Flat Earthism

There are lots of stories around flat Earth theories – so many that I’ve lost interest in keeping up with all the various debunkings and origin stories. Since Ptolemy was working on longitude and latitude in the 2nd century AD, I’m willing to say our knowledge goes back at least that far and probably much farther.

Not to re-ignite the debate… I’d appreciate feedback as to whether or not my own personal debunking of flat Earth works or not. To describe it, I will have to resort to power-point, the premier tool of conspiracy theorists, everywhere.

When the moon blocks the light by getting between the sun and the Earth, we get a shadow. That’s an “eclipse.” When the Earth blocks the light falling on the Moon we have a “lunar eclipse”…

Let’s zoom in and look at what the eclipse would resemble if Earth was flat (assuming it’s not a pixel-thin plane!)

I just now realized that there’s a problem with the whole “sun rising, sun setting” thing if Earth is flat. What makes that happen? It seems that the only way that’d work would be if Earth-disk is flipping on an axis so it flips toward the Sun. Which would mean that if we saw a lunar eclipse we’d see Earth’s shadow looking kind of like an oblate spheroid.

Wow, stupid orbital dynamics are complicated! It seems a lot easier if you have more-or-less round things because they cast more-or-less round shadows always.

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Do the flat Earth people have an explanation for why it’s hotter at the equator?

I’ve been unable to determine if flat Earthers actually believe this stuff, or if it’s just a surrealist pantomime. If it’s a surrealist pantomime, I’m OK with that, but it seems that they’ve missed a point: earth is shaped like a Urinal. That explains a lot, especially Alabama.

I freely admit that I may have some of the thinking wrong. I’m just a computer programmer, not a physicist or a philosopher or a real scientist or anything like that. So please school me gently.

How deep would we have to dig the holes to get a smiley face-shaped shadow? (I realize we could do that if we still suppose a round Earth, but getting all the dirt out would be a lot more work than with a thin, flat Earth)


  1. says

    Anything that simple geometry can’t explain is subject to explanations with extreme hand waving, optical illusions and magic. You can’t win against a mind made of cement.

  2. felicis says

    So – the flat-earth eclipse – a line only works if it is edge-on to the moons orbit, but what if Urth is a disc (not square, as you have it), and the shadow is cast from behind onto the moon over the surface? You would get a curved shadow on the moon that way also…

    My simple response has been a rehash of Eratosthenes:

    In Syene, the sun is directly overhead. In Alexandria (500 mi N), it is about 7 degrees off. If the Earth is flat, what would the angle be in Byzantium? What about if the Earth is (roughly) spherical? Let’s go look at what it is.

    Or – vice-versa, given Syene and Alexandria, we can calculate the distance from the Urth to the Sun easily – how high is the sun using Syene and Byzantium? It’s different. How can there not be a consistent height for the sun?

    The response is that the Urth’s atmosphere distorts the path of light, or that it doesn’t make sense to assume the light rays are parallel, or – oh, gods know what… It’s too early to put myself in that mindset.

  3. komarov says

    Er, what if we rotate your model earth by 90° (make the plane vertical in the diagrams) and have it spin about the same vertical axis once per day? Sun- and moonrise should work as normal, then. So should eclipses, even if the moon is a (tidally locked) flat disc, too.*
    As for the temperature zones, the question is where the axis tilt goes – if any – and how the surface is mapped onto the disc. I don’t think something boring like “South Pole in the centre” would work, it probably would have to be something more complicated and fun, if you enjoy projections and coordinate transformations. (I’ve recently learned that I don’t)
    But if you keep the axis tilt (slightly off the vertical) and put both poles on the disc’s edge along the spin axis right on the edges then at least the seasons should still make some sense, at least in parts of the world. I just realised that I’m simply terrible at mentally modelling spinning disc-shaped map-projections.

