## What-if 0092: "One-Second Day"

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dalcde
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### What-if 0092: "One-Second Day"

One-Second Day
Dylan wrote:What would happen if the Earth's rotation were sped up until a day only lasted one second?

—Dylan

Citation 2 should link to http://xkcd.com/852/

Istaro
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### Re: What-if 0092: "One-Second Day"

This centrifugal force isn't strong enough to overcome gravity and tear the Earth apart, but it's enough to flatten the Earth slightly and make it so you weigh almost a pound more at the Equator than you do at the poles [emphasis mine].

Isn't that supposed to be the other way around?

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### Re: What-if 0092: "One-Second Day"

I was wondering the same thing, but he seems awfully sure as he goes on to make a Canadian-food-will-make-you-fat joke.
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### Re: What-if 0092: "One-Second Day"

Google says you're right - he has it backwards, backwards, you're (slightly) heavier at the poles than at the equator. Which makes the aforementioned Canadian food joke make more sense in context.

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`enum ಠ_ಠ {°□°╰=1, °Д°╰, ಠ益ಠ╰};void ┻━┻︵​╰(ಠ_ಠ ⚠) {exit((int)⚠);}`
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sehkzychic
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### Re: What-if 0092: "One-Second Day"

I'm just a lowly biologist, so please correct me if I'm wrong about this. It sounds like the Moon, rather than being disintegrated is being ejected from the solar system (I guess from some combination of momentum transfer and ablative stuff on the Earthward side). If that's the case, how long would it stay bright for? (And just how bright would it be? Clearly it's many, many times greater than the Sun's output [since from 1AU it outshines the Sun at point-blank range]. But what's a reasonable estimate?) Basically, I'm wondering what an alien astronomer might see. Spectral analysis aside, how much brighter would the SuperMoon be than the Sun in terms of energy output per second, given an equal distance (say 1AU).

On an unrelated note, I just want to say that despite all the comparisons of how big the Sun is compared to the Earth (Bill Nye filling a model Sun with thousands of model Earths stands out), a quick check on Wolfram|Alpha says that you couldn't make the Sun spin at 1rev/sec, because that would make the equatorial rim travel at over 14 times the speed of light. Even Saturn is too big to have a one-second day (CSaturn = 1.26 lightseconds).

Not sure if I even want to know the amount of damage the Sun would do if it were spinning fast enough that the equatorial edge were moving at the speed of the OMG-particle. I suspect that it would exceed the rule of thumb about comparisons to a supernova though. By a lot.

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### Re: What-if 0092: "One-Second Day"

sehkzychic wrote:Not sure if I even want to know the amount of damage the Sun would do if it were spinning fast enough that the equatorial edge were moving at the speed of the OMG-particle. I suspect that it would exceed the rule of thumb about comparisons to a supernova though. By a lot.

I don't know the details about what would happen in such a situation, but I do know that if you have an object rotating at relativistic speeds, then weird things start to happen...

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keithl
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### Re: What-if 0092: "One-Second Day"

I suppose you could call it centrifugal force - or you could think of all the particles of the earth suddenly moving radially outward at 2π d meters per second, where d is the distance from the rotation axis in meters). If you were two meters tall and standing on the equator (d=6378 kilometers), your feet and the surface just underneath them would go in an approximately straight line in The Direction Formerly Known As East at 40074 kilometers per second, and your head and the air around it would go at that speed plus 12.6 meters per second. The rock underneath would indeed fracture into chunks and tumble, as would you, in a cloud of fast moving air and gravel. Nearby stuff will be moving at similar speeds and tumbling once per second. Deeper material, relieved of hydrostatic pressure, will explode into shrapnel and mix with other nearby stuff to the north and south. But it is all spreading apart so fast into a 12,700 km thick disk/cloud that distant regions will never interact.

If you were strapped in the middle of a sturdy space capsule with a good heat shield, you would tumble but survive as you zoomed out of the solar system surrounded by a dissipating cloud of atmosphere and bouncing gravel.

