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Out there in the vastness of space there is a colossal machine by unknown makers. An entire artificial planet that, underneath the initial crust, has massive systems of clockwork with the topmost pieces being continent-size gears that are slowly ticking.

By ticking, I mean that over the course of some amount of time, they will slowly start turning, turn for a while, then stop again.

What I want to know is, how fast could this rotation possibly be without destroying a modern city or even a city similar to Rome at the height of the Roman Empire with the city located at the edge of the gear?

Additional Information:

  • The planet is approximately the size of Earth.
  • The continental gears are around the size of Europe or, about 4 million miles squared.
  • The gears are made of a material that acts similarly to steel except strong enough to endure the massive scales of all this.
  • The gears are not directly exposed, they are beneath a large layer of rock and soil that acts as a crust.
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    $\begingroup$ Pretty sure that at continental scales, the gears' teeth would simply bend and smash rather than turn the wheels. $\endgroup$ – ApproachingDarknessFish Nov 15 '16 at 20:11
  • $\begingroup$ There isn't enough information in this question for any kind of specific answer. How big are the gears? What are they made out of? How large is the planet? ...and so on. $\endgroup$ – Green Nov 15 '16 at 20:15
  • $\begingroup$ Tried to add some additional information to hopefully solve this problem. $\endgroup$ – santyclause Nov 15 '16 at 20:25
  • $\begingroup$ Ocean of WD-40... $\endgroup$ – user6760 Nov 16 '16 at 6:27
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Gears of that size are of course impossible, but we are ignoring this, they are strong enough, etc.

On the inside, you can move them however you want, but you could get funny effects like from gyroscopes (i.e. influence the planets movement/rotation).

On the outside there will be two zones:

  • Around the edges/between the gears
  • Everything else

For the latter part, you should check how Earth quakes' strength is measured, that way you could calculate how much movement (accelerating force to be exact) would be which kind of Earth quake. You could move much, much faster than the Earth's plates.

For a rough approximation, calculate how fast the edges of the gears change (circular) speed. This is the acceleration which you compare to Earth quakes' acceleration, the effects on the gear will be less than the Earth quake with that acceleration.

In the areas between the gears/on their edges, you would best have some Oceans to conveniently hide them away, or you'll have deep abysses (because whatever is above them inevitably falls down) and even with only very little movement you won't be able to live on the edges because everything just falls away into the abyss (you also need to solve the problem of why the gears don't choke on the earth and stuff which falls in between).

You can't easily have the edges covered by crust (although with enough hand waving...) because either they are covered, that means the crust doesn't move with the gears and you are basically getting whatever seismic events you want from the gears because you are already hand waving a lot. Or the crust turns along with the gears below it, and then you are tearing it up along the edges. You can minimize the tearing, though (by just saying the tears fill back up with soil or something), but then this will be the limiting factor for you gear movement speed, and not the seismic effect part.

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Plate tectonics

Continents themselves do move, so at the minimum, the world is probably safe if the gears are moving as fast as continents would otherwise move. This amounts to 10 cm/year. For a gear the size of 'Europe', lets say a 2500km diameter (the distance from London to Moscow) and 10 cm/year is equal to 4$\times10^{-8}$ radians/year. Ludicrously slow, about 157 million years per rotation.

Earth's spinning core

On the other hand, the inner core of the earth is spinning at a different speed than the surface. The nice buffer zone of outer core and mantle makes sure the two can rotate independently. Supposing your gears are submerged in a liquid metal core/mantle it could spin a different speed too. No one knows for sure how fast the core is spinning, but this article says the solid inner core is superrotating, completing one rotation 2/3 of a second faster than the rest of the earth. That works out to a quarter turn every 100 years, according to the article, or 0.016 radians per year, or 5$\times10^{-9}$ RPM. As a surface speed, that works out to 0.00062 meters/sec.

At the speeds I listed, the residents of the surface would not even know that the core/gears were rotating at a different speed from the planet, just as we didn't until a few decades ago.

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  • $\begingroup$ 10 cm a year is the fastest moving continental plate the average is 3cm/yr. on earth most of the mantle is more like a plastic but the layer of molten rock (upper asthenosphere) just below the crust is very fluid. plenty of tectonic plates are rotating so that is not a problem. $\endgroup$ – John Nov 15 '16 at 22:41
  • $\begingroup$ I’ve never heard of different rotation rate of the core before! What you list doesn’t seem significant with respect to the motion causing the geodynamo. $\endgroup$ – JDługosz Nov 15 '16 at 22:52
  • $\begingroup$ After looking at your link: the solid inner core’s motion does not cause the magnetic field. It’s being turned due to exposure to the magnetic field. And the mantle does not buffer the motion, which is between the inner and outer core, not the crust. $\endgroup$ – JDługosz Nov 15 '16 at 22:55
  • $\begingroup$ It says it quite directly: «The magnetic field pushes eastwards on the inner core, causing it to spin faster than the Earth, but it also pushes in the opposite direction in the liquid outer core, which creates a westward motion.’ The solid iron inner core is about the size of the Moon. It is surrounded by the liquid outer core, an iron alloy, whose movement generates the geomagnetic field.» $\endgroup$ – JDługosz Nov 15 '16 at 22:58

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