# Q: If Earth was flat, would there be a horizon? If so, what would it look like? If the Earth was flat and had infinite area, would that change the answer?

Physicist: There’d definitely still be a horizon if the Earth were flat.  It would be in almost exactly the same place, and look essentially identical.  While the Earth isn’t flat, adherents to that theory are correct in that it’s nearly so, and if you’re standing on the surface of a round something the size of the Earth it’s difficult to tell the difference (in fact, mathematically you can make the argument that a flat Earth acts the same as an infinitely big Earth).

Who would even notice?

For someone around 5’6″ tall, if the Earth were perfectly flat the horizon would be about 0.04° higher.  That’s about the width of a (mechanical) pencil lead held at arm’s length.  Unless you have short arms, in which case you’ll need to shave down the lead a little.

Even if the Earth were perfectly flat and went on forever, the horizon would still be exactly level: 180° of sky and 180° of ground (instead of the paltry 179.92° of ground we have).  The only difference between a finite flat Earth and an infinite flat Earth is that no matter how tall you are on an infinite flat Earth, the horizon always stays in the same place.

However, even though the horizon of an infinite and flat Earth might actually be in the same place, it wouldn’t appear to be.  An infinite plane has an extremely simple gravitational field; uniform and exactly the same regardless of distance.  Normally the higher you are the weaker the gravity, but for a flat Earth that isn’t the case.

As such, light, which drops only imperceptibly under Earth’s gravity, has an infinitely great distance over which to do its dropping.  The effect would require tremendous distances (as in; interstellar distances), but if you’ve got an infinite plane, that kind of distance is cheap.

Given enough time and distance light will eventually curve back toward an infinite plane of matter. So if you’re standing somewhere on the surface and you look up you’ll see light that started somewhere else on the surface.  Instead of a horizon, the world would look like it rises up on all sides and encloses you.

When you look up from what should be the horizon you’ll just see more of the infinite-flat-Earth.  The one exception is what you’d see if you looked straight up.  Directly above you you’d find the entire horizon bunched up at that point.

Answer gravy: It’s not interesting enough to include in the post directly, but here’s how the math above was done:

If you’re standing on a sphere with radius R and you’re H tall, then the distance from your head to the middle of the sphere is R+H.  Your line of sight to the horizon is a tangent line to the sphere.  This allows you to draw a right triangle and do a little trigonometry.

θ is the angle between the “true horizon” and the perfectly level “ideal horizon”.  Coincidentally, it’s also the angle between where you’re standing on a sphere and the farthest thing you can see on the surface.

So, $\cos{(\theta)} = \frac{R}{R+H}$ and $\theta = \arccos{\left(\frac{R}{R+H}\right)}$.  Plug in R = 6,378,100 meters and H = 1.68 meters (which is 5’6″), and you find that θ = 0.04°.

By the end of college, electrical engineers and physicists get sick to death of the example of the infinite plane of anything (be it matter, electrical charge, kittens, whatnot).  The reason an infinite plane is useful is that it has some nice symmetry.  You can argue that, since no direction is special (by being close to an edge for example) gravity always points straight into or out of the plane-o-stuff.  Symmetry is useful when you use a Gaussian surface, because you can ignore buckets of math.

Basically, draw a “bubble” around a lump of matter.  The total gravitational field pointing through that bubble will be proportional to the amount of matter inside.  So, the more matter, the more gravity.  The bigger the bubble, the less the strength of the field through any particular part of the surface (by the by, there’s an example of this in action here).  If the Gaussian surface you choose is a rectangular box that punches through the flat-Earth, then you find that it doesn’t matter how tall the box is.

The total amount of gravity pointing into any imaginary box you can draw is always proportional to the amount of matter in that box. In this case, no gravity points through the sides (by symmetry) so it all points through the top. But if you make the box taller that doesn’t change. As a result, for an infinite plane gravity stays the same forever. QED y’all!

Uniform and infinite sheets of matter or charge have gravitational or electric fields that extend, without changing, forever.  Of course, there are barely any infinite planes of stuff out there, so this isn’t a situation that ever actually comes up.  However!  If you’re close enough to a surface it can seem to be nearly infinite, so the infinite-plane solutions are often good enough.

And often as not, “good enough” is good enough for physics.

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### 50 Responses to Q: If Earth was flat, would there be a horizon? If so, what would it look like? If the Earth was flat and had infinite area, would that change the answer?

1. In a related question, at what altitude does it become visually apparent that the Earth is a sphere?

2. The Physicist says:

If the Earth is perfectly round (trying this in the middle of the ocean is a good way to approximate that), then you should see a noticeable deviation (a few degrees) when you’re a few kilometers up.

3. Locutus says:

Funny how you don’t need a black hole to keep light from escaping…you just need something infinitely big. Of course that would have infinite gravity…which would be a black hole. I think.

Love Long and Prosper

4. Will says:

Black holes don’t have infinite gravity; if they did they’d crush the entire universe. A Black hole actually has slightly less gravity than the star it was created from (due to losing some matter).

The key is that Black holes are infinitely -small-.

5. Goodwill says:

There should be a limit to what we can see(in the infinite flat earth case)? B/c speed of light is finite and it would take an infinite amount of time for light from the edge(of the infinite flat earth) to reach the centre of this flat earth?

6. The Physicist says:

That’s exactly what you’d have to take into account when you think about what you’d see almost directly above you.

