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Assume Earth has been wrenched out of the Sun's orbit and has become a rogue planet, with its surface equilibrium temperature falling to ~-240C.

At what depth will temperatures remain "comfortable" for human life (i.e. = current surface temperature of ~15C)?

  1. In areas where today the average geothermal gradient is 3.5C/100m [red line].

  2. In geothermally active areas, where the geothermal gradient is much flatter [green line].

Geothermal gradients

In other words, how will a radical cooling of the planetary surface affect Earth's current geothermal gradients?

Will the gradient lines just be shifted 255C left? Or will it be a sort of gradual convergence like in the following diagram?

enter image description here

Thanks in advance for your input!

Optional, closely related question: I assume solid ground reach its equilibrium state much faster than the oceans due to the latter's vast latent heat capacity. But once the oceans do freeze over, after 100,000's of years, would the ice henceforth behave about the same as completely geothermally inert soil, and hence trend towards -240C as well (i.e. in areas of ice far from hydrothermal vents where liquid water may remain indefinitely)?

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  • $\begingroup$ I always though Friesland was in the Netherlands... $\endgroup$ – L.Dutch - Reinstate Monica Oct 26 '19 at 3:33
  • $\begingroup$ inclination of lines on plots will stay about the same so it means plus about 10km crust under which it will be more or less okayish temperature $\endgroup$ – MolbOrg Oct 26 '19 at 7:55
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Initially only the upper most part of the crust would be affected, but as time progressed the new cold boundary would spread downward. This process would be very slow due to the depth of rock and rocks insulating effect.

Making the Earth a rogue planet would in all likelihood also lead to considerable gravitational upheaval which in the short term at least would lead to a lot of volcanism which would delay things further in some locations.

Ultimately the gradients would shift to the left with the surface at -240C (with some volcanic variations) and similar gradients that we see today depending on the underlying geology. However the process might take a very long time indeed to run to completion especially at the deeper levels, possibly billions of years.

Most of the upper parts of the oceans would freeze relatively quickly and spread downwards over time, taking long and longer to freeze as the process continued due to the insulating layer of ice above. There might well be sufficient convection circulation driven by plate tectonics in parts of the oceans to keep significant parts of the lower abyssal plains free from ice. The ice that formed away from ocean vents would eventually be more rock like than soil like at such deep cryogenic temperatures.

I assume the Moon was lost when the Earth escaped the solar system, but in the unlikely event that it was retained possibly with an altered orbit it could be responsible for a degree of energy input by tidal forces.

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  • $\begingroup$ Thanks! What do you mean by "very slow"? (In terms of orders of magnitude). For instance, I have read elsewhere that the oceans will take on the order of 10^5-10^6 years to freeze solid all or most of the way down. I would imagine that the process for the ground will be much quicker - perhaps by two orders of magnitude - since unlike with water one wouldn't need to do any phase transitions. But you seem to disagree ("the process might take a very long time indeed to run to completion especially at the deeper levels, possibly billions of years"). $\endgroup$ – ak7 Oct 26 '19 at 23:52
  • $\begingroup$ Given the scenario it’s difficult to be precise but I suppose it depends on what "deep down" means. The oceans are only a few miles deep whereas the planet is thousands of miles deep. Also although most of the heat from Earth’s interior is from radioactive decay a small but not insignificant part is from accretion that heat has been there for 4.5 billion years $\endgroup$ – Slarty Oct 27 '19 at 10:01
  • $\begingroup$ I think you are right about the latent heat in the oceans. I am not certain, but I do wonder about how the calculations for the oceans freezing was carried out? It very much depends on what assumptions and simlifications are made. Does the calculation include heating from below? Is it just a rudimentary energy balance calculation? It might be worth checking it in detail the oceans must take longer to freeze than you think... $\endgroup$ – Slarty Oct 27 '19 at 10:07

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