# Does planet size affect mountain formation?

I just wanted to know if the size of a planet would affect the size of its mountains. For example, I know Mars has larger mountains than our own despite being 1/3 our size. Do planets that are larger than earth have different shaped mountain formations and if so, did the planets' size have anything to do with it?

• Not the first (or second) time this question has been asked. See: Mountain heights - theoretical limits. In short, it depends on gravity, rock's tendency to flow under pressure - and the thickness of the planet's crust (the crust being too thin, the mountain sinks). Commented Feb 5 at 5:59
• It also depends on things like meteors, volcanism, and erosion (how old the planet is vs. its atmosphere). The size of the planet certainly does have something to do with it, as does its density, chemistry, etc., etc. What doesn't really exist is a trivial answer. Olympus Mons, on Mars, is 2.5X the height of Everest... and it's a shield volcano from Mars' distant past, and since the planet's atmosphere is long gone along with any water, nothing has worn it down. In other words, you can have almost anything you want. Do you have a specific Q?
– JBH
Commented Feb 5 at 17:53

## 2 Answers

Here's one of Willk's answers on what a 30-kilometer-tall mountain would look like. The equation in it is somewhat mangled but the gist of it is that mountain height directly depends on planetary gravity. More gravity, less mountain, and vice versa to a certain extent.

Now, about that "certain extent" thing: a crossposted chunk of another answer of mine to "How might planet size affect volcanic activity?":

## Rayleigh number

The competition between forcing by thermal buoyancy and damping by viscosity and thermal diffusion is characterized by a dimensionless ratio called the Rayleigh number.

In other words, a Rayleigh number represents the ratio between how much hot mass in a convection current rises and how much the viscosity and thermal conductivity of the mass stop it from rising and bleed away its heat, respectively. In this case, the mass in question is the mantle of a terrestrial planet, and the convection current in question is mantle convection.

𝑅𝑎 (Rayleigh number) needs to exceed a certain value, called the critical Rayleigh number [𝑅𝑎𝑐], in order to excite convective flow. The value of 𝑅𝑎𝑐 is typically on the order of 1,000, with the exact value depending on the thermal and mechanical properties of the horizontal boundaries, (e.g., whether the boundary is rigid or open to the air or space, see Chandrasekhar, 1961).

Therefore, it can be concluded that, if, within a body's mantle, the ratio of "stuff-forcing-its-way-up" to "stuff-being-held-down" is ≤ ~1,000, said body won't experience convective flow in its mantle. As far as I know, convective flow in the mantle is necessary for a body to have plate tectonics; this is supported by the fact that the Earth and Venus, with the highest Rayleigh numbers calculated in Mantle Convection in Terrestrial Planets, are fairly volcanically active, whereas Mercury, with the lowest one, is a dead rock, and Mars, with the second-lowest one, features stagnant-lid tectonics, if I recall correctly.

Assuming their material properties are similar to Earth’s, we can estimate the Rayleigh numbers for the mantles of other terrestrial planets: $${10}^4$$ for Mercury, $${10}^7$$ for Venus, and $${10}^6$$ for Mars. With the exception of Mercury, whose $$Ra$$ is at most an order of magnitude above critical, the mantle of the rocky planets in the solar system appear to be cooling predominantly by convection.

The equation for finding a Rayleigh number is: $$Ra = \frac{ \rho g \alpha \Delta Td^3 }{\upsilon \kappa}$$ where:

• $$\rho$$ = density of mantle
• g = planet's gravity
• $$\alpha$$ = thermal expansivity of mantle
• $$\Delta T$$ = difference in temperature between top and bottom boundaries of mantle
• d = thickness of mantle
• $$\upsilon$$ = viscosity of mantle
• $$\kappa$$ = thermal diffusivity of mantle

So, within the range of planets with supercritical Rayleigh numbers like that of Earth — i.e. around $${10}^7$$ — it directly scales with Wilik's answer.

Below that Rayleigh number — at least $${10}^6$$ or less, there is some wiggle room — you begin seeing stagnant-lid tectonics, where the crust basically thickens and does nothing, meaning no continental plates smashing into one another to build mountain ranges and no volcanic activity capable of breaking through the crust to form solo volcanic mountains. Perhaps some mountains will form early in planetary development but they will likely weather away over time once the processes to make more mountains break down as the planet cools.

Above that Rayleigh number, things begin getting chaotic. Even if the gravity's the same as the Earth, you start getting one hell of a lot more tectonic/volcanic activity, meaning there are going to be volcanoes popping up all over the place and mountain ranges being formed faster than on Earth as the mantle plays bumper cars with tectonic plates. The answer to that Astronomy Stack Exchange question of mine concludes that the largest possible Rayleigh number is about $$3\times{10}^8$$, on a hypothetical super-Earth with 7 times the mass, thrice the radius, and about twice the gravity of Earth, while being made of the same stuff and having twice the temperature differential between the top and bottom of its mantle. That 2x gravity is going to limit the maximum height of mountains, but there are going to be a lot more of them because tectonic plates are colliding very quickly and there's plenty of upwards convective motion in the mantle to feed volcanoes.

It is important to remember that Rayleigh number does not directly correlate to planet size. What it's made of is also important. You can have a smaller planet with less surface gravity than the Earth, but which has a lower Rayleigh number and therefore has smaller mountains than the Earth.

## Here are some general trends you might like:

1. Greater radius means greater Rayleigh number and therefore more mountain-building activity.
2. Greater radius relative to mass (i.e. lesser density) means less gravity and therefore higher mountains, as well as lower Rayleigh number and therefore less mountain-building activity.
3. Greater radius means increased volume relative to surface area, and therefore more time for heat to escape, and therefore a longer time for mountain-building to occur.
4. A less viscous and less thermally conductive mantle (represented as a higher Rayleigh number) means more magma moving around and therefore more mountain-building via tectonic and volcanic activity.
5. A thicker mantle means a higher temperature difference between the top and bottom of the mantle and therefore a higher Rayleigh number, as well as a longer time to build mountains because it takes longer for all the heat to leak out.

The inverse of all of these is also true.

# Yes

The higher the gravity on a planet, the closer its surface will come to being "smooth". As has been commented, there are lots of answers about "biggest possible mountain" on this site that make it clear that the prevailing characteristic is whether the crust and the material of the mountain can sustain its own weight - so the more massive the planet, the shorter its mountains will likely be (proportionately).

The reason Olympus Mons can exist on Mars is because of the lower gravity (and lack of weathering or tectonic activity that might wear it down/erase it after its formation).

When planets/planetoids get small enough, the meaning of "mountain" starts to break down, since the entire body can be irregularly shaped. At that point, though, it starts to violate part of the definition of "a planet":

Object has sufficient mass for its self-gravity to overcome rigid body forces so that it assumes a hydrostatic equilibrium (nearly round) shape

It's always worth remembering that Earth's highest mountain (Everest) is still only about a tenth of one percent (0.1%) of Earth's radius above sea level. On a macro scale, Earth is pretty smooth.

• An additional factor that allowed Olympus Mons to get to its height is the reality that Mars's crust was a lot thicker when it was forming. Not only did this keep the fault in one place (as opposed to Mauna Loa's fault, which is still moving), but it supported a much higher mountain without sinking. Commented Feb 5 at 22:46