A relative of mine has recently introduced me to the modern flat earth theory, which she believes in. Setting aside for the moment that it is ridiculous, and that sending up some balloons with cameras on would provide evidence to the contrary, how could one evidence that it is in fact spherical from ground based observation?

I immediately thought about citing the observations of Aristotle and measurements of Eratosthenes, something that one can do themselves, but of course they have an answer for that regarding curving light to explain variation of the sun's elevation with latitude. Also refraction backed up by observations of ships on the horizon appearing to be above the horizon (due to refraction) and so light-based observations of a curved body of water are out. To make it even harder, the belief has been adjusted to allow for a flat earth that curves slightly but is not spherical, so objects gradually disappearing over the horizon aren't proof and neither is observing the curvature from a plane! For every argument there is a counter argument, and I, as a layman, don't know how to prove e.g. that the light isn't curving as described.

Without getting into countering non-scientific flaws such as the massive amount of government-level collusion that would be needed to maintain this conspiracy, how might one go about demonstrating it or designing a practical experiment for which the conclusion cannot be refuted. Is this even possible when someone can claim e.g. light curving through the atmosphere in a particular way, without having to back it up? I'm not familiar enough with scientific theory to know how one establishes certainty, or if it is based on a balance of probability (i.e. more proof of one theory than of the contrary).

Note: This is a thought exercise only, I do not expect to actually convince my relative while she is going through a personal crisis for which this is one of many symptoms, that is a separate issue. She holds a degree in aeronautical engineering so it isn't caused by a lack of intelligence.

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    $\begingroup$ Some suggestions here: physics.stackexchange.com/questions/26427/… $\endgroup$
    – user2821
    Dec 10, 2015 at 19:59
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    $\begingroup$ related: earthscience.stackexchange.com/questions/4999/… $\endgroup$
    – casey
    Dec 10, 2015 at 20:01
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    $\begingroup$ To be pedantic the Earth is an oblate spheroid, rather than spherical. But I think the simplest is the angle of sun to the observer at the same time (midday is easiest) depending on latitude. To get the a 90 degree angle at the pole (assume equinox day), the flat earth would have to be much larger than we see, though I expect this is covered in greater depth in the answers noted in the other suggested SEs. $\endgroup$
    – Siv
    Dec 10, 2015 at 21:21
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    $\begingroup$ Isaac Asimov wrote "When people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together." $\endgroup$ Dec 29, 2016 at 9:35
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    $\begingroup$ Once you are at the stage that somebody is finding ways to disbelieve good evidence ("answers involving curving light" and so forth), I'm not sure there's much point in searching for more evidence. As with so many issues today, if somebody is determined to ignore scientific method, then offering them more science is not going to help. $\endgroup$ Jan 7, 2017 at 17:01

12 Answers 12


To answer my own question based on the useful comments here, my favorite methods were:

