Can you tell the earth isn't flat by eyeballing its curvature?
October 13, 2021 3:34 AM   Subscribe

An argument sometimes brought to bear against flat earthers is that one can supposedly detect “the curvature of the earth” by observing it from a high enough vantage point (e.g., from a MiG29, or from the ISS). And I’ve heard flat earthers state that they would concede that the earth is spherical if they were shown its curvature in this manner. But what visual impressions exactly is a spherical earth supposed to yield, which could be described as resulting from its “curvature”, that would distinguish it from a circular disk-shaped earth (one that looks like a pancake)?

The visual aspect created by a sphere, when seen from a sufficient distance, is circular. But the visual aspect created by a circular flat disk, when seen from a point high above its center, is also circular. So the curved outline of earth against the background of space can’t be the “curvature” they're talking about.

I also don’t think the answer lies in depth perception. True, the edges of the visible part of a sphere are further away from the observer suspended above the sphere than is its center, and this to a greater degree than the edges of a flat disk are, since the surface of the sphere curves away from the observer. But I doubt that, at the scales we are talking about, it would be possible to observe this difference, say, by considering the apparent size of known objects or their blurriness. There’s discussion on how far above the earth’s surface you would have to go to observe its curvature, but it’s apparently pretty high [paywalled].

Another option is the angle of observation. When looking down at a disk, a tall tower right at its edge would be seen at an angle < 90 degrees, with both its side and the rooftop visible. Whereas a tower at the visible edge of a sphere would stick out at a 90 degree angle, with only its side visible. But where would you find a tall enough tower?

Samuel Shenton, the father of modern flat earthism, is quoted as saying “"If they show us a very clear picture of the earth from space […] and the edge of the picture is out of perspective, then that would prove that the earth is round”. But how would he be able to tell?

I realize there are other things you can see from high above the earth that will reveal it to be a sphere – for instance, the fact that at most half of its surface is visible at any one time – but that’s not observing its “curvature”, so this can’t be the answer I’m looking for. (This guy supposedly tried to prove the earth is flat by building a rocket that would photograph the entire earth’s surface at once.)

So, tl;dr: what is it that one is supposed to be able to see from high above the earth, that can be attributed to its “curvature”, that would reveal it to be a sphere?

Final note: I’m not asking for proofs that the earth isn’t flat. I’ve got that covered.
posted by bleston hamilton station to Science & Nature (26 answers total) 2 users marked this as a favorite
 
Here's one thing I've always found compelling: when you see a boat sailing away from you over the horizon, the bottom of it disappears before the top does. There's really no way to explain that other than the curvature of the earth; if the earth were a circular pancake, the boat would just disappear all at once when it went off the end (and before that all the parts of it, bottom and top, would get smaller with perspective in the same way).
posted by contrapositive at 3:41 AM on October 13 [10 favorites]


It's quite easy to see the earth's curvature at the beach. Watch a boat sail over the horizon - or, look at a boat that's near the horizon from a vantage point that's right beside the water - and then again from up on the pier or from the top of a cliff.

When sailing away from an island on a clear day - watch the island slip over the horizon until only the hilltops are visible. I recommend the Hebrides as the ideal location, but any long-enough ferry ride will show the same.

on preview: jinx!
posted by rd45 at 3:42 AM on October 13 [1 favorite]


While I completely concur with the preceding answers...

So, tl;dr: what is it that one is supposed to be able to see from high above the earth, that can be attributed to its “curvature”, that would reveal it to be a sphere?

Perspective.

Similar to the previous (correct) answers, any motion of view-point from a significant height will present a difference between a disc and a sphere.
posted by pompomtom at 3:49 AM on October 13 [2 favorites]


I also agree, as I think most people who live near the ocean would. I actually remember standing by the North Sea as a child and asking why I couldn't see England on the other side, and getting the explanation and also understanding the ships sailing over the horizon. Just like children have probably standing on that beach with adults for thousands of years.
Maybe this is relevant? Myth of the flat Earth (wikipedia)
The myth of the flat Earth, or the flat earth error, is a modern historical misconception that European scholars and educated people during the Middle Ages believed the Earth to be flat
posted by mumimor at 4:23 AM on October 13 [2 favorites]


Maybe being high enough up and watching it rotate with continents gradually coming into view and out again?

