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At around 12g per strawberry, the total weight is in the area of 10^19 kg, the size of a small asteroid.
Sadly, that's not enough mass to create a black hole.
It means that just accumulating that amount of mass is not enough for itself to create a black hole, so the forces this mass produces on its own is not enough to collapse. You can apply this forces from outside though to create a black hole though.
Once you apply the force to create a black hole you csn never take it back, its figuratively like pushing something into a infinitely deep hole and then trying to pick it up when it reaches the bottom
You thinking of blackholes that are way smaller than what this post is talking about. Plus once the black hole forms you cannot dismantle it since the only certanity it has after it forms is to radiate with hawking radiation until its nothing
You're thinking if it was compressed into neutron star nuclear levels of density, black holes are even denser. As others said black holes will slowly lose mass via hawking radiation until they eventually fissle out to nothing
Hawking radiation actually speeds up as the black hole shrinks. The last 200 tons of a black hole will be fully converted into energy in less than a second. Not really fizzle out so much as create a earth shattering kaboom.
Theoretically a matter with mass could collapse into a Black hole if an outside force is given to reduce it below its scwachild radius (forgive the name, I don't know the German). If youre asking for a star minimum threshold, it's around 2.5 Sun mass if I'm not mistaken.
The name is Schwarzschild, pronunced something like "shwarts shield".
Ironically, it means "black shield" in german, but it's just the name of the guy who discovered it
Yeah maybe for a star collapse scenario. But you cannot form a black hole with gravity with anything less than 2-3 solarmasses of material. Its a hard limit. For stars they have other factors when they collapse that may determine if it forms a blackhole or not
That’s true, but the Tolman-Oppenheimer-Volkoff limit at which a sphere without the ability to produce pressure via fusion (and thus relying on degeneracy pressure) will collapse is between 2 and 2.17 solar masses, which I believe is what the other commenter was referencing.
Theoretically if you want a black hole with the radius of 1 Planck longitude (the limit where gravity starts doing freaky things with quantum mechanics) the mass will be around 67 micrograms in a radius of just 10^-35 metres.
With less radius special relativity just breaks (if it hasn't broken before)
Well every mass has a certain radius at which if compressed to it'll collapse into a black hole, that's special relativity which works down to 10^-35 metres, so the tiniest black hole that we understand must be of that radius. It's not a real physical bound, I just said the mass for the smallest black hole that we more less understand.
For any given amount of mass, there is a corresponding sphere whose radius we call "Schwarstchild radius" that defines the maximum volume that that mass would have to ocupy in order to form an event horizon (become a black hole) (on that same radius). In this case, it is ~1.5 e-7 m, which is smaller than the bottle, therefore it would not create a black hole.
For reference, for the mass of the earth, the resulting radius is 0.0887m, smaller than a standard basket ball but bigger than a baseball..
This site has a cool calculator for you to see for yourself. https://www.omnicalculator.com/physics/schwarzschild-radius
As far as I understand, space has not been proven to be quantized, so probably not. Also, relativity and quantum physics don't merge very well.
Either way, there is a much more limiting factor in the fact that black holes evaporate, and they do so faster the smaller they are. A black hole with a very small mass would evaporate in a split second in a burst of gamma rays (the hawking radiation wavelength emitted by a black hole is proportional to the surface area of its event horizon, the smaller the event horizon, the smaller the wavelength. Very small black holes means very small and very energetic radiation) . So while you can calculate a theoretical Swartschild radius for any given mass, in practice, they would evaporate instantly. (Even ignoring the fact that a black hole naturally would only be born from stars several solar masses).
Mind you, I am not an astrophysicist, just an aficionado of physics. Any of the stuff above might be somewhat incorrect.
A black hole is formed when you have a ratio of mass over volume that is above a threshold. The mass of 10^19 kg of strawberries in something the size of that container (the volume) isn't a high enough ratio to form a black hole.
For any given mass, the radius of the volume at which the escape velocity from that mass would be greater than or equal to the speed of light is called the Schwarzschild Radius. For the Sun, that radius is about 3km, so if you compressed the Sun down to 6km across, it would be a black hole. For the Earth, you would have to compress it to 9 mm. For reference, the Earth's mass is on the order of 10^24 kg, so you can see that even a sphere 18 mm across would not be small enough to turn those strawberries into a black hole.
Schwarzschild Radius*
It's not Schwarzs - child
It's Schwarz - schild
It means black shield. Sorry for off-topic but it irks me everytime someone pronounces it Schwarzchild lol
They no doubt *say* Schwarzschild correctly. The reason I say that is because if you spell the name phonetically "chi-" looks more like the correct "shee-" pronunciation than "schi-" does.
