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Scenario: While poking around in an alien ruin, scientists discover a gateway which offers instant transportation to an Earth-like world.

The Observed World: The gateway leads to an area that is temperate (let's say it's similar to east coast of America, like Virginia/Maryland/Pennsylvania, for simplicity). The air is breathable, and there is an ocean visible within less than a mile. The gravity and day/night cycle almost exactly matches Earth. The planet has no visible satellites, natural or otherwise. There is flora and fauna, but no intelligent life.

The Actual World: The "planet" is actually an artificial construct—a flat (coin-shaped) world created through technological (rather than supernatural) means. The size is similar to what Earth would be, were its surface peeled open like an orange, and flattened into a disk. Gravity is artificially generated and regulated to mimic Earth (so you won't be pulled at an angle as you approach the edge). The atmosphere is held in by an invisible field which forms a dome over the livable side of the world.

The world orbits a yellow star similar to the Sun, and also rotates (like a spinning coin), so the sun will appear to rise and set.

Question: If a team of scientists are sent through the gateway with the purpose collecting flora/fauna/air/water samples, and observing the night sky (to determine the planet's location relative to Earth), what would tip them off that they're not on a typical spherical planet?

Particularly, what would stand out to someone with a good grasp of general physics, or astrophysics, even if they had no reason to suspect that the planet was anything other than a typical sphere?

I'm not looking for a mathematical proof, but rather something that visibly stands out and would make a scientist decide to perform such a proof in the first place.

Their available technology is modern-day: telescopes, laptops, quadcopter-mounted cameras, etc.

Liesmith
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    If they looked over the side and saw a turtle. – Comic Sans Seraphim May 28 '16 at 11:40
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    No time an not enough physics to follow this up with an answer: what about Foucault's pendulum? https://en.wikipedia.org/wiki/Foucault_pendulum (They'd have to suspect something to set up the experiment.) – Ethan Bolker May 28 '16 at 20:00
  • I think the only way would be through edge. Any other measurements can be just because radius is sufficiently bigger - and I'd assume the accuracy of the off-hand calculation wouldn't give radius which would gave mass bigger then 75 times Jupiter. Dome could be explained to exists over part of planet. Both are much simpler explanation then disks so they would be preferred over it. Only edge is a definite proof. – Maja Piechotka May 30 '16 at 05:09
  • So the surface area would be the about 500x10^6 km2, giving a radius of about 13,000km, and a maximum distance of 13,000 to an edge. Without atmosphere, the telescopes should be able to see the highest points, and the highest points would see the edges. It isn't initially mathematical, but the distance to horizon would not get significantly larger no matter how high you flew your drone, keying one into working out the d=sqrt(h*(D+h)) math. – Dave X May 30 '16 at 23:51
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    Wouldn't star trails ( https://en.wikipedia.org/wiki/Star_trail ) be another give-away? I wonder if aiming straight away from the surface would produce straight lines, as opposed to curved lines when on a spherical world (when not on the equator). – frozenkoi Jun 01 '16 at 02:16
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    I wonder how you peel an orange and flatten it so that the result looks like a coin. – RemcoGerlich Jun 01 '16 at 09:11
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    @RemcoGerlich: Step 1? Believe in yourself. – Liesmith Jun 01 '16 at 10:43
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    I am surprised no one mentioned Discworld yet. A quote from one of the first books: "Since the disc's tiny orbiting sunlet maintains a fixed orbit while the majestic disc turns slowly beneath it, it will be readily deduced that a disc year consists of not four but eight seasons. The summers are those times when the sun rises or sets at the nearest point on the Rim, the winters those occasions when it rises or sets at a point around ninety degrees along the circumference." And I would make this into a much more elaborate answer, but alas, this questions is protected against new users. – The Square-Cube Law Jun 01 '16 at 16:05
  • One option is to calculate the curvature: https://en.wikipedia.org/wiki/Curvature – Erel Segal-Halevi Jun 03 '16 at 09:51
  • @Studoku whats that a reference too? – Vajura Jun 03 '16 at 12:18
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    @Vajura Discworld – Comic Sans Seraphim Jun 04 '16 at 08:03
  • @RemcoGerlich, Flattening the peel must change its geometry. There are no parallel lines on a sphere : The " line segment" from A to B is the shortest path from A to B. – DanielWainfleet Jun 04 '16 at 19:28
  • Lets hope the exploration party does not get into a heated debate on the subject like they did here on planet earth – Forward Ed Jun 15 '16 at 23:52
  • What is the reason for why they don't send in drones to explore to begin with? This would be a cost efficient and practical option when you can launch them from right outside the portal, or if necessary from right inside it. – Martine Votvik Jun 16 '16 at 05:24
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    @EthanBolker: Foucault's pendulum would still precess on a rotating disc. There's a latitude-dependent effect on the Earth (basically, because the rotation axis of the Earth is oriented at different angles to the surface at different latitudes); the scientists could try to measure the difference of the precession period at different locations, but at that point they're just as well off cribbing from Erasothenes. – Michael Seifert Jun 16 '16 at 14:19
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    As a matter of comedy, I saw the link to this question on the sidebar and thought "Ugh this is in physics, Im going to yell at this person". Ok, World building, much relief, go ahead..... – Shayne Oct 27 '20 at 03:54

21 Answers21

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Apart from the horizon topic that was already covered by Separatix and Ctouw, they could quickly verify their observation by measuring the angle towards the sun at different points of the planet at the same time).

Those angles will, much unlike at home, be almost identical, since they are measured from a plane a large distance from the observed object (the sun), while comparably close to each other, even if they are on different continents.

Also, they will quickly notice that they won't have time zones, for exactly the same reason.

As a result, all programmers of earth will, almost immediately after that discovery, migrate to the new planet, and will forever be happy coders that don't have to deal with time zone handling any more.