Or seeing nighttime? E.g. here, I'm not sure what can explain the curvature of the night part of the world without it being a sphere, not a disk?

And on your point about a big enough tower, maybe mountains, or more specifically their shadows? Their shadows should be non parallel when viewed from above, assuming you're not in a similar sky position as the sun so you can see shadows.
posted by Boobus Tuber at 4:39 AM on October 13 [1 favorite]


A curved horizon. As in, you're still standing on Earth, or at least in the atmosphere, and you look out to the "edge" and instead of being flat, it dips down on the sides. Ideally it'd also be seen to curve up in the middle but at least some are willing to believe that the sheer scale makes it hard to perceive that with just the eyes. But there should definitely be warped ends.

Source: my dad's whacky friends from the Navy who grudgingly conceded that their careers were difficult to reconcile with their beliefs and that the planet was indeed best navigated and weather best predicted under the assumption that it was spherical, but they still didn't like it and would grouse about "curvature" and faked NASA footage when drunk.
posted by teremala at 4:48 AM on October 13 [3 favorites]


No, you can't prove the earth is round by eyeballing the curvature of the horizon from high altitude.

The circular area occupied in the observer's field of view by a sphere, is identical to that occupied by a flat disc where the observer is above the centre of the disc - just as you say.

The position of flat earthers that they would be convinced, if they could only see curvature from high altitude, is chosen so as to be unfalsifiable.

In fact, the burden of proof is really in the other direction. If the earth were a flat disc, then it should be possible to observe that this is the case from high altitude, above any point other than at its centre.

If you were positioned high above a flat Earth, at a position offset towards its rim, you would see different curvature in different directions. Consider the extreme case, with an observer positioned near the rim: the horizon would be almost horizontal looking toward the centre, but almost directly downwards towards the rim, following a curve in between these two extremes.

I will believe in a flat earth when shown this curvature.
posted by automatronic at 4:53 AM on October 13 [6 favorites]


A snapshot from a high vantage point can't be definative. A movie from the ISS is something different; it would demonstrate that you can reach the west by going east. (Even more of a problem is keeping the ISS from crashing to earth without a notion of orbital mechanics,.)

Of course, sailors have been familiar with the phenomenon of seeing boats go hull down at distance since ever, but I will remark that the optics of seeing something from a great distance are not always the same. Different temperature gradients cause light to be bent in different ways, leading to mirages in the desert and on the ocean.
posted by SemiSalt at 5:04 AM on October 13 [1 favorite]


No, you can't prove the earth is round by eyeballing the curvature of the horizon from high altitude.

The circular area occupied in the observer's field of view by a sphere, is identical to that occupied by a flat disc where the observer is above the centre of the disc - just as you say.


One might eyeball from more than one position. Indeed, it would be difficult not to.
posted by pompomtom at 5:27 AM on October 13


You're looking in the wrong place.

In Search Of A Flat Earth
posted by krisjohn at 5:38 AM on October 13 [1 favorite]


Remember that Alfred Russel Wallace ultimately lost the wager that resulted in the Bedford Level Experiment. You might be able to see the curvature, but convincing someone with that level of buy-in won't be as easy
posted by scruss at 8:00 AM on October 13 [2 favorites]


This YouTube video with Hannah Fry and Matt Parker shows the difficulties of determining the radius of the earth by observations in one place.
posted by SemiSalt at 8:12 AM on October 13 [1 favorite]


On a flat Earth, the horizon would be at eye level. As it is, you have to look slightly down. Now, you might attribute that to not being able to see far enough due to atmospheric haze (which isn't an entirely unfair point), however, you can do one better. If you go up on a mountain then the horizon drops lower.

You can make a simple sextant to measure this. The biggest trick is finding a convenient mountain from which you can take clear measurements.

But, let's go back to your original question:

But what visual impressions exactly is a spherical earth supposed to yield, which could be described as resulting from its “curvature”, that would distinguish it from a circular disk-shaped earth (one that looks like a pancake)?