An armored space capsule at the rotation pole would have an easier time of it. The Debris Cloud Formerly Known as Earth (DCFKAE) is going away very fast, so you are unlikely to be struck by most of it. The column density of incandescent material between you and the x-ray emitting satellite collisions will shield you from most of those emissions - mass will move radially stratified by initial radius and won't mix much during the first second.

Flywheels can move at rim speeds above a kilometer per second. A carbon-fiber-hulled space capsule at the pole could be could be 50 meters radius and remain intact. If it was a kilometer tall above the pole, and contained enough fuel to slow down with thrusters, it might contain enough material to make a survivable space colony. Sturdy machinery, seeds, and well packaged components could be stored outwards to 25 meters (100 gees) radius, with fuel and water and LOTS of carbon fiber support beyond that. Rather than one continuous column, divide it into a stack of disks, because one tall cylinder will tend to pitch over and rotate end over end.

There will also be a column of DCFKAE chunklets with relatively little velocity, most of the mass formerly along the line between the poles. A few hundred meters of crust, maybe? Most of the stuff within 4km of the rotation axis will remain in solar orbits in the same 1AU zone, almost a million cubic kilometers of material in this new asteroid belt, spreading out fast.

You will need a lot of fuel, and very good radar, so you can dodge big chunks over future years. Space is big, and they will scatter over a volume of more than 1E21 cubic kilometers, so big collisions won't be that frequent.

Or, you can avoid all the bother by telling Dylan that he can't ride in YOUR cylinder if he does this annoying thing. Chastened, perhaps he will go play relativistic baseball instead.

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### Re: What-if 0092: "One-Second Day"

phlip wrote:
sehkzychic wrote:Not sure if I even want to know the amount of damage the Sun would do if it were spinning fast enough that the equatorial edge were moving at the speed of the OMG-particle. I suspect that it would exceed the rule of thumb about comparisons to a supernova though. By a lot.

I don't know the details about what would happen in such a situation, but I do know that if you have an object rotating at relativistic speeds, then weird things start to happen...

So if I'm understanding the article correctly, are you saying that calculating the energy of any chunk of the Sun is non-trivial since it's not just accelerated by the increased rotational velocity, but its mass is changed by relativistic effects? (Any by extension, the total kinetic energy of the SuperSun becomes some weird mix of integrals and Lorentz equations?)

PayasYouDraw
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### Re: What-if 0092: "One-Second Day"

Oh god why did I click the [citation needed] thing? I was expecting a joke, not the madness of Timecube.

Well I guess that depends on your interpretation of Timecube.
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### Re: What-if 0092: "One-Second Day"

Every surface in the Solar System—Europa's ice, Saturn's rings, and Mercury's rocky crust—would be scoured clean ...

... by moonlight.

So in other words: that's some serious moonlight.

mathmannix
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### Re: What-if 0092: "One-Second Day"

Thoughts:

1. I had to wiki poutine, but it seems like it would make you gain weight? Unless his point is that it is so disgusting that you would stop eating, but it sounds like something I want to try!

2. I'm pretty sure Santa is a time lord. So, he would have regenerated by now.
I hear velociraptor tastes like chicken.

speising
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### Re: What-if 0092: "One-Second Day"

mathmannix wrote:Thoughts:

1. I had to wiki poutine, but it seems like it would make you gain weight?

yes? that's what he's been saying.

mathmannix
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### Re: What-if 0092: "One-Second Day"

speising wrote:
mathmannix wrote:Thoughts:

1. I had to wiki poutine, but it seems like it would make you gain weight?

yes? that's what he's been saying.

But he said that being Oop North, where you would be offered poutine, is one of the reasons you would "weigh almost a pound more at the Equator than you do at the poles." Thus, I deduced that eating poutine (or at least, being offered poutine) will make you weigh less. Which doesn't seem like it would be true, but even if true, it doesn't support his argument. So, shouldn't he have said something like "being closer to the equator in North America increases your chances of being offered jambalaya", or deep-fried crawfish and hush puppies, or something like that?
Last edited by mathmannix on Wed Apr 16, 2014 12:52 pm UTC, edited 1 time in total.
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### Re: What-if 0092: "One-Second Day"

Except, if you read the thread, people are saying he got that backwards.
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mathmannix
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### Re: What-if 0092: "One-Second Day"

Istaro wrote:
This centrifugal force isn't strong enough to overcome gravity and tear the Earth apart, but it's enough to flatten the Earth slightly and make it so you weigh almost a pound more at the Equator than you do at the poles [emphasis mine].

