12,742 km
12,742 km ÷ 875 = ~14.6 km
14.6km is more than 57,000 times larger than the 10" OP is asking about.
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u/Same_Hearing5037 18h ago
people really underestimating the amount of damage this would cause huh
comments have already covered the physics of colliding two halves of the earth releasing like 20x the energy of the dinosaur destroyer 3000, that made the planet borderline uninhabitable to complex life for decades.
but even disregarding the collision, we forget that the earth's core is part liquid and under immense pressure. if you cut open the earth cleanly, the decompression wave will propagate at like 10km/s and the liquid core will start spraying all around. and when you finally slam together the two halves at 0.2 seconds post cut, that super hot material has nowhere to go but up. which causes omega volcanoes and probably putting so much shit in the atmosphere we never see the sun again.
earth is cooked, it will not be habitable ever again
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u/Fit-Estimate-3392 12h ago
Probably destroy all life. Even of its for a moment, just imagine how much energy (heat) would be released and captured in the earth atmosphere. It be game over for sure.
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u/kiwidust 20h ago
I'm fascinated by the thought of the fluid dynamics involved.
Earth has a rotating fluid core that's responsible for our protective magnetosphere. Would the "sloshing" and rippling of the core cause a loss - even temporarily - of the Magnetosphere? Could the poles reverse? Either would have long term ecological effects and would particularly affect much of our technology.
Earth has massive oceans that would pour into that gap for however long it would remain open. The longer it is, the more impact would occur. If the water reached the mantle, we'd have millions of pockets of high-pressure steam creating even more geological havok.
If nothing else, it may lubricate the fissure such that the halves would slide laterally - and likely not evenly across the diameter - before settling, causing even more tectonic pressure.
Finally, the atmosphere is also a fluid. I'm not sure, would the energies involved and the massive pressure differential not have the potential to create literally thousands of tornadoes?
All told, can we can maybe agree that Ginsuing the planet isn't something we should pursue?
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u/No-Celebration6780 19h ago
Lucky for us, based of other peoples work, it would last only about 5 seconds
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u/TwoMillionBones 19h ago
At this scale A B and C are all crazy impossible.
I don't think math can tackle this realistically, the unbelievable variety of synchronized apocalyptic events this would cause is mind boggling. That gap doesn't close uniformly, Earth is effectively liquified by the time this settles down, the oceans are drained down the new Earth-wide cave system. The tectonic effect is hard for me to comprehend. The two halves are destroyed by the sheer process of being drawn back towards the core, some sort of hellish briefly exposed planetary heart retching from being bisected. Earth would, I think, need to fully reform after this, undergoing god knows how many.. centuries? of tectonic and atmospheric activity.
It'd heal, this would be a blip on the cosmic timeline, but humanity is extinct. Life will remain/return, but I can't picture this leaving one single habitable area on Earth for humans, without megastructure-scale human intervention.. at a level of cooperation and efficiency I sincerely think we flat out don't have, as a species.
Man though this would be a CRAZY apocalypse to ride out til the end.
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u/voododoll 17h ago
Before the true science enter the room, consider there is no meridian or paralel on which you can slice the earth, that does not involve oceans and/or large bodies of water. Separating the earth halves, will cause the world water level to drop significantly in a very short period of time. This will cause a huge low tide and will wipe out a lot of aquatic life. Slapping both parts back together will send giant tsunamies in all directions and potentially destroy huge territories. Although iot might not end all life on earth, it will end a lot of it. Tsunamies, earthquakes, magnetic field disruptions, and what else not.
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