# How long would we live without the sun

I was trying to come up with a solution to the timeline when hypothetically speaking the sun would stop shining ( or emitting radiation). Now, gravitational issues aside (the sun as a body still there), how long would it take for median temperature to drop beyond freezing point around the globe? How long would it take for the oceans to completely freeze, and how long would it take for the air to become liquid or solid?
I'm wondering if anybody did a research on this topic, I searched the internet but could not find anything about the subject.

Also, as the sun burning hydrogen in its core it becomes more efficient, therefore, gets hotter (as I understand). Somewhere I saw that it increasing its output about 10% in billion years. How long would animals have left on this planet, and how would it affect us humans in.... let's say 10,000-50,000 years from now.
Thank you very much

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russ_watters
Mentor
The timeperiods where the sun's output varies enough to matter enough to worry about killing us is in the billions of years. And what is going to kill us is the increase in output and volume of the sun. The sun is literally going to swallow the earth.

Assume earth is a black body radiator, calculate rate of energy loss. Multiply the latent heat of freezing water by the seven oceans.

If the sun stopped shining, animals would run out of plants within the season. A small human population might last long enough to harness fusion themselves, though it sounds like a tenuous existence. Bit pointless though, since that isn't the predicted fate for the sun; provided we can start colonies extraterrestrial colonies in the near future, we'll likely have time to find other suns.

I saw another notion that as the sun expands in size it would "push" the earth beyond its present orbit....
Now, back to my freezing question: What would be immediate effects of absense of sunlight and how long do you think it would be before our world would become a perfect cryogenics lab?

chroot
Staff Emeritus
Gold Member
Well, the Earth would initially lose energy at the rate given by the Stefan-Boltzmann law, or something on the order of about 2.3 x 1017 watts, with some (slightly unreasonable) assumptions. This is a high estimate.

Assuming the Earth were a solid ball of iron, it would have a heat capacity of 0.450 J/g-K. Other materials have larger heat capacities, so this is a low estimate of the heat capacity of the Earth: 7.2 x 1029 J.

http://en.wikipedia.org/wiki/Heat_capacity#Heat_capacity

Solving the differential equation gives me a cooling time, from 300K down to 270K (the freezing point of water) of some five thousand years. This means almost nothing though, since it doesn't really matter when the entire Earth's volume reaches the freezing point of water; the crust would long ago have become so cold that life could not exist on it. It's not really all that calculable (there are too many heat transfer questions I cannot answer), but I'd bet the surface would be inhospitable to most life in a matter of days.

Solving it down to 2.7K gives me a time of about 6 x 1017 seconds, or about 20 billion years. This is not a very accurate calculation, but the true value will certainly be in the billions of years.

In other words, it won't support life for more than a couple days, but it'll be "hot," relative to the vacuum of space, for an extremely long time.

- Warren

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How much heat does earth radiate into space (as black body). Would you please specify a formula for that..
Thank you.

mgb_phys
Homework Helper
Power = sigma * T^4 * 4pi R^2

Where sigma = stefan boltsman constant 5.670 ×10−8 Wm-2K-4, R is the radius of the earth ( about 6400Km)
So currently about 2 x 10^17 Watts but this will decrease as the temperature drops

The earth is mixture of silicon/iron so has a specific heat capacity of around 500J/kg/K, and has a mass of 6 x10^24 Kg
So it has to lose 3X10^27J to drop 1 degree C

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chroot
Staff Emeritus
Gold Member
Moderator note: I have merged these two threads into one. Alex Nesh, please do not post the same question in more than one place.

- Warren

Would heat capacity of air and water play a major role in the heat "giveaway" since the earth crust acts as a good insulator from its interior and covered substantially by water. Also, would the temperature on "dark" earth resemble the temperature of unlit side of the moon? Do "airless" planets experience heat exchange from the dayside to the night side to any measurable extend?
Thank you. (sorry I have many questions)

chroot
Staff Emeritus
Gold Member
Since the volume of air and water are so tiny compared to the volume of rock, it would make little difference. Besides, the dominant mode of heat loss from the surface would be radiative, not convective, so the material is irrelevant.

The surface temperature of the Earth would rapidly approach that of the surface of the unlit side of the Moon, yes.

Planets without atmospheres still have heat exchange through their volume; through the rocks that make them up. This is a larger effect than that of the atmosphere.

- Warren

The temperature of unlit side of the moon is not low enough to liquify any of the air components, correct? Now, the lowest point (of rapidly desending temperature) will reach in a matter of a few days? The presence of atmosphere on the outer planets or satellites (like Titan) makes litte difference on it's surface temps?
Thank you. (it's hard to get some anwers on myspace, you know)

chroot
Staff Emeritus
Gold Member
I'm pretty sure the temperature on the unlit side of the Moon would be low enough to liquify any component gas of air, but I'd have to check on that.