Isn't that supposed to be the other way around?

Pfhorrest wrote:I was wondering the same thing, but he seems awfully sure as he goes on to make a Canadian-food-will-make-you-fat joke.

I interpret these comments to say that, yes, the physics are backwards and Randall should have said that you weigh more at the poles. However, he seemed to be (illogically) supporting his (incorrect) assertion with the idea that poutine makes you fat.

So did he somehow make two wrongs and get a right?
I hear velociraptor tastes like chicken.

stib
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### Re: What-if 0092: "One-Second Day"

My RSS reader shows the page saying that you'd be heavier at the equator, but on the page the goof has been fixed, and the poutine reference removed altogether, which was probably unnecessary - if they sold that stuff where I live my mass would be appreciably slowing down time, I'm sure.

Now it says:
but it's enough to flatten the Earth slightly and make it so you weigh almost a pound less at the Equator than you do at the poles

Edit: the poutine is still there in the citation popup. So you may now go about your business calmly.
Last edited by stib on Wed Apr 16, 2014 1:13 pm UTC, edited 2 times in total.

speising
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### Re: What-if 0092: "One-Second Day"

stib wrote:Looks like the heavier at the equator goof has been fixed now, and the poutine reference removed altogether.
but it's enough to flatten the Earth slightly and make it so you weigh almost a pound less at the Equator than you do at the poles

i only saw this version. the poutine ref. is in the annotation popup thingie.

Whizbang
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### Re: What-if 0092: "One-Second Day"

I have nothing of value to add other than to say poutine is just amazing. Don't try it at home, though. You can't just put any ol' cheese and gravy on "french" fries and call it poutine. Well, you could, since poutine means "pudding" and is a name given to all sorts of dishes that are just mish-mashes of food, but it wouldn't be the same as the stuff you get in Canada (Quebec, at least. I haven't been to the other parts.).

You need poutine gravy1, and cheese curd. The nice thing is that you can add your own toppings. I like sweet italian sausage and grilled peppers and onions.

1My family uses this one. It is not quite the same as ordering poutine from a stand or restaurant, but its close enough.

stib
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### Re: What-if 0092: "One-Second Day"

I have a local Lebanese bakery that does fatayer bil jibneh (cheese pies), made with a squeaky cheese called jibneh which sounds similar to cheese curds. The Cypriot take on squeaky cheese is called Halloumi, which even the mainstream supermarkets sell here in Melbourne, Australia.

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### Re: What-if 0092: "One-Second Day"

Use to get fries with cheese and gravy at both Rutt's Hut in New Jersey and Original Hot Dog's in Pittsburgh going back more than 30 years ago. We just didn't give it a fancy French name. It's the kind of thing that got lost when chain store fast food replaced the local burger and hot dog joints.

JetstreamGW
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### Re: What-if 0092: "One-Second Day"

I had the misfortune of clicking on the "Citation Needed" bit.

What bugnuts insanity is this?

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### Re: What-if 0092: "One-Second Day"

The site is blocked at work for 'Violence/Hate/Racism'.

Now I am very curious.

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### Re: What-if 0092: "One-Second Day"

Time Cube
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### Re: What-if 0092: "One-Second Day"

sehkzychic wrote:Not sure if I even want to know the amount of damage the Sun would do if it were spinning fast enough that the equatorial edge were moving at the speed of the O-M-G-particle. I suspect that it would exceed the rule of thumb about comparisons to a supernova though. By a lot.

I don't have enough maths to calculate relativistic rotational momentum, so the best comparison I have is the amount of energy of the entire Sun moving at the speed of the O-M-G-particle, relative to its neighbourhood.