MrCodeWeaver
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Burki
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    This. Kill all timezones. And the people who think "daylight saving time" is a good idea. – Tim B May 27 '16 at 13:41
  • What if it's a flat world that rotates? Then you'd have timezones, wouldn't you? – TylerH May 27 '16 at 14:23
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    @TylerH Not according to the programmers that inhabit it. – IllusiveBrian May 27 '16 at 14:48
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    This assumes that they travel far enough to experience the lack of timezones, or split up and take measurements. I think OP wants something that will be a trigger like "Hey guys! I think we are on a flat planet because I just unexpectedly noticed XXXX" – Trenin May 27 '16 at 18:02
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    I think this is a good follow up experiment once they suspect something is up. But initially, the horizon distance and lack of dawn/twilight would be a bigger clue that doesn't even require their action, only their observation. – Trenin May 27 '16 at 18:09
  • If you look at pictures of what people who believe the earth is actually flat looks like then you will see time zones are technically still possible. Not sure if it would still work with a flat earth that is orbiting a star thought. And it also depends on the size of the earth, but if the individual feels it is big that it to should have timezones then it is safe to assume it is. – thebigtine May 27 '16 at 18:24
  • @yobddigi checked that. To me, the Flat Earth society timezoned model would have terribly different sunsets as well, with the Sun going away, but not going down. – svavil May 27 '16 at 20:43
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    The no-timezones feature could be the reason this planet was created in the first place. – Emilio M Bumachar May 28 '16 at 00:38
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    You think time zones are bad? How about the fact that this newly discovered planet has no moon? There are 5 types of astronomical months, and at least 20 different ways of designating civil months. – Michael May 30 '16 at 05:46
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    Since the new world would not have (known) GPS satellites deployed, they would most probably initially try to use old techniques (sextant - using the sun and a chronograph) to determine the longitudes, for navigation. Then they would notice that there is no (an very very small, at most about 0.005°) difference, hence no longitudes, hence no curvature. – frIT May 30 '16 at 07:53
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    @timb Daylight savings time is an atheist plot to screw up church schedules twice a year. – Jay May 31 '16 at 13:41
  • An even more insane idea than time zones is leap seconds. Whoever thought that having seconds added to the calendar at essentially unpredictable times was better than having the time when the Sun is directly overhead at the center point of a timezone be different from 12:00 by a second or two ... why? I think programmers should just ignore these people and create our own calendar. – Jay May 31 '16 at 13:45
  • tut, just more examples of programmers putting their own desires above that of their users! :-) – gbjbaanb May 31 '16 at 15:55
  • Wouldn't this planet have two timezones: the day side and the night side? – Gavin S. Yancey Jun 01 '16 at 03:34
  • @TimB If we were sensible and had an absolute universal time, measured relatively to a start point, we could get rid of leap years/seconds/time zones e.t.c and each country/spaceship/colony/place could then implement its own method of extracting an arbitrary local time from the absolute time. Then all machines can run on absolute time which helps with GPS (leap seconds are a nightmare), time conversions with future space colonies or starships operating on different day/night cycles. – Troyseph Jun 01 '16 at 11:13
  • @Tim B and death to the swine who drew the international date line and made it crooked. – RedSonja Jun 02 '16 at 13:19
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Daybreak and nightfall would be spectacular

A flat coin shape would have a day face and a night face with sudden transitions because unlike a sphere, it blocks all sunlight with its own shadow, there is no refraction around the sphere. The sunlight also passes through much more air when close to the horizon.

If you start at noon, things would appear quite normal and stay so into twilight as the suns moves lower in the sky. A few minutes before sunset the sunlight starts fading much more rapidly than it would on Earth. The effect would be like the sun sinking into clouds even on the clearest day, until the sun barely outshines our moon and the sky would be as dark as night while the sun is still above the horizon.

The moment the sun passes the horizon, it will be completely dark. There are no shimmering clouds or scattered glow, only pure darkness. The scattered light from the edge simply can't reach you through thousands of km of air.

Daybreak would arrive just as suddenly, with what looks like a moon rising in the night suddenly increasing in brightness until normal sunlight a few minutes later.

If the observer would be very close to one edge of the world, sunrise and sunset would be asymmetrical, with the closer one fading closer to the horizon.

No scientist is going to take long in figuring this one out.

EDIT: I've updated my answer for a bit more scientific accuracy, as many comments pointed out the effects should be noticeable even before the sun sets, and they are right. Below is the science behind the answer, that I could find online.

The air in our atmosphere reduces the intensity of light going through it by scattering, absorption and reflection. Even at the shortest path (straight down when the sun is at zenith) only about 75% of visible light makes it to the surface. This is a well-known and important effect in Astronomy and other fields of science and modelled as "Air Mass" (wikipedia). The lower the sun is in the sky, the higher the amount of air mass the light travels through. On Earth, the air mass is about 38x higher when the sun is at the horizon, resulting in a drop in light intensity in the environment from 100k+ lux to only ~400 lux on a clear day.

On a flat world with a similar atmosphere this would be about the same until the sun gets close to the horizon. Then the light needs to pass through much more atmosphere making it much darker. I drew this for a visual impression. The blue and purple areas show the atmosphere of a round and flat world respectively. The curve is exaggerated for clarity. It's roughly to scale for a 100 km high atmosphere, but only the lowest few km have enough density to matter.

diagram of sunlight at various angles on a flat vs curved world

It's easy to see that the difference in air mass is unnoticeable until about 85 degrees from zenith (5 degrees above the horizon). This is 20 minutes before sunset on Earth. 12 minutes before sunset (87 degrees) the difference is perhaps 20%, noticeable but easily dwarfed by variation due to atmospheric conditions (hazy sky). 6-7 minutes before (88-89 degrees ) it's already as dark as it should be as sunset and then in the next few minutes the sun and daylight will fade to perhaps only the strength of a full moon before setting.

To back this up with some numbers: The Wikipedia article has a graph with several models. Conveniently, the most basic one is the "plane parallel" which is a flat world. It's given only as a reference because it is invalid at high angles, but exactly what we want to compare. When looking at the graph, the air mass at sunset (90 degrees) is ~38 for most models, a value the plane parallel line already reaches between 88 and 89 degrees. The air mass then increases rapidly, approaching infinity because it doesn't account for the limited radius of the flat coin world in this question :-).

