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As you know, Earth has active and moving techtonic plates known as the lithosphere. They float on the asthenosphere and slowly move about. Here's my question:

Can a planet with a hot molten core have a lithosphere-like layer where all pieces are solidly connected and are stationary? I would also prefer if you could provide what would have to happen during the planet forming process that didn't occur for Earth to make this possible

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This is a complicated matter of planetary geology. Some guidance can be found by looking at the solid planets in our solar system, specifically the planets of the inner solar system.

The simple answer is yes, but this comes with caveats. Namely, something like this can occur, but it may not be that simple. Particularly if comparisons are made with the planets Mars and Venus and our own Earth.

Let's start with the planet Mars.

No current plate tectonics: The giant volcanoes of the Tharsis Bulge tell us much about Mars' lithosphere:

  • It's not moving: On Earth, rising mantle plumes cause volcanic hot
    spots like the Hawaii hot spot. When lithospheric plates move over a
    hot spot, a chain of extinct volcanoes results. Each volcano is of a
    finite size because it only has limited time in which to grow before
    it is move away from the hot spot. On Mars, there are no chains, only extremely large volcanoes, suggesting that individual volcanoes sit
    on top of their hot spots forever and are not moved aside by
    lithospheric motion.

  • -

It's thick: On Earth, the weight of the relatively modest volcano
Mauna Kea pressing into the lithosphere creates a measurable dimple
in the ductile mantle. The giant Olympus Mons and its companions do
not. Mars' lithosphere must be considerably thicker than Earth's. Not surprising considering that Mars is so much smaller and consequently
has a higher SA/V ratio.

enter image description here

In summary, Mars lacks plate tectonics and continental drift because of its small size and the formation of a thick mantle. However, this is complicated by early subduction during martian geological history.

The geochemical comparison of Mars surface (observed by rovers) and deep (sent to Earth as Mars meteorites) rocks by Tuff et al., 2013 suggesting active subduction during Mars' first 0.5 gy.

Now let's look at the planet Venus and this is different from both Earth and Mars.

On Earth, plate tectonics involve:

  • The subduction of cold lithospheric plates at convergent boundaries.

    • Subducting slabs are "lubricated" by partial melting of adjacent mantle rocks as a result of the infusion of water from the subducting slab.

But consider:

Q: What happens if the surface is too hot for oceans to exist?
A: No melting occurs near subducting slab, so slab is not lubricated and can't move.
Q: What happens if the lithosphere stays very hot because of surface conditions?
A: Lithosphere doesn't subduct because it is not relatively cool. 

That sums up the situation on Venus, where there seems to be lithospheric movement, but no subduction zones or clear plate boundaries.

Subductions zones and their volcanic arcs are the "refineries" at which continental and oceanic crust are differentiated. Lacking them, Venus lacks the global dichotomy (maybe) of continents and ocean basins that characterize Earth, even though it has continent-like elevated regions. (Compare this image of Earth surface elevations to this one of Venus.)

enter image description here

In summary, while Venus has plate tectonics they are radically different from those of planet Earth.

Th key factors for plate tectonics on any planet can be summarized as the following.

Necessary planetary differences:

Factors that make each world unique.

Heat sources: Magnitude and relative contributions of different heat sources (primordial, radiogenic, tidal)

Size: Surface/vol ratio determines rate of cooling.

Resurfacing: Presence and rate of resurfacing processes like impacts or erosion, transport, and sedimentation that mask crustal tectonic processes.

Rate and extent of cooling: How prevalent is volcanic activity? How thick has the lithosphere become. Does an asthenosphere exist at all?

These factors can be compared with those of Earth's.

Earth: Recall the distinctive features of Earth's lithosphere:

Active plate tectonics: Rigid lithospheric plates move over asthenosphere

Volcano distribution: Volcanic activity concentrated at plate boundaries and hot spots

Oceanic vs. continental crust: Dichotomy between continental and oceanic crust yields bimodal hyspography. (Surface elevation is either low or high but not much in between.)

Constant resurfacing: Plate tectonics drive processes like subduction and erosion that result in destruction of old features like impact craters, which are scarce.

Source: Planetary Geology

Please note all material quoted in this answer was drawn from the source in the link. This is a lecture in a course on planetary geology at the University of Maryland.

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Yup!

If the planet is too much smaller than Earth (or really, really old), it's outer layers may cool off faster than the interior, producing plates that are too thick to move around. This is what happened to Mars- it does have a hot, molten layer in the interior, but no plate tectonics.

If the planet is too hot, the lithosphere may be insufficiently brittle, and just end up stretching and folding in response to mantle currents, rather than separating into distinct plates with trenches and ridges in between. This is what happened to Venus. Different pieces of the crust can move relative to one another, though, in this scenario, so it might not be quite what you're looking for.

If the planet is too large, such that the lithosphere is too thick, or simply has an unfavorable composition such that the light, continental crust is too widely spread and too darn thick, then plates won't be able to subduct beneath each other, which will freeze them in place.

And finally, if the planet is just the right size, with the right composition of crustal rocks, and the right temperature, but is too dry, then plates will end up fusing together without sufficient fluid to lubricate their movements.

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  • $\begingroup$ Darn, you beat me to the Mars example! $\endgroup$ – Dubukay Nov 6 '17 at 0:47
  • $\begingroup$ In other words, plate tectonics are more of an exception than a rule. They need quite specific conditions to occur. $\endgroup$ – Gryphon Nov 6 '17 at 0:48

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