If you look at the Earth from the ISS (or Blue Origin spacecraft, if you are William Shatner) then you'll see a disk and you could just claim "Aha, the Earth is a flat disk". The problem there is that you can never see all of the planet. Most of the continents are missing.

None of this will convince anyone, IMHO. There are already enough conceptual problems with the flat Earth theory that people who could be convinced by the evidence have already been convinced. Hell, you can't even explain sunset with a flat Earth.
posted by It's Never Lurgi at 9:28 AM on October 13 [1 favorite]


"If they show us a very clear picture of the earth from space […] and the edge of the picture is out of perspective, then that would prove that the earth is round"

Well, you know, we have such pictures, and they have such a distorted perspective. Compare the linked picture to a map of Mexico or South America. (Maps can be made, and were for centuries, simply from ground observations.) There's also the little fact that the photo doesn't show half of the Earth.

If in fact you make a map using east/west as defined by sunset/sunrise, and north defined by Polaris, you'll find that the flat map gets distorted away from the equator. E.g. at 70° north, a 1° E/W distance is only 43% as long as 1° of N/S distance. If you marked out 1 minute of arc at that latitude in both directions, you could see even from ground level that the E/W markers are far closer together.

(It's hard to take the flat earthers seriously if they can't produce a photograph of the rim. Or even tell us where it is.)
posted by zompist at 9:39 AM on October 13 [2 favorites]


A variation on what folks have said above:

Can You See France From England?

Why Are the Dover Cliffs the Best Place to See France From England?

The perfect place to view France is on top of the Cliffs of Dover. The reason being, the cliffs are at an ideal height for you to see farther.

A short Geography class here: If you are standing at any beach in the area (or at the base of the cliffs), you are only likely to see up to 3 miles away. This is due to the curvature, or the round shape of the earth. This shape determines how far the horizon appears.

That said, even with the help of a binocular or telescope, you can’t see France (21 miles away) from the shores of Dover. However, for every foot that you climb up, the horizon moves further away, meaning that you get to see further and further.

Now, if you are standing at the top of the cliffs (350 feet above the sea level) and assuming your height is 6 feet, then the horizon will appear about 23.1 miles away- and that’s how far you can see on a clear day.

This explains why the Northern Coast of France (21 miles away) is visible from England, but only when viewed from the top of the cliffs. Like I said above, climbing up the castle or any ground higher than the cliffs adds a few more miles to how far you can see across the strait.
posted by polecat at 9:52 AM on October 13 [1 favorite]


The podcast Oh No Ross and Carrie did a long series on flat earthers where they conducted experiments with a group of people from “both sides”. The results of which yet again don’t act the way the flat earthers predict and (gasp!) somehow act the way the science of a round earth predicts! Experiments such as how high a target would have to be off the surface of flat water to see it form a certain distance away. If the earth was flat, as long as the surface between you and the object is flat (water) and the atmosphere is clear enough, you can in theory see it at any height from the surface. Of course, in realty the visual target has to be higher than the surface by a minimum, calculable amount to accommodate the curve between the viewer and the target.
posted by Crystalinne at 11:33 AM on October 13 [1 favorite]


Addendum to krisjohn's comment: the lake experiment (in which the curvature of water can be observed) has a separate, more in-depth video
posted by O9scar at 1:14 PM on October 13


This YouTube Video does a nice job of covering the various aspects (in my opinion).
posted by forthright at 3:22 PM on October 13


Best answer: I am dumb, so I just spent 2 hours putting together a Sketchup model that allows you to stand at a given altitude and see, simultaneously, what a flat-disc earth would look like, what an infinitely extended flat disc would look like, and what the actual spherical earth looks like. This was actually interesting to me, because even though I spent some years of my life doing grad work in math, thinking all day long about spheres and planes and geometrical things, the exact outcome of what to expect in the spherical vs flat disk situation was not all that obvious.

Takeaways:

* The difference in the height of the horizon, pointed out by It's Never Lurgi, for the Flat Disk vs Spherical Earth situations is very, very, very large and noticeable. It is LARGE - not subtle at all.