7. Robert Constant says:

I don’t believe it is correct to say you need to raise your eye height a few kilometers to see that the Earth is a sphere. Standing on the beach on a clear day, or on the deck of a ship at see, it is plainly apparent that the horizon curves off in all directions.

I think it is a common misconception that you have to go high to see the curvature of the Earth; I have even heard the Space-X guy, as well as Richard Branson, talk about their “space tourism” vehicles going so high that you can “see the curvature of the Earth…” When I first heard these statements I recall saying (to no one in particular), “Hell, you can see the curvature of the Earth on any clear day standing on the beach!”

Depending on the size of the hypothetical flat plane on which one was standing, it would appear that you were standing inside a shallow bowl — with the bowl appearing deeper and steeper the larger the plane and the lower the eye height. You can see a similar optical illusion looking down a long runway at the airport.

8. Daraje Garba says:

I think there is no change day to night also seasons.

9. The Cool Dude says:

I calculated the downward gravity you would experience on this hypothetical infinite plane, for anyone who was curious.
Since I don’t know the height or density of the infinite plane, only the length and width (infinite), I used infinite sums to add up the downward gravity caused by infinitely smaller segments of a cylinder of a height H, a radius R, and a density D, even taking into consideration the decrease of gravity over distance, as well as the angle of gravity for each point, which would alter the total downward gravity, and after much calculation, my conclusion is that the gravitational acceleration (In m/s^2) is:
GπD(atan(H/R)R²-atan(R/H)H²+RH)
Where G is the gravitational constant, 6.67384*(10^-11).
The limit as R goes to infinity, unless either H or D are zero, is infinity, which means if the plane is infinite in size, which it is, and has any height and density, then it has an infinite downward gravitational force. Further, it has zero horizontal gravitational force, since there is “equal” stuff on all sides.

Elaborating on the Physicist’s answer to Goodwill’s question, gravity is a function of distance, so the farther out a thing goes from a source of gravity, the less gravity affects it, and the velocity required for an object to completely escape a source of gravity is called escape velocity. Escape velocity is the one reason you would still be able to see the entirety of the infinite plane while looking higher and higher up, because the light doesn’t HAVE to come back down, since the speed of light is definitely greater than the escape velocity of any hypothetical object with the same gravity as Earth.

Though I suppose if you really want to consider all the mechanics of light, you would have to assume that it would be mostly black, unless the plane its self emits light, since the plane will definitely be almost all you see, except for a near single point directly above the observer, of course, but the real question is how much ambient light that will actually be.

10. Robert says:

I am not sure the gravitational bending of light, as Cool Dude calculates, is a substantial phenomenon in such a small scale system.

Surely, gravity effects light, and we often measure the effect to make measurements in deep space.

However, the biggest factor bending sunlight as observed from Earth is the density of the atmosphere and not gravity.

Returning to the main subject of this conversation, IE The optical properties of the horizon if the Earth were flat, I was just re-considering this only yesterday as I sat with my kid on the bluffs overlooking the Pacific ocean at Dockweiler Beach in Los Angeles.

Looking out at the horizon, it curved off in all directions, a result of the dipping of the earth at a (virtually) uniform rate in all directions. If instead Earth were flat, I don’t see how it is possible for the horizon to appear “essentially identical” as the physicist claims in the original answer to the hypothetical…

11. The Cool Dude says:

I am extremely sorry,
I redact my previous math which calculates for the gravity caused by an infinite plane, due to a slight mathematical error.
I rechecked my calculus, and through the accidental loss of an exponent, it turns out, as the plane gets increasingly larger (to infinity), the acceleration (m/s^2) is actually equal to 2πDHG, where D is density (kg/m^3), H is the height of the plane (m), and G is the gravitational constant, 6.67384*10^-11 (m^3/(kg*s^2)), meaning it is proportional to the height times the density, assuming the density is uniform.

This means that the infinite plane does NOT have infinite gravity, despite being infinitely large, unless it is already infinitely dense.

12. The Cool Dude says:

Also, Robert,
The plane in question is infinite, and with a finite gravity, light bouncing from any place on the plane would have the ability to reach you, so long as it was angled correctly. While ignoring air shenanigans, the entire plane would appear to bend upward into the sky, where the infinitely far away edge would be nearly directly above you.
I don’t really know how air works with respect to light, and over long distances it would definitely increase the effect, but it’s probably more likely that everything would just look really blurry.

13. The Cool Dude says:

Looking at my equation, the properties of the infinite plane allow that your distance from the plane would not actually matter.
Since if you are Y distance off the surface of the plane height H, then the actual downward acceleration you would experience would be equal to the acceleration you would experience if the plane were height Y+H, minus the acceleration you would experience if the plane were height Y, since all of Y is empty space. Because the function is multiplicative in nature, you could factor out all the multipliers to simplify to get it to the exact same gravitational acceleration as if you were right next to it, which means all things in the universe would be attracted to it at the exact same rate, and more important to the problem we are considering, all light would experience the same acceleration regardless of distance from the plane, and would inherently NOT have an escape velocity, as previously assumed.

As for how that makes any sense, I do not know, though I have reviewed the Calculus numerous times, and do not see any further errors. I will notify if I do, or at request, can post the math here for the peer review of anyone who understands the properties of this particular situation better than I do.

