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Suppose you have a planet large enough to support life, with water and air all that, but old enough that it has exhausted its internal heat supply, the core is frozen solid, and there is little to no volcanic or plate tectonic activity.

What sorts of geological / tectonic processes would still occur on such a world, in a steady state (i.e., after all of the mountains formed by volcanoes or crumpling plates have worn away), powered solely by solar energy? Could, e.g., wind sculpting or dissolution and re-deposition of chemicals in the seabed produce a landscape that continues to evolve significantly over time?

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Solar energy does not penetrate the crust for more than few meters. Furthermore is way too diluted to have any plastic effect on rocks. Look at Mercury, it's still solid despite being really close to the Sun. Nor has Venus rivers of liquid rocks.

Furthermore, based on the current theories, a solid core would mean no magnetic field, and no magnetic field would mean no shield from solar wind: bye bye atmosphere and bye bye life.

The only tectonic process which could still occur would be the contraction due to cooling, which would be less powerful than the convective flow.

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  • $\begingroup$ Mercury also doesn't have any fluids on its surface. That seems to me like a significant complicating factor. $\endgroup$ – Logan R. Kearsley Jun 24 '17 at 6:06
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    $\begingroup$ Actually you can have an magnetosphere and atmosphere without tectonics and active core! Venus is an example. See my question on astronomy.se asking just that! astronomy.stackexchange.com/questions/18573/… $\endgroup$ – EveryBitHelps Jun 24 '17 at 9:12
  • $\begingroup$ @EveryBitHelps but not a strong enough magnetosphere to protect life that uses DNA. $\endgroup$ – John Jun 24 '17 at 14:45
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    $\begingroup$ @John You don't need a magnetosphere to protect life from radiation. A sufficiently thick atmosphere or ocean will do that just fine. The benefit of a magnetosphere is primarily to avoid hydrodynamic stripping of the atmosphere by stellar wind. $\endgroup$ – Logan R. Kearsley Jun 24 '17 at 16:42
  • $\begingroup$ and having oxygen and water are essential to life, by just making the atmosphere thicker you also change surface conditions as the atmosphere will get much thicker as you travel back in time especially if it also has to act as the modern radiation shield. This will begin to create more and more of an impediment to photosynthetic life and thus free oxygen in the atmosphere. Also the magnetosphere is a major component of our protection from high energy cosmic rays. $\endgroup$ – John Jun 24 '17 at 23:13
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Contraction due to cooling might change a lot of your landscape over time and some changes might be introduced through "external heat" other than photons like meteorite impacts and tidal forces from moons, suns or other big objects around.

But you may get a lot of things done directly or indirectly through solar energy too, like

  • wear down through erosion through wind, water (think Grand Canyon) and photons
  • build up through (shifting) dunes, sand banks, river deltas
  • freezing and melting cycles for "ice sculptures" like the glacier on kilimanjaro or apparently some mountains on pluto
  • coral reefs, stromatolites, bogs, termite hills, waste dumps and other "biological buildings"

and then you might want to combine such things like freezing water, putting sand on top and fixing it with plants.

There should be many more possibilities.

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Exhausting internal heat happens because the isotopes capable of radioactive decay have spent their vigor. But you could bring back volcanoes via tidal heating.

From https://en.wikipedia.org/wiki/Tidal_heating_of_Io

Tidal heating (also known as tidal working) occurs through the tidal friction processes: orbital and rotational energy are dissipated as heat in the crust of the moons and planets involved. Io has a similar mass and size as the Moon, but Io is the most geologically active body in the Solar System. This is caused by the heating mechanism of Io. The major heating source of Earth and its moon is radioactive heating, but the heating source on Io is tidal heating. As Jupiter is very massive, the side of Io nearest to Jupiter has a slightly larger gravitational pull than the opposite side. This difference in gravitational forces cause distortion of Io’s shape. Differently from the Earth’s only moon, Jupiter has several moons (i.e. Io, Europa, Ganymede and Callisto). As Io is the innermost moon of Jupiter, Jupiter pulls Io inward and other moons pull Io outward. This causes Io’s orbit to be elliptical and eccentric. The distance between Jupiter and Io changes all the time and the distortion of Io likewise changes all the time. The constant change in the shape of Io results in a large amount of friction in the moon and the friction-induced heating drives strong volcanic activities on the surface of Io.[1]

If your planet has company capable of gravitationally flexing it back and forth, that will heat it up and restart some of the geologic processes which on Earth are driven by a molten core.

A different scheme to fire up your planets tired cold core might be inductive heating. A planet with a conductive core traversing a strong magnetic field would heat the core and power up geologic processes. Clearly inductive heating is a thing but I could not find that it is known to happen to any planets. That was my answer to Can you replace a sun with a burning moon?

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    $\begingroup$ Do not know why someone downvoted this answer. Upvoted for the mention of tidal heating. $\endgroup$ – VampyreSix Jun 29 '17 at 15:05
  • $\begingroup$ The downvote is mysterious to me as well. $\endgroup$ – Willk Jun 30 '17 at 0:07

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