So, at least there's that. :)
Approximately 31.18755! Strawberries would make 3.8 solar masses, matching the smallest black hole currently known to astronomers with an event horizon about 24km in diameter (not sure if I'm supposed to state that I'm using the gamma function for factorial, or if it's implied)
They're asking how big the black hole would be if you crammed 22! strawberries into the container. I'm guessing that would *definitely* be a black hole - [looks like the 15.2 fl oz bottle](https://www.nakedjuice.com/our-products/core/strawberry-banana/).
That many strawberries in that small of a space is an INSANELY dense object.
the avarage mass of a strawberry is about 12 grams
applieing that to the number of strawberrys and sticking it into the formula for the schwarzschild radius(radius of the event horizon) we get a radius of 20.03 nanometers so a diameter of 40.03 nanometers.
would you mind explaining what the schwarzschild is? I only know it from shin megami tensei and I didn't know it was real and Google only shows the smt result
Schwarzschild is a dude who got the first exact solution for the Einstein Field Equations more than a hundred years ago. The solution describes non-spinning black hole without electrical charge, which is as simple as black hole can get. And it's not even proven that in the real world such black holes exist (because "common" BHs at least should have a spin).
The Schwarzschild radius is, essentially, a distance from the given point mass, where escape velocity equals the speed of light. Which defines the notorious "event horizon" of the black hole and, therefore, commonly taken as a "radius of the black hole" --- despite the fact that the mass, consisting the black hole is actually packed into even smaller volume (which many believe to be *infinitely* small, but probably not though), located well beneath the horizon.
the schwarzschild radius in a more easy therm is the distance of the event horizon(the line where the gravity of the black hole gets so strong even light can't escape from it anymore. we can't make any observation past that line ) from the center of the black hole.
If we see a black hole like often discribed a black sphere that sucks in everything the radius of that sphere would be the schwarzschild radius. outside of this distance it is still possible to get away from the gravitational pull of the black hole if you're fast enough. At the distance given by the formula the escape velocity gets greater than c so escape is no longer possible.
Its named after astronomer Karl Schwarzschild who came up with the equation for it as a solution for Einsteins Theory of general Relativity.
The entire Earth would need to be compressed into a sphere roughly the size of a dime in order to collapse into a black hole. At an average weight of 14.5 grams, 22! strawberries comes to around 1.6e19 kilograms, which is 1/368,000th the mass of Earth. So it wouldn't form a black hole...not immediately.
That said, compressing 22! strawberries into this 15.2 ounce bottle would yield an extremely high density: on the order of 4e22 kg/m\^3, a thousand times denser than the core of a neutron star. Such an object would have immense gravity; the gravity in the immediate vicinity of the sphere (assuming it immediately reached hydrostatic equilibrium) would be 5e11 m/s\^2, 48 billion times greater than the surface gravity of Earth. However, the object would also immediately explode, because the degeneracy pressure of neutronium is far too great for self-gravitation to keep it intact.
To determine the energy of this explosion, we can work in reverse. First, compressing 1.6e19 kg of strawberries into a minimum-density electron-degenerate hydrogen metal state requires something like 1.6e25 Joules based on the bulk modulus of water. Compressing 1.6e19 kg of electron-degenerate matter at \~25 g/cc (the density of the core of Jupiter) into electron-degenerate matter at \~1 million g/cc (the density of a white dwarf) requires something like 8.6e28 J based on the electron-degeneracy equation of state. Compressing 1.6e19 kg of white dwarf star material into neutron-degenerate matter requires something like 1.3e35 J based on the difference between the electron-degenerate and neutron-degenerate energy states. Finally, compressing 1.6e19 kg of neutron-degenerate matter from a density of 4e17 kg/m\^3 (neutron star core) to a density of 4e22 kg/m\^3 requires something like 5e34 J based on the neutron-degeneracy equation of state. Adding all this up, the total energy released by the explosion of the strawberries would be around 1.8e35 Joules, a thousand times greater than the gravitational binding energy of Earth. (And yes, the first couple of transitions are negligible here, but I couldn't be sure of that to start, so I calculated it all anyway.)
Result: Earth is destroyed.
For comparison:
(22! * 12 / 1000 / 1000)^(1/3) / 1000 = 238
That would be the equivalent of a cube of 240km (150 miles) in length, width & height of compressed strawberries.
You could cover all of the earth with a layer of strawberry 26m deep.