  1. The earth's shadow cast on the moon during an eclipse. It is easy to observe and the flat earth counter argument is so insane that if it is offered you should just walk away.
  2. Shadows differ from place to place. The same experiment as Eratosthenes but you can carry this out locally with a piece of large card, 2 obelisks and a light source casting a shadow. Now bend the card and observe the change in shadows. The same effect could then be observed on the earth's surface. The counter argument of curved rays of light is weakened by the fact you can reproduce it locally.
  3. triple-right triangle: You move in a straight line for a long enough distance Turn right 90° degrees, walk in that same direction for the same distance Turn again to the right 90° degrees and walk again the same distance After this you'll end up at the starting point. This is not possible on a flat surface since you'd just be "drawing" a half-finished square. Not sure how practical this is as you'd have to walk a long way!
  4. Although not technically about the earth being flat, in a flat earth theory the sun orbits, or at least moves over the earth. A simple way to discount this is observing parallax with surrounding stars.
  5. It is not too difficult to prove the earth curves at least, such as by observing more objects over the horizon the further you go up. And even measuring the curvature is not difficult. Thus I believe a person could drive the length of the African continent, observing the curvature and measuring the straight line distance, and modelling that alone would show the earth curves beyond what could be acceptable on a flat earth, without all the water running off the edge!
  6. One I haven't seen mentioned yet is showing that the flat earth map cannot work. In a flat earth, apparently, the north pole is at the centre and south pole is a ring around the outside. Pick a land mass close to the south pole, and another on the opposite side of the map. The distance you would need to travel to reach one from the other by e.g. flying east around the map would be enormous and not congruent with the flight times or shipping times in real life.
  7. Earth is warmer near the equator, for obvious reasons in a non-flat world but the counter argument would have to be pretty imaginative.
  8. Sunrise and sunset do not happen at the same time for everyone on earth. The difference in timezones, which can be observed by taking a trip to different countries, cannot reasonably be explained by a curved but nearly flat earth.
  9. Experiments with gravity, but flat-earthers reject the complication of gravity (things drop just because). So I avoided this one, but it would be a compelling way to demonstrate why people on the other side of a spherical earth are not on their heads.
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    $\begingroup$ The eclipse shadow could be the result of a disc-shaped Earth. It proves the Earth is shaped like a circle, but not necessarily spherical. $\endgroup$ Dec 11, 2015 at 9:50
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    $\begingroup$ As the moon moves across the sky, and especially when it is closer to the horizon, the shadow cast wouldn't be consistent with a disc shaped earth. $\endgroup$
    – dutch
    Dec 11, 2015 at 10:04
  • $\begingroup$ Also, if the Sun were to orbit a supposedly flat Earth, it would rise & set at the some point on the horizon. However, the setting & rising points of the Sun change with the seasons because the Earth is spheroidal, its axis is tilted & it orbits the Sun. This is additionally supported by the angle the Sun makes with the horizon as it passes overhead: in winter it is low & in summer it is high. $\endgroup$
    – Fred
    Dec 11, 2015 at 10:15
  • $\begingroup$ @Matt: True, a vertical circular disc would cast a curved shadow, but how then would we & all other life forms on Earth live on a vertical plane, wouldn't we slide off? As far as I'm aware flat earth believers hold that the Earth is horizontal & flat. $\endgroup$
    – Fred
    Dec 11, 2015 at 10:21
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    $\begingroup$ Observing two shadows isn't sufficient to prove a spherical Earth: you can get the same effect with a nearby Sun. You need a minimum of three shadows to prove a non-flat Earth, and infinitely many to prove a spherical one. $\endgroup$
    – Mark
    Jun 19, 2017 at 6:11

I'm sorry that this answer will be unsatisfactory and, strictly spoken, off topic, but I want to give it anyway.

The answer is: You can't. Don't waste your time. Your relative has developed a paranoia. Not only is this not an isolated earth science issue; it is not even an issue with science at all. Instead, she has dismissed our common everyday frame of reference wholesale. She must assume a lot of things along with a flat earth:

  • As you say, a massive conspiracy dating back hundreds of years, involving governments as varied as absolute monarchies, Hitler's and Stalin's regimes and modern democracies. This conspiracy involves government fraud on a large scale, and a secret cooperation between all governments in the world. This renders all of our commonly accepted news meaningless, including news about economics and politics.
  • No moon landing, of course. No ISS. No astronautics as we know it whatsoever. Half of NASA's employees are liars, the other half are being lied to like everybody else and duped into performing an elaborate cargo cult.
  • Meteorology and climate models are based on the concept of a solar system with a near-spherical earth. Their predictions are therefore meaningless.
  • Relativity, and physics in general, is wrong (light bends, the direction of gravity towards the edge of a flat earth is obviously not as it should classically be, whatever).
  • If the earth is not a round body shaped by gravitation, all cosmological theories about the formation of star systems, and thus cosmology as such, must be wrong. (That also follows from her rejection of the Relativity Theory.) Then she'll have a hard time with the age of earth as well as the fossil and geological record (oh, all of geology is wrong as well!). Why don't you ask her who created the earth?

This belief of an alternate reality behind the scenes is paranoid. It also lets other conspiracy theories latch on with ease:

  • Climate change is not happening, or is not happening the way we are being told, or is not happening for the reasons we are being told.
  • Ask her about chem trails. They may be needed to adjust a few things. And since all commercial aircraft pilots are undercover government agents anyway lest they betray the fact that they actually do not cross the poles on certain intercontinental flights, they can as well produce chem trails on the side.
  • Ask her if the lying government also keeps people intentionally sick (maybe with the chem trails!) and suppresses simple, cheap medicines.
  • On a more unappetizing note, because major players in the sciences and finance system are Jews, there is an overlap with classical anti-semitic conspiracy theories (who else would secretly rule the world?).

