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Red Giant
2009-Feb-22, 12:51 PM
If the sun shut off how long would it take the Earth to freeze? (I know it's not possible)

astromark
2009-Feb-22, 06:01 PM
Eleven point three days... given the thermal spreading of frozen oceans and atmospheric distrabution... Wind. I will note that the measurement of the time period of Earths atmosphere and oceanic freezing could not be pinned down to hours of accuracy as the variable movement of warmed currents both liquid and gas is inconsistent. It would get very cold very quickly and the weather would be hell.
In as little as seventy hours catastrophic cold would be obviously spreading.

EDG
2009-Feb-22, 06:13 PM
Eleven point three days...

Is that a guess? If not, what heat loss calculations are you making to arrive at that number?

astromark
2009-Feb-22, 06:32 PM
Is that a guess? If not, what heat loss calculations are you making to arrive at that number?

... HOW DARE YOU QUESTION ME... Lol:) YES, it is a of the shelf guess. based on not a single known parameter or fact...

Ken G
2009-Feb-22, 06:57 PM
It depends on what you mean by "shut off". Some might mean that the nuclear reactions that power the Sun shut off, but if that happened, there would be no impact on the earth for many thousands of years, and the Earth wouldn't "freeze" for maybe a few million. However, if you mean by "shut off" that the surface of the Sun is instantly transported to absolute zero temperature, or the Sun is removed completely, then it would obviously happen much faster! It would take just over 8 minutes for us to notice the Sun was gone (the light travel time), and after that it would start cooling off even faster than day cools after sunset (in the latter case, we are still warmed by air currents from the day side). The issue is then, how much warmth is stored beneath the top layers of soil, rock, and ocean, and how long would it last as the Earth radiates its heat into empty space? If you want real numbers, you'll need to do your homework on the question, someone might find a source that has worked it out. Until then, astromark's numbers seem plausible to me, though I suspect it would happen a bit faster than that.

EDG
2009-Feb-22, 07:40 PM
There was an account in Graham Greene's book "Frozen Star" that explored what would happen if the sun rapidly (and for no good reason) collapsed to become a black hole. The day side of the Earth got roasted during the collapse, but when the sun "winked out" everything else froze pretty quickly... it's been ages since I read it but IIRC the earth was a frozen iceball (with the atmosphere freezing out) within a couple of weeks.

mugaliens
2009-Feb-22, 07:56 PM
Well, parts of the Earth are already frozen. The poles. The crust. The mantle. The inner core (we think).

Most of the unfrozen parts of the surface would progressively freeze over the course of a couple of weeks. The oceans would take much longer. The molten portions inside might not freeze for thousands if not millions of years until the radioactives ran out.

Red Giant
2009-Feb-22, 10:02 PM
Thanks for this.

Jens
2009-Feb-23, 08:25 AM
If the sun went out, it would perhaps not be appropriate to ask "how many days". Maybe better to say, "how many nights"? :)

antoniseb
2009-Feb-23, 09:59 AM
If the Earth were suddenly far from the Sun, people could stay comfortable living not too far underground for many generations... Long after the Oxygen in the air turned to snow. I'm not sure where they would get power to drive equipment though. We'd probably have to rely on nuclear & geothermal... Solar would be right our, and the air supply would be precious.

timb
2009-Feb-23, 11:42 AM
If the Earth were suddenly far from the Sun, people could stay comfortable living not too far underground for many generations... Long after the Oxygen in the air turned to snow. I'm not sure where they would get power to drive equipment though. We'd probably have to rely on nuclear & geothermal... Solar would be right our, and the air supply would be precious.

You're dreaming. Humans would be extinct within weeks. If the sun went away today, who would be the people living comfortably underground? coal miners? They have nothing with them underground to equip them for survival. For example, they wouldn't have any food.

Ronald Brak
2009-Feb-23, 12:04 PM
With warning people could set up heat exchangers that operate off geothermal warmth and the freezing surface, but without warning I think the liquid oxygen rain would finish off most survivors within perhaps a week, leaving a small number of people in submarines, really well built air-tight survival shelters and on the international space station who would have no hope of lasting longer than their supplies.

Red Giant
2009-Feb-23, 12:06 PM
timb is right on this. Now if we had warning we would stand a chance.

heldervelez
2009-Feb-23, 04:00 PM
We live an interglacial period.
The humanity will have to prepare to the cold future. The Sun will not disappear but the cold will came anyway. The geothermic energy will be a must.

antoniseb
2009-Feb-23, 04:23 PM
You're dreaming. Humans would be extinct within weeks. If the sun went away today, who would be the people living comfortably underground?...

