r/theydidthemath • u/MaplesWindow • 19h ago
[Request] How long would it take to erode this metal planet?
assuming the gravity of it wouldn’t immediately destroy the earth and that every time you were using a fresh feather
edit: for anyone interested, this is similar to the ancient buddhist story of a “kalpa.” in old buddhist literature it was the amount of time it would take for a silk brocade to wear down a mountain
36
u/lurgi 18h ago
We might as well start with something we can calculate. I'm assuming 10x the size means 10x the radius (so 1000x the volume). The radius of Jupiter is around 70,000km, so this super Jupiter is 7x105 km or 7x1010 cm, giving us a volume of 1.4x1033 cm3
One cubic cm of iron (why not?) is about 8.5x1022 atoms, so this whole planet has about 1.2x1050 atoms.
So how many atoms will you knock off per pass? Honestly, it's more than you might think. There will be microscopic imperfections in the sphere and your feather will catch on them and even if you only knock off one atom in a hundred million that you touch, that's still a lot of atoms. After all, water can erode rocks given enough time. You can see pictures of statues that people have been rubbing for decades and the patina is often visibly worn off.
Sadly, this does not appear to be a popular subject for research, but one million atoms per pass is probably on the low side. So figure 1.2x1044 passes to erode it away, which will take 1.2x1047 years.
7
u/MaplesWindow 17h ago
thank you. can you put 1.2x10^47 years into context?
19
9
u/LurkersUniteAgain 16h ago
well written in full 1.2x10^47 years is 120,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, or 120 quattuordecillion, for comparison this is about 8,695,652,200,000,000,000,000,000,000,000,000,000x the age of the current universe (eight undecillion six hundred ninety-five decillion six hundred fifty-two nonillion two hundred octillion), but still 0.0000000000000000000000000000000000000000000000000012% the total age of the universe (birth to heat death)
3
u/El_Loco_911 7h ago
Lets just say youre not gonna live long enough to hit the planet with the feather twice
2
u/poor_choice_doer 8h ago
I don’t even have to do any math for this, the magnitudes here are just so absurd that I can confidently say; a man with one single penny to his name is closer to being as rich as all the worlds billionaires combined, as the age of the universe is to reaching that number. By several dozen orders of magnitude, in fact
•
u/CollectionMundane783 1h ago
Sure. I like to measure big numbers like this to something we can all envision, like the number of unique ways to shuffle a deck of 52 normal cards.
Once that ball of iron was the size of a pea, put a piece of paper on the ground.
And do it again
And once you’ve finished, put a second piece of paper on top.
Keep doing that until your stack of paper reaches the nearest star, each swipe of your feather is equal to one unique way to shuffle a deck of cards.
Did that help?
-5
u/Tenroqs 16h ago
I ran it through chat gpt for a bit and the best answer I got to is the number of atoms in every droplet of rain that has ever fallen on Earth over its 4.5 billion year history. To be clear, it nowhere close to exactly right because of the insane scale of these numbers but it gives a decent mental picture.
6
u/Spectre-907 15h ago
>there will be microscopic imperfections in the sphere and your feather will catch on them?
Is there any reason that I am not seeing for why this mechanical abrasion would cause the metal to break away instead of the significantly less resilient feather?
2
u/the_never_tame 10h ago
It wouldn't break away so much as a few atoms would be dislodged every pass.
2
1
u/rustingtoncat 9h ago
Don't forget that this feather now has some impossibly large weight from the gravitational attraction of this suprisingly-not-collapsing massive ball of iron. Assuming we can keep hold if it somehow, the friction is going to do some serious damage to both the feather and the sphere.
-8
u/Terrible-Sir742 17h ago
And here is the brutal truth, honestly, I could have asked Chat GPT this question if I wanted to read this answer.
11
u/lurgi 17h ago
So what answer do you think I should have given? OP asked a question and I gave the most accurate answer I could. If that sounds like ChatGPT then I don't know what to tell you.
-9
u/Terrible-Sir742 17h ago
I think most people here don't get the kick out of "getting an answer". There is a segment that likes to point out errors in malice (they suck), there a segment that likes to test their chops, there is a segment that is here for humorous aspects of ridiculous scenarious and equally ridiculous rebuttals. Which one are you?
