What would the horizon look like when standing on a very large planet?

Question

Scifi describes the Mars horizon as closer than on Earth since Mars is smaller. On Earth at sea we can watch sailboats gradually drop behind the horizon. The horizon also appears to us quite clearly because it is not far enough for the atmosphere to mask it (but for bad weather). How would the horizon appear to us on a much larger Earth-like planet endowed with a similar atmosphere (in clear weather)? (This might be a theoretical impossibility considering the mass of a larger Earth and the gaseous composition of ours.) Objects would gradually recede and fade away behind the atmosphere, without neatly dropping out of sight. The horizon itself would be blurry or invisible so that we could not ever neatly distinguish Earth from sky. This might induce psychological/cultural effects in human-like observers. Are there visual depictions of and/or fiction about such a scenario?

EDIT: As suggested, I guess a sufficiently large planet would be indistinguishable from a sufficiently broad flat Earth, from the observer's perspective. I'm trying to get a more visceral, and if possible visual, feel for what such an experience would be. The referenced prior question is more about long lines of sight to singular objects on our Earth, that is almost the opposite of a broad sweeping vista of a planet's surface fading out toward an infinitely distant horizon. I don't know how to put it better than this although I realize it may not fulfill whatever criteria you have around here for well worded questions.

Answer 1

This isn't as hard as people are making it

The perceptual effect of the arc would become less distinctive, but still be there.

1. Let's ignore atmosphere for a moment. We have an airless rock in space, plenty of light, a great telescope... what happens? The smaller the diameter of the planet the more noticeable that arc is. In other words, the smaller the diameter, the easier it is to see the gradual process of the "ship" (ok "land rover") sinking out of sight. As the diameter increases, that effect is less distinguishable (you can think of it as "there's not enough resolution to easily see the gradual sinking-out-of-sight effect), but it still happens. As the diameter increases, it will appear more and more like the land rover just pops! out of sight. If I'm making any sense, the effect becomes more and more sudden as the diameter increases because it's harder to perceive the arc in relation to the distance you're looking through.

2. Compare this to an actual flat surface where you never see the land rover sink out of sight. It gets smaller with distance, but so long as you use ever-better telescopes, you can see it forever. No matter how large the planet is, there will always come a moment (despite needing a honking powerful telescope) when you can't see the land rover any more.¹

So... big planet, harder to see the effect... pop! and it's out of sight. Note that if you had a telescope with the ability to clearly observe an object at any distance, you'd still clearly see the sinking-out-of-sight effect... the problem is that the human eye itself just ain't that good.

3. Now, let's add atmosphere. For the sake of argument, let's say that no matter the diameter of the planet (or its gravity), the atmosphere density is always the same as we experience here on Earth. What happens then? As diameter increases the ability to see clearly through all that atmosphere decreases, so you're right about that. Given a large enough planet you won't see the effect at all. You'll lose sight of the land rover (ok, now it can be a ship on an ocean!) before the effect occurs due to atmospheric density.

But there are some other problems, too.

• We humans sometimes forget that light passing through a gas causes grief. That's because we evolved/grew-up in it, and so we "see" perfectly fine for the distances we generally care about. It doesn't help that when we use satellites, they take pretty clear pictures (when there aren't clouds...), but they're looking through the thinnest layer of atmosphere (perpendicular to the surface). Rayleigh scattering is what you get when light passes through a gas — and it's what makes the sky look blue. The more atmosphere you must look through, the worse that scattering gets in the way of what you're trying to see. It's basically the reason terrestrial observatories are put on mountains or a long way from any city — because the "light pollution" (local rayleigh scattering) gets in the way of a clear image.

• Also, let's not forget gravity. We sometimes read about giant mega Earths in the news, but the problem is that nothing's free. You can reduce the planetary density only so much. From a practical perspective, as diameter increases, so does gravity. Gravity is the one thing we know of that can bend light in a homogeneous medium. Light refracts ("bends" for lack of a better word) when it passes from one medium, like air, to another, like water... that's not what we're talking about. Gravity actually causes the path of photons to arc, not unlike a bullet dropping to the ground after being fired. So, as the diameter of your planet increases, so does the fact that the light's bending ever-so-gently, which can contribute to not clearly seeing the sinking-out-of-sight effect.