14. The Cool Dude says:

I checked the equation for gravitation caused by standing on top of a cylinder by summing the equation to create the gravity caused by a sphere, (Like a planet), and it resulted in M*G/R^2, which means the equation holds true, and the properties I mentioned in my previous comment should be correct.
This would imply, however that you would not be able to see the entire plane, as previously suggested, because there would be no escape velocity, and instead you would see that at a certain point, the plane would begin mirroring its self, and so directly upward would in fact be the exact point the observer is standing at, but some time in the past, due to the time it would take light to decelerate back down.

15. The Cool Dude says:

Anyway for anyone wondering, here’s a link to the proof Calculus on that, if I am allowed to post links on this site, that is.
http://tinyurl.com/p6hmy5k

Though I realize that the math is somewhat irrelevant in proving that the plane has a finite gravity, due to The Physicists Imaginary Box explanation, but I found the problem interesting, and it allows one to find the exact gravitational acceleration based on the density/height of the plane, which leaves room for further consideration, as well as the method of calculating the gravity having many other, perhaps more realistic applications.

16. Setuben says:

So ah – for there to be a finite gravity on a infinite flat plane…My guess there would be an identical “mirrored” plane on the opposite side correct?

17. The Physicist says:

Nope. The math just works out this way or an infinite plane.

18. The Cool Dude says:

I think Setuben is referring to what’s underneath the infinite plane. If the plane has a finite depth, then there’s a mirrored plane on the other side, with an inverted gravity. If it has an infinite depth, it’s the same as being on an infinitely large planet, so the gravity is also infinite. Unless the material has an infinitesimal density, the plane should have a finite depth, but having an infinitesimal density causes a lot of problems with firmness, so you would just fall through it forever, and it would be more like an infinite vacuum plus gravity.

On the other hand, the density could be shaped in such a way that it gets lesser the deeper in the plane it is, but after a while it would act like a fluid or a gas, so there would still sort of be another surface on the other side, it would just be muddy, or fuzzy.

In the end though, if you wanted it to be infinitely thin, then it would have to have an infinite density, and in that case although there would be another side to it, the plane would be infinitely hard, so you could never penetrate it, so the other side would be irrelevant.

19. Mark says:

I liked the explanation of how a plane would actually appear to be a bowl, due to gravitational bending of light rays. It should have made sense before, but now I understand why the natives of planet Mesklin thought their poles were located at the bottom of a bowl.

20. Brian says:

Isn’t that kind of like Gabrael’s horn which has an infinite surface area and a finite volume ?

21. Happy Forever says:

Yes for sure. It looks exactly like what you see. Actually we live in a the flat earth and the round earth theory is fake.

22. Anders says:

If the Earth were an infinite plane then it’s radios would be infinite and so it would take an infinite velocity to stay in orbit and to escape the planet so it would be a black hole.

23. James says:

For a 25,000 mile circumference sphere, there should be a 600 FOOT drop in curvature over 30 miles. It would be very noticeable with the naked eye and even more so at 20,000 foot elevation. The fact remains, that you will NEVER see the curve of the earth or buildings/terrain curving away from you no matter what the elevation. That is because the earth really is flat, and the sky is a Dome that separates Water Above from Water Below.

“And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters. And God made the firmament, and divided the waters which were under the firmament from the waters which were above the firmament: and it was so. And God called the firmament Heaven. And the evening and the morning were the second day.” Genesis 1:6-8 KJV

Notice, it says IN THE MIDST of the waters.

“And God said, Let the waters under the heaven be gathered together unto one place, and let the dry land appear: and it was so. And God called the dry land Earth; and the gathering together of the waters called he Seas: and God saw that it was good. And God said, Let the earth bring forth grass, the herb yielding seed, and the fruit tree yielding fruit after his kind, whose seed is in itself, upon the earth: and it was so. And the earth brought forth grass, and herb yielding seed after his kind, and the tree yielding fruit, whose seed was in itself, after his kind: and God saw that it was good. And the evening and the morning were the third day.” Genesis 1:9-13 KJV

Take a look at the first photo from space:
http://www.airspacemag.com/space/the-first-photo-from-space-13721411/

The Horizon is Flat and perfectly at Eye Level.

Here is a video that compares the Red Bull jump with an amateur rocket launch at 120,000 feet elevation:

And lastly, here is the math:
http://www.sacred-texts.com/earth/za/

24. Robert says:

You can stand at the beach on a clear day, at sea-level, and looking out at the horizon you can see the curvature of the Earth. No need to go to higher elevations.

25. michael ward says:

I’m not sure that’s entirely true or, more to the point, if that covers everything.

As an artist, I’ve always wondered why throughout history more people didn’t intuitively understand the earth was round. After all, for a person around 6 feet tall, the horizon is only around 3-4 miles away (looking out on a surface like the ocean or the great plains in the US). But you would expect to be able to see much further than that if the earth were flat. At some point the atmosphere would be the determining factor in exactly how far you could “see out” but like the title of that musical, on a clear day you can see forever.

26. I do think the Earth is round. Personally drone footage debunks many of the arguements. However, or sake of being thorough is it possible for the Earth to be flat while the atmosphere is round and therefore that would give a type of reverse optical illusion of looking downward seeing a round Earth?

27. AerialImagery.org says:

Michelle Carmela,drone footage only proves that all commercially available drones use wide- angle or fish eye lenses,distortion is so great that even the roof of a house will show apparent curvature.Drone imagery shot through lenses corrected for inherent distortion show no such curvature,perplexingly this is true at any altitude.