The O-M-G Particle (assuming it was a single proton) had a mass on the order of 10^-27 kg, and the relativistic energy of 50 J ( http://en.wikipedia.org/wiki/Oh-My-God_particle ). If the Sun (with mass on the order of 10^30 kg) would move at the same speed, it would have relativistic energy on the order of 10^58 J.

The closest Order of Magnitude comparison ( http://en.wikipedia.org/wiki/Orders_of_ ... de_(energy) ) shows that this would have roughly as much energy as the total mass-energy of the Milky Way (10^58 J). This is the energy of 100 trillion supernovas (a single supernova being 10^44 J), or one-trillionth of the total mass-energy of the Universe (10^69 J).

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### Re: What-if 0092: "One-Second Day"

gene123 wrote:
sehkzychic wrote:Not sure if I even want to know the amount of damage the Sun would do if it were spinning fast enough that the equatorial edge were moving at the speed of the O-M-G-particle. I suspect that it would exceed the rule of thumb about comparisons to a supernova though. By a lot.
I don't have enough maths to calculate relativistic rotational momentum, so the best comparison I have is the amount of energy of the entire Sun moving at the speed of the O-M-G-particle, relative to its neighbourhood.
The problem is that this vastly overestimates the total, because on a spinning sphere only the outermost edge would have that kind of energy, and once you move 14% of the way from the equator toward the center, the mass around you isn't "even" moving fast enough to have more kinetic energy than rest-mass-energy.
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### Re: What-if 0092: "One-Second Day"

mathmannix wrote:I interpret these comments to say that, yes, the physics are backwards and Randall should have said that you weigh more at the poles. However, he seemed to be (illogically) supporting his (incorrect) assertion with the idea that poutine makes you fat.

So did he somehow make two wrongs and get a right?

No, it supports the corrected assertion. He's saying that anyone who passes through Canada to get to the North Pole will find themselves heavier at the pole than what they were when they started their journey, due to the irresistible poutine along the way.

ilduri
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### Re: What-if 0092: "One-Second Day"

The best (worst?) thing about that timecube website is that once you scroll all the rambling, incoherent way down to the bottom, there's actually a link entitled "NEXT PAGE."
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### Re: What-if 0092: "One-Second Day"

Whizbang wrote:The site is blocked at work for 'Violence/Hate/Racism'.

Now I am very curious.

RationalWiki has an amusing Time Cube page.

ilduri wrote:The best (worst?) thing about that timecube website is that once you scroll all the rambling, incoherent way down to the bottom, there's actually a link entitled "NEXT PAGE."

Gene Ray's an old-fashioned kinda guy.

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### Re: What-if 0092: "One-Second Day"

PM 2Ring wrote:RationalWiki has an amusing Time Cube page.

Thanks. Great read. I ended up visiting the Time Cube website when I went home, and promptly shared it with all (1) my friends.

PM 2Ring wrote:
ilduri wrote:The best (worst?) thing about that timecube website is that once you scroll all the rambling, incoherent way down to the bottom, there's actually a link entitled "NEXT PAGE."

Gene Ray's an old-fashioned kinda guy.

I like that, at least on the second page (I didn't check the first after I noticed it), a lot of the "sections" are just a single line hyperlinked to an Index(#).html page, with just more of the same but with a different background. These other pages are only as long as most of the other sections, and so can fit easily in the parent page, but he must have felt a different background image would somehow help his case.

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### Re: What-if 0092: "One-Second Day"

gene123 wrote:
sehkzychic wrote:Not sure if I even want to know the amount of damage the Sun would do if it were spinning fast enough that the equatorial edge were moving at the speed of the O-M-G-particle. I suspect that it would exceed the rule of thumb about comparisons to a supernova though. By a lot.

I don't have enough maths to calculate relativistic rotational momentum, so the best comparison I have is the amount of energy of the entire Sun moving at the speed of the O-M-G-particle, relative to its neighbourhood.