Cyrus
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    This for sure. The other things might go unnoticed, but the first day/night transition would be an dead give away. After, they could perform all kinds of experiments to confirm. – Trenin May 27 '16 at 18:07
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    You probably would see something of a twilight as the sun goes down. You go from very little distance through the atmosphere at noon (~16 km) to approximately the entire radius of the disk (~ 12000 km, if it's the same surface area as earth). That's a lot of light attenuation. Wikipedia indicates that at the clearest, max visibility is ~300 km. From the angles, you should reach that at about 12 min before sunset. So you'd get fading light for about a half hour before "true" sunset. Perhaps a bit longer, if the air is cloudy/dusty. – R.M. May 27 '16 at 18:44
  • It was hard to pick an answer, since they were all so good, but I think this one best fits what I was looking for. Thank you for the suggestion! – Liesmith May 27 '16 at 22:16
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    No. There will be a difference but you aren't going to get the sudden effect unless you're near the edge already. Rather, the sun will fade in/fade out due to the huge amount of atmosphere it's going through. – Loren Pechtel May 28 '16 at 00:19
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    I guess nobody who ever thought the Earth was actually flat realized this... – Michael May 30 '16 at 05:43
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    @Michael People who thought the Earth was flat thought the sun was smaller than Earth and just circled above it. – nmclean May 30 '16 at 18:57
  • @nmclean Then why would it go in a straight line across the sky? And why would it ever set? – Ovi May 31 '16 at 00:01
  • @Ovi http://www.theflatearthsociety.org/tiki/tiki-index.php?page=The+Setting+of+the+Sun – nmclean May 31 '16 at 12:35
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    Also the sun is very big[citation needed], so it takes up a significant portion of the sky. The sun's angular diameter is about 32 minutes, or half a degree. For that reason alone, sunrise/set will not be instantaneous, but will take at least 1/720 of a day, provided that the sun is the same size and distance as on Earth. (On Earth this is about 2 minutes.) – Devsman May 31 '16 at 18:46
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    Apart from the already mentioned points (atmosphere, solid angle of the sun), there is also Lambert's law (https://en.wikipedia.org/wiki/Lambert%27s_cosine_law), which means the surface will softly transit from lit to unlit. The moment the last sun ray hits the surface, it is already almost dark. You completely ignore that on the micro scale we live at, a disk is already a very precise approximation. – phresnel Jun 02 '16 at 08:07
  • Place giant prisms at the edge of the disk to generate fun sunsets/sunrises. You know, for aesthetics. – Yakk Jun 02 '16 at 15:07
  • @nmclean I don't really get that explanation. "Usually it is taught in art schools that the vanishing point is an infinite distance away from the observer [...] However, since man cannot perceive infinity due to human limitations, the perspective lines are modified and placed a finite distance away from the observer" Huh? That doesn't make sense at all. Are they proposing some sort of modification to the laws of physics or mathematics which allows for a limited line of sight like that? There doesn't seem to be any explanation of such a modification on that page. – Ajedi32 Jun 02 '16 at 18:31
  • It's a little like this near the ecuator in real life. Every day, it's fully light at 6pm, a bit of golden sunset at 6:30pm as the sun gets very low in the sky, twilight at 6:45pm as the sun starts to dip under the horizon, some minutes of moderate darkness as the sun disappears but light still refracts and reflects off clouds, then bam, pitch black by around 7:10pm. Even just this is very noticeable to someone used to dusk in temperate climates. – user56reinstatemonica8 Jun 02 '16 at 22:51
  • @Ajedi32 I can't say I understand it myself, but yes they do modify the laws of physics (gravity doesn't exist, among other things) ... I think the explanation for limited line of sight is this one: Electromagnetic Accelerator - also known as "bendy light". – nmclean Jun 03 '16 at 12:33
  • "The atmosphere is held in by an invisible field which forms a dome over the livable side of the world." A dome atmosphere would refract, would it not? – C. Tewalt Jun 03 '16 at 18:50
  • What color will the sky be? – Readin Jun 06 '16 at 05:57
  • I'm not completely convinced. Refraction slows the apparent rising/setting of the sun, making it appear to move across the sky very slightly slower when rising/setting, but it's only visible for an extra 2 minutes or so. I don't see why nightfall would be more "sudden", all you'd lose is illumination of the clouds in the upper atmosphere after the sun dipped below the horizon, but on a cloudless day I don't see much effect. Once the sun is occluded (whether apparently or truly), it's dark. Would you really notice that the sunset was a mere 2 minutes shorter than usual? – Nuclear Hoagie Aug 12 '22 at 13:40
  • If I read it correctly, the graph from wikipedia comparing different models essentially invalidates your answer. It shows that the airmass increases faster on the plane than on the sphere: light starts to be attenuated sooner (at lower angles) on a flat world. It suggests that the transition from day to night will be spread out over a longer period of time (relative to your rotational period). Of course it is hard to tell how much of that is an artifact of considering the plane infinite. But geometrically, the optical path will indeed be asymptotically longer on the plane than on the sphere – Barbaud Julien Aug 19 '22 at 11:48
  • @BarbaudJulien Airmass does increase faster on the plane and it gets darker "earlier" at sunset, but the whole graph only covers 5 degrees above the horizon (from 85-90 degrees from zenith). So the main difference is exactly what my answer now says: It gets dark a few minutes earlier and critically, before the sun reaches the horizon. – Cyrus Aug 19 '22 at 12:29
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Horizon effects would be the first signal.

As a quick and dirty calculation, the distance to the horizon in miles is half your height in feet.

Given their visual range is going to be far greater than that, you have two options, either the world is absolutely vast (even though gravity is Earth normal) or it's flat.

They'll quickly realise something strange is going on, after that it's a matter of working out what. Spread out, do some triangulation and they'll find the answer.

Then the sunset will be all wrong.