28. Emeth Aletheia says:

I would like to see a factual response to James. I am not yet convinced that the earth is flat or a sphere. Of course I believed it to be a sphere my whole life because that’s what I was told. That’s what NASA shows us. But I have recently discovered through many unrelated accounts and research that NASA cannot be trusted. The most damaging of these accounts was seeing the unedited reel of the Apollo 11 astronaughts faking the footage of “Earth from space” through the shuttle window. If you haven’t seen this I urge you look it up. But I’m not the type of person who just runs to the nearest opposition when I find out that one sources credibility is completely mangled. But the more I look into the flat earth the more I see that there are actual “proofs” that it might be the case. I see NASA going through a lot of extra unnecessary effort to make the earth look round in their videos using fish eyed lenses like in the red bull jump. Why would they need to do this if they could easily prove why the horizon looks flat at these altitudes. I have seen amateur balloon footage at similar heights which show the horizon perfectly flat. Some say you must go much higher for the curvature to be seen but others, even on this thread are saying you don’t have to go that high to see it. I have yet to see any credible photo or video showing any curvature at all. I would like to. lol It would finally put me at easy, but so far I have not seen anything. Wouldn’t the horizon at least lower in the frame of the camera, even a little, at 30miles above the surface? As I said I am still not convinced either way.
I’ve seen a lot of comments saying you can look out at sea level to see the curvature, but that is simply what we have been told. I have seen lots of footage with long range zooms where a ship that appeared to curve over the horizon is brought back into full view, hull and all. The explanation I found was that the lowest part of our atmosphere is the most dense and when they appear to dip down over the cure they are actually just fading out of site. It’s silly to think that our eyes would just be able to see forever if the earth was flat. Looking at contrails of airplanes would, would they be at an altitude high enough that they should also look curved? I’m not some nut I’m just slowly learning that in the majority of aspects of our life we have been lied to. And I am simply seeking truth for myself rather than going along with the heard and eating up everything we are told without questioning it. I’d be more than happy to find out that yes the earth is a ball. But I would be just as happy to find out the world is flat, just as it seems, motionless, just as it seems, and that the stars revolve above and around us, just as they seem.

Thank you all for this great thread and to anyone who takes the time to read and or respond to this.

Emeth Aletheia

29. Carefree Mathematician says:

@James do not tell people the Earth is Flat, that is wrong, and some people will believe you, please don’t troll.

You don’t need to go to space to prove the Earth is round. If the Earth were flat, then either it’s infinite in horizontal directions, or it’s finite and has edges. The gravity for both of these models is actually extremely easy to calculate with calculus, because they are essentially two-dimensional shapes with height. If either model has an infinite depth, then the gravity is infinite, and we would be dead. If the Earth were flat and infinite, then it’s gravitational field would be constant at ALL altitudes, meaning every celestial body would be gravitationally attracted to the Earth, and things like The Moon and The Sun would have crashed into the surface shortly after the beginning of time, in addition to the fact that you could never see the whole of the Earth at once. Even light cannot escape an infinite plane’s gravity, so as the topic has said, Earth would appear to be a bowl, instead of flat, but that is obviously not true. Any picture of Earth that shows it being circular, even if it’s distorted, still proves that the Earth is finite. Even if the Earth were flat and infinite at one point in time, then the structural integrity would be comparably infinitesimal, and it would snap into tiny, planet sized pieces, very quickly.

The Earth is Flat theory comes from the belief that ships on the horizon fall off an edge, because they cease to be visible as they move along the curvature of the ocean, which means that the original theory supports a finite model as well. If the Earth were flat but finite, then it would need edges, but because gravity is radial, the atmosphere and the water would still be semi-spherical, and the edges would act like extremely high mountains, as gravity pulls you to the center of the mass, rather than just being normal to the surface, which is proven by literally any hill which has a slope. Because of this, these edge mountains would be very unstable, and collapse down into the center of Earth’s mass, into a spherical shape, which would also kill everyone on the planet. Earth is Flat theory can also be disproved via airplane or boat, and is constantly disproved by airline companies and cargo boats many times every day, because as it happens, despite people going around the world in all directions on airplanes AND boats all the time, nobody has ever found a giant edge.

Finally, there is literally no social bonding force that keeps this conspiracy possible. There is absolutely no reason that every single pilot, scientist, space agency engineer, physics teacher, geography teacher, and overseas ship crews would all collectively keep this secret, in addition to the fact that there’s no reason any of those people would individually keep that secret, but I’d doubt you can find almost anyone with much experience in any of those groups who legitimately claims to believe the Earth is flat, so in addition to being physically impossible, the theory is also socially impossible. If you honestly believe the Earth is flat, then you’re ignoring monumental evidence from all scientific directions, and the only way you can support your theory is by proving it your self. Get a pilot/boat license, rent, buy, or become employed to pilot a plane or an ocean fairing boat, and navigate the globe your self. Miraculously, you will find no edge, you will not find a new continent, and you will not find an infinite ocean.

30. Emeth Aletheia says:

@Carefree Mathematician

The flat earth model and flat earth researchers seem to claim that gravity does not even exist. And that gravity is only there to explain things IF the earth is a ball. And that on a flat earth they say this is all explained by density and buoyance. That things rise and fall depending on the density weight and buoyancy of the object and what ever is around it ie air water ect. Basically they claim that IF the earth was flat there would be no need to account for gravity.

