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As the core and mantle of the earth cools, it will reach a point where new crust cannot be produced.

How can this point be calculated?

If we can, has anyone done such calculations?

Thanks!

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  • $\begingroup$ I would imagine that the proximity to a star and speed of rotation probably comes into play with the tidal force on the crust. Interesting question, though! +1 $\endgroup$ – Richard Nov 19 '14 at 12:42
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One permanent threat to plate tectonics is the oceans vanishing. The scientific jury may still be out on this matter, but most geologists and geophysicists consider water to be the lubricant that makes plate tectonics possible. In a billion years or so, the Sun will have become 10% more luminous. This is conjectured to make the Earth to undergo an unstoppable moist greenhouse / runaway greenhouse, and the oceans will vanish.

The core is still emitting residual heat from the formation of the Earth. As the core cools, iron in the outer core freezes onto the inner core. This is freezing is an additional source of heat. The solidification of the Earth's core thus represents another permanent threat to plate tectonics. The liquid outer core is conjectured to have frozen solid less than three billion years from now.

A nearer term threat is the formation of the next supercontinent. Plate tectonics may operate in fits and starts. What makes subduction zones form is not known. What is known is that a major subduction zone vanished when India collided with Asia, and no new subduction zones formed elsewhere to take its place. If this conjecture is true, plate tectonics will temporarily stop in a few hundred million years when the next supercontinent forms, only to restart later when too much heat stress builds up inside the planet.

This is all highly conjectural. No scientist will live to see their conjectures falsified.


References:

Kasting (1988), "Runaway and moist greenhouse atmospheres and the evolution of Earth and Venus," Icarus 74.3 : 472-494

McDonough (2003), "Compositional model for the Earth's core." In Treatise on geochemistry 2 547-568.

Silver & Behn (2008), "Intermittent plate tectonics?" Science 319.5859.

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    $\begingroup$ The implication that subduction stopping when super continents means an end to plate tectonics I think is a bit of a stretch. Certainly, you can imagine a unique world where the world is filled with transform boundaries and rifts, and actually growing in crustal for a small period of time (100-300myrs). $\endgroup$ – Neo Nov 19 '14 at 19:33
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    $\begingroup$ @Neo - That's exactly what Silver & Behn said in their paper, that plate tectonics is not a continuous process. It instead operates in fits and starts. $\endgroup$ – David Hammen Nov 19 '14 at 20:35
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The whole plate tectonic system is good for a few billion years yet. David is correct that water, as a lubricant, is needed to keep the system moving, but a 10% warming of the sun isn't enough to completely destroy the oceans. That will occur, but not until the sun moves close to, or into its red giant phase several billion years from now. The other factor is uncertainty as to how long there will be sufficient radioactive heat to overcome viscous drag of the convective cells which underlie the crustal plates. There has been much speculation, but I am not aware of any convincing analysis of how long this will take.

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  • $\begingroup$ Regarding "but a 10% warming of the sun isn't enough to completely destroy the oceans" : I can give plenty of citations that say that this is indeed the case. I already gave one in my answer (Kasting, 1988); there are plenty of others. Can you give one that backs your claim? $\endgroup$ – David Hammen Oct 17 '16 at 19:19

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