Separatrix
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  • There will probably also some strange things going on with the weather considering the lack of Coriolis force and possibly strange weather phenomena at the edge of the disk. I am not planning to write an answer so if you find this point valid you could add it to yours ;) – Jaywalker May 27 '16 at 13:23
  • @Jaywalker, as you say, the weather could be a mess, but I would expect it to take a few days for that to show. Weather is much more subtle in that regard. – Separatrix May 27 '16 at 13:30
  • True, also there are other reasons why a planet's weather could be weird such as being tidally locked to the parent star. – Jaywalker May 27 '16 at 13:32
  • Option #3: it's ~6 miles wide and you're 5'7". If you're not standing in the center the distances won't equal. – Mazura May 27 '16 at 16:09
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    Due to my hobbies I am liable to notice within a few hours the hull-down effect just isn't there. Depending on where I'm let down I might well notice immediately. – Joshua May 29 '16 at 03:00
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    Why would they be expected to assume that the planet is the same size as Earth? Might it be a much larger planet (with much farther horizons) made of less dense material? – Readin May 29 '16 at 04:01
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    @Readin, first judgements are always based on experience, Earth gravity would initially imply Earth radius so you'd expect the same horizon line. – Separatrix May 29 '16 at 15:40
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    This was my first thought also, though one must concede there's a catch: If the terrain is hilly, or they're in a thick forest, or some other situation where you don't expect to see all the way to the horizon, you might not notice. If you're on the coast of the ocean or in a wide flat desert, would you notice if there were no obvious landmarks? I'm not sure. – Jay May 31 '16 at 13:48
  • @Readin Can't find where I read it, but a planet that massive would surely be a gas giant. Main reason for NASA to completely obviate planets that massive in their search for life-suitable planets. I think it would surely not be earth-like. (Found it! this SO answer covers it) – tfrascaroli May 31 '16 at 16:52
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An Edge

Not sure why this has not been said, but when you go for a long enough walk and get to the perimeter of the disk planet, there is an edge.

In the Truman Show, the edge looks like this:

The Edge

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Forward Ed
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  • Fair point, but I think it will be a night time before we reach the edge, and see how the sun is setting... So we will stop walking. – zx8754 May 28 '16 at 07:08
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    Given the specified size of the flatworld you might need to travel quite a long way to find an edge. – Sean Condon May 29 '16 at 06:57
  • I dont recall a time limit for the discovery nor did the OP state that the new gateway was far from the edge. – Forward Ed May 29 '16 at 07:21
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    ROFL, by far the most humorous answer. +1 (Also, it works!) – minseong May 30 '16 at 10:48
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    It's worth noting, that most current "flat earth theorists" say that the edges are all at water. That is, all the continents are surrounded by water, and far after the water comes the edge – Cruncher May 30 '16 at 13:01
  • I guess I should add sail, swim, or paddle. Kind of like the "Trueman Show" – Forward Ed May 30 '16 at 14:46
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    Though it's the most blunt solution and requires the least scientific insight, this is for sure the most dramatic solution. – Devsman May 31 '16 at 18:52
  • What happens if you jump off the edge? – Darthg8r Jun 02 '16 at 15:03
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    You find out the gender of A'Tuin – Raphael diSanto Jun 02 '16 at 15:48
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    @zx8754 we're talking about scientists here. Right after they discovered the sunset thing, they will indeed stop walking, and start running, to see what the edge looks like. – Burki Mar 08 '17 at 16:00
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Triangles

Most of the methods posted involve the sun or the sky, but since the planet was created using some very advanced technology, it's possible these effects are hidden.

Instead, a simple and foolproof method is to measure a (sufficiently large) triangle.

Why?

You might think the angles of a triangle add up to exactly 180°, but this is only true on a flat surface. On Earth (and any sphere) the angles of a triangle actually always sum to more than 180° (up to 540°). There are similar distortions in area, and other properties.

So, as soon as they seriously consider any 3 points on the planet that are far enough apart, someone clever will notice something is unusual (180° triangles).

As a bonus, because this is a purely mathematical property of flat surfaces, there is absolutely no way to hide the flatness of the world.

LaDeDaDo
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    If the triangles are line of sight, you get 180º even on the surface of the Earth. Measuring an angle surplus has to be done with lines that follow the contours of the surface itself, and will be rather confounded by any hills and slopes present. –  May 27 '16 at 17:46
  • If you're going to invoke godtech as a reason why other measurements might not work, you have to consider the possibility of being in a funky universe. Like if the EM and gravitational fields aren't divergenceless, you could get all kinds of wackiness, including a world that seems flat but is actually curved. – MackTuesday May 27 '16 at 19:43
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    Hurkyl, it of course has to be over a large enough distance that Hills and slopes are negligible. It wouldn't be something you'd notice walking down the street, but any attempt to map the area will reveal the flat nature (and it IS an exploration mission ). – LaDeDaDo May 28 '16 at 12:08
  • If someone's constructed this elaborate rotating flat world, it's reasonable there might be a false sky and atmosphere , if only for an aesthetic reason by the designers. God tech is necessary for such a world in the first place, so there's a lot of flex room for what's possible. And like I mentioned this is purely a mathematical property, so even in a universe with different physics it would work. – LaDeDaDo May 28 '16 at 12:15
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    But why would they want to do the triangle test in the first place, if they were not already suspicious about the "planet's" form? – vsz May 29 '16 at 17:21
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    They're on an exploratory mission, so it makes sense they would try to draw maps. The person doing this would find it odd that the world perfectly maps to a flat plane (this isn't supposed to happen which is why there are all sorts of complicated projection schemes). Admittedly, the effects from the sun people mentioned would be noticeable before this. So if nothing hides those, this would merely be a confirmation of what they already figured out. As a historical note, people have done this sort of test as far back as ancient Greece. – LaDeDaDo May 30 '16 at 04:41
  • @Hurkyl In geodesy, triangles aren't line of sight. Triangles are line of sight projected on the surface. This way (in Earth) they are spherical triangles, not plane triangles. – Pere Jul 19 '18 at 16:15
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There will be no horizon line or it would look way further than on actual Earth

The horizon line is caused by the Earth being a sphere, so that when you look straight in front of you, at a certain point you can't see things because they are hidden by the curvature of the Earth itself.

