# Does a planet's mass or gravity affect the height of it's mountains?

According to this Wikipedia page, the top five highest mountains on Mars (and the highest on Venus) are all taller than Mount Everest (and Mauna Kea as measured from the ocean floor).

Does a planet's mass or gravity affect the height of it's mountains? Is there an upper limit that a mountain can reach given the mass or gravity of a planet?

• Good question and there is a good answer in part here physics.stackexchange.com/questions/47159/…
– user8
Nov 13 '13 at 11:54
• An interesting / relevant aside: arxiv.org/abs/1004.1091 Nov 14 '13 at 0:22
• @UV-D: The question is good, and the answer you are pointing at is also good. However, the latter is given for a different question. There is just a bare minimum of useful information there on the matter. Nov 14 '13 at 15:48

Yes, gravity definitely affects the maximum heigh of mountains.

Think on a solid bar of steel. It sticks straight because of the electronic forces. But when you make it larger and larger gravity makes it bend: gravity starts being considerable, but still smaller than electronic forces.

If you make the bar larger, there will be a moment in which the weight of the whole bar will be larger than the short-range electronic force: your bar will break purely due to gravity.

Exactly the same happens to mountains made of solid rock (as opposed to sedimentary ones quoted by Hobbes). There is a point,k depending on the strenght of planetary gravity, where it takes over short-range electronic forces, making the mountain collapse.

This is exactly the force that "rounds up" the planets, as opposed to the non-spherical asteroids.

In addition to the answer quoted by @UV-D, gravity affects the height of mountains composed of loose material (e.g. sand, volcanic ash). In a pile of loose material, the height is determined by the angle of repose, i.e. the steepest angle at which material will stay in place rather than roll down the sides of the mountain. This angle depends on gravity.

• Nice point, though: 1) Would be great to see at least some quantitative discussion, 2) Mountains tend to be tectonic, not sandy in nature Nov 14 '13 at 15:49
• I agree with @AlexeyBobrick, I don't think this actually answers my question. It's unlikely that there will be a mountain of loose material that rivals the height of the solar system's highest mountains. Can you link to any evidence that gravity affects the height of actual mountains? Nov 14 '13 at 23:11

For those who wanted a complete mathematical answer and were also dissatisfied with the previous answers, see answers to How high can a mountain possibly get? in Earth Science SE.

I adjusted a few numbers in the linked equation to more accurately reflect compression strength and density of granite ($$2.5 \times 10^8$$ and $$2.75 \times 10^3$$ respectively).

A quick 'n dirty equation to determine max height for any planet with a granite mountain:

$$H(g) = 0.909 \times 10^5 / g$$

Some quick maths:

max height of a (granite) mountain on Mars (1/3 earth g): 24.5km (incredible! - mount olympus close at 21.9km)

max height of a (granite) mountain on Earth: 9.3km (Everest is close at 8.8km)

max height of a (granite) mountain on Kepler-452b (2 earth g): 4.8km (pathetic!)

• This is a really helpful answer! I would be even better if you mentioned the units that the numbers use.
– uhoh
Sep 23 at 6:56
• See also this other question at Earth Science SE: earthscience.stackexchange.com/q/20242/18081 Sep 23 at 8:17

Yes, gravity plays a role in how high mountains can get. Additionally, the chemisty via the strength and elasticity of the material of the lithosphere plays a role how mountains can get.

The word to look for is "Isostasy". There's two basic processes howThis is a common problem in geophysics, especially in gravimetry where these give information about the crust and upper mantle.

Assuming that gravity at the surface and near the surface is relatively constant for any given terrestrial planet, the weight which needs to be supported by the basement rock due to a mountain depends on both, the size (mass) of the mountain as well as the acting gravity. Thus for a planet with a smaller surface gravity a larger mountain can be supported without the underlaying material cracking or being compressed or slowly being pushed away resulting in the mountain subsiding slowly until it is (again) in equilibrium with the strength of the material it rests on.

The mountains actually form as a result of the tectonic plates' movement at the earth mantle. Suggesting that a new mountain would be formed tomorrow, during the tectonic activity rock from the mantle and above moves upwards, only the tip of the newly formed mountain would consist of sediments like sand or soil.

So, I don't think that the gravity or mass of a planet affects the mountains' height.

Plus, Earth is the only known planet to be affected by plate tectonics. So, the 'birth' mechanisms must be a lot different and cannot be compared with the ones' acting on our planet.

• "Earth is the only known planet to be affected by plate tectonics" - do you have a reference for this? Nov 20 '13 at 19:16
• Trust me I'm a geologist! wwnorton.com/college/geo/egeo2/content/ch02/article_2.htm Nov 21 '13 at 18:27
• Sounds trustable! Though, it is not clear, why wouldn't gravity affect either mountains as we know them on the Earth (Earth-like planets), or mountain-like structures on other types of planets. Nov 21 '13 at 19:38
• I wanted to make clear that earth's mountains are not the same as other planets' mountains, thus they can't be compared. Nov 22 '13 at 20:19
• It does not matter which the birth mechanisms are in order to assert if there is a maximum size. While I agree with you in that mountaingenesys mechanisms are very different on a techtonic planet like Earth than in a non-techtonic one like Mars, basic Physics are the same. For planets with same radious, that one with bigger gravity will be more round, that is, mountains will have smaller maximum possible (note possible does not mean actual) height. Nov 24 '13 at 13:32