# How to prove the earth and moon isn't flat? **URL:** \ **Category:** Factual Questions\ **Created:** [March 4, 2014, 11:41am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819 "2014-03-04T11:41:09Z")\ **Posts on this page:** 20\ **Page:** 3
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 5, 2014, 3:02pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/41 "2014-03-05T15:02:24Z")
> [@Saint\_Cad](#): > > You’ll note in my post about it, I went further and calculated the distance to the Sun assuming a flat Earth. > > Absolutely wrong. A person at elevation can look over the lip of the flat Earth and see the Sun earlier. Do this. Draw a segment (representing the flat Earth and label the endpoints A and B. Draw the perpendicular bisector and label the intersection M. Now draw a point on the bisector above M and call it N. > Draw ray NB and label any point past B as O. > Extend the segment AB past B to make it ray AC. > > If the sun is anywhere in the angle CBO then person at point N sees it and a person at point M does not. > > This can be generalized to any perpendicular to segment AB except at the endpoints. > Therefore the Earth is flat. > Quod Erat Demonstrandum You’re correct. I was thinking of an infinite plane. > [@Saint\_Cad](#): > > Oh and by the way on the real round Earth - the person on top of the pyramid sees sunlight before the person on the ground - not the way you describe it. I described a setting sun. The person on the ground would see the sunset before the person at the peak, and therefore wave their flag before the person at the top. It would, of course, be opposite for a sunrise. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 5, 2014, 3:04pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/42 "2014-03-05T15:04:23Z")
> [@njtt](#): > > Aristarchus’ estimate of the distance of the Sun (or, rather of the relative distances of Sun and Moon) was however, hugely inaccurate, whereas Eratosthenes estimate of the size of the Earth was amazingly good. Aristarchus estimated the Sun to be only about six times as far away as the Moon is. His mathematical analysis of the problem (which does not require trigonometry of the modern type - which was not developed until many centuries later) was sound. However, his measurements were not so good, and this is one of those situations where a tiny error in measuring can lead to a huge error in the final result. > > In any case, Aristarchus, like Eratosthenes, was living at a time when the sphericity of the Earth had long since been taken for granted. Agreed, which is why I mention using trigonometry and Huygens’s method. But, with that, you’d need telescopes. They didn’t come around until the early 1600s; though, grinding and polishing your own lenses wouldn’t be impossible. ---
**Author:** ![ftg](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ftg/32/2801_2.png) [@ftg](https://boards.straightdope.com/u/ftg)\ **Post date:** [March 5, 2014, 6:00pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/43 "2014-03-05T18:00:06Z")
Re: a Foucalt pendulum. > [@Mangetout](#): > > I think that would demonstrate that it’s in motion, but not its shape. But the period of rotation changes with respect to latitude. You’d have to move it around and get different timings, but it would show that something was happening wrt latitude. The simplest explanation being a round Earth. On a flat Earth, it would rotate at the same rate regardless of location. (With the rate being 0 for a fixed Earth.) BTW: The ancient Greeks were also aware that sundials at different latitudes had to be locally calibrated. E.g., archaeologists found one in [Alexandria the Farthest](http://en.wikipedia.org/wiki/Alexandria_Eschate) that had been badly “adjusted” due to having been originally located somewhere else. ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 5, 2014, 6:59pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/44 "2014-03-05T18:59:43Z")
Another, semi-practical proposal: [See this diagram first.](http://s33.photobucket.com/user/cmykev/media/Flat_vs_Round_Earth_Diag_zps6ee58c4e.jpg.html) Step 1) Erect a tall enough tower to maximize the parallax effect on the raised platform. The large platform would have a bright red edge, and a bright green underside. Step 2) Work out the angles over the decided distance, so that the platform would be seen edge on from POV1. Step 3) From POV 1 (but really POV 2) observe under magnification (if necessary) whether or not the green underside of the platform can be seen. If the earth is curved, an experiment like this can be performed over and over, so long as finding an adequately level surface of land, like the salt flats, is practical enough. ---
**Author:** ![Saint\_Cad](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/saint_cad/32/18907_2.png) [@Saint\_Cad](https://boards.straightdope.com/u/Saint_Cad)\ **Post date:** [March 5, 2014, 8:12pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/45 "2014-03-05T20:12:28Z")
> [@cmyk](#): > > Another, semi-practical proposal: > > [See this diagram first.](http://s33.photobucket.com/user/cmykev/media/Flat_vs_Round_Earth_Diag_zps6ee58c4e.jpg.html) > > Step 1) Erect a tall enough tower to maximize the parallax effect on the raised platform. The large platform would have a bright red edge, and a bright green underside. > > Step 2) Work out the angles over the decided distance, so that the platform would be seen edge on from POV1. > > Step 3) From POV 1 (but really POV 2) observe under magnification (if necessary) whether or not the green underside of the platform can be seen. > > If the earth is curved, an experiment like this can be performed over and over, so long as finding an adequately level surface of land, like the salt flats, is practical enough. At 10 miles along the arc instead of the plane, the difference would only be 0.076 degrees. Can you make a board and paint it and have it that rigid and square? ---