In the world you describe, you would see what is in front of you up to the edge of the "planet"; or, depending of its span, instead of having a horizon line, distant objects would progressively disappear into "distance fog". But you would see way further than on actual Earth anyway.

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Eratosthenes made the first estimate of the size of the spherical earth. He did so by measuring the length of the sun's shadows while at two different locations. One location was much further north than the other, and the length of shadow told him how much the earth surface curved between the two. His measurments were both performed on the summers solstice when the sun was at it's highest point in the sky. The known distance between the measurement points and his calculated difference in the sun's shadow angle allowed him to calculate the curvature (size) of the earth, within 5-15% of its true value.

So if you are limited to low tech, the way to measure a planet's curvature is if two people were to measure the angle of the sun's shadow at noon on the same day at two distant points (exactly north-south of each other), and if that angle is different at the two locations, that would imply that the earth is curved and probably spherical, or at least curved in the north to south direction. The time-zone answers given by other answers here would prove the earth is also curved in the east-west direction, but to use that method requires precise/reliable clocks for the two measurements to occur at the same time but east-west from each other.

Which is also one of the reasons why sailors historically needed precise clocks for navigation; this allowed them to know how far east-west they were when out of sight of land. What time noon occurs at depends on how far east-west you are. If you know the time, the sun's position tells you where you are (east-west). If you know where you are (east-west), you can use the sun to tell you what time it is.

Given your premises of scientists with higher tech, I would say one tip-off to them of the flat planet scenario would be if one scientist were to video-call another while they were located at widely different points on the flat planet, and one of them notices that the sun's shadows appears to fall at the same angle at the same time in both locations.

Mark Ripley
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    +1 for the plausible scenario for making that accidental discovery. – frIT May 30 '16 at 08:07
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    +1 for pointing out that east-west curvature could be different from north-south curvature. If ellipsoid / sphere isn't the only option, then cylinder is possible as well as flat. – Peter Cordes May 30 '16 at 17:24
  • +1 for historic reference to how our civilization figured it out – Atog Aug 12 '22 at 23:05
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No clouds near the horizon
On a cloudy day when you look at the horizon where the sky meets the water over the ocean, you see clouds appearing to touch the water even though those clouds are in the air. On a flat world the clouds would not do this. They would get close to the horizon, but never touch.

Readin
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    Wouldn't perception of perspective make the things almost the same? You may see farther, but water and clouds will eventually look as if they're touching (since you can't really know which side of a cloud you're seeing). – Kamen Minkov May 31 '16 at 06:32
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    @KamenMinkov: I think you'd lose vision in haze at a short enough distance that you could tell the difference. For example if the clouds are at 1km and you can't see much beyond about 300km then there would still be a discernible angular "distance" between the sea and the sky except that air isn't transparent enough. But I might be wrong. – Steve Jessop May 31 '16 at 09:01
  • This is the same phenomenon as a ship appearing to be low in the water when it is a few miles offshore. Take a sailing ship a bit further out and you see the sails but not the hull, though you can climb a hill or tower to peer slightly further over the horizon. Sailors knew the world was round long before learned men accepted it! – nigel222 Jun 17 '16 at 11:01
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Atmospheric readings would be weird

On Earth, the atmosphere is a spherical layer around a spherical earth. However, you say that the atmosphere is a dome over the world. If the dome is a physical object, it would have to be close to round to be able to support its own weight. If it's held there by the gravity, most of it would spill over the edges. If it's an invisible force field, the easiest way would again be a spherical field.

Assuming the dome is round...

  • Either the entire atmosphere weighs just as much as Earth, which leads to a much thinner atmosphere;
  • Or the atmosphere is just as dense as on Earth, which leads a much larger atmospheric pressure;
  • Or the atmosphere changes density in a different way than on Earth, which means that incoming light is diffused differently.

Assuming the dome is a fixed-height force field, then the lower view angles would have to travel through far more atmosphere to reach you compared to on earth, again affecting diffusion.

Compasses would not work like they do on Earth

Earth's magnetic field is caused by molten metal deep inside the core moving around and generating electric currents. Because of the Coriolis effect, this field is roughly aligned with Earth's rotational axis.

However, on a flat disk, there probably is no molten core, and even if there was one, it wouldn't generate a magnetic field in the way that we know it on Earth, because the molten metal would flow differently and there wouldn't be as strong a coriolis effect.

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Nzall
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  • It isn't the atmosphere that's a dome. The dome is a field surrounding the entire disc. That will give the atmosphere the same exponential pressure gradient we have on Earth. (By the way, how can a dome over a disc be a fixed-height force field?) – MackTuesday May 27 '16 at 20:16
  • @MackTuesday Are you saying that the artificial earth-surface-normal artificial gravity works on the atmosphere above it, and hence causes the same type of atmosphere, rather than the atmospheric pressure being caused by the dome? That could work. – Dewi Morgan May 28 '16 at 00:08
  • @DewiMorgan -- I don't see why gravity would affect people but not the air, but let's say that's true. This hemispherical dome is big and holds a lot of gas. If the pressure is the same throughout, light will be maximally scattered across the visible spectrum, making the sun indistinguishable in a fantastically bright sky that dims near the horizon. – MackTuesday May 28 '16 at 01:40
  • "Artificial gravity" just means "a downward force not caused by gravity": spinning, etc. Assuming a hemispherical dome with a radius of about 8000km (based on it covering a disk with earth's surface area), and gravity reducing at an earthlike rate from the surface to about 2m/s/s by 8000km, that's enough height to encompass the exosphere and the atmospheric properties should be about earth-normal, I think.

    But if it's a dome filled with gas and an artificial gravity effect that only operates near the ground, or which applies with the same force throughout the dome, then it would get weird.