The crust of the earth would cool well below the temperatures required to sustain life in only a couple of days without any sunlight, yes. (Maybe a week.)

The presence of atmosphere on moons like Titan makes an enormous difference on the surface temperatures there; it just won't make too big a difference in how fast Titan would cool if there were no sunlight. Keep in mind that cooling is an exponential process; it occurs very, very quickly at first and gradually slows down.

- Warren

.... and ambient temperature of space in solar system is 2.4K, so that's the temperature the earth would eventually reach at infinity, correct?

chroot
Staff Emeritus
Gold Member
2.725K. It would cool exponentially toward this forever, without reaching it. Yes.

- Warren

do you think the earth would change its orbit as the sun becomes red giant, or would it be engulfed by the "surface" of the sun altogether?

chroot
Staff Emeritus
Gold Member
I know of no mechanism that could push its orbit out. Neither radiation pressure nor the solar wind should have any meaningful effect on a body as large as the Earth.

- Warren

For what I understand, at the last stage of its cycle the the sun will lose almost a quater of its mass as the result of outer layer expansion, that would (in my opinion) change solar system orbits of the planets, do you think that would make sence?

chroot
Staff Emeritus
Gold Member
You didn't really specify exactly what stages you're talking about, though. I thought you were simply talking about its gradual expansion.

The Sun will indeed go through a series of pulsations, shedding mass each time. These will occur very late in its life, though, on its way to becoming a so-call planetary nebula. The Earth will be completely gone (absorbed into its outer layers) long before these pulsations even begin to occur.

Also, the solid angle of the Earth as seen from the Sun is so small that only a miniscule fraction of any ejected mass is going to actually impact the Earth. I cannot personally say what effect it would or would not have on the Earth if it miraculously still existed then; perhaps a more educated planetary physicist could say.

- Warren

Sorry, I was talking about the first red giant phase ( when it depletes hydrogen). With very strong solar winds it will lose quater of its mass in the course of a few million years, that in turn will result in lower central gravity in the solar system, and planets in response will move outwards of their original orbits.......

russ_watters
Mentor
Hmm - I'd never heard that before, but that's what wik says:
The Sun is expected to become a red giant in about five billion years. It is calculated that the Sun will become sufficiently large to engulf the current orbits of some of the solar system's inner planets, including Earth.[6][7][8] However, the gravitational pull of the Sun will have weakened by then due to its loss of mass, and all planets but Mercury will escape to a wider orbit. That said, Earth's biosphere will be destroyed as the Sun gets brighter while its hydrogen supply becomes depleted. The extra solar energy will cause the oceans to evaporate to space, causing Earth's atmosphere to become temporarily similar to that of Venus, before its atmosphere also gets driven off into space.[9] Venus will become a burnt out planet; its atmosphere having long been driven off, and its rock will melt.[1]
http://en.wikipedia.org/wiki/Red_giant

Horrible to read, although facinating :=\

I was trying to come up with a solution to the timeline when hypothetically speaking the sun would stop shining ( or emitting radiation). Now, gravitational issues aside (the sun as a body still there), how long would it take for median temperature to drop beyond freezing point around the globe? How long would it take for the oceans to completely freeze, and how long would it take for the air to become liquid or solid?
I'm wondering if anybody did a research on this topic, I searched the internet but could not find anything about the subject.

Also, as the sun burning hydrogen in its core it becomes more efficient, therefore, gets hotter (as I understand). Somewhere I saw that it increasing its output about 10% in billion years. How long would animals have left on this planet, and how would it affect us humans in.... let's say 10,000-50,000 years from now.
Thank you very much

In a couple of billions of years, the oceans will start boiling, and that is when the life on Earth will end, do not worry about the Sun exploding in 4 billion years, life as we know it will end in 2

do you think the earth would change its orbit as the sun becomes red giant, or would it be engulfed by the "surface" of the sun altogether?
it is hardly so that the earth will cahnge its orbit but there maybe some truth in it too. but most likely, the sun may die out before it can 'burn' our planet:rofl:
(visit my blog!)

In a couple of billions of years, the oceans will start boiling, and that is when the life on Earth will end, do not worry about the Sun exploding in 4 billion years, life as we know it will end in 2
yea. it is true but we wont live to see it though. maybe scientist have found a way to this problem by then. but do you know that the earth itself is already dieing? changes may happen!
(visit my blog!)