The O-M-G Particle (assuming it was a single proton) had a mass on the order of 10^-27 kg, and the relativistic energy of 50 J ( http://en.wikipedia.org/wiki/Oh-My-God_particle ). If the Sun (with mass on the order of 10^30 kg) would move at the same speed, it would have relativistic energy on the order of 10^58 J.

The closest Order of Magnitude comparison ( http://en.wikipedia.org/wiki/Orders_of_ ... de_(energy) ) shows that this would have roughly as much energy as the total mass-energy of the Milky Way (10^58 J). This is the energy of 100 trillion supernovas (a single supernova being 10^44 J), or one-trillionth of the total mass-energy of the Universe (10^69 J).

It would not make any explosion though. It would just become a super massive black hole. One to mach the biggest we have seen*, with its milky way sized mass. (*Or well not seen, you know what i mean.)

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### Re: What-if 0092: "One-Second Day"

Wouldn't that imply that the Sun itself looked like a black hole to the oh-my-god particle?
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### Re: What-if 0092: "One-Second Day"

Now I'm curious... if you spun the Earth up over time, rather than instantaneously, how fast could it go before bits started flying off? (I guess I should clarify that I mean bits of the Earth, not trifling little things like cows and people. I imagine they're a lot easier to fling into the depths of space.)

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### Re: What-if 0092: "One-Second Day"

If Earth didn't change shape at all from what it is now, stuff at the equator would become weightless at a bit upwards of 17 rotations/day (=sqrt(9.78/6378137)/(2*pi)*86400). (This is of course equal to the orbital speed at the equator.)

However, if it happened very slowly, so that the oblate spheroid shape had time to reach hydrostatic equilibrium, things are a lot more difficult to calculate, because the equator would bulge out as the speed increased, so you ultimately wouldn't have to spin quite so fast for stuff to start floating off.
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### Re: What-if 0092: "One-Second Day"

Jamaican Castle wrote:Now I'm curious... if you spun the Earth up over time, rather than instantaneously, how fast could it go before bits started flying off? (I guess I should clarify that I mean bits of the Earth, not trifling little things like cows and people. I imagine they're a lot easier to fling into the depths of space.)

gmalivuk wrote:If Earth didn't change shape at all from what it is now, stuff at the equator would become weightless at a bit upwards of 17 rotations/day (=sqrt(9.78/6378137)/(2*pi)*86400). (This is of course equal to the orbital speed at the equator.)

For "bits of the earth", gmalivuk's speed covers non-trifling things like "the atmosphere" and "the oceans" and "all the loose dirt". And once the dirt goes, forests and boulders and everything else that the dirt was holding down can go. Given enough time at that speed, you'll strip the equator to the bedrock.

If you mean "what'll it take to orbit all of Ecuador, and none of Peru", just work out the additional speed needed given the effective tensile strength and mass of Ecuador. Determining those may be non-trivial. I'm not sure there's a speed that will separate mountains and countries from the rest of the crust without just peeling the whole crust off the mantle like an orange rind, though.

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### Re: What-if 0092: "One-Second Day"

gmalivuk wrote:Wouldn't that imply that the Sun itself looked like a black hole to the oh-my-god particle?

No, because to the OMG-particle the sun was moving along linearly.

In this example the sun is rotating, in every inertial frame there will be enough energy within a little enough radius to be a black hole.

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### Re: What-if 0092: "One-Second Day"

You replied to calculations about the sun moving linearly, though.
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### Re: What-if 0092: "One-Second Day"

gmalivuk wrote:You replied to calculations about the sun moving linearly, though.

I took it to mean still rotating, just giving every individual particle the energy of the OMG-particle.

Anyway, jupiter is close enough and massive enough that as long as it was not also accelerated, the sun-jupiter system would still form a black hole, now just one moving at terrifying speed.

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### Re: What-if 0092: "One-Second Day"

I can't quite keep up with this busy thread... the first thing I thought of with this latest thought exercise from Mr. Munroe, is a similar, but opposite thought exercise by EducationDocumentary. I'm not sure if I'm the first to mention Doomsday Prophecies: When the Earth Stops Spinning.