People insisting on the Flat Earth scheme just don't really know what an actually Flat Earth scenario would look like. But in reality, Flat Earth would look really, really different even in a low-level ocean view, and vastly, vastly different in any view from say 10,000 ft / 3000 m and up

* There is in fact a really huge difference in curvature between the Flat Disk Earth and Spherical Earth. It is noticeably visible even at 10,000 feet / 3000m altitude but it is very, very, very visible and obvious at 30,000 feet / 10,000m, which is a common cruising altitude for commercial airliners. At that altitude the Flat Disk Earth has a completely flat horizon (to the naked eye - with precise instruments you could detect a minuscule bit of curve) while the Spherical Earth has a very visibly curved horizon.

* The one that surprised me the most is that you can see obviously, dramatically more land at much, much, much greater distance in the Flat Disc Earth scenario than on actual Spherical Earth. Compare this Flat Earth image with this Spherical Earth. The squares shown are about the same size in both. The view is about what you would see at 45,000 feet / 14,000 m. So obtainable by commercial jetliners.

In Spherical Earth, you can count about 1.5 squares going front to back. After that it just rolls right over the horizon.

In Flat Disk Earth, you can pretty easily count 7 or 8 squares going back. If you had binoculars or a telescope, you could see even more. They are just lined up in a straight line, all visible, all the way to the edge.

Point is, in a Flat Disc Earth scenario our view from the top of the Tetons or the Alps or the Himalayas, or out the window of an airliner, would be vastly, vastly different than it actually is.

The horizon would come more up to the aircraft's wingtips all the time, no matter how high you flew, and the space between the "real" horizon and that horizon, which on Real Earth (tm) is filled with clouds and sky and stuff, would be filled up with 3-4-5X as much land that you just look over and see.

Just for example, in this photo from the Space Shuttle the entire U.S. west coast would be far more straight down instead of being all foreshortened, and in addition you would be able to see several states further over than you actually can.

In short, Flat Earthers look around and say "I don't see any proof whatsoever of Spherical Earth. Everything looks 100% Flat to me."

But in reality, their idea of what Flat Disc Earth would look like is wildly, wildly wrong.

It would in fact look noticeably different from Real Earth, particularly at any altitude at all.
posted by flug at 1:18 AM on October 14 [10 favorites]


>If they show us a very clear picture of the earth from space […] and the edge of the picture is out of perspective

Well, here you are, rather exactly. This shows all the cloud layers, atmospheric layers, etc that we think of as being stacked straight vertically from the ground up - and would be in that orientation, if the photo were taken from the top down - but shown exactly side-on, because it's a photograph from space of the earth's limb. Meaning that this is as photo of those cloud and atmospheric systems from the side.

This is exactly as striking as if you'd taken a photo of a building's roof when it was directly under the Space Station, and then another horizontally into a side window a little later when it had rotated over to the limb.

Here is an explanation and photos of the same phenomenon on the moon (scroll down a couple of pages for the photos). Craters that are actually round circles become severely crimped ovals when they are near the moon's limb, precisely because of this same effect. Mountains that are actually rising up look to be rising horizontally across, and so on.

Point is, we can see all those same effects on similar photos of the earth.

Another really nice example. Towards the bottom of the photo you are looking down on the top of clouds and thunderstorms. Towards the back there is a mid-sized one almost from the side and then to its left is a smaller thunder cloud that is pretty much broad-side.

Similarly with this one. At the bottom of the photo you're looking down on cloud tops, at the limb you're looking broadside at the same types of weather patterns. Also if you look carefully along the limb you can see mountain ranges and such from the side - very similar to the lunar photos above.

Same here - weather patterns a viewed from the top down near the bottom of the photo, then side-on at the limb. So . . . just what you would expect in Spherical Earth, and just can't do on a Flat Disc Earth.

This is not an obscure or seldom-seen phenomenon. It's like in every photo ever taken of Earth f from space.