Whatever you come up with will be countered with a new idea; you give a few examples of that pattern in your question. Occam's razor alone would do away with such complicated nonsense.1 It was sufficient to convince the catholic church, eventually.

xkcd illustrates this nicely:

enter image description here

A paranoid person is actually not really interested in science. A scientific answer is simply inadequate: It does not address the issue! (An example for an adequate answer is "If the earth were flat, all your horoscopes would be wrong!").

One possible psychological trigger for the paranoia is when one learns that long-held supposed truths are actually wrong. Developing scepticism as a response is in order, but the pathological response is to suddenly see all of reality differently, like in an ambiguous picture:

enter image description here Let me add that there are plenty of reasons to be sceptical, because there is so much bad science out there -- most nutritional advice of the last 50 years is nonsense, for example, and most cancer screening did more harm than good. To me, that is an incentive to work towards better science; for others, it's a stumble which makes them see the world differently when they look up from it.

1 Occam's razor is actually the answer to your question, which only makes it to a footnote in my answer. Assuming roughly spherical bodies which follow gravity's pull in free fall makes a lot of observations fit very elegantly. It is difficult to come up with a *single* (or a handful of single) irrefutable proofs; defending its alternate reality, the paranoid mind is inventing counter-arguments to any single argument. But comparing the two theories *in toto* makes the judgement irrefutable. It is, in essence, the difference between the Ptolemaic and Copernican models of the world, and the jury is not out any longer: Copernicus' model is constructed "procedurally" on the basis of a few basic principles. Ptolemaeus' model, by contrast, needs many arbitrary, intricate rules for the movement of celestial bodies. Occam's razor shaves all that away.— This combining of many observations into a theory is how the scientific method works in practice. Single contradicting observations do in practice *not* immediately disqualify a theory, how ever much the mathematicians among us would prefer that. This could be seen as a generalization of Truzzi's principle: Extraordinary claims need extraordinary proof.
  • $\begingroup$ Although not directly an answer, a very good answer nonetheless. Take my upvote. $\endgroup$
    – Gimelist
    Feb 5, 2016 at 9:56
  • $\begingroup$ That picture is so ambiguous, its purpose defeats me -_- $\endgroup$
    – cr0
    Aug 23, 2016 at 22:51
  • $\begingroup$ I think you're right that you can't prove Earth is round. According to youtube.com/watch?v=JHQOX8EVNmE, banks were cheating so information about what people saw that demonstrats it's round could be a lie as well. The pendulum in the experiment precessed because it didn't start with a position and velocity that would make it exactly pass through the point at the bottom. I have proof that Earth is round which is that I saw a cloud cut off by the horizon of a lake but I don't suggest that dutch prove it to their relative because they might really not want to learn that Earth is round. $\endgroup$
    – Timothy
    Nov 29, 2016 at 23:20
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    $\begingroup$ Unfortunately, people who ascribe to these "theories" tend to follow Trump's Razor rather than Occam's. To review, Trump's Razor: ascertain the stupidest possible scenario that can be reconciled with the available facts. $\endgroup$
    – Tim Nevins
    Sep 20, 2017 at 17:24
  • $\begingroup$ The idea that the Catholic Church condemned the idea that the earth is round is revisionist pop history at worst, and a gross oversimplification at best. Not sure why you felt it necessary to say. $\endgroup$
    – Jeh
    Jun 21, 2021 at 14:33


Skype someone at least 10 time zones away. Ask them to point the camera at the sky.


This actually works really well for a psychological reason as well. Its easy to deny abstract arguments, its difficult talking to someone and denying what they claim is their experience.