I’m not sure how you could prove the earth is a sphere using a plane. If anything, a plane how shown me nothing but a continuously flat horizon that remains at eye level no matter how high you rise. if it was a sphere wouldn’t the horizon lower as you rise? Even just ever so slightly? footage from low earth orbit amateur weather balloons show a still flat and at eye level horizon. Planes and boats circumnavigated east to west but never north to south. Circumnavigation east to west is possible on the flat earth model as well. Where the north pole is the magnetic center and as long as you keep your compass with the needle pointing to the right you can fly in a circle and circumnavigate. GPS was designed and put in place by the same people that stop anyone from flying or sailing around the globe north to south. Just thought that was kind of suspicious. I see no real reason for the south pole to be quarantined off the way that it is. I also find it strange that those few that have explored the Antarctic wall and sailed around it claim that they traveled around 60,000 miles when it is said to only have a circumference of about 18,000 miles.

This edge you speak of seems to be the Antarctic ice wall. Which in their model surrounds us in 360 degrees like a wall holding in the oceans. More of a barrier than an edge. But people aren’t aloud to go their and have been escorted away at gun point while being threatened. Admiral Byrd announced on national TV that the Antarctic is full of resources yet nobody to this day is aloud to touch it mine it or even go look at it. Corporations included. Countries are fighting at each others boarders but down there they are all friends with a common goal of keeping everyone from exploring.

To address your final paragraph, pilots wouldn’t know, following GPS and believing gravity keeps them from having to slope as they fly over the surface of a curve they wouldn’t know any different. Computers for the most part get planes and ships where they need to go. I follow the blogs of a radio host who has lots of experience as a pilot and he is even now questioning the heliocentric model. He doesn’t believe it to be flat but he is at least looking at it as a serious question and trying to prove it for himself.
Scientists theories and years of work are based on the idea that gravity is there. Their work is still valid IF gravity exists. So they wouldn’t have to be “in on it”. Just because a model works doesn’t mean it is what we live on. But that of course goes both ways.
And for the social aspect NASA does have every reason to hide this. NASA is why we believe the earth is a ball. Their pictures and footage have proved that. But now I see errors in their proofs. Like their first footage of the ball earth rotating. the footage shows a 1/2 – 3/4 rotation of the earth but the clouds do not morph or change at all. Over a time frame of 12- 18 hours you would expect clouds to change shape, even slightly. There is also footage of the astronauts faking footage of the earth from space using a round window, a darkened cockpit and cutouts. https://www.youtube.com/watch?v=mCHG6uJH5L8
Why would they go through all this trouble if it was so easy to prove the ball is a sphere? Why don’t they just simply use their video camera to take pictures or video of the earth from space? Nasa themselves admit that they have to composite their images from ribbons of imagery that they put together in photoshop and have to paint certain sections. Why can’t they just go to space and take a simple photo or video? We give them billions of dollars and they can’t do that?

31. Carefree Mathematician says:

Gravity was first conceptualized as a dynamic force when it was applied to celestial bodies, I.E. with the Heliocentric model. It was a logical consequence that gravity works the same way on Earth as it does for other stuff in space. If you believe the Earth is Flat, you probably also have to believe in the Geocentric model, which some people also believe in, because it’s the logical consequent.

From any height, a spherical Earth appears to be a circle, because eyes take pictures, and pictures are two dimensional. As you get higher or farther away from the surface, the circle image projected into your eye gets smaller, and as such, you see the curvature of the Earth. From very low heights, you don’t see the curvature of the Earth, because if you look straight down, the Earth takes up half of a spherical radial view, and so the edge of the Earth traces a line in 360 degrees, which is why the Earth looks flat when you’re standing on it, or very low. Assuming Earth is a sphere, the angle the diameter of the circle image of Earth you see when looking directly at it takes up is roughly equal to:
2*asin(r/(y+r))
Where ‘r’ is the assumed radius of the Earth, and ‘y’ is your altitude. Because r=3959 miles, at 120,000 feet, which is about 22.7 miles, the resultant angle is 2.9 radians, over 93% of the average person’s field of view, which is not too different from what you see typically. Even if the Redbull video compared had distorted lenses, which is actually very typical, because it gives cameras a wider field of view while it’s predictable curvature and can be computationally removed when needed, the comparing amateur video doesn’t prove anything, because it uses a camera pointed straight at the horizon. You would not see the curvature of the Earth at that height without using a wide FOV camera pointed down, as in the Redbull video.

Additionally with that equation, it proves that the actual horizon doesn’t curve very much until you’re several times higher above the surface, but you can see the surface of the Earth curve away, and it’s sufficiently easier to see the curvature of the Earth that way, rather than by using the horizon, because when you look directly at the horizon, it looks much straighter than if you look directly at the Earth, because of math.

Actually, people have thought the world was round for thousands of years. NASA did not first prove the world was round, far from it. In fact, historically, people have believed that the Earth was at best an upturned bowl, not flat, since you can see the curvature of the Earth from on top of a mountain. The Flat Earth theory was never actually popular. Planes were invented in 1903, and GPS was invented in 1995. The first flight around the world was in 1923, so the idea that pilots wouldn’t know if the Earth is round or not because they use GPS is bust. Furthermore, the circumference of the Earth is almost 25000 miles, not 18000. Additionally, there are continents in the way of traveling straight around the world on a boat, in addition to the fact that they would need to take stops due to probably are going around the planet for a specific purpose like delivering cargo, so taking a circuitous path would actually result in a total distance around 60000 miles.