    Oh, but I did just realise there’s another issue this model (and perhaps other models) have: equatorial velocity. It’s very useful for launching rockets into space, which is why spaceport are preferably places close to it. But in this model the equator is basically the disc diameter running half way in between the poles. That means equatorial velocity actually changes as you move along the equator, getting slower as you get closer to the disc’s centre, where it’s essentially zero. That means you can’t just set your spaceport up anywhere on the equator but want to be on both the equator and outer rim.
    If you actually do enjoy mapping challenges, this gives you another contraint to work with. Hence the world map has to fit on the disc such that:
    1) Both poles lie on the spin axis and the edge
    2) You can sail around the world, west to east (whatever that means) without turning into space debris midway
    3) Time zones, temperature zones and seasons still work
    4) The KSC, Baikonur and Guiana Spaceports (among others) all have to lie reasonably close to the equator and the disc’s edge

    Nonsense theory or not, there’s probably a PhD in it for whoever manages this. Bonus points for figuring out how on (flat) Earth a geosynchronous orbit is supposed to work in all this.

    *It’s the real secret NASA’s keeping** and what actually went wrong on Apollo 13. They missed their landing site close to the edge, so they just pretended to have an accident that required re-routing straigth back home.
    **Not counting Aliens, Global Warming and the fact that The Soviets Were First But Forgot To Bring Their Flag And Were Too Embarrassed To Say Anything. You can tell it’s true because of all the capital letters.

    Re: Lofty (#1):

    Anything that simple geometry can’t explain is subject to explanations with extreme hand waving, optical illusions and magic. You can’t win against a mind made of cement.

    If I may be so bold, I believe quicksand is a more appropriate analogy. The more you struggle the worse it gets, right until you suffocate. I should know, I just accidentally did it to myself…

  4. felicis says

    One interesting aspect of Geometry (from Gauss) is that using only intrinsic measurements, we can determine global (well – large scale) curvature. A simple example – construct a straight line running E-W at the equator (say 6 miles), turn right angles at both ends and head North – again, 6 miles. The ends of those two sides will not be 6 miles apart, though you can turn a right angle from either end and get to the other side. That is – you create a 4-sided figure with four right angles and exactly three sides of the same length – such measurements imply positive curvature (such as a sphere).

    Consistency of such measurements taken anywhere on the earth also imply a high degree of symmetry, yet another argument for (rough) sphericity.

    Very fine measurements actually show the Earth as kind of pear-shaped. There is no way at all to get the Earth is flat, even with relatively short measurements (six miles is the length of the edge of a township – and in Illinois, the state roads follow these lines and every six miles you have to turn right, travel a bit, then tun left to get onto the nest northward township line (a relic of how the townships were laid out originally in the 1800s, itself caused by the curvature of the Earth).

    You could probably reasonably measure the curvature with as little as a half-mile edge and non-specialized equipment.

  5. Dunc says

    Other problems with a flat Earth: integrate Newton’s law of gravity over a finite plane, and you find that the gravitational force vector points to the centre of the plane. This is also (partly) why most forms of sci-fi artificial gravity don’t actually make any sense…

  6. Rob Grigjanis says

    If you’re actually interested in debunking flat earth (and I can’t imagine why you would be), you should research what the believers say, rather than tossing out your off-the-cuff ideas to a roughly-spheroid audience. Maybe send an email to the Flat Earth Society?

  7. Rob Grigjanis says

    felicis @4: Or you could arrange an experiment with distant friends. Call them and ask for the angle between their horizontal plane and an agreed-upon celestial object right after making your own measurement.

  8. Rob Grigjanis says

    Dunc @8: It doesn’t point to the centre of the plane except at the centre. It tilts as you go away from the centre, like this. That’s for an electric field, but it is also a 1/r² force, so the integration would be proportional, just in the opposite direction.

  9. NYC atheist says

    No, no, no, the north pole is the center and Antarctica is a circular ice wall keeping the ocean in. Gravity isn’t real, the earth is accelerating upward at about 9.8 m/s^2. And no-one has ever been to space, NASA is a sham. Wake up sheeple!

  10. Pierce R. Butler says

    A flat disc with a rim around it (see # 12 above) practically demands to be flung with a high rate of spin.

    The most urgent issue of our time is whether our planet will be caught by another God, or a Dog – or get stuck up on some cosmic Roof for the next several eons.

    (I asked a small-d dog for his prognosis, and he replied, “Roof! Roof!”)