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### Re: What-if 0092: "One-Second Day"

Tass wrote:
gene123 wrote:
sehkzychic wrote:Not sure if I even want to know the amount of damage the Sun would do if it were spinning fast enough that the equatorial edge were moving at the speed of the O-M-G-particle. I suspect that it would exceed the rule of thumb about comparisons to a supernova though. By a lot.

Spoiler:
I don't have enough maths to calculate relativistic rotational momentum, so the best comparison I have is the amount of energy of the entire Sun moving at the speed of the O-M-G-particle, relative to its neighbourhood.

The O-M-G Particle (assuming it was a single proton) had a mass on the order of 10^-27 kg, and the relativistic energy of 50 J ( http://en.wikipedia.org/wiki/Oh-My-God_particle ). If the Sun (with mass on the order of 10^30 kg) would move at the same speed, it would have relativistic energy on the order of 10^58 J.

The closest Order of Magnitude comparison ( http://en.wikipedia.org/wiki/Orders_of_ ... 40;energy&#41; ) shows that this would have roughly as much energy as the total mass-energy of the Milky Way (10^58 J). This is the energy of 100 trillion supernovas (a single supernova being 10^44 J), or one-trillionth of the total mass-energy of the Universe (10^69 J).

It would not make any explosion though. It would just become a super massive black hole. One to mach the biggest we have seen*, with its milky way sized mass. (*Or well not seen, you know what i mean.)

Ohhh! Is this a Schwarzchild radius thing? (I was wiki-tabbing the origins of the universe literally 2 days ago and ran into it.) In what I read, it seemed like it was saying that a black hole happens whenever you have enough mass in a small enough space. (So everything "could" become a black hole if you squished it "enough," though for most objects, "enough" would be physically unheard of since the universe was less than a second old.) So, since mass ~ energy, does having enough energy (kinetic in the SuperSun) in a small enough space also produce the black hole effect? If so, is this to do with the whole "mass-increases-at-relativistic-speeds" thing?

speising
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### Re: What-if 0092: "One-Second Day"

sehkzychic wrote:
Tass wrote:
gene123 wrote:
sehkzychic wrote:Not sure if I even want to know the amount of damage the Sun would do if it were spinning fast enough that the equatorial edge were moving at the speed of the O-M-G-particle. I suspect that it would exceed the rule of thumb about comparisons to a supernova though. By a lot.

[spoiler]I don't have enough maths to calculate relativistic rotational momentum, so the best comparison I have is the amount of energy of the entire Sun moving at the speed of the O-M-G-particle, relative to its neighbourhood.

The O-M-G Particle (assuming it was a single proton) had a mass on the order of 10^-27 kg, and the relativistic energy of 50 J ( http://en.wikipedia.org/wiki/Oh-My-God_particle ). If the Sun (with mass on the order of 10^30 kg) would move at the same speed, it would have relativistic energy on the order of 10^58 J.

The closest Order of Magnitude comparison ( http://en.wikipedia.org/wiki/Orders_of_ ... 40;energy&#41; ) shows that this would have roughly as much energy as the total mass-energy of the Milky Way (10^58 J). This is the energy of 100 trillion supernovas (a single supernova being 10^44 J), or one-trillionth of the total mass-energy of the Universe (10^69 J).

It would not make any explosion though. It would just become a super massive black hole. One to mach the biggest we have seen*, with its milky way sized mass. (*Or well not seen, you know what i mean.)

Ohhh! Is this a Schwarzchild radius thing? (I was wiki-tabbing the origins of the universe literally 2 days ago and ran into it.) In what I read, it seemed like it was saying that a black hole happens whenever you have enough mass in a small enough space. (So everything "could" become a black hole if you squished it "enough," though for most objects, "enough" would be physically unheard of since the universe was less than a second old.) So, since mass ~ energy, does having enough energy (kinetic in the SuperSun) in a small enough space also produce the black hole effect? If so, is this to do with the whole "mass-increases-at-relativistic-speeds" thing?

what do you mean by "also"? mass and energy are equivalent, so "enough mass" and "enough energy" are exactly the same condition.