TL;DR

As the 13th century friar William of Ockham once suggested (in a much lengthier treatiese), all other things being equal, the simplest answer is usually correct. As the diameter of a planet increases, the sinking-out-of-sight effect can still be seen — it just gets harder to see.

As for what the horizon, itself, would look like (your title question)? It would look like what it looks like now, a basically flat line, only more so and harder to see. But it would still be there.

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_{¹ And this is the point the flat-earthers don't get or refuse to understand. From the top of the Rockies I should be able to see the Himalayas... but I can't. And the pesky interference of atmosphere isn't the reason why. Oh well, at least they're fun to argue with.}

Answer 2

The thing about Earth like atmospheres is that there is no hard answer to this because there is no constant for vapor/aerosol content. Depending on what is in the air at any given time your meteorological optical range (MOR) could be anywhere from less than 1 meter to about 240km.

Then there is the second variable which is that the distance to horizon is based on how high your point of observation is. This is found using the formula d = R*arccos(R/(R+h)) where d = distance to horizon, R = planetary Radius, and h = height of the observer.

For purposes of your question, I will assume you want a planet where the horizon is never visible on a perfectly clear day when you have a MOR of 240km for a person of average height (1.7m) standing on ground that is perfectly level relative to the planet's center of gravity.

For this you need a world with a radius of about 17,000,000km

To find out if this is possible, we must now look at how big your planet can be.

In this related question, I answered the question that the maximum size a naturally forming 1G planet could theoretically be is somewhere on the order of a radius of 70,000km (140,000km across) assuming you have a planetary structure similar to Hyperion. This is probably an over estimation since Hyperion is probably made of highly porous ice that would compact under its own gravity at that scale. A fully compacted ice world would have a radius of 35,000km; so, the size of a world you can stand on probably tops out somewhere in that range.

You could try playing with planets of much higher gravities, but this tends to also affect the way atmospheres are compressed against the surface; so, it would not really be an Earth like atmosphere any more. Gravity and pressure would also crush your observer long before you could get to that radius; so, this does not seem like a viable solution.

Instead the most Earth like you could get the atmosphere is to leave the light gases alone and just add more vapors/aerosols. Infact, Earth's actual average MOR is only 30km, way less than an ideal maximum; so, if you were to take a 140,000 km wide icy world with an Earth like atmosphere and add just a bit of extra vapors/aerosols to the atmosphere. You could further reduce the MOR to never exceed 15.5km in which case you would never see the horizon line... or you could keep a rocky Earth like world and reduce the max MOR to 4.7km. Either way, Earth experiences these levels of light scattering all the time under normal conditions; so, making an Earth like world that does this on the norm could still be in every way human habitable. For example, Cloud Forests here on Earth never approach enough visibility to see the horizon (even if those darn trees were not in the way).

Answer 3

I will dive into the psychological side of the problem. Take it with a grain of salt, as we don't have enough experience especially with far horizons.

Close horizons

The horizon on the Moon feels unnervingly close. Visually, the horizon is as close to you on Earth only if you are climbing a hill or you find yourself at a bottom of a mild pit. That's what it probably (I haven't been there myself) feels like to look at the horizon on the Moon: You are always surrounded by non-existent hills blocking your view. Look how anticlimactic it feels when the astronauts finally get on top of a real hill on the Moon.

With Mars, it's similar, although less noticeable than on the Moon. The horizon is unnaturally close.

Because we are programmed by evolution to like great views (you see enemies and predators from far away), this might actually be a big problem for the psychological health of the future inhabitants of Mars and the Moon.

Far horizons

Now, what would the horizon look like on a livable big planet (let's say Jack Vance's Big Planet)? We can describe it mathematically, but can only guess psychologically. My educated assumption is that the feeling will be similar to looking from a hill down to a valley. If the weather is good, the view will always be as magnificient as a view from a hilltop, even if you find yourself on a vast flat surface.

As mentioned, because we are programmed to enjoy those views, living on such a planet might be exhilarating, at least if there are interesting objects to see around and until the brains of the colonists get used to the effect.