# Thousand Plate World: Formation

I have found this idea on a discussion on /r/worldbuilding. Anyway, the premise is as follows:

• The planet is earth-like in terms of size and mass.
• The planet has a very large amount of small, active, mobile tectonic plates (several hundred to several thousand).

My question here is:

• How could a world such as this form?
• Planets form in basically the same way. You're asking for details about the geology of a fictional world which is beyond what current knowledge would have. So the question is either too broad or opinion based. Questions on WB SE need to be more focused than this. – StephenG Oct 30 '18 at 11:04

As a geologist I found this an interesting question so I started theorizing on it.

Plate tectonics is a complex system with multiple variables affecting the system, but in order to have many plates you essentially need a weaker crust than the earth's. This is so that the plates break earlier and into more segments.

Linked article describes a 3D modeling exercise on this topic.

In order to have a weaker crust consider something like this:

- Different composition

The composition of your planet is different form the earth's, meaning different dominant rock types in the oceanic/continental crust making it weaker.

- Faster convection*

Mantle convection in your planet is quicker; oceanic crust has less time to cool, keeping it thinner and more weak.

This could be caused by more internal heat being generated from i.e. tidal forces from several moons, or a large moon at close distance. Or lots of radioactive elements in you planet's mantle.

Faster convection would also allow for some interesting water chemistry scenario's; it is generally assumed that the ubiquitous carbonate deposits from the late cretaceous era are partly due to more calcium entering the oceans from very active (compared to present day) mid-ocean ridges.

*note that the relative influence (and nature) of mantle convection versus other mechanics driving plate tectonics is still under debate, but it consider it a starting point.

Let's do a 0th order approximation: the size of a tectonic plate depends on the size of the underlying convective cell (image source).

If we look at the distribution of flow velocities across the cell, we see that the velocity is higher at the borders and practically null at the center. This is due to the shear stress between the upward and downward flow.

One can easily imagine that if the cell is too compact, the convection motion will be hampered by the friction, and thus won't happen.

To understand which of the two phenomena prevails, one can refer to the ratio between the Reynolds number

Reynolds number is the ratio of inertial forces to viscous forces within a fluid which is subjected to relative internal movement due to different fluid velocities, which is known as a boundary layer. $$Re = \rho \cdot u \cdot L \over \mu$$

and Nusselt number,

Nusselt number (Nu) is the ratio of convective to conductive heat transfer across the boundary layer. $$Nu =h \cdot L \over K$$

$$Re\over Nu=\rho \cdot u \cdot K \over h \cdot \mu$$.

Where:

• $$\rho$$ is the density of the fluid
• $$u$$ is the velocity of the fluid
• $$K$$ is the thermal conductivity of the fluid
• $$\mu$$ is the dynamic viscosity of the fluid
• $$h$$ is the convective heat transfer coefficient of the flow

If the ratio is bigger than 1, it means the viscous forces are not strong enough to stop the flow, while on the other case, when the ratio is lower than 1, it means that the viscous forces stop the flow and heat transfer happens mostly by conduction.

To have convective cells one need to be in the first case, so, once the material is chosen, this practically set a limit on how small the cell can be.

The parameters affecting the phenomena are listed above, and again all depend on the material. Therefore it might be possible that, with the right materials, convective cells can be small enough that they can be counted in the order of thousands.

However, since you specify that

The planet is earth-like in terms of size and mass

I am afraid there are no knobs to turn, and for such a planet the size of the plates is bound to be similar to what we have on Earth, where one of the smallest one is the Juan de Fuca Plate

One of the smallest of Earth's tectonic plates, the Juan de Fuca Plate is a remnant part of the once-vast Farallon Plate, which is now largely subducted underneath the North American Plate. Approximate area 250,000 $$km^2$$