     – Dewi Morgan May 30 '16 at 20:59
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    Using rotation, acceleration is higher the closer to the hub you go, so "gravity" would go up, not down, as you rose. Still, just in case it's of interest, to get 9.8m/s of acceleration with a rotational period of 24hrs, you'd must rotate about a radius of 1.8 million km. With a "moon" or other massive object as a counterweight, it's feasible... handwaving away that the moon wouldn't move in the sky (paint it black?) and the whole "what kind of tethers could hold that weight" problem, and the atmospheric issues. But at least it's not handwaving away "artificial gravity". – Dewi Morgan May 30 '16 at 23:00
  • This answer made me try to imagine the conditions required to make a compass needle spin like a dervish (for humorous effect, of course). Maybe a spinning giant magnet floating just below the underside of the flat earth. [https://en.wikipedia.org/wiki/Spin-stabilized_magnetic_levitation] – Mark Ripley Jun 03 '16 at 10:42
  • @MarkRipley I'm not even sure there would be any magnetic north that a compass could point to. Earth has 2 magnetic poles because there is a large amount of metal in the core and it spins. A large disk probably wouldn't generate any worthwhile magnetic field. – Nzall Jun 03 '16 at 10:50
  • @Nzall: I agree that unless a large bar magnet or something similar were part of it's construction, a flat earth would have very weak or no magnetic field. I was imagining the humorous look on the face of the scientists when they arrived and looked at a compass only to see the needle spinning around, especially spinning at high speeds, and then thinking about what conditions might cause a compass to do that on a hypothetical flat earth. – Mark Ripley Jun 03 '16 at 12:43
  • @MarkRipley Why would the needle spin? Wouldn't the needle just stay in the same position relative to the compass itself? Or does a compass needle just start spinning erratically without a magnetic field to control it? – Nzall Jun 03 '16 at 12:49
  • @Nzall: Look at the URL I included above. Now imagine a giant spinning magnet like that underneath a flat earth that creates a powerful spinning magnetic field. That field would affect the entire flat earth and would not only spin a compass but if powerful enough spin any ferrous metal object. Imagine wrenches and pipes spinning in place everywhere due to the rotating magnetic field. It would take a special breed of engineer to deal with conditions like that. I didn't say this was at all plausible, but this is world-building after all; it's about what kind of world makes for the best stories. – Mark Ripley Jun 03 '16 at 13:11
  • What about noticing that the flushing toilet water isn't spinning? – Sirat Aug 06 '19 at 19:05
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First, why would it be spinning? Consider a coin spinning clockwise from your point of view. The leading (top left) edge moves with the spin, as does the bottom right. Someone standing at either point would experience higher gravity than someone in the centre. An observer at the trailing edge would experience negative gravity. It's the same concept as spinning cylindrical space stations to generate artificial gravity-it varies according to your direction of movement. A disk spinning like a coin would be obvious the moment you take a few steps orthogonal to the spin axis. If it's spinning like a flat top, centripetal force increases as you travel closer to the edges. Again that should be fairly obvious. Not to mention the sun travelling the other way at "night". If anything, the only way for this to work is with the classical flat earth model, where the disc is at rest and everything rotates around it.
So, now that we have a stationary flat disc, under a VR dome, how does the air and water circulate? Cold generators at the poles and heat generators at the centre? Pressure generators at the rim? As someone pointed out, if we assume godtech, anything is possible. Assuming a circular world however, geometry would indicate everything moves either to or away from the centre.

nzaman
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    Also, everything would be perpetually sliding toward the edge. – Devsman May 31 '16 at 19:04
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    If it's spinning like a phonograph record, perhaps the density (and surface gravity) is adjusted at different radial distance to compensate for the centrifugal force. Something similar might work for spinning like a coin on a table; but you'd have to somehow keep the axis from podholing. – JDługosz May 31 '16 at 21:36
  • @JDługosz: You'd still see the sun going both ways – nzaman Jul 13 '16 at 13:09
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Weird atmospheric effect.

We have a disc-shaped world which is either illuminated (albeit with varying angle) or in the dark. There is no circulation between Lightside and Darkside.

As a result, the atmosphere gets very little horizontal circulation, or none (this depends on how thoroughly the gravity generators compensate with height the centripetal force from the world's spinning: they would need to shoot upwards on the axis and shoot at an angle, and more powerfully, nearing the edges). Vertically, there would be only convection.

Now during the night the heat escapes into space, and the atmosphere cools off. During the day it warms up starting with the lower layers.

Under these conditions, light gets refracted in the atmosphere and gets bent upwards. This, combined with a horizon much farther than the Earth value of around 5 km, would cause the illusion of being at the bottom of a shallow cup.

At that point, I'd expect that the curiosity of pretty much any scientist regarding the actual shape of the world he's on would be quite aroused. Travelling some fifty kilometers with some device capable of measuring the Sun's angle with a high time precision would then quickly hint about what's happening. More subtle tests with the local intensity of the gravitational field would show it's artificial (actually, I suspect an artificial field with the needed characteristics of directionality just can't be produced. Perhaps, the disc might be made to orbit a massive black hole orbiting around the sun, so that it doesn't spin around its axis like a coin. The disc would need to be slightly rounded or the black hole very far, though).

LSerni
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One example of a similar scenario I've read is "Missile Gap", a short story by Charles Stross. This follows the reactions of the Cold War superpowers to the entire planet being transplanted onto the surface of a disk with the mass of 50,000 suns just after the Cuban missile crisis. The main effect observed is the altered geography, which shifts the balance of power as ICBMs become no longer in range, and the near-uniform gravitational field, which prevents any further space exploration.

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    Wow, thanks for this! I hadn't expected such a specific situation to already have a short story...I'll definitely be giving it a read. – Liesmith May 31 '16 at 13:13
  • And termite-beings, and the motives of the aliens who built such a thing... – JDługosz May 31 '16 at 21:30
  • Minor note: it has no effect on the story (because the characters aren't aware of it), but the planet wasn't transported: the planet was scanned by Sufficiently Advanced Aliens and then copied on to the Alderson Disk where the story takes place. – Keith Morrison Nov 25 '18 at 01:26
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Other clues will show up before this one does, but it's worth noting anyway.

Gravity might be weird anyway.