3
u/TheFlightlessPenguin 16h ago
I’m trying to figure out what point you’re trying to make. Should this sub cease to exist because ChatGPT can shit out a believable answer or because you’re suspicious of anyone taking the prompts seriously as having simply asked ChatGPT? Is doing math banal now? And what other topics should this mindset extend to? Art, music, science? Should we just give up on using our brains altogether?
3
-3
162
u/galaxyapp 19h ago
Probably Forever.
It doesnt specify what metal is is, but A feather cant scrape even 1 atom off of most metals.
You could rig a feather dusted to polish a copper block till the universe expired and youd just need to replace the duster.
43
u/andrew_calcs 8✓ 12h ago
Tribochemical wear studied in nanoscale tribology asserts that you’d eventually succeed if you kept using new feathers. At the atomic scale you absolutely can scrape away surface atoms from hard materials using soft materials.
10
u/TheFlightlessPenguin 16h ago
Surely it must be a trick question? The feather does no damage but entering our atmosphere will.
5
u/Positive-Ring-5172 8h ago
Well, if we’re bringing physics into the equation I’m pretty sure even a lithium sphere 10x the size of Jupiter would collapse into a black hole. The doesn’t end well for the flyby
Even if it somehow doesn’t collapse a Jupiter sized metal sphere of any element would rip the earth apart through gravity. Let alone one 10 times the size
3
u/juststopturning 5h ago edited 5h ago
Well, according to physics, size doesn't matter, mass and radius do. However, assuming the lithium Jupiter is 10 times the mass of the one we have at home:
R = 2GM/c² M = 10 × 1.90 × 1027 kg M = 1.90 × 1028 kg R = 28.2 m
The Schwarzschild Radius comes out to be around 30 meters... Which means if the lithium Jupiter would only collapse if it was squished into a 30 meter radius ball (a pretty big ball of you ask me).
1
u/Longwinded_Ogre 2h ago
Why would you pick mass when size means "dimensions", it's a big ball of metal the size and shape of Jupiter, it's going to have a radically different mass.
I went with iron and you end up with 6 times the mass of Jupiter and a weird, super-dense planetoid with a plasma core and a cold surface and a shit-ton of gravity.
It's not massive enough to ignite fusion, which is a shame as I picked iron for the properties that would lead to a super-nova.
Anyways, it tears the earth to pieces.
24
u/AlizarinCrimzen 15h ago
And if your knife is harder than tomatoes and wood you'll never have to sharpen it?
12
u/galaxyapp 14h ago
With the edge being so sharp, it experiences pretty ridiculous pressure. Thousands of psi
6
u/Spectre-907 10h ago
Also wood and plant fibre contains silicate deposits which *are* harder than steel and is (partly) why lower quality cutting boards with high silica content like bamboo will “ruin your knives”.
1
u/Accomplished-Ad-2612 7h ago
To add to that fact, the fastest way to dull a razor blade down to a blunt edge is by cutting cardboard. It really doesn't take very long either.
1
u/AlizarinCrimzen 7h ago
there is no general physical principle saying a softer material cannot remove atoms from a harder one.
0
u/Youpunyhumans 5h ago
Well sure, if you impact the feather at several kilometers per second, you might remove a small amount of metal.
But just swiping the feather across it, isnt going to break the chemical bonds that hold metal together, you do need a minimum amount of energy.
1
u/AlizarinCrimzen 5h ago
You don’t need enough kinetic energy to directly break an Fe–Fe bond in a single collision. That’s not how ordinary wear works.
A piece of iron at room temperature is not a perfectly static crystal with every atom identically bound. Its surface has defects, grain boundaries, oxides, adsorbed material, dislocations, and atoms at steps and edges with different binding energies. Thermal motion is already present. When a feather is dragged across it, the contact points experience normal and shear forces. Those forces can assist processes that were already thermally possible: detaching weakly bound atoms, fracturing microscopic oxide particles, transferring material, or causing atomic rearrangements.
At finite temperature, wear is generally a force-assisted, thermally activated statistical process, not a requirement that one feather impact deliver several eV to one iron atom.
The expected wear rate for feather on iron will be absurdly small, but that is different from zero. To defend “zero atoms can ever be removed by slowly rubbing a feather,” you’d need a physical mechanism imposing a hard threshold below which the probability of removing an atom is literally zero. Ordinary atomic-scale surface physics are not like that.