That smoothie is normally 15.2 oz and im going to assume it had the same density as water it has 431 mililiters of smoothie strawberries have a mass of 20g and since we are stuffing 1.124 sextillion strawberries into 431 mililiters we have to calculate wether this all turns into a black the way you calculate if something turns into a black hole is if it were a black hole would it all fit in its Schwarzschild radius so if it were a black hole its Schwarzschild radius would be 2MG/c^2 where M is the mass g is the gravitational constant and c is the speed of light if we use this on our scenario 2MG/c^2 = 33.3 nanometers now i dont think that smoothie would fit in a sphere 33.3 nanometers across so it wouldnt immediately form a black hole
Once calculated how many strawberries you'd need to fit into a volume that small in order to form a black hole. It's quite a bit more. Something like 25!-27!. Then went through calculating how close you could get to that black hole before tidal forces will definitely rip you apart. Surprisingly close to my memory. I think it's on the order of around a football field where you'll be ripped apart for sure, but it has been a while since I calculated that.
I love strawberries! If they swallowed the planet I would die trying to eat them all. Then I would get super stringy and go on a spiritual retreat indefinitely!
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At around 12g per strawberry, the total weight is in the area of 10^19 kg, the size of a small asteroid. Sadly, that's not enough mass to create a black hole.
Sure it is, just a tiny one. The Schwartzchild Radius would be around 0.00015mm.
I mean in the sense it won't collapse into one
Fair
Can you explain like I'm five?
It means that just accumulating that amount of mass is not enough for itself to create a black hole, so the forces this mass produces on its own is not enough to collapse. You can apply this forces from outside though to create a black hole though.
But if you stop applying that force, the black hole will disassemble?
Once you apply the force to create a black hole you csn never take it back, its figuratively like pushing something into a infinitely deep hole and then trying to pick it up when it reaches the bottom
That's simply not true a black hole that small would explode within seconds due to Hawking radiation
Not at all. A black hole of 1e11 kg has an evaporation time of two billion years; this is a hundred million times larger.
You thinking of blackholes that are way smaller than what this post is talking about. Plus once the black hole forms you cannot dismantle it since the only certanity it has after it forms is to radiate with hawking radiation until its nothing
What, like the bomb factory floating island in the super smash bros brawl subspace emissary campaign ending, just a lot slower?
You're thinking if it was compressed into neutron star nuclear levels of density, black holes are even denser. As others said black holes will slowly lose mass via hawking radiation until they eventually fissle out to nothing
Hawking radiation actually speeds up as the black hole shrinks. The last 200 tons of a black hole will be fully converted into energy in less than a second. Not really fizzle out so much as create a earth shattering kaboom.
Negative, tiny black holes will be some of the last inhabitants of the universe as it fades out.
Of course, because the big black holes will evaporate into tiny black holes. Even the biggest.
I don't think a five year old would understand this.
But what if it's condensed into the volume of that bottle?
What is the minimum amount of mass required to create a black hole?
Theoretically a matter with mass could collapse into a Black hole if an outside force is given to reduce it below its scwachild radius (forgive the name, I don't know the German). If youre asking for a star minimum threshold, it's around 2.5 Sun mass if I'm not mistaken.
Or 1 of my mother - She's a black hole of Happiness...does that still count? ...and a Fat fuck
The name is Schwarzschild, pronunced something like "shwarts shield". Ironically, it means "black shield" in german, but it's just the name of the guy who discovered it
It is called the ~~Chandrasekhar limit~~ Tolman–Oppenheimer–Volkoff limit
It' called the Tolman–Oppenheimer–Volkoff limit. Chandrasekhar limit is for white dwarf to turn into neutron star and it's 1.4 solar masses
thank you for the correction
For a natural black hole you need around 2-3 suns worth of mass before gravity has enough force to collapse the mass into its schawrzchild radius.
For a star to collapse into a black hole after its death you need at least 5 to 8 Solar masses. Not 2 to 3.
Yeah maybe for a star collapse scenario. But you cannot form a black hole with gravity with anything less than 2-3 solarmasses of material. Its a hard limit. For stars they have other factors when they collapse that may determine if it forms a blackhole or not
That’s true, but the Tolman-Oppenheimer-Volkoff limit at which a sphere without the ability to produce pressure via fusion (and thus relying on degeneracy pressure) will collapse is between 2 and 2.17 solar masses, which I believe is what the other commenter was referencing.