  • $\begingroup$ Curious why the -1? $\endgroup$ Dec 2, 2016 at 18:44
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    $\begingroup$ I'm not the -1, but I'm not a +1 either. You don't go into how it proves it. The fact the sun and other objects are in different spots in the sky in different locations would be explained away by a near-Earth sun causing daylight differences (or by a rotating flat Earth). I think with 3+ properly selected locations, you could start to disprove flat Earth with the equivalent of the three sided triangle on a sphere reality, showing the sun positions don't line up right. $\endgroup$ Jul 2, 2018 at 11:16
  • $\begingroup$ @JeopardyTempest daylight differences, but not sunsets and sunrises, if the sun is rising at bobs house and still high in the sky at your house the only explanation is you are both living on a curved surface. $\endgroup$
    – John
    Feb 20, 2021 at 14:14
  • $\begingroup$ @John looks like they try to form an answer for that here. Regardless of its validity, it may make it hard enough to convince people on that topic :-( $\endgroup$ Feb 20, 2021 at 23:31
  • $\begingroup$ @JeopardyTempest I know a few flat-Earthers but none of them believe in a rotating flat Earth. All of them believe that it's the Sun that orbits around the Earth. I suspect above 90% of flat-Earthers think this way. $\endgroup$ Aug 13, 2023 at 8:18

Just after sunset, call a friend some number of time zones to the west and ask them where the sun is in their sky. Or, just before sunrise, call a friend some number of time zone to the east and ask them where the sun is in the sky. Then, think about why the sun is at different heights for you and for your friend. The more time zones this experiment crosses, the harder it will be to explain this as a feature of a flat earth.

  • $\begingroup$ I believe they explain this away by using a sun very near Earth, such that it can't be seen beyond a certain distance from it. But indeed, it's a start, as with enough observations you should be able to show the flat-Earth map/sun model don't line up, and they have no way to rectify this without using a 3-D Earth. $\endgroup$ Jul 2, 2018 at 11:20
  • $\begingroup$ Indeed, if the Earth were flat, although sunrise on the near side might occur slightly before the far side, due to mountains etc. as soon as it reached any appreciable height it would be visible everywhere, certainly mid-day should occur for everyone at the same time. I've also heard it argued that the sun is a "spotlight" only pointing at parts of the Earth at a time. But then the sun would appear to "rise" in the middle of the sky as it came into view for you, not always at the horizon. $\endgroup$
    – komodosp
    Jul 15, 2022 at 12:44

The simplest method I can think of is to observe a hand-held global positioning system ('GPS'), which shows the position of visible satellites, directly overhead, and at various angles from the vertical. Once satellites disappear over the horizon, they reappear again exactly in accordance with an orbital trajectory around a sphere. Secondly, go to Google Earth - a composite of satellite photographs - and take a spin around the world. At all points the Earth appears as a globe. How is this possible if the Earth is flat? Thirdly, there are more than 100,000 commercial flights per day, which can be tracked on sites such as Flight Aware. Not one of these flights has ever seen an edge to the Earth. How come, if the Earth is flat? Fourthly, the sun and all the planets and dwarf planets have all been examined by probes and found to be spherical (more or less). On what basis should one expect the Earth to be any different? Fifthly, apart from minor purturbances caused by local geology, the Earth's gravity is pretty much uniform everywhere. How can this be possible in a flat Earth where the mass distribution would be very heterogeneous?

There are many more possible tests, but as you say, one can't change the minds of such people. 'Flat Earthers', like creationists and climate change deniers, have already made up their mind, and don't want to be confused by the facts.

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    $\begingroup$ Thank you for your thoughtful comment, however the use of GPS technology and looking at a website isn't really a way to observe a spherical earth for yourself as you are relying on data and images from a third party. I realize the idea of the data being faked is preposterous, but the exercise was about how one could determine it for themselves. $\endgroup$
    – dutch
    Dec 11, 2015 at 9:48

Major problems with sunlight\energy\temperatures for the "southern Hemisphere". The Flat Earth Society offers this suggested map of a flat Earth and a rough idea of how seasons would work:

enter image description here enter image description here

But because of the larger radius of the SH Summer circle, the sun would have to move faster to complete a circle in 24 hours during December. That would mean less sunlight per area in the southern hemisphere (or putting it another way, the same amount of solar energy is given onto a larger area in the southern hemisphere, meaning less energy per location). And that means colder temperatures.

For that matter, that larger circle should mean the sun moving through the sky more quickly there, and thus shorter days despite being nearer to the central path?

The one option to keep seasonal temperatures balanced would be moving the sun closer to give more heat, but that would mean even shorter daytimes. And either would cause more asymmetry in seasons, day length, etc at the Equator and between the summer and winter comparisons.