Well, this is a dreaming kind of question. I suppose that I was imagining that we had a lot of time to prepare. If it was an unexpected change of venue for the Earth, you're absolutely right about humans being extinct (not counting the all-male crews of some nuclear subs. They might last months).

heldervelez
2009-Feb-23, 04:50 PM
The humanity will prepare is own future, and the future of Life, in another planets far away. Other Suns will be shinning in our future.

Bob B.
2009-Feb-23, 06:40 PM
... and on the international space station who would have no hope of lasting longer than their supplies.

The ISS is solar powered, so it would be nothing but a tin can in space. I think the crews would subcomb to hypothermia long before the supplies ran out.

Bob B.
2009-Feb-23, 08:30 PM
As the nerdy engineer that I am, I’ve tried to put some numbers to this problem. Heat transfer problems are not something I normally do, so if anyone finds an error in my logic, please correct me.

Let’s say we want to figure out how long it would take for the Earth’s atmosphere to cool to a global temperature of zero degrees Celsius. The mean air temperature at sea level is about 15 C. Although the temperature drops with increasing altitude, most of the atmosphere’s mass is near the ground. Therefore, let’s call the atmosphere’s temperature 15 C. (Since this is a bit on the warm side, it should account for some heat radiated from the ground.)

The atmosphere has a total mass of about 5.15E+18 kg. The specific heat capacity of air is about 1 kJ/kg-K. Therefore, the amount of heat the air must lose to cool to 0 C is

5.15E+18 kg * 1 kJ/kg-K * 15 K = 7.725E+19 kJ

We can use the Stefan-Boltzmann law to determine the power of energy radiated:

P = A*epsilon*sigma*T^4

Where,
P = power radiated, in watts (or J/s)
A = surface area = 4*pi*6371000^2 = 5.10E+14 m^2 for Earth
epsilon = emissivity = about 0.6 for Earth
sigma = Stefan-Boltzmann constant = 5.67E-8 W/m^2-K
T = temperature, in K

Since we’re cooling from about 288 K to 273 K, let’s use an average of 280.5 K. Therefore,

P = 5.10E+14 * 0.6 * 5.67E-8 * 280.5^4 = 1.1E+17 W

The amount of time needed to cool the atmosphere is, therefore

7.725E+22 J / 1.1E+17 J/s / 86400 s/day = 8 days

This is a very crude estimate and is intended to simply get us somewhere in the ballpark.

There is, of course, also heat in the ground and heat in the oceans that would have to radiate away. However, I think that once the air loses enough heat that global freezing temperatures are the norm, the surface will freeze over pretty quickly.

slang
2009-Feb-23, 08:47 PM
(not counting the all-male crews of some nuclear subs. They might last months).

Oh wow, imagine their surprise when they come to periscope depth! "Umm.. captain, wasn't it supposed to be daytime right now?" or "How did we end up under the arctic ice?".

Arneb
2009-Feb-23, 08:52 PM
IF we are dreaming about survivors living in old mines on geothermal, nuclear and hydroponics - We might as well speculate they found a way to make sorties to the atmosphereless surface and actually shovel their oxygen into cryotanks for consumption below.

Now all they had to do would be finding a way of venting the CO2 away from their O2 sources everyone would be a green very soon...

I also think they would start to ponder ideas about interstellar travel seriously even sooner...

Bob B.
2009-Feb-23, 10:27 PM
Using the same equations given in my previous reply (#18), I calculated the temperature of the Earth's atmosphere as a function of time. As the atmosphere cools, the rate of heat loss decreases. The temperature, therefore, drops quickly at first and then may take years to cool just one degree. Here are the results integrated over time:

Initial Temp. = 288 K
After 1 day, T = 286 K
After 1 week, T = 275 K
After 1 month, T = 245 K
After 3 months, T = 202 K
After 6 months, T = 171 K
After 1 year, T = 141 K
After 2 years, T = 114 K
After 3 years, T = 100 K
After 5 years, T = 85 K
After 10 years, T = 68 K
After 20 years, T = 54 K
After 50 years, T = 40 K
After 100 years, T = 32 K
After 200 years, T = 25 K
After 500 years, T = 18 K
After 1000 years, T = 15 K

These temperatures ignore heat added by geothermal sources.