If you’re simultaneously arguing for the Heliocentric model, the Earth is Flat model, a fake moon landing, and a wide-spread technology conspiracy, I think what you are doing is what is formally referred to as “reaching.” The world isn’t as complicated as you need it to be. There are literally millions of professional and amateur mathematicians, physicists, geographers, pilots, ship captains, engineers, programmers, air traffic controllers, etc. How is it even remotely possible that nobody, in the history of the planet, has ever obtained proof that the Earth is flat?

“And for the social aspect NASA does have every reason to hide this.”
You said this, and then proceeded to NOT give a reason. All you did was explain why and how you think they are hiding it, but not for what reason. NASA doesn’t have an incentive. There’s no profit in a huge lie like that. If anything, it’s an extremely hard to keep secret, and it wastes monumental amounts of money. Additionally, the theory that NASA or the American government alone is capable and responsible for keeping this entire theory is extremely America-centric. 9 other countries are capable of sending satellites into orbit, and 2 other countries have landed on the moon, America alone has done 6 manned moon landings, and there are over 1000 mechanical satellites in orbit, many owned and orbited by privatized companies. Are they ALL also in on the conspiracy? The theory falls apart when you consider the fact that power groups other than the American Government exist. Fun Fact: The American government is composed of real, human people, just like you. It is not an omniscient, hyper-competent entity. Many people argue that the American government is actually incompetent due to its inability to solve even the most basic of problems. It actually has sufficiently less power than many billionaires who own large companies simply due to its inability to organize, and the fact that it hobbles its self while *attempting* to work for the people.

Out of all the billions of people on Earth, very very very few people believe that the Earth is Flat, and of those people, almost none of them have any legitimate scientific experience. Why do you think that is?

32. Mike Ochoa says:

Would the horizon appear the same, if we where on the inside of a infinitely hollow flat plane that gradually curved over onto itself forming the sky? And could this relate to Einstein curvature of of space time in special relativity?

33. Emeth Aletheia says:

As a videographer I know that using wide a angle lens like they do for the exterior shots of the RedBull video, you get curved footage. This is an effect. It’s not showing the real curvature. It’s a result of the lens only. At one point in the RedBull video the camera is pointed at an angle that makes the earth look concave because it is inverted. Why do they always feel the need to use these lenses and make us think we are seeing the curve of the earth? You can still use a nice wide lens to get a great view but they go to the extreme with their angles to always give that effect. Or why not use the tool that comes with these cameras to remove the curve effect in post? It is just very deceptive to those who don’t know how wide angle lenses work.

The amateur footage uses a camera pointed straight out. Why does the horizon remain at eye level at these altitudes? If the earth was a ball wouldn’t the horizon line lower even just a little as you climbed to these altitudes?

And yes there were a lot of people who believed this before NASA came along. But there were still very strong arguments for the flat earth. The Bedford level experiment was not able to measure any curvature in all of their tests. But it was NASA that claimed to fly out into space and take a picture of the earth as a ball so that it could be proved visually once and for all. See is believing for most people. But if this act of them filming and photographing the earth from space then questions need to be asked. Why did they fake this footage? Why can’t they take a non composite picture of the earth from space in full view?

How do you see curvature of the earth from a mountain top? And you misunderstood me, I said the circumference of Antarctica is about 18,000miles, not the earth. Yet they traveled over 60,000 miles. Enough to go around the earth many times. And these explorers, not delivery men, had a purpose, finding an inlet into the Antarctic ice wall. And as I said they traveled around Antarctic claiming they traveled 60,000 miles around the ice wall never finding a passage inward. Why has nobody circumnavigated North to south? Why are civilians not aloud to explore the poles independently if no country has a claim on Antarctica?

I am not arguing for either just looking to answers as to why the geocentric model seems to make more sense then the heliocentric model. And if people are working their theories on the wrong model they might still work and calculate correctly but if the model is wrong then they wouldn’t know the difference.

And I thought the motive of why NASA would do this is obvious. They collect billions of dollars and then pump out easily provably fake photos and videos. Cheaply made I might add. If they collected all this money to start a space program and then realized they weren’t able to make it out of our atmosphere, do you really think they would tell people? With NASA’s nazi influences I think it’s safe to assume that they would continue to collect billions of dollars and continue to use the tiniest percentage of that to make fake photos and video of our cosmos. How can you say there is no profit from this lie? The Astronauts from Apollo 11 said there was no effect from the Van Allen radiation belt and that they did not have to take any precautions to pass through it and he wasn’t even sure that they did go through the belt. Which they did, twice, if they did go to the moon. And now they are trying to figure out how to plate the Orion shuttles so that they can get people through the belt unharmed. But at the same time they are claiming they went through it many times back in the 60’s? Why is it such a problem for them now?

I don’t believe I even brought up the American government. If anything this is a global conspiracy. The same countries involved in the Antarctic treaty, keeping people away at gunpoint, are the same countries feeding us cheaply and sloppily done photos and videos from space. Air bubbles escaping from their helmets, sudden unexplained moments where gravity seems to spontaneously appear on the space station, all the female astronauts perming their hair so that it gives the illusion that it’s floating.
Most major corporations have the same goal and come out of the same think tanks. And if you understand how the military works then you can see how compartmentalizing information and clearances makes keeping this secret very possible. I suppose you believe ISIS and America are mortal enemies, the same way Bush and the bin laden’s were enemies. Sorry I am getting away from the subject here.

Over the years I’ve come to believe that what the majority of people believe has been fed to them and is not to be believed at all. Most of the people who believe the earth is flat are the ones who aren’t going to tell you. It’s too profitable for them to hid it and continue their space programs which have yet to provide any real photos of the earth in full view. The researchers who are coming forth trying to spread this info right now have some very shocking information. It took a while for me to even believe that it was a possibility for the earth to be flat. But after studying their work I was left with more questions on how the ball earth is provable.

