So, for some reason the sun has randomly disappeared. The earth, along with the rest of the solar system, have been thrown out into interstellar space.

Obviously, temperatures will plunge to levels beyond "cold", but what will happen? For the sake of answering the question, we'll ignore the fact that all life forms have probably died or gone into stasis if they're lucky. What will happen to the atmosphere, the oceans, the planet's core? Essentially, I'd like to know what would happen to the earth if there was no energy coming in from the sun.

Also, the moon would still be in orbit around the earth if that changes anything.

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    $\begingroup$ I think the question is just "what happens if the sun disappears", the title is a bit misleading. How long after the event are we talking about? A couple of minutes or 3 billion years into the future? $\endgroup$ – Raditz_35 Feb 9 '18 at 10:21
  • $\begingroup$ Surely the question is what would happen if the sun should suddenly disappear? Isn't interstellar space just space between star solar systems which, by definition, we would exist in if our own star (the sun) disappeared? We are not just going to be thrown somewhere (although that may be an effective consequence) $\endgroup$ – Lee Leon Feb 9 '18 at 10:28
  • $\begingroup$ google.com/… returns a lot of good articles, and this question shows no sign of reading any of them. Also related: physics.stackexchange.com/q/18174/104551 earthscience.stackexchange.com/q/4498 worldbuilding.stackexchange.com/q/9679/809 $\endgroup$ – Mołot Feb 9 '18 at 10:39
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    $\begingroup$ I decided not to vote this as a duplicate, based on its specified focus on atmosphere oceans and core. $\endgroup$ – kingledion Feb 9 '18 at 10:43
  • $\begingroup$ en.wikipedia.org/wiki/A_Pail_of_Air for a short story set roughly in the situation described by the OP $\endgroup$ – NofP Feb 9 '18 at 10:50

The atmosphere will stay

It has become something of a running joke to see how many times I have posted this picture.

enter image description here

The mass of Earth will stay the same, so will its escape velocity. The temperature will drop, moving to the left on the chart. This will make the Earth's atmosphere easier to hold on to. In fact, the Earth will retain helium and even hydrogen too, after it gets cold enough.

The core will stay hot

It won't cool down that fast. The Earth's core has essentially been cooling down for the past 4 billion years, and still is pretty hot. Two laws govern here.

The loss of energy from the surface is dominated by the Stefan-Boltzman law for blackbody energy emission in the infrared range. The equation for this emission is $$j* = \epsilon\sigma T^4.$$ Here, $j*$ is radiant emittance, $\epsilon$ and $\sigma$ are constants, and $T$ is temperature. As temperature decreases, emittance decreases as the fourth power of $T$.

As the planets surface drops from its current ~285 K to 200 K, heat loss drops by a factor of 4. By the time temps get down to 150 K, heat loss drops by another factor of 3. The cooler it gets, the less the Earth will cool.

This also applies to heat transfer from the mantle to the crust. The heat equation in one dimension is $$\mathbf{q} = -k\Delta u,$$ where $\mathbf{q}$ is power of the heat transfer, $k$ is a constant, and $\Delta u$ is the temperature difference across the mantle, in this case. The outer core is 4000 K; the surface is about 285 K. Since heat transfer scales linearly with temperature differential, if the surface temps drop to 200 K, then heat transfer will increase by a factor of $1.022$.

So basically, the crust will stop losing energy quickly as it cools, but heat loss from the core won't speed up much at all. So, the core will remain hot for billions more years. No promise of plate tectonics or a magnetosphere for any length of time, but both seem likely for many millions of years.

The oceans will freeze

I estimated in this post that in a little under a year the oceans would freeze over to a depth of tens if not hundreds of meters.

Once the top layer freezes and temperature drops, heat loss to space will be reduced significantly. The rest of the oceans store a lot of energy and will take decades to centuries to freeze solid.

  • $\begingroup$ Could you please clarify what remains from atmosphere? I suppose it will freeze much faster than oceans and many gasez will drop to rain. But I can't estimate how cold it would be and how fast it would be changed $\endgroup$ – ADS Feb 9 '18 at 12:05
  • $\begingroup$ If the temperature drops, wouldn't Earth move to the left in the chart (not the right)? Also, I'm not sure what the chart is meant to relay. How are escape velocity and temperature related? $\endgroup$ – Frostfyre Feb 9 '18 at 13:47
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    $\begingroup$ @Frostfyre Yes, of course, that is what is says, look :) $\endgroup$ – kingledion Feb 9 '18 at 13:52

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