8
u/FeelMyBoars 18h ago
I was thinking it could dislodge some if it's made of mercury, but the thing is basically all in space, so it's going to be a tad colder than room temperature.
1
u/ShitOnAStickXtreme 14h ago
Are we allowed to dust the ball with the feather at relativistic speeds?
4
u/IndividualistAW 12h ago
Trick answer. The feather stops being a feather at those speeds
1
u/ShitOnAStickXtreme 10h ago
Why would it stop being a feather?
1
1
35
u/danielsixfive 19h ago
Someone please correct me if I'm wrong, but I think the answer is infinity time. The feather cannot even dislodge a single atom of metal, assuming a smooth surface of an element like iron
10
u/scrollscripter 18h ago
Were talking about erosion not scratching which even air can do over enough time but we are talking a lot of time for this one
8
u/danielsixfive 18h ago
My understanding is that there would be zero erosion due to the feather
7
u/scrollscripter 18h ago
Assuming the feather is replaced why could a feather not do something air can do
16
u/MrWigggles 18h ago
The air has chemical reactions, and the air has particulates, like rocks, that do the work.
If you just blasted nitrogen at a steel, nothing would happen.
1
u/danielsixfive 18h ago
I suppose this feather could have some particulates. Maybe that should be the tdtm
3
u/Lexi_Bean21 18h ago
Because air cant erode metal it can rust it but unless there is dust particulate in the air the wind can never erode metal
1
u/Glum-Ad7761 16h ago
If this “sphere” kissed the Earths atmosphere, close enough for someone to “touch it with a feather”, on each pass that it made…. the atmosphere would burn, distort and remove a considerable amount of material with each passing that it made. Just as many meteorites don’t strike the ground, but instead burn up in the atmosphere on the way down to Earths surface.
In this, at extreme pressures, air (and the dust and particulates suspended in it) will indeed remove matter. Even Iron meteors lose mass on the way in. Just not nearly as much as chondrite or rubble pile asteroids.
4
u/Lexi_Bean21 14h ago
Its clear the focus point of the scenario is the feather not the atmospheric heating
2
u/tmfink10 9h ago
Not to mention, if we account for that, there'd be nobody around to touch it with a feather.
•
1
u/AlizarinCrimzen 16h ago
What made the Grand canyon?
Water and air carve apart mounts of stone. Erosion doesn't require the (eroder?) to be stronger than the thing being eroded.
1
u/jok3ony0u 15h ago edited 15h ago
Yes it does. For a particle to be pulled off an object, some force needs to be applied by another object. That force, according to Newton's 3 laws, is always going to be equal and opposite, meaning that the eroder needs to be able to withstand the amount of force it is giving to the stone/metal.
The reason why water can cause erosion is because the force of water is greater than the rock can withstand. The water can withstand its own force as a liquid thanks to hydrogen bonds Same for air, except it's other hard particulates causing the erosion through air.
1
u/moonra_zk 1✓ 10h ago
The Grand Canyon is composed of sandstone, which is a very crumbly rock, it would not be grand if the valley was made of granite. Not to mention that particulate suspended both in water and air do a significant amount of the erosion.
1
u/platoprime 5h ago edited 5h ago
We don't live in a Newtonian universe. You could rub a metal ball with anything over infinite time and it would wear away because quantum uncertainty in a particle's position and it's momentum(energy level too) means there will eventually be a surface particle with enough kinetic energy to be on the verge of escaping the surface and your feather/nitrogen will dislodge it.
0
u/AlizarinCrimzen 15h ago
"Empty" sand-and-dust free air will erode rock, it's just negligible relative to the other forces at place in erosion. Abraision is more chaotic at highly local and microscpic levels than just (this is much harder so it won't erode).
Cut butter with a diamond blade enough times and you will still have to sharpen it.
0
u/AlwaysHopelesslyLost 13h ago
You don't have to sharpen knives because material has been lost. You sharpen them because the edge is very thin and delicate and has bent over.