34. Carefree Mathematician says:

@Emeth Aletheia, I noticed you didn’t actually address any of my primary arguments or responses to your initial statements. Specifically, the following:

1) Why don’t pilots know the Earth isn’t round if they’ve been flying around the planet for almost a century before GPS? Why don’t sailors know the Earth isn’t round if they’ve been sailing around the planet for five hundred years?
Addendum: As a programmer, I know that computer programs can be extremely easy to dissect if you apply logical effort and have skill in the language. Why has that literally never happened? Are all engineers, programmers, pilots, captains, in on it? Or do you mean to imply that in all of human history, none of those people can reasonably be assumed to have any two skills at once?

I mathematically showed that the Earth would take up 93% of a person’s lateral view (180 degrees) while looking straight down at a height of 120,000 feet, which is only 3.5% per side, so if the camera is looking straight at the horizon, it would only lower by about 6 degrees, which is greater than the average visual wobble of the amateur craft in the video, thus disproving its purpose.
Addendum: the atmosphere in the amateur video is thicker than 6 degrees, so it’s impossible to tell if the horizon/edge is curving or not, but ironically, you can actually see the curvature of the surface of the Earth in the very same video, via really simple graphic analysis. I took a screenshot of the video, pulled it up in photoshop, grabbed the filler tool, selected red color, and clicked randomly on the picture: http://prntscr.com/7lrg74
Notice how all the lines curve toward the horizon? It’s subtle, as I mathematically showed it would be (6 degrees is small), but it’s still very much there. Do it your self, you’ll probably end up with a similar image.

And again, you seem to believe that NASA gets ridiculous amounts of profit. Surely you understand that many astronauts die, and that rockets cost ridiculous quantities of money? The entire crew that it takes to make up NASA is huge, and they aren’t cheap either. Even if literally every single one of them had benefit for keeping the secret, it’s statistically impossible that none of them would have slipped up by now. The only way it would logically make sense for that many people to all congregationally deceive the entire planet is if it created insane amounts of power, but the thing about insane amounts of power is that it is extremely sloppy, and extremely easy to identify.

Finally: I asked you why you thought you need to believe in so many conspiracy theories simultaneously. I didn’t mean your logical reasons, but your personal reasons, for why you even care. You keep saying how difficult it is for Ball-Earth theory to be provable and that’s why you don’t believe it, and yet your entire argument for Flat-Earth hinges on the fact that it’s impossible to prove. The double standard is indicative that you have underlying, personal biases for believing this, that are completely outside the realm of the logic of the problem. Is your life so easy that you need the entire planet to be a hoax to satiate your desire for a plot in your life? There’s more than enough social injustice in the world to have something to fight for, so why is it that you would rather pretend that a vague yet menacing government agency controls all information of the structure of the planet of the entire species?

As a final addition to what I’ve said, I’d like to ask you, what makes you believe you have any more understanding on any of the following related subjects than anyone else:
Computers
Physics
Mathematics
Rocketry
Military structure
Sailing
Flying an airplane
Political science
Social science
Psychology
Personally, I happen to go to college for half of those, and associate primarily with students of a completely different half. I am literally in the process of becoming the very type of person who would be “in” on your grand conspiracy, and yet, here I am, being no different than you. Or would you instead argue that the system makes me part of keeping the conspiracy without me knowing it? In which case, WHO exactly is keeping the conspiracy if NOBODY ever finds out?

35. A says:

I know nothing of calculus nor am I a maths genius. However, if you see a curve on the horizon it is your BRAIN that is curving it. It does not curve.
Experiment.
Lay on the ground in a park or a large field.
It curves upwards.
Your brain doesn’t realise you’re upside down and your eyes don’t know what to do with the information, so they bend the horizon upwards.

It’s our reverse lens/retinas that distort the horizon.

The horizon itself does not curve.

36. R says:

Why do people keep repeating the 3-4 mile horizon limit? It’s been said that a person standing on a beach for example looking over the water can only see out 3-4 miles to the horizon. It’s at least 3x that and provable to anyone. Simply go to Westerly, RI, Misquamicut Beach and you will see Block Island (12 Miles away), and not just because its elevated.. you can see it’s sandy beaches meet the water. I’ve been to both beaches. When at the Block Is beach at the water’s edge you can also look over to see Misquamicut beach. — On a clear day mind you. Through strong binoculars you can see people on the beach. Check any map to confirm distances.

37. Carefree Mathematician says:

@R While it’s true that the furthest a person of normal height can see from sea level to another point also on sea level is about 3 miles, it’s also true that if two points were 12 miles away on the open ocean, they would only need to be 24 feet elevated from sea level to be able to see over the ocean. The higher either point is, the further you can see, and the lower the other point needs to be.

If you have two points on a circular (spherical) planet of radius ‘r’ at sea level, and one of them is ‘h’ distance from sea level, and the other is ‘H’ distance from sea level, then the relationship that describes the maximum arc distance ‘D’ they can be apart and still see each other is as follows:
r*acos(r/(H+r))+r*acos(r/(r+h))=D
If you plug in the radius of the Earth, and you set both h and H to 24 feet (make sure to use all the same units!), then D becomes about 12 miles! It could be very easy to think the last 24 feet of the beach simply aren’t there, especially if the beach is long and tall.
Also, due to tidal range, which can be as much as 38 feet on the coast, and tides in general, where low-tide makes the ocean look the most flat, it’s very possible for the ocean to appear much flatter than it actually is, and thus allow you to see significantly further!