Again, though: a big part of the problem is you have to know what you are looking for. If you're convinced that "Flat Earth" looks like "A sphere curving off into the distance" there is not much that can be done.
posted by flug at 2:54 AM on October 14 [3 favorites]


flug, bravo for making that! In that first Imgur page, can you add some text for what are the elevations of views #2, #3, and #4? Maybe they're in there somewhere, but I couldn't find them.
posted by polecat at 2:27 PM on October 14


Just saw a meme on fb, picture of William Shatner, The Earth is not flat; I checked! and many people have gone far enough into space to confirm this, we have satellite, rocketship and other photos. Anybody choosing to believe the Earth is flat will choose to disbelieve any evidence presented. It utterly baffles me, along with many other things.
posted by theora55 at 9:15 AM on October 15


Hey flug, that is some very nice work with the 3D model. However, it makes assumptions about the size of the disc.

From any of the vantage points you have included, you should find that you can resize the disc such that the visible horizon from the disc follows the same line as that of the sphere.

It's still not possible, from any individual view of a sphere, to prove based on outline alone that the object is a sphere, rather than a disc of some arbitrary size with the observer above its centre.

This is why the flat earthers' demands, for a single view showing curvature that is consistent with a sphere but not a disc, are impossible to satisfy.
posted by automatronic at 12:28 PM on October 15


Say that you have levelled a very large field of dirt. You or your interlocutor have personally inspected enough of it with a level to agree that it is completely flat with respect to gravity. (Do flat-earthers have fun ideas about what direction gravity pulls toward?)

You (or they) sketch out a grid system across the entirety of this field of dirt. Squares about 1 mile wide by 1 mile long would match a lot of the farmland covering middle america, but they might be a little small for the height we'd need to attain. This grid is completely straight and all the lines are either parallel and non-intersecting or perpendicular (incidentally, if this field were to cover the entire earth, what would happen to those parallel lines on a flat earth?)

Now, we rise high into the air, as high as we need to, perfectly perpendicular to our completely flat field (which, again, was confirmed to be completely flat at every point according to our level; also of note is the fact that the atmosphere right now is so clear that your grid is perfectly clear at any height you wish to view it from). Hold up one of those right-angle rulers (preferably one that you and they used to construct the grid in the first place) with inches or centimeters, or really any regular spaced interval, align the bottom with the closest line of your grid you see, then tilt the ruler outwards until the next tickmark aligns with the next line of the grid.

Better double check your initial point of reference, they're still aligned right? So you have one inch on your ruler lined up with one square of your grid. How does inch 2 look? Pretty close, right? How about inch 12?

You and your companion may find that your carefully constructed grid seems rather short when it gets further out, how strange. The ruler gets shorter looking too, because the effects of perspective and foreshortening are fairly well understood, but still, not as fast as the grid seems to be shrinking.

When you go back down from your height to double check the spacing of the lines, take the opportunity to install a mirror at the intersections of grid lines. After you've satisfied yourselves that the grids are in fact equally spaced, head back up to your previous vantage point. This time, take a laser and a stopwatch.

Now, we know that the grids are equally spaced, regardless of what we thought we saw up here before. And to prove it, we will measure the distance between us and each of those vertices where we placed mirrors using this laser (do proponents of flat-earth theory have any doubts as to the speed of light in our very clear atmosphere in non-relativistic settings?). By the way, those mirrors are all connected via 5G so that we can maintain a perfect angle of reflection, just in case some stray animal has knocked them around while we were ascending, or we decide to ascend higher or lower than before.

You send a request for all of the mirrors to point to your position by providing them the height you'd reached and they already know their position in the grid as well as where you went up from. Trigonometry easily describes your exact position-- your height divided by their distance from your grid coordinate equals the tangent of whatever angle theta they need to aim themselves to be looking straight at you.

Your companion has the laser and is getting frustrated that it doesn't seem to be working--the light is being reflected, but other than the first couple of mirrors, it seems to be reflecting lower and lower the further out they aim, instead of at the same place each time. No worries, these mirrors have an auto-adjust feature, and with one command, begin to align themselves as your companion shines the laser at them.

Satisfied that they are all capable of reflecting light back at you, you hold a very precise stopwatch; it can measure a millionth of a second! Which is good, because we have reasonable measurements that the speed of a laser approaches 182,000 miles per second, and while your grid is indefinitely large, 182,000 miles is still rather a lot. Too bad the air has to be so clear for you to see the grid, otherwise it might have slowed the photons down a bit.