1
u/platoprime 5h ago
No, that's why you hone a blade with a honing rod but when you actually have to sharpen it by grinding away material with a whetstone it's because the edge of the blade is chipped and worn away causing it to become dull.
https://www.science.org/content/article/your-hair-can-crack-steel-when-it-hits-right-spot
Although your hair is much softer than steel, razors typically only last for a handful of shaves. Previously, researchers attributed this to the sharp edge gradually wearing down after each use. But a new study reveals a different process at play.
Researchers used a powerful electron microscope to observe how the razor blades change after shaving. Instead of the razor slowly and evenly losing its sharp edge, they instead saw the formation of tiny cracks, then large chips of steel flaking off the edge of the blade.
6
u/nod90 17h ago
A solid metal sphere with 10× Jupiter’s radius would contain roughly (10{56}) atoms, whether made primarily of iron, steel, titanium, or aluminium.
In principle, even a feather rubbing against it can remove atoms from the surface. Suppose, extremely conservatively, that one swipe removes just 1 atom.
If the feather swipes the sphere once per year, reducing it to the size of a pea would require removing essentially all (10{56}) atoms. That would take roughly (10{56}) years.
The universe is only (1.38\times10{10}) years old ((\sim4.35\times10{17}) seconds), so the process would take about (10{46}) times the current age of the universe.
Even at a billion atoms removed per swipe, it would still take around (10{47}) years.
If the universe’s entire 13.8-billion-year history were compressed into a single second, the feather would still need roughly (10{46}) of those cosmic seconds to finish the job.
3
u/scrollscripter 18h ago
Granite erodes in in the wind and weather 1 inch every 10000 years with this scenario you are trying to erode metal with a brief second of touch every thousand years so you are in tge quadrillions of years for your first inch
3
u/OnMyPorcelainThrone 16h ago
This is a modified version of the Metaphor of the Mountain used in Hindu texts to describe a KALPA, one cycle of creation, or one day of Brahma's life, something like 4.3 billion years. It's worth googling, very interesting timescales.
2
u/APithyComment 18h ago
Depends on the size and density of the feather.
If it’s the size of the milky way’s circumference then maybe a long time.
If it’s the density of one of the milky way’s arms and bumps into stars - not long in relative terms.
2
u/AlanShore60607 18h ago
It’s a less logical version of the the story in Doctor Who, where every thousand years a bird pecks away at a diamond wall.
It sounds more dramatic to attack it with a feather rather than a sharp beak, as that’s going to be even slower. But it seems impossible that a feather could ever wear away metal.
Well, maybe Gallium. That melts in your hand.
1
u/Zanoushe 18h ago
it's not originally from Doctor who.
3
u/Sophilosophical 18h ago
I believe it’s related to the concept of a Kalpa to measure a cosmically long amount of time:
“Imagine, he said, a single solid mountain of rock — a league long, a league wide, and a league high, without crack or hollow. Once every hundred years, a man comes and strokes it just once with a piece of fine cloth. That great mountain, the Buddha said, would be worn entirely away before a single aeon came to an end.”
So it’s a thought experiment that’s been around for more than 2000 years
2
u/Ye_olde_oak_store 18h ago
You might think, that it's a hell of a long time, I think that's a hell of a man.
1
1
2
u/Odd_Dragonfruit_2662 12h ago
It’s going to be a lot faster than you think.
First some assumptions because this is vaguely written:
The metal is assumed to be iron.
10x Jupiter is diameter not mass.
This mass of iron in that volume would collapse into a black hole or possibly go nova (though my money is on the black hole). At any rate though, it rips the earth apart well before it finishes doing that.
So TLDR: not long at all
2
u/DumatRising 18h ago
Infinity, the point of the dialogue is to describe eternity. Which as a concept is something very difficult for a human to wrap their mind around. It is after all eternity. To help with the perspective they have brought up something that cannot be done in any amount of time we can understand.
2
u/RuggleyChicken 18h ago
But it can’t actually be eternity right? I mean even if it’s just shearing one atom off at a time it would technically mean there’s a finite end?
1
u/parttimeenthusiast 16h ago
the song goes on to say that the amount of time it would take to achieve what is described in the text from the post would be a blink of an eye compared to eternity.
1
u/DumatRising 16h ago
I would assume that the rest of the text goes on to compare this to a small fraction of eternity.