38. Andy says:

Interesting discussion guys! I have always accepted the heliocentric view of the universe but similair to Emeth I now find that doubts have crept in and I find myself in a place where for the first time in my 42 years I have major doubts about who we really are and where we really live. I am not interested in taking one side or the other in this debate, I used to think that the idea that we live on a flat earth with a dome above it was stupid but now I realise that this is no more fanciful than the alternative model of an infinite universe of dead matter which despite being infinite was created in an instant from nothing and also despite being infinite is expanding (expanding into what?). I am also highly sceptical of anything NASA has to say, there’s just too many secrets and lies with them and I do believe that money and power are at the root of their agenda.
All of this being said, at the end of the day, whether the Earth is a ball planet in the ‘scientific’ model or a flat earth in the ‘creation’ model. Life and conciousness are/is amazing and more than anything we should appreciate that we’re all ‘in it together’ and that we’re more alike than different despite the best efforts of our ‘leaders’ to inspire mistrust and division between us.
peace
Andy

39. steve says:

Please explain how Water can curve.? Let’s say from Japan to California, the Pacific ocean would have a Hugh curve or hump in it if the earth was a sphere. Yet the physics of Water doesn’t do this, water always goes to the lowest point and is observed flat. Lakes, ponds, etc….
The Earth is NOT a sphere.

40. Carefree Mathematician says:

@Steve
Oceans being curved IS the lowest point. That’s how pressure works. The points on the surface of a contiguous fluid in equilibrium all has the same potential energy. That’s what equilibrium means. Equal energy. Gravity wells of finite objects are spherical, therefor, points of equal radius from the center of the gravity well have the same potential energy. That’s why objects in space are spheres. That’s why Earth is a sphere. That’s why the ocean is a sphere.

In order for flat earth to make sense, mass would need a short cylindrical gravity well, but if that were the case, then all heavenly bodies would need to be short cylinders. Unless every heavenly body in the universe is in rotation lock with the Earth, the theory is impossible, because short cylinders only look circular from the front, and every heavenly body looks circular. Additionally, every object in the universe would need to be on the same inclination, which is obviously not the case. The theory is implausible.

41. John says:

are you kidding me? I’m not a proponent of flat earth, BUT this story is 100% false. AND it’s all just assumptions about gravity and such, theres not facts behind ANY of this… this is ALL just someone’s idea, and almost every point they made is NOT sound…

42. Anonymous says:

If the luminaries are rotating in concentric circles above the flat earth, closer to the Arctic in summer, and then closer to the Ice Wall in Winter,

how can a typical sunset be explained,
when the sun is seen as a red globe sinking below the horizon,

43. w Math says:

Carefree Mathematician, please do not give up, I will be collecting all of your arguments to understand them better and eventually use them as means of educating some of the believers in this nonsense. You’re doing a good thing.

44. Karmen says:

Someone mentioned from which hight does Eart appear round, well, Ive been to Adriatic sea many times from my childhood, and when you look at the horizon from the shore, you can see it is curved. No need to climb anywhere.
What makes me wonder though is, why does it always look straight on photos?

Karmen, the horizon looks straight on photos because the angle of view of a camera is very limited, compared to our eyes. https://en.wikipedia.org/wiki/Angle_of_view suggests that normal lens have 40~62°, while http://www.cambridgeincolour.com/tutorials/cameras-vs-human-eye.htm says our eyes have 120~200° each, around 130° for overlapping vision of both eyes.

46. Karmen says:

I guess this might explain why I see the curvature if the Earth is flat. Which is easy to accept since eyes are easy to deceive. And it just might be flat, because Ive been going through some slope angle calculations with some mathematician friends and the numbers dont match the actual distances by far. So either Earth is indeed flat or it is way way bigger than what we are being told. Which still wouldnt explain how do all the huge water surfaces manage to remain perfectly horizontal on the spherical shape of the Earth. Wrapping around a sphere and staying horizontal, I dont think so. And some say, ah its cos of gravity, so gravity is some kind of magic?

47. Leif says:

So, it would look like the whole thing would enclose you. Great.
Reminds me of Halo, but…
What would happen if you tried to reach the ‘top’ of the sphere by going up in a straight, vertical, line? Would it just uncurl into a flat plane?

48. KEN GIBBS says:

THE ONLY THING I KNOW BOYS AND GIRLS IS THAT WHEN I WAS IN THE NAVY, 1959-1962, I COULD NOT SEE A SHIP BEYOND THE HORIZON WITH THE NAKED EYE, “B U T”, WHEN I LOOKED THRU THE SIGNALMANS
VERY HIGH POWERED BINOCULARS I COULD WATCH A SHIP GO BY AND BECAUSE IT WAS SO FAR AWAY, ALL I COULD SEE WAS THE TOP OF ITS MASTS OR FUNNELS GOING BY. I WAS ALSO TOLD THAT THE CURVATURE WAS NOTICEABLE AT FOURTEEN MILES. REMEMBER GUYS A WWII USA BATTLESHIP COULD SHOOT A 16″ SHELL IN EXCESS OF 20 MILES, SO EVEN THOUGH THEY COULD NOT SEE THE SHIP IN ITS ENTIREITY THEY COULD HT IT. KEN