It would take a little over 4 years for the oxygen to rain out of the atmosphere (boiling point = 90.2 K). The nitrogen would rain out of the atmosphere by 7 years (boiling point = 77.4 K). The atmosphere would freeze solid after about 19 years.

I used an emissivity coefficient of 0.6 in my calculations, which is the approximate current value. As the surface freezes and the atmospheric gases condense, the emissivity will surely change (by what amount, I don't know).

mugaliens
2009-Feb-23, 11:18 PM
You're dreaming. Humans would be extinct within weeks.

Most of them, yes. And frozen.

If the sun went away today, who would be the people living comfortably underground? coal miners? They have nothing with them underground to equip them for survival. For example, they wouldn't have any food.

Not live food, anyway. There'd be lots of frozen food lying around... :shifty:

Ronald Brak
2009-Feb-24, 02:12 AM
It would take a little over 4 years for the oxygen to rain out of the atmosphere (boiling point = 90.2 K). The nitrogen would rain out of the atmosphere by 7 years (boiling point = 77.4 K). The atmosphere would freeze solid after about 19 years.

Wow, I thought the atmosphere would cool much faster, simply based upon how much the temperature can drop overnight in a desert.

Peter B
2009-Feb-24, 02:21 AM
IF we are dreaming about survivors living in old mines on geothermal, nuclear and hydroponics - We might as well speculate they found a way to make sorties to the atmosphereless surface and actually shovel their oxygen into cryotanks for consumption below.

Now all they had to do would be finding a way of venting the CO2 away from their O2 sources everyone would be a green very soon...

I also think they would start to ponder ideas about interstellar travel seriously even sooner...

Sounds like a cross between Fritz Leiber's short story "A Pail of Air" and Dave Dvornik's novel "Core Heat".

Ronald Brak
2009-Feb-24, 02:33 AM
The ISS is solar powered, so it would be nothing but a tin can in space. I think the crews would subcomb to hypothermia long before the supplies ran out.

Very good point. However, since the ISS is designed to be in shade almost half the time, I think body heat might be enough to keep them alive until their oxygen ran out. And since their emergency solid oxygen system also generates heat (and flames on Mir) that would also help, for a while.

Bob B.
2009-Feb-24, 03:32 AM
Wow, I thought the atmosphere would cool much faster, simply based upon how much the temperature can drop overnight in a desert.

So did I until I started working the equations; of course I may not be using the equations correctly. Although I studied this stuff decades ago, heat transfer is not something I normally do so I'm pretty rusty. I invite anyone with a knowledge of this to double-check my results.

Also note that I'm using a very simplified model; there's a whole bunch of stuff I purposely ignored. The real answer is probably much different than my results; I just hope I got the order of magnitude right.

heldervelez
2009-Feb-25, 01:46 AM
...
It would take a little over 4 years for the oxygen to rain out of the atmosphere (boiling point = 90.2 K). The nitrogen would rain out of the atmosphere by 7 years (boiling point = 77.4 K). The atmosphere would freeze solid after about 19 years.
...

Exercises like the OP are good to try to explain observations:

...We can say that the athmosphere of Mars(*) is now freezed and it was not so in the past...

and reasoning along the OP the most probable cause could be :
Less solar flux now than in the past.
Why ?

May be we will have the need of equate the Star travelling sooner than we tought.
(*) also past climate on Earth was warmer.

Gandalf223
2009-Feb-25, 02:18 AM
As I've gotten older, I find my appreciation of cold weather has lessened, so the idea of the sun turning itself off does not warm the cockles of me heart.

But at least we could expect a couple days of outstanding seeing before we all became corpsicles...

neilzero
2009-Feb-25, 04:50 AM
I agree with Astromark. 90% of Earth's ocean would have ice on the surface at 11.3 days. Dry ice would fall from the sky about the 12th day and liquid nitrogen and liquid oxygen would fall as rain the 13 th day in some locations. Very few locations would be warmer than 100 k = -173 c, by the 50th week, but there might still be lots of 4 degree c water at the bottom of the ocean, insulated by very thick ice, and frozen nitrogen on the surface. Neil

qraal
2009-Feb-26, 12:55 AM
The oceans store a lot more heat than the atmosphere or the land. Air currents might cause the very upper layer of ocean to freeze over quite quickly, but long term heat loss will be very, very slow because of the ice. The oceans are, on average, at 278 K - most of the ocean is "cold" for humans. That still represents, taking 34.5 K as the zero, about 3.5 terajoules of heat to lose to space. If the surface was at 273 K - i.e. frozen, but 'warm' ice - then the heat loss rate is 315 W per square metre over 4300 metres of ocean. That's a characteristic time of 362 years. Assuming the whole lot was isothermal then it would chill to 34.5 K in about 140,000 years - ignoring things like the insulating effects of ice and geothermal heat etc. In actuality it would probably take a million years to hit equilibrium.