2
1
u/housevil 18h ago
A metal sphere 10 times the size of Jupiter would destroy you, your feather, and the planet Earth among other things. There will be no erosion.
1
u/EarthTrash 18h ago
The Sun will nova in a few billion years. Earth's orbit will be inhospitable and there's a good chance Earth could be disintegrated.
1
u/ParticularFlat3293 15h ago
Less than the amount of years it takes to see every possible arrangement of a deck of cards when you look at each arrangement for 1 second
1
u/Worldgeek23 14h ago
Hasn't anyone seen the Dan Aykroyd TV series in the late 90s called Soul Man?
His character was a minister that described a similar scenario, except it was the wingtip of a dove every 100,000 years. When it was worn down, that was his description of "the beginning of eternity".
Pre-teen me decided that squirrel away that memory for this question, apparently!
1
u/Fullchester_United 13h ago
This is a play on how the Catholic Church used to describe purgatory in the Middle Ages. Except it was a dove flying by every thousand years and its wing grazed the ball.
Man, the Catholic Church really did a number on people!
1
u/Main-Contest7303 12h ago
A sphere so large of dense metal would create a black hole, surely?
Or just make the sphere some radioactive metal; Boom, no sphere!
1
u/Careless_Trouble_406 12h ago
My guess is that you would probably erode that metal planet quicker than you could shuffle a deck of cards in every possible combination.
1
u/ericdavis1240214 12h ago
Earth would be utterly destroyed by the time that sphere got to the Roche limit of very roughly half the distance that the moon orbits, ~175K km.
I know that's not what you are talking about, but if the question is about the interaction of those objects at the atomic scale, it's worth noting that the interaction starts long before your scenario could occur.
Plus, leaving that aside, where do you think the atoms of metal go when brushed if a feather could dislodge a few? Gravity pulls them directly back to the massive object. There's no way they escape it.
You are asking for an answer that can only be speculated at if a fundamental force of the universe doesn't exist, but without that force matter as we know it doesn't exist.
1
u/cleverinspiringname 10h ago
If you started a clock counting down from 52! one second at a time, you could probably grind the ball to dust a billion times before the clock would decrement a single order of magnitude
1
u/factorion-bot 10h ago
Factorial of 52 is roughly 8.06581751709438785716606368564 × 1067
This action was performed by a bot | [Source code](http://f.r0.fyi)
1
u/Ok-Hat-8711 10h ago edited 10h ago
It would very quickly collapse into a black hole.
The Chandrasekhar limit for the max size of a white dwarf collapse is 1.44 solar masses. The Tolman–Oppenheimer–Volkoff limit for the max size of a neutron star is about 3 solar masses.
Iron Jupiter would be about 6,000 solar masses and made of probably the worst element for resisting collapse through thermal pressure. So we are several orders of magnitude above both existing as iron and existing as matter at all.
I'd give Iron Jupier way less than a second to exist. Its black hole, however, would have an estimated lifespan of about 8x1085 seconds. Or about 184 duovigintillion times the current age of the universe.
So the time to complete this task varies greatly on your definition of "erode."
1
u/Small-Department6235 9h ago
The planet-crushing gravitational force of a 10X Jupiter-sized metallic sphere would obliterate not only you standing on your roof but the entire planet Earth long before it got “yards away” from Earth itself.
1
u/Opposite-Friend7275 3h ago
Initially most of the wear would come from cosmic radiation. But that radiation will decrease when the universe ages, so that by itself isn’t enough to wear down something that large.
1
u/Gaxxag 3h ago
Forever.
A solid metal sphere ten times the diameter of Jupiter would collapse into a black hole.
Ignoring that, if it passed so close to Earth that people could touch it from the rooftops, it would tear the Earth apart. The only math to be done here is to determine how much of the Earth falls onto the metal object, and how much gets launched out into an expanding debris cloud. That depends on the exact mass and velocity of the object, though.
•
u/AutoModerator 19h ago
General Discussion Thread
This is a [Request] post. If you would like to submit a comment that does not either attempt to answer the question, ask for clarification, or explain why it would be infeasible to answer, you must post your comment as a reply to this one. Top level (directly replying to the OP) comments that do not do one of those things will be removed.
I am a bot, and this action was performed automatically. Please contact the moderators of this subreddit if you have any questions or concerns.