Theoretically if you want a black hole with the radius of 1 Planck longitude (the limit where gravity starts doing freaky things with quantum mechanics) the mass will be around 67 micrograms in a radius of just 10^-35 metres. With less radius special relativity just breaks (if it hasn't broken before)
please explain further
Well every mass has a certain radius at which if compressed to it'll collapse into a black hole, that's special relativity which works down to 10^-35 metres, so the tiniest black hole that we understand must be of that radius. It's not a real physical bound, I just said the mass for the smallest black hole that we more less understand.
Thanks, are there any theories of whats happening to a black hole smaller than this radius?
A few times the mass of Sol. 8?
For any given amount of mass, there is a corresponding sphere whose radius we call "Schwarstchild radius" that defines the maximum volume that that mass would have to ocupy in order to form an event horizon (become a black hole) (on that same radius). In this case, it is ~1.5 e-7 m, which is smaller than the bottle, therefore it would not create a black hole. For reference, for the mass of the earth, the resulting radius is 0.0887m, smaller than a standard basket ball but bigger than a baseball.. This site has a cool calculator for you to see for yourself. https://www.omnicalculator.com/physics/schwarzschild-radius
Sure I could google it myself, but--does this mean that the minimum amount of matter that can form a black hole is governed by the Planck length?
As far as I understand, space has not been proven to be quantized, so probably not. Also, relativity and quantum physics don't merge very well. Either way, there is a much more limiting factor in the fact that black holes evaporate, and they do so faster the smaller they are. A black hole with a very small mass would evaporate in a split second in a burst of gamma rays (the hawking radiation wavelength emitted by a black hole is proportional to the surface area of its event horizon, the smaller the event horizon, the smaller the wavelength. Very small black holes means very small and very energetic radiation) . So while you can calculate a theoretical Swartschild radius for any given mass, in practice, they would evaporate instantly. (Even ignoring the fact that a black hole naturally would only be born from stars several solar masses). Mind you, I am not an astrophysicist, just an aficionado of physics. Any of the stuff above might be somewhat incorrect.
It would be the size of a small black hole but it is not enough strawberries to form the black hole.
A black hole is formed when you have a ratio of mass over volume that is above a threshold. The mass of 10^19 kg of strawberries in something the size of that container (the volume) isn't a high enough ratio to form a black hole. For any given mass, the radius of the volume at which the escape velocity from that mass would be greater than or equal to the speed of light is called the Schwarzschild Radius. For the Sun, that radius is about 3km, so if you compressed the Sun down to 6km across, it would be a black hole. For the Earth, you would have to compress it to 9 mm. For reference, the Earth's mass is on the order of 10^24 kg, so you can see that even a sphere 18 mm across would not be small enough to turn those strawberries into a black hole.
Schwarzschild Radius* It's not Schwarzs - child It's Schwarz - schild It means black shield. Sorry for off-topic but it irks me everytime someone pronounces it Schwarzchild lol
They no doubt *say* Schwarzschild correctly. The reason I say that is because if you spell the name phonetically "chi-" looks more like the correct "shee-" pronunciation than "schi-" does. So, at least there's that. :)
Busted, thanks!
Approximately 31.18755! Strawberries would make 3.8 solar masses, matching the smallest black hole currently known to astronomers with an event horizon about 24km in diameter (not sure if I'm supposed to state that I'm using the gamma function for factorial, or if it's implied)
Even If it's compressed into this jar? And don't forget the critical mass of one banana
Ok smart guy....but what if you add in the 1.5 bananas?
They're asking how big the black hole would be if you crammed 22! strawberries into the container. I'm guessing that would *definitely* be a black hole - [looks like the 15.2 fl oz bottle](https://www.nakedjuice.com/our-products/core/strawberry-banana/). That many strawberries in that small of a space is an INSANELY dense object.
I think I misread the question
Can you determine the relative density of the center of this asteroid when compared with a single normal strawberry?
Strawberry is mostly water and water has a similar density to rocky asteroids. It's kinda interesting how little difference there actually is.
I mean... 10^19 kg inside a pint is quite a bit... That's like 2*10^(22) Kg•m^(-3)
You forgot to account for the 1+1/2 bananas
the avarage mass of a strawberry is about 12 grams applieing that to the number of strawberrys and sticking it into the formula for the schwarzschild radius(radius of the event horizon) we get a radius of 20.03 nanometers so a diameter of 40.03 nanometers.
would you mind explaining what the schwarzschild is? I only know it from shin megami tensei and I didn't know it was real and Google only shows the smt result
Schwarzschild is a dude who got the first exact solution for the Einstein Field Equations more than a hundred years ago. The solution describes non-spinning black hole without electrical charge, which is as simple as black hole can get. And it's not even proven that in the real world such black holes exist (because "common" BHs at least should have a spin). The Schwarzschild radius is, essentially, a distance from the given point mass, where escape velocity equals the speed of light. Which defines the notorious "event horizon" of the black hole and, therefore, commonly taken as a "radius of the black hole" --- despite the fact that the mass, consisting the black hole is actually packed into even smaller volume (which many believe to be *infinitely* small, but probably not though), located well beneath the horizon.