Let's see what results as it all cools down to an equilibrium driven only by Earth's geothermal output. A square metre of water-ice one metre thick will radiate 4 Watts of heat for every degree of heat differential between it and the heat-sink. Frozen N2 and O2 will let 0.4 Watts through per metre per degree. Assuming about 10 metres of cryo-snow then 0.04 Watts per degree will get through. Assuming the cryosnow is at 34.5 K at top and the water is at 277 K at the base of the water ice, then there's a 242.5 K differential.

Earth's geothermal output over oceanic crust is about 0.08 Watts per square metre of surface. Thus, at equilibrium, the cryosnow creates about a 2 K differential between it and the water-ice. Between the top and bottom of the water ice there's a 240.5 K differential across the ice. To reduce the heat-flow to 0.08 W means the ice, at equilibrium, will be 12 km thick... just a bit too thick for a long term global ocean. The best that can be hoped for is melt-pockets around geothermal vents, following the oceanic ridges where new oceanic crust is being exuded. A network of meltwater channels in the ice could form connected across the frozen globe but deep below.

That assumes non-convecting ice - a "stagnant lid" layer - which seems possible given our ignorance of water-ice's low temperature bulk rheology. Convection would hasten heat-loss and reduce the melt volume, but a network following the mid-oceanic ridges might still form. Something might live down there indefinitely until the Earth gets too cold. The concentration of the salt as the ocean froze might keep it liquid down to 250 K or so, but just what would survive in such a super-saline mix is anyone's guess. If ammonia was allowed to build up and creatures could adapt then a liquid ocean would remain down to 176 K. Such oceans might exist under the ice on many of the large moons of the Outer Planets.

Bob B.
2009-Feb-26, 02:01 PM
The oceans store a lot more heat than the atmosphere...

In fact, if I'm working the numbers correctly, the ocean contains about 1,200 as much heat as the air.

Total mass of air = 5.15E+18 kg
Specific heat capacity of air = 1 kJ/kg-K
Average temperature of air* = 250 K

Total heat = 5.15E+18 x 1 x 250 = 1.29E+21 kJ

(* This is a weighted average based on the "Standard Atmosphere".)

Total mass of oceans = 1.4E+21 kg
Specific heat capacity of sea water = 4 kJ/kg-K
Average temperature of oceans = 278 K

Total heat = 1.4E+21 x 4 x 278 = 1.56E+24 kJ

qraal
2009-Feb-28, 12:01 AM
That's why oceanic currents make parts of the world warmer than they have any right to be. Coldest part of Eurasia is in the middle of Siberia away from the oceanic warmth. If there was a supercontinent over the north pole the ice would be immensely thick and... a lot like Antarctica, in fact, but much larger. While the Arctic ocean is coated in ice there's still some current flow keeping it a bit warmer than it would be if land-locked.

In fact, if I'm working the numbers correctly, the ocean contains about 1,200 as much heat as the air.

Total mass of air = 5.15E+18 kg
Specific heat capacity of air = 1 kJ/kg-K
Average temperature of air* = 250 K

Total heat = 5.15E+18 x 1 x 250 = 1.29E+21 kJ

(* This is a weighted average based on the "Standard Atmosphere".)

Total mass of oceans = 1.4E+21 kg
Specific heat capacity of sea water = 4 kJ/kg-K
Average temperature of oceans = 278 K

Total heat = 1.4E+21 x 4 x 278 = 1.56E+24 kJ

timb
2009-Feb-28, 12:41 AM
That's why oceanic currents make parts of the world warmer than they have any right to be. Coldest part of Eurasia is in the middle of Siberia away from the oceanic warmth. If there was a supercontinent over the north pole the ice would be immensely thick and... a lot like Antarctica, in fact, but much larger. While the Arctic ocean is coated in ice there's still some current flow keeping it a bit warmer than it would be if land-locked.

There would be no Arctic sea ice if the Arctic Ocean weren't nearly land-locked. Its only deep water connection to another ocean is the GIUK gap.