The generator accounts for essentially all of the gravity, and somehow projects* it up like a floodlight so you feel gravity only from the surface within meters of you. This will make the strength of gravity independent of altitude within a cone thousands of kilometers high. The tighter the floodlight, the taller the cone. The wider the floodlight, the farther from the edge gravity stops pointing down.

If you decrease the width near the edge, you can make a roughly dome-shaped region above the disc where gravity is actually stronger along the "surface" of the dome than within.

If you don't want this stuff to be true, then the generator has extra magic that makes its field violate the inverse-square law.

*It's a static field so nothing's really being "projected", but the floodlight analogy holds up pretty well otherwise.

MackTuesday
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  • The change in the earth's gravity as you go up is so small that by the time you notice it, you can already just see the shape of the world by looking down. In the international space station the strength of earth's gravity is still 90% of what it is on the surface, but in orbit you don't notice because you are constantly falling around the earth. A much weirder effect would be gravity suddenly ending when you leave the gravity generators 'projection'. – JanKanis Aug 15 '20 at 21:29
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Euclidean Geometry

On a sphere a triangle's interior angles add up to more than 180 degrees because of the curvature.

On a flat world, Euclid would rule supreme. An accurate survey would reveal that triangles have 180 degrees hence no curvature.

enter image description here

chasly - supports Monica
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  • this may sound esoteric but if scientists find themselves on a new world they will likely try to calculate this fairly quickly to find out how big a planet they are on. this is how we confirmed THIS planet is round. – John Aug 12 '22 at 13:35
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Most was said, but nobody spoke of seasons. If axial tilt is zero (the "coin" stands perpendicular to the orbital plane and spins like a top), there would be no season. However, if the planet is tipped and spins on a diagonal axis, it will be the same season everywhere. I agree, though, that other effects mentioned will catch the eye more quickly.

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It's the same time everywhere!

The expedition arrives. One person begins taking pictures of the night sky, rapidly determining the location of the celestial equator. I'm assuming the pole stars are harder to find, because they will be directly in the plane of the coin. They conclude they are on the equator.

The rover teams branch out in different directions in motor boats, hover craft, ultralight aircraft, and optionally robotic walking vehicles. They use inertial navigation (accelerometers) as a substitute for GPS, generating an accurate map of the landscape.

But which way is North? They are going in all directions. If they move east or west, the star overhead at base camp will have gone overhead already or not yet arrived, giving a sense of the planetary radius. If they go north or south, the celestial equator will appear tilted and a pole star will become apparent. NONE of this happens. The planet has an infinite radius and the local time is the same everywhere! (Infinite until they fall off the edge, anyway)

First they may consider something is wrong with their measurements, it's a very large world, they're in a Mimas-like flat spot. But the further they go the more impossible the data looks: no way to tell latitude with a mariner's astrolabe or any more sophisticated instrument. No way to tell longitude by the time. The world... is flat!

Mike Serfas
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The Clouds

Due to effect of the horizon, there'd be clouds approaching it. Since this place is flat and not round, it cannot have a horizon. So there wouldn't be clouds on the horizon. (There wouldn't be a horizon :O)

Atmospheric Effect

There wouldn't be day and night at the same time. The entire disc (if you will) will be either be at day or night.

The edge

There'd be an edge. Since it's not round and there aren't any buildings like in Pennsylvania or Virginia, it'd be easy to see too.

Vincent
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    Hi Aravind Suresh, and welcome. We like answers to add something not previously said in response to a question. This answer appears to merely repeat things that have already been said, though perhaps worded slightly differently. I would recommend that you add something not previously mentioned to this answer, such that it stands out more. That way, it is likely to be better received by the community. – user May 29 '16 at 16:06
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    Welcome to Worldbuilding Aravind! Several answers before yours seem to include all of the points you've listed here, so please check that your content in your answer has not been posted already before you post an answer to a question. – fi12 May 29 '16 at 16:23
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My first thought was observing the horizon, but others have mentioned that.

Second thought: You say there is artificial gravity, which I presume means a uniform force over the entire surface. Then you say there is a dome to hold in the atmosphere. If by "dome" you're implying a curved surface, then the dome is closer to the ground near the edges than at the center. Which means there is a taller column of air near the center. Which means the air pressure must be higher. If the scientists travel far enough, the difference in air pressure will be noticeable.

If the scientists travel far enough, sooner or later someone should notice that there is a fairly uniform average temperature over the entire world, rather than cold poles and hot equator.

Which brings to mind that sooner or later someone is going to try to figure out their latitude and longitude and calculate the size of the planet, at which point they're going to figure it out geometrically.