  • $\begingroup$ As far as I've seen Flat Earth subscribers often suggest that planes not flying between southern Hemisphere locations hints at a conspiracy by suggesting they are much further apart than indicated on a globe. But the sun does the work for us, traversing that same path every day, and if those locations were truly further apart as suggested, there would be large consequences in day length\energy\temperatures that don't appear at all in places like Sydney, Buenos Aires, Sydney, and especially at the more distant parts of southern Chile\Argentina $\endgroup$ Feb 22, 2021 at 21:50
  • $\begingroup$ I found youtube.com/watch?v=f8DQSM-b2cc gave some interesting thoughts on the worth of skepticism, even if at times venturing off a bit, and some other thoughts on the topic worth consideration. $\endgroup$ Feb 22, 2021 at 21:50
  • $\begingroup$ Of course another easy way to dispute a map like the one shown above, without being unduly hindered by the silly "they don't fly direct longhaul flights across the Southern Hemisphere" (so it must be a conspiracy?), and without having to resort to your own boat trip... is to just verify the distances across places like South Africa, Patagonia, and Australia... they aren't the great expanses compared to the northern NH that this map shows. And if that fails to convince, take a boat around the globe at = latitude (verified by things like stars?) and can see it's not enormous compared to the NH. $\endgroup$ Mar 17, 2023 at 23:15
  • $\begingroup$ More of direct examples: it's only under 2k miles from SW coast of Angola to NE coast of Mozambique straight across... 2500 mi from US WA coast to E ME, or 2800 mi from AK panhandle to E Newfoundland, or ~1000 mi from Norway to White Sea. And about 300-400 mi across the heart of Patagonia vs 250 mi across UK from SW Wales to Yarmouth or 300 mi across Iceland. This map just doesn't suggest that (and can't, since SH is required to be bigger to make the shape). They can prove/disprove in 2 trips if they are vehement, or offer to together call random people in those spots to ask how long a trip. $\endgroup$ Aug 13, 2023 at 8:48
  • $\begingroup$ I'll throw out one more thought. What would explain the Northern Lights??? Can't be things particularly from the sun, as the North Pole is the littlest exposed to the sun when night if it's a small nearby object? $\endgroup$ May 11 at 6:21

If you can get one dumpy level (surveyor level), it is very easy.

Place the dumpy level in one flat area and take the level from one point and transfer to another one. Try to do it as far as possible. At this stage it is suppose that you have 2 points on the same level.

Then place the dumpy level as close as you can to one of this points and transfer again.

You will get a deviation of 1.5 mm at 100 meters.

Why? The Earth is an spherical body so the gravity is radial. The gravity in one point have no the same direction that the gravity at 100 meters...

How can you explain this gravity deviation on a flat body?

The funny issue is that it happens in the complete planet... How flat-Earth defendors can explain it?

Yo can do the same issue with a laser level, even, with a hand level and one laser pointer.


On a flat earth, pendulus will maintain its normal direction, on a rounded Earth, this normal direction is changing as well as the difference of elevation between 2 points, as the pendulus become tilted.

Automatic level

Regarding this 1.5 mm every 100 meters... Mathematics: 100 meters * Atan (100 m / 6370000 m). Assuming an average radius of 6370 km for Earth, every 100 meters at the surface you are tilting the gravity 1.5 mm from the gravity 100 meters away in any direction. This phenomena it is registered in the whole planet.

  • $\begingroup$ Perhaps you could explain a little more for us general public (on this topic) of how a dumpy level works in basic, so that it gets this 1.5 mm difference? I guess the picture kind of does. But how do you know you're at the same elevation at each point? Just helps to have a small bit of background to surveying equipment for those of us who have no clue! $\endgroup$ Mar 11, 2023 at 0:12
  • $\begingroup$ A dumpy level works with a glass prism suspended, so gravity can pull from it. Main idea is that it is a telescope with this prism on its internal mechanism, so when you are close to an horizontal position, telescope level itself to ensure a completelly horizontal view against gravity. As Earth is not a flat surface, as soon as you transfer elevation between 2 points, the position of the level is relevant, as the gravity will not exactly match and the difference of elevation too. $\endgroup$ Mar 12, 2023 at 2:11

How's the weather?

