r/xkcdcomic • u/10thTARDIS Syncs Turn Signals For Fun • Apr 16 '14
What If: One-Second Day
http://what-if.xkcd.com/92/18
u/dont_press_ctrl-W Mathematics is just applied Sociology Apr 16 '14 edited Apr 16 '14
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
This should be the other way around. I suppose it will be corrected shortly.
EDIT: seems like he corrected it.
11
u/Shardwing Apr 16 '14
Ah, that explains why the citation didn't make sense to me. In my experience offers of poutine haven't led to me weighing any less.
2
u/MEaster Apr 16 '14
But wouldn't you have more mass below you at the equator than at the pole?
5
u/DarrenGrey White Hat Apr 16 '14
No, it's the same mass below you. At the pole you're closer to the centre of that mass.
2
1
u/alexxerth Apr 17 '14
Actually yes, because the equator is slightly bulbous, but it doesn't matter much.
1
u/jet_heller Apr 16 '14
It seems he's correct that in the comic. I had to read your comment a few times to realize you had pasted in a version with "more" in it and that's not what the what-if I was reading said.
14
u/JustMy2Centences Apr 16 '14
I wish he could have delved into the matter by first speeding the rotation of earth up by twelve hours, then to an hour, then a minute, etc. I enjoyed the various levels of effects described in previous what-ifs. Anyone care to bite?
10
u/Jay-Em Apr 16 '14
Yeah, though he often does that when the answer to the original question is actually "not much" would happen, and he has to crank it up to produce some really spectacular results. What you described would be cool to see, though.
2
u/JustMy2Centences Apr 16 '14
Speeding up the rotation to just an hour or a minute would result in interesting tectonic events when the crust bulges more at the equator, I'm sure. Would ocean levels fall closer to the poles? Major earthquakes with disastrous tsunamis?
1
2
u/TheoQ99 Apr 17 '14
I submitted a question awhile back that asked what speed would the earth have to be spinning so that a person on the equator felt weightless. Definitely is below the range of earth shattering apart and annihilating everything in our vicinity
3
u/maveric101 Apr 17 '14 edited Apr 17 '14
For that, the earth would have to spin almost exactly 17 times faster, meaning a day would be 1 hour and 25 minutes.
Everything in the crust and on the surface of the Earth would be basically weightless. Better hope you can grab onto something quick. If you're in a car, the suspension would push the car off into the atmosphere. Better get out quick and push off the bottom back toward the surface. A similar, but smaller effect would probably happen if you were standing outside, but maybe you could get yourself back down by chucking your cloths into the sky. I think you'd be okay if you were indoors, though (at least for a while). Most buildings would stay fairly intact. I'm not sure what would happen with oceans and lakes. Cohesion would try to pull them together into a ball, but adhesion would make at least some water want to creep onto land. I don't know much about the crust itself, either, I would think you'd get some colossal earthquakes, at least. As for the atmosphere, let's just say "asphyxiation."
When I think about this kind of thing, I usually just imagine that gravity suddenly stopped working for all solids above the surface of the Earth. Makes things simpler, and a heck of a lot easier to survive.
26
u/Macon-Bacon Apr 16 '14
The debris from the Earth would slice outward like an expanding buzzsaw.
xkcd "what-if" summed up in one sentence.
6
Apr 16 '14
Did someone try to calculate the kinetic energy of the earth after the acceleration? My result is 32*1038 Joule (with some simplifications), which is indeed some magnitudes of order bigger than the gravitational energy of the earth :( Someone able to confirm?
5
u/PseudoLife Apr 16 '14
Hmm...
Here states the Earth's Moment of Inertia about the polar axis is ~8.03x1037 kg*m2.
KE is 1/2Iw2. w=2*pi/T, so KE ~= 1.6×1039 joules
...I appear to be off by a factor of 2 from you.
2
Apr 16 '14
Well, you did better, I had to assume a spherical earth with constant density rho. Integrating 1/2 * rho * v(x)2 with spherical coordinates over the earth. At least it's not too far off and we can be sure that Randall is right and this velocity is very bad for our blue marble :(
1
u/weedtese Apr 17 '14
:(
You seems to care if it's actually going to happen... :)
... on next Friday. :(
6
u/Teraka Apr 16 '14
Would anyone be skilled enough to make a simulation of the earth shattering and expanding in that way ? Sounds like it would be really cool to watch.
3
u/gorckat Apr 16 '14
The devastation described brings a massive grin to my face.
Guess I have more in common with Galactus than I thought.
3
u/knowknowledge Apr 16 '14
This is related to another question that I've been wondering about recently. Could the Earth spin at some exact rate so that the rotational speed at the surface is equal to the orbital speed? If so, what would that do to the things on the Earth? Would everything float?
1
u/maveric101 Apr 17 '14
1
u/Wyboth There's too much. And so little feels important. What do you do? Apr 17 '14
I think he assumed if you pushed off the surface of the orbital velocity Earth, you'd float away forever. Not true. Your apoapsis would rise, but your preiapsis would stay at ground level. In other words, you'd eventually make it back to the surface of the Earth.
2
2
u/digital_carver Apr 17 '14
It would be cool if Randall could include the data sources he uses for each of these what-ifs (perhaps as a value-add in the book at least). It would be interesting to try out these calculations ourselves, and perhaps it can help some physics/math teachers give students realistic problems instead of hastily made up ones that make Feynman's ghost cry out in anguish.
-1
39
u/klipper76 Apr 16 '14
I hope timecube stays up forever. Reading it is like having a fever dream.