No, we're talking about a satellite forming into a sphere under its own gravity, not the planet's. Given a large enough lump of matter, gravity will overcome structural strength and force the material to flow into a roughly spherical shape. On Earth, this happens with the maximum mountain height being a few kilometers, but on Mars' moons, which are much smaller, the gravity is far too weak to overcome the rock's structure, and they are basically strange shaped rock things.

Mars' moons are really nothing more than captured asteroids. They look like "strange shaped rock things" because that's exactly what an asteroid is: just some random piece of rock.

As for the spherical shape, the term there is hydrostatic equilibrium: https://en.wikipedia.org/wiki/Hydrostatic_equilibrium.

> Mars' moons are really nothing more than captured asteroids.

Keep in mind it's not actually possible to just "capture" an asteroid. The object needs to lose speed somehow in order to be captured.

Most likely via collision - something large hitting the planet, or two other moons crashing.

So the story of the moons is much more complicated than just "random piece of rock".

Given enough time [1], all solid objects become perfect spheres, no matter their size.

[1] 10^65 https://en.wikipedia.org/wiki/Timeline_of_the_far_future

I am comfortable with a definition of "moon" that does not involve extrapolating 10^65 years into the future.

That's what they said about IPv4

Well, then you'd need to define an arbitrary time limit for how long it would take to form a sphere. In which case, you might as well have just defined a size/mass limit in the first place.

I think the definition would be that they're presently a sphere, that was formed under its gravity. That way objects could possibly become moons in the future, but the timescales are so long it's mostly irrelevant

That's technically correct (the best kind of correct!), but I think it's a misleading thing to state. The reason all objects eventually become spherical is because they eventually disintegrate into the nearest significant source of gravity, which will itself be a sphere. It's not as if, hypothetically speaking, an immortal human being floating through space without orbit would eventually morph into a sphere under the pressure of its own gravity. Rather any object is naturally going to decompose into parts which will be spherical or adjoined with an already spherical object.

Even if the conjecture that sufficiently high entropy causes quantum physical effects to dominate macro-physical spacetime is correct, long before that happens there won't be any objects left which aren't already spherical.

Actually, not always. A mass orbiting close enough to a planet is subject to tidal forces that will rip apart and eventually flatten a round body into a ring.

https://en.wikipedia.org/wiki/Roche_limit

If body is in a strange orbit taking it in and out of the roche limit, it will adopt some strange middle ground between bring a round moon and a flat ring. Inside the limit, material will be ripped away from the body and flattened towards a ring. Outside the limit, that material will fall back nearer to the equator. So you get something like a ball with a belt.

Whew, how you can possibly wrap your mind around 10^10^120 is a mystery to me.

I can't wait to be a ball!!

Is the maximum height of mountains on Earth really due to gravity or a limit imposed by geological weathering?

According to quite a lot of comparative planetary geology work, Mt. Everest, Mauna Kea, etc. are pretty close to the height limit imposed by gravity and structural strength. On some objects (like Mercury or the Moon: see https://arxiv.org/pdf/1511.04297.pdf) there aren't any mountains high enough to hit that limit, but Earth seems to have active enough tectonics to push up at that limit despite weathering.

A bit of one, a bit of the other, AFAIK. Of course, having geological weathering is also a function of gravity; small objects don't have the atmosphere for it.

The tallest planetary mountain in the solar system is Olympus Mons on Mars, about 2.5x as tall as Mount Everest (as measured from sea level). This is only possible because Mars has 1/3 the gravity of Earth.

https://en.wikipedia.org/wiki/Olympus_Mons

Aren't all moons natural satelites?

That's no moon!

Pop culture references aside, yes, a moon is defined to be a natural satellite.

It's a space station.