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I'm relatively new to all this. I'm thinking of studying a little Earth sciences in the hope that it tells me but, up front, I want to know if I'm completely off. I want to know if a world with no high altitudes can be habitable. What leads me to think it might not be is that mountains are indications of

• tectonic activity and so a liquid core generating a magnetic field repelling radiation,


• low meteorite activity.

The amount of activity sufficient to result in a world with only large hills and low peaks that never rise above the "tree line", that is the altitude at which plants grow. Can anyone tell me if such a world is feasible? Can I have a habitable world which also has nothing in the way of mountains without constant battering from meteorites? Am I overthinking this and I could just have tectonic plates that don't really move in a way so as to produce mountain ranges? Sorry if this is far too many questions for a single post.

This is actually a more thought provoking question than it seems at face value. You are not overthinking things and if anything by overthinking it you make it worth exploring.

Though the first challenge is the ambiguity in the usage of habitable. Starting with Europa, it potentially meets all the qualifications. I believe Europa's surface meets the shape requirements. As for habitability. Scientists believe that beneath the ice there is likely lots of liquid water with the possibility for life. If that is the case that then could be habitable with undersea colonies. Kinda like Rapture.

So Europa or a similar setup potentially passes the test Also extends to water worlds

If you meant more conventional habitability with land then that is much more difficult. NO It shouldn't be possible. To better understand tectonics imagine a balloon deflating. when it reaches a certain size you begin to see ripples and sag marks as the material contracts with no where to go but bulge. This is similar to what happens as a planets core cools. The rock contracts resulting in mountains forming. Even on Mars this process is still happening.

Point is a planet would have to be completely cold for tectonics to stop. Therefore it would be inhabitable.

The other way to achieve this and be geologically active would be to have hyper erosion. The chemistry and energy needed to make this happen would be in-hospitable for non microbial life.

The smoothest planet in the solar system is probably, AFAIK, Europa. It does have plate tectonics, of a sort, but it's ice plates floating on a water ocean. In terms of habitability, not great. Also, smoothness is here defined as maximum deviation from ellipsoid, not how steep those deviations are. I recently read (I forget where) that it might have fields of knife-like ice projections (which have a name that I also forgot) metres high and quite impassable.

Since you're probably looking for something more earth-like, I would guess that you can't avoid mountains. To develop complex life, you need a healthy mix of elements on the surface, plus a reasonable protection from radiation. You get the first from tectonics and volcanism, and the second from a molten ferromagnetic core that provides a magnetosphere. You also need surface volatiles (water, atmosphere) which in Earth's case got there from cometary bombardment, if memory serves. Someone correct me if I'm wrong.

Finally, I would think that thermodynamics on a flat planet would be too bland. We have no idea how life got started (ok, we have too many ideas), but what is sure is that you need an mixture of gradients: one chemical species diffusing from A to B, a temperature gradient going in a different direction, a liquid current carrying everything the third way etc. That is why all models of biogenesis, starting with Darwin's warm little pond are on some kind of interface. If the planet is too flat, I suspect the conditions might be too uniform. I haven't checked this suspicion in any way, and I doubt anyone has, so it could be completely wrong. But I have a hunch.

Of course, you might not want life to develop there, just to be able to terraform and settle it. In that case, apart from probable lack of magnetosphere, I don't see any objections. Your ecosystems might be a bit boring, though.

Follow-up

An idea that might work: take an old planet around an old sun, and make it the only planet in the system. You could have a red dwarf that got too close to some energetic young suns and had the rest of its planets stripped away. Leave a circum-stellar dust ring that provides just enough micro-bombardments for any mountains to be eroded to low hills.

Now you have the right shape, but you lack water and atmosphere. No problem: the micro-bombardment has gradually shifted the planet's orbit outward (would that happen? Um...) and the outer layers of the dust ring are water-rich (which would happen). So a layer of water accumulates on the planet. Take it from there.

What leads me to think it might not be is that mountains are indications of a) tectonic activity and so a liquid core generating a magnetic field repelling radiation,

That's correct.

and b) low meteorite activity.

I don't think that's correct. (Low circular hills, yes, but mountains? No.)

Earth was like this sometime in the Archean Eon

Life started in the early Archean (Earth was habitable in the Archean).

The first continents formed in the Archean. Mountains are caused by two continents colliding or rubbing together.

Some continent had to be the first continent. So there was a time when Earth was habitable but couldn't make a mountain because it didn't have two continents to rub together.

Less likely,but not improbable. And habitable for what? Life is not all about humans. Meaby you have more or less flat continent and all that not-so-common activity is down below in your oceans. Harsher weather is not something you can not overcome and adapt to.
If you fear meteors better to have less them in your solar system and have good pal gas giant collecting them for you.