Jay
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  • Hmm...that's a very good point about the air pressure being very different in the center column...thank you very much for pointing it out! – Liesmith Jun 01 '16 at 06:39
  • If the center column has higher pressure, then it would expand outwards, creating a wind that radiates from the center to the edges in all horizontal directions. Either that would cause the air pressure to equalize in horizontal layers, or loop back up to the top and fall down again, creating a massive warped donut-like wind system covering the entire planet. However, since the central column of air would push outwards at every elevation, there would probably be no way for air to cycle back to the top, meaning equal air pressure at equal elevations. – Darcinon Jun 01 '16 at 18:29
  • @Darcinon I'll readily yield to someone with a better knowledge of the physics of this. But my thinking is: Say the dome is a mile high at the center. At the edges the height is zero. So at the middle you have a 1-mile high column of air exerting a downward force on anything beneath. Near the edges you have the weight of a few feet of air. The weight of the air will be proportional to the height of the column at any given point. This wouldn't create a wind because the force is pressing downward, and the ground is exerting an equal and opposite force upward. – Jay Jun 02 '16 at 05:30
  • ... The force I'm describing is vertical, due to the pseudogravity, not lateral. I presume the lateral force would be constant because of pv=nrt and all. – Jay Jun 02 '16 at 05:31
  • I'm no physics expert, so I can't say I'm completely sure I'm right. I think that the vertical gravitational force would compress the gas until the pressure of the gas counteracts it. The increased pressure in the center column would cause an outwards force as the system tries to equalize the pressure. It's not like the air molecules are in vertical stacks that can support their own weight without the molecules trying to escape; each air molecule's weight is supported by all the other air molecules at lower elevations. – Darcinon Jun 02 '16 at 16:25
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    The pressure will be the same along the entire surface. As an analogy: back in the day when the water mains was pressurized by a water tower, do you expect the pressure to only exist at the bottom of the water tower, with other water pipes having close to no pressure because they only have the few cm of the diameter of the pipe as head? – JanKanis Aug 15 '20 at 21:42
  • @JanKanis The forces exerted by an object are not equal in all directions. When gravity is pulling something down, it exerts a greater force downwards than upwards or to the sides. But an ounce of experiment is worth a pound of theory. Fill a dishpan with water. Submerge a glass in this dishpan so that it fills with water. Then turn the glass bottom side up and lift it so that it's half out of the water. What happens? You'll see that the water will stay in the glass even as that level rises about the level of the surrounding dishpan. ... – Jay Aug 16 '20 at 00:48
  • ... It doesn't create a downward current forcing the surrounding water up. (I'm trying to think of a way to measure the water pressure under the glass versus in the dishpan outside the glass with things I have handy at home.) – Jay Aug 16 '20 at 00:49
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    @Jay The force caused by pressure in a fluid is the same in every direction. The pressure depends on the height of fluid (directly or indirectly) above the point where you're measuring. In the case of the glass in the dishpan things get more complicated because there is also the atmosphere applying pressure to the water, and the glass is blocking some of that pressure. – JanKanis Aug 16 '20 at 12:08
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    As a different experiment, if you have a rainwater tank with a tap in the side, you can easily verify that the water pressure at the tap is caused by the height of the water above the tap level, even though there is no water directly above the tap. If the tap can be rotated you can verify that the pressure is mostly independent of if the tap is pointing upward, downward or sideways. Any other water container with a tap on the side will also work. – JanKanis Aug 16 '20 at 12:10
  • @JanKanis True, but like your water tower example, the water is pushing against air, which exerts much less force than water. Presumably the air is subject to exactly the same gravitational force as the water, so I don't think this experiment proves your point. – Jay Aug 16 '20 at 23:10
  • Agree with most of the comments that this makes no sense. If pressure was higher at the center than the edges, that by definition means there is an imbalanced net force pushing the atmosphere outward from the center. The result would be a perpetual wind radiating outward, but that would obviously eventually result in equilibrium - otherwise, the center would be sucked completely empty and yet still somehow have higher pressure. Pressure is only related to the depth from the highest point, not the depth directly above. – Nuclear Hoagie Aug 11 '22 at 17:38
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[The portal outlet would have to be near the centre; if it is near the edge, space will immediately look different in different directions, to the visitors, because of the different thickness of the air. (...Unless the air is perfectly translucent... which would raise suspicions.)]

[The disc must spin around its diameter, not its centre; otherwise, there will be dramatic centrifugal force differences with very obvious effects near the centre.]

[Anyone who looked through a telescope from a high point would be able to see (not automatically implying notice) that the horizon was infinite. The aliens would presumably compensate for this by making the landscape universally hilly (or perhaps slightly curved (inwards or outwards), or completely flat). Regardless, at least one scientist would probably start to wonder...]

I am thinking that the immediate obvious difference will be in the types of animal and plant. (If they are imports from a spherical world, then they will be okay initially.) The seasons have to do with, not only the axial tilt of the Earth, but also the differential sun heating from north to south... which would not work with a flat surface. That is... there would be no seasons. The scientists would begin to notice this after a number of weeks, but the animals would be obviously relevantly very different from Earth animals from day one; they would neither migrate nor change with the seasons. There would be only one mode of life, for every single plant and animal... not to mention the terrain. No scientist studying the flora or fauna could possibly miss this -- at least subconsciously initially, and probably consciously within 24 hours. (From there, I would guess it would be only a few hours until someone suggested the obvious but fantastic explanation, and only a few hours more until someone started working on checking it.)

[Of course, if there is anything that would give the game away easily, the whole scenario is suspect.] One might expect the aliens to compensate for this. The obvious easy way would be to make the ground more reflective in the north and south, but I imagine that that (in concert with the atmosphere issues) would have undesirable effects. However, nothing along those lines would work anyway, as seasonality near the equator depends on the sphere thing.

The aliens have to either engineer a whole artificial seasons system or just leave the thing as it is.

In turn, then, the obvious inference is that the homeworld of the aliens does not have an axial tilt. It would still have cold poles, though. Thus, that difference remains -- no seasons, but latitude temperature variations. This gives us a variety of different animals and plants, every last one of which is suited to only one temperature.

...And I shall stop there.

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The planet's magnetic field would be a lot different/non-existant

I think this is plausible, but I'm not sure about the specifics.

The Earth has a magnetic field because its full of churning molten iron. This makes compasses work, protects us from some radiation from space, and sometimes makes auroras.

I assume a flat artificial planet would not have any volcanic or tectonic activity, and thus no magnetic field. (Maybe there is an artificial one?)

But without one, everyone would be getting blasted with a lot more radiation every second, and some instruments might pick that up.

If they don't have proper detectors, then they could still see the effects indirectly. Maybe over time a lot of people get skin cancer. Maybe the radiation causes a much higher rate of computer errors than they expect. Airplanes usually have triple-redundant processors for essential computations because there is a higher likelihood of this kind of thing happening at 30,000ft than on the surface.

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There would be a few things, but one of the major ones would be an appeared incline as you moved away from the center. There is a great youtube video on this topic, and it's how I got this idea.

https://www.youtube.com/watch?v=VNqNnUJVcVs

The main point is up to about 1:53.

Jonah Cote
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    Could you talk more about this in your answer itself? We prefer answers to not be link-only - they should be able to stand on their own as an informative source without leaning on a link they're pointing to. – doppelgreener May 31 '16 at 08:30
  • This has been mentioned on other questions. The disk coukd be built to compensate by having more mass near the rim. – JDługosz May 31 '16 at 21:32