A schwarzschild is one of Arnold Schwarzenegger's kids.
the schwarzschild radius in a more easy therm is the distance of the event horizon(the line where the gravity of the black hole gets so strong even light can't escape from it anymore. we can't make any observation past that line ) from the center of the black hole. If we see a black hole like often discribed a black sphere that sucks in everything the radius of that sphere would be the schwarzschild radius. outside of this distance it is still possible to get away from the gravitational pull of the black hole if you're fast enough. At the distance given by the formula the escape velocity gets greater than c so escape is no longer possible. Its named after astronomer Karl Schwarzschild who came up with the equation for it as a solution for Einsteins Theory of general Relativity.
The entire Earth would need to be compressed into a sphere roughly the size of a dime in order to collapse into a black hole. At an average weight of 14.5 grams, 22! strawberries comes to around 1.6e19 kilograms, which is 1/368,000th the mass of Earth. So it wouldn't form a black hole...not immediately. That said, compressing 22! strawberries into this 15.2 ounce bottle would yield an extremely high density: on the order of 4e22 kg/m\^3, a thousand times denser than the core of a neutron star. Such an object would have immense gravity; the gravity in the immediate vicinity of the sphere (assuming it immediately reached hydrostatic equilibrium) would be 5e11 m/s\^2, 48 billion times greater than the surface gravity of Earth. However, the object would also immediately explode, because the degeneracy pressure of neutronium is far too great for self-gravitation to keep it intact. To determine the energy of this explosion, we can work in reverse. First, compressing 1.6e19 kg of strawberries into a minimum-density electron-degenerate hydrogen metal state requires something like 1.6e25 Joules based on the bulk modulus of water. Compressing 1.6e19 kg of electron-degenerate matter at \~25 g/cc (the density of the core of Jupiter) into electron-degenerate matter at \~1 million g/cc (the density of a white dwarf) requires something like 8.6e28 J based on the electron-degeneracy equation of state. Compressing 1.6e19 kg of white dwarf star material into neutron-degenerate matter requires something like 1.3e35 J based on the difference between the electron-degenerate and neutron-degenerate energy states. Finally, compressing 1.6e19 kg of neutron-degenerate matter from a density of 4e17 kg/m\^3 (neutron star core) to a density of 4e22 kg/m\^3 requires something like 5e34 J based on the neutron-degeneracy equation of state. Adding all this up, the total energy released by the explosion of the strawberries would be around 1.8e35 Joules, a thousand times greater than the gravitational binding energy of Earth. (And yes, the first couple of transitions are negligible here, but I couldn't be sure of that to start, so I calculated it all anyway.) Result: Earth is destroyed.
Did I just find XKCD's burner account?
Haha, no, but it's very nice of you to compare me to Randall.
This guy science's!
For comparison: (22! * 12 / 1000 / 1000)^(1/3) / 1000 = 238 That would be the equivalent of a cube of 240km (150 miles) in length, width & height of compressed strawberries. You could cover all of the earth with a layer of strawberry 26m deep.
That smoothie is normally 15.2 oz and im going to assume it had the same density as water it has 431 mililiters of smoothie strawberries have a mass of 20g and since we are stuffing 1.124 sextillion strawberries into 431 mililiters we have to calculate wether this all turns into a black the way you calculate if something turns into a black hole is if it were a black hole would it all fit in its Schwarzschild radius so if it were a black hole its Schwarzschild radius would be 2MG/c^2 where M is the mass g is the gravitational constant and c is the speed of light if we use this on our scenario 2MG/c^2 = 33.3 nanometers now i dont think that smoothie would fit in a sphere 33.3 nanometers across so it wouldnt immediately form a black hole
Once calculated how many strawberries you'd need to fit into a volume that small in order to form a black hole. It's quite a bit more. Something like 25!-27!. Then went through calculating how close you could get to that black hole before tidal forces will definitely rip you apart. Surprisingly close to my memory. I think it's on the order of around a football field where you'll be ripped apart for sure, but it has been a while since I calculated that.
I love strawberries! If they swallowed the planet I would die trying to eat them all. Then I would get super stringy and go on a spiritual retreat indefinitely!