  11. says

    To believe in the concept of a flat earth, you would to have to actively deny the existence of gravity as we understand it, and make up some new forces to keep us on the disc.
    Only on a sphere would gravity always point down. On a disc, gravity would be tilted towards the disc center. At the equator it would be tilted 45% to the “flat” ground, making walking really tricky. And it would get even worse farther south (or north if you put the Antarctic
    in the middle).
    But throwing out Gravity means also throwing out Relativity (both Special and General).
    Which, besides many other things, means we are not longer able the explain the color of gold.
    So, dear flat earthers, how do you explain the color of gold?

  12. says

    @NYC atheist
    The accelerated disc explanation is the funniest flat earther idea of them all.
    An object accelerated by on g would reach light speed after only a year. After 4 billion years you would be 4 billion times faster than light*, making it quite strange that other light sources outside earth are visible to us. The physics you would need to assume to make this possible is mind boggling.

    *Relativity has already gone out the window of course, so no universal speed limit.

  13. Rob Grigjanis says

    Turi1337 @14:

    But throwing out Gravity means also throwing out Relativity (both Special and General).

    Since Special Relativity is formulated without any reference to gravity, how is it thrown out?

  14. says

    Rob Grigjanis@#9:
    If you’re actually interested in debunking flat earth (and I can’t imagine why you would be), you should research what the believers say, rather than tossing out your off-the-cuff ideas to a roughly-spheroid audience.

    I wasn’t interested in debunking flat Earth – I’m just playing with ideas. As John Morales pointed out at #2, they probably already have some ‘explanation’.

    The real question I’d like a straight answer on is the one I probably can’t get, which is: “are you kidding?”

  15. Rob Grigjanis says

    Marcus @18: They’re talking about a situation in which both sun and moon can be seen above the horizon during the lunar eclipse;

    A selenelion or selenehelion occurs when both the Sun and the eclipsed Moon can be observed at the same time. This can happen only just before sunset or just after sunrise, and both bodies will appear just above the horizon at nearly opposite points in the sky. This arrangement has led to the phenomenon being referred to as a horizontal eclipse. There are typically a number of high ridges undergoing sunrise or sunset that can see it. Although the moon is in the Earth’s umbra, the Sun and the eclipsed Moon can both be seen at the same time because the refraction of light through the Earth’s atmosphere causes each of them to appear higher in the sky than their true geometric position

  16. says

    Rob Grigjanis@#19:
    I didn’t even know that was possible! Thanks for the explanation.
    (I thought they were talking about refraction through water, because they started giving the example using water, and that didn’t make sense to me)

  17. Dunc says

    Rob, @11: Yeah, that’s basically what I meant… It’s just is been nearly 30 years since I did the relevant maths / physics, and I was very drunk at the time. Thanks for the clarification.

  18. StevoR says

    @Siobhan : “what happened to the flat earther guy who built a rocket to “prove the earth was flat”

    Latest I’ve seen :


    NPR reports that the Bureau of Land Management (BLM) “got wind” of the plan after the Associated Press reported Hughes’ announcement. The agency shut down Hughes’ launch, which would have taken place on public land.

    See also : https://www.youtube.com/watch?v=xDmL6Qjkbfg

    & via space dot com’s article on it (Flat-Earther to Launch Himself in Homemade Steam Rocket Saturday
    by Mike Wall, Space (dot – Ed) com November 22, 2017 06:49 am :

    Update for Nov. 26: This launch has been postponed to no earlier than Tuesday (Nov. 28) after a federal agency refused to grant the stuntman permission to conduct the experiment on public land. He is now moving the launch site to privately-owned land a few miles up the road on Route 66, he told The Washington Post.

    Plus via David McAfee :

    So the launch has been postponed. Whether it will happen at all whether he was sincere or just out for publicity & bucks is, uncertain I’d guess. He has made previous similar launches to his proposed one in the past (complete with pretty poor parachutes) so, maybe?

  19. says

    I didn’t realize his launcher was an old trailer home. How… creative.

    My guess is he’s the Ken Ham of rocketry. Hey, maybe they should team up!

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