The circulation of winds around high and low pressure centers is driven by the Coriolis force, which occurs on rotating bodies. This of itself does not exclude a flat Earth, for the Coriolis force can occur on a rotating disc (and that model actually does account for the stability of the Lagrange-point objects in space that are now known to follow the orbits of most planets). But the Coriolis force on a rotating disc is uniform in magnitude and direction, and weather observations on Earth disagree with both claims. The apparent dependence of wind circulation on latitude and the reversal that occurs when you move from the Northern to the Southern Hemisphere are instead more consistent with a rotating sphere.


I proved this to myself during a fishing trip a couple of years ago. I took a sequence of pictures of a well-known suspension bridge that could be seen from miles away (the boat actually passed under it). The suspension part in the middle is much higher than the ends.

first in sequence

As I got farther and farther from the bridge, first the ends disappeared beyond the horizon, as did the lighthouse and bottoms of the suspension section's massive concrete anchors.

second in sequence third in sequence fourth in sequence fufth and last in sequence

If the Earth were flat, good binoculars could have picked out the features that disappeared. But the curvature of the Earth was in the way. Eventually the bridge disappeared altogether.

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    $\begingroup$ I love it! Kudos for data! Of course, there could be a high density unobtaium shelled alien spacecraft under the water so vast that its gravitational mass perturbs the local geopotential and induces a local curvature only, but... :-) $\endgroup$
    – uhoh
    Aug 13, 2023 at 7:51

There are some recommendations in the following videos:

and especially

which includes suggestions like repeat Eratosthenes' experiment using three wells instead of two

enter image description here

watch an eclipse

enter image description here

or watch a ship sail off into the distance slowly drop below the horizon.

enter image description here


One of the simplest ways (not working I think): Ask them how can the Moon shine like a crescent if it's a flat shape like the Earth?

A little harder (better working): Go on a ship journey with your flat-Earther friend from a port and come back to the same port after months. Also, in this way they will find out there is no sudden edges on Earth.

The hardest way (works I think): Ask them to become astronauts so that they go to space to see the Earth as a sphere by their own eyes (a sphere has shadows and/or lights on the edges just like a ball; just like a crescent Moon). Also, they can orbit around the Earth as astronauts parallel to the Equator or the Greenwich meridian. If parallel to the equator they will come back to the same spot after completion of an orbit just like the ship journey (of course, this time with a little error because of the rotation of Earth). And if parallel to the Greenwich meridian they will see the North and South Poles in each semi-orbit respectively.


We can see the Moon's shape, right? We can see the Sun's shape too, right? And lots of other planets through telescopes? Does any of those looks flat to anyone? I guess not! Then, thinking further, I guess Earth cannot be flat...

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    $\begingroup$ We can see that they are circular; however, they are not obviously spherical. If you have some methods to prove that they can appear spherical, then please edit your answer to include these sources. $\endgroup$
    – L.B.
    Jul 4, 2016 at 0:06
  • $\begingroup$ @L.B. But the Moon moves, right? Any doubt about this fact? I guess not... Then, you can establish a fixed point on the Moon. Wait about 24 hours, and in the meantime, you can see the Moon moving in a circular manner, then suddenly, the fixed point re-appears. What this can mean? That the Moon is flat? $\endgroup$ Jul 5, 2016 at 20:12
  • $\begingroup$ Yes, but, theoretically, do we have a way to prove it doesn't simply move side to side? (By the way, I do not support the flat earth theory, I simply wanted to make a point). $\endgroup$
    – L.B.
    Jul 6, 2016 at 21:10
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    $\begingroup$ @L.B. Ohh, that's for sure! I didn't meant to consider myself a smart person. I did not made any research in this domain, and even if I would, there is no way I could find the ABSOLUTE truth. And I do too consider the humans aren't no were near to find that ABSOLUTE truth. Those are just approximations, which can be closer to the truth, or light years far. $\endgroup$ Jul 9, 2016 at 15:57
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    $\begingroup$ @DanCostinel coincidentally, the moon would just wind up frustrating your argument! A point on the moon actually won't ever rotate behind the moon from our perspective... look into the concepts of dark side of the moon and even libration if you want to get more detail, but basically you'll see the face never change, except over days it slowly wobbles (upload.wikimedia.org/wikipedia/commons/e/e6/…). Over the course of a night, you'd see basically the same surface at moonrise as at moonset. So this might not be the best demonstration to use! :-D $\endgroup$ Dec 1, 2016 at 8:13

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