The distance between each mirror and your viewing point again is a matter of not even trigonometry, but mere geometry. Your height (h) times itself plus the distance of each mirror (m) times itself will equal the distance your laser beam will travel times (l) itself. Oh, and the laser has to actually go there and back(2l), so the time it takes to complete a round trip should be about equal to the square root of (h2 + m2) * 2 divided by 182,000 (to whatever precision you can agree on).

The laser and stopwatch are coordinated so that as soon as the laser fires, the timer begins, and the timer stops the instant the return beam arrives. The times for the closest mirrors are very good, and you take a few minutes to review the angles that the mirrors have indicated they have self-adjusted to. Some of them seem rather steep, actually, surely they would be aiming too high, but your companion reports that they are still getting measurements, although the values are a little less accurate now, when suddenly they express consternation and reveal that the latest mirror, the furthest out so far, didn't return a beam.

You share your concern about the steep angle of adjustment, and the two of you agree to ascend a bit until this mirror responds to the laser. Once you do, they resume aiming at the next mirror out, but it too is not responsive.

You check the program for the auto-adjustment, but there are no errors in the math, other than it thinks you are much higher than you know you are. Your companion admits they've started having difficulty, even with their great visual acuity and the clarity of the atmosphere, discerning the individual mirrors, and they were really aiming at where they assumed the next ones would be.

You decide that the time for experimental methods is over. It is time to take matters into your own hands. You hated to do it, but you had been saving a very special filament, infinitely long and malleable, yet extremely light weight and resistant to tear or sagging. You ask your companion to stay aloft with one end of the filament, and you set off to check the orientation of this mirror yourself.

When you reach the mirror, you see your companion up where you had just come from--it's funny, the distance makes their height seem so much less, and you smile and wave to them, then check the inclination of the mirror. It matches what the program said it was. You perceive a flash of monochrome light across your vision, and you laugh. You begin to pull the filament taut. It is actually marked with measurements itself, just like the ruler was, that match the increments of the grid. When you have it taut and begin to take the reading, you realize that the mirror is mounted on the ground, while you stand a few feet high. So you lie down next to it and take the measurement which seems to be a little longer than trigonometry had told you, but perhaps there was a little sag in your filament, after all. You roll over and start to get up, but to your horror, your companion has vanished.

All you see are your grid lines, rising away (but they were supposed to be flat), blocking all of your view of your companion (they were so high up, though).

You pull out your level, and the grid field still claims to be perfectly flat.

You pull out your ruler, and the lines in the distance seem to mock you, in every direction you look, insisting on being closer together than they really are.

You look back at the line in your hand, drawn taut, and realize that it seems to be catching on something; you can draw it tighter if you raise it a little ways above the ground.

Late in the evening, you have slumped back to the origin of your grid system. Your companion is there, weeping. They scream when you arrive--they thought you had died when you vanished. Privately, you had had the same thought. The two of you huddle together in the cold and dark, at the center of a desolate plane of not-quite squares, at the foot of a dizzying obelisk, alone on a planet that obstinately refuses to be flat. Too disturbed to sleep, you anxiously trade theories that could explain the lunatic observations made on this day. Tomorrow, you will build a flatter field, a straighter grid, a more precise ruler, more sophisticated mirrors, a narrower laser beam, and a filament that doesn't sag in the middle.

When sleep takes you both regardless, you dream of an existence that would allow itself to be modeled and justified more easily.
posted by rubah at 3:54 PM on October 15 [1 favorite]


automatronic, I agree that a flat-earther would probably never agree to any such mathematical proof, since they can always argue about the radius of the fictional disc. However, I was thinking that if we follow the assumption that the disc is like so, then the radius of the disc should be twice the radius of the true globe (while flug assumed the two radii were the same), and therefore the differences should be more dramatic than what flug illustrated.
posted by polecat at 5:30 PM on October 15


By the way, those mirrors are all connected via 5G

You've not met many flat earthers, have you?
posted by automatronic at 4:57 AM on October 17


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