**Author:** ![Chief\_Pedant](https://avatars.discourse-cdn.com/v4/letter/c/a6a055/32.png) [@Chief\_Pedant](https://boards.straightdope.com/u/Chief_Pedant)\ **Post date:** [March 5, 2014, 8:18pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/46 "2014-03-05T20:18:10Z")
> [@Saint\_Cad](#): > > Except that is begging the question. Eratosthenes assumed the Earth was round and didn’t prove it. The same results (7 degrees 5000 stadia away) can be achieved with the Sun as a point-source approximately 40720 stadia from the flat Earth. Well but then how does the Sun rise and set? ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 5, 2014, 8:44pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/47 "2014-03-05T20:44:32Z")
> [@Saint\_Cad](#): > > At 10 miles along the arc instead of the plane, the difference would only be 0.076 degrees. Can you make a board and paint it and have it that rigid and square? You could use supports and braces from above the plane to keep it square I imagine. I haven’t the time to work out the math, but how much distance would be feasible to put between yourself and the tower? ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [March 5, 2014, 9:46pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/48 "2014-03-05T21:46:02Z")
> [@Chief\_Pedant](#): > > Well but then how does the Sun rise and set? It is drawn by chariot on paths around the sky and under the earth. A better question is why it is not put out when it sets in the ocean. ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [March 5, 2014, 9:48pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/49 "2014-03-05T21:48:12Z")
> [@Saint\_Cad](#): > > At 10 miles along the arc instead of the plane, the difference would only be 0.076 degrees. Can you make a board and paint it and have it that rigid and square? A lot of these methods get frustrated by these small things and fine measurements. I would think that findings 10 miles of perfectly flat ground (that everyone involved would agree is perfectly flat) would be the major challenge. Maybe a large lake or a small strait would do. ---
**Author:** ![Blue\_Blistering\_Barnacle](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/blue_blistering_barnacle/32/3386_2.png) [@Blue\_Blistering\_Barnacle](https://boards.straightdope.com/u/Blue_Blistering_Barnacle)\ **Post date:** [March 5, 2014, 9:49pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/50 "2014-03-05T21:49:51Z")
There is at least one other thread on this site that discusses this issue at length. I have no luck when I try to search up threads, though. ☹ ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 5, 2014, 10:22pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/51 "2014-03-05T22:22:49Z")
> [@Blue\_Blistering\_Barnacle](#): > > A lot of these methods get frustrated by these small things and fine measurements. I would think that findings 10 miles of perfectly flat ground (that everyone involved would agree is perfectly flat) would be the major challenge. Maybe a large lake or a small strait would do. This was my thought as well. I had wondered about about using barges on a large, calm sea somewhere, which might mitigate any margin of error. What’s more, the further the distance, the more drastic the parallax. But of course, you’d lose resolve, unless you built a more massive structure. Wind might be an issue too, but this can be mitigated by perforating the plane’s surface with holes. ---
**Author:** ![APB](https://avatars.discourse-cdn.com/v4/letter/a/8e8cbc/32.png) [@APB](https://boards.straightdope.com/u/APB)\ **Post date:** [March 6, 2014, 9:55am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/52 "2014-03-06T09:55:27Z")
> [@Blue\_Blistering\_Barnacle](#): > > Maybe a large lake or a small strait would do. Such as the [Bedford Level](http://en.wikipedia.org/wiki/Bedford_Level_experiment). ---
**Author:** ![cmyk](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/cmyk/32/3353_2.png) [@cmyk](https://boards.straightdope.com/u/cmyk)\ **Post date:** [March 6, 2014, 4:04pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/53 "2014-03-06T16:04:14Z")
> [@APB](#): > > Such as the [Bedford Level](http://en.wikipedia.org/wiki/Bedford_Level_experiment). Clever: 3 floating poles of equal length and a surveyor’s scope. Can we bring a theodolite back in time? ---
**Author:** ![Aquadementia](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/aquadementia/32/555_2.png) [@Aquadementia](https://boards.straightdope.com/u/Aquadementia)\ **Post date:** [March 8, 2014, 4:01am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/54 "2014-03-08T04:01:08Z")
If the world was flat wouldn’t there be equal amounts of day and night no matter how far north or south you were? ---
**Author:** ![Kobal2](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/kobal2/32/20_2.png) [@Kobal2](https://boards.straightdope.com/u/Kobal2)\ **Post date:** [March 8, 2014, 4:16am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/55 "2014-03-08T04:16:14Z")
> [@The\_Controvert](#): > > Hmm, how about a variation on this [xkcd strip](http://blog.xkcd.com/2009/04/06/a-date-idea-analyzed/)? Instead of a cherry picker, just observe the sunset laying down on the ground, then get up really fast and observe it from standing height. > > I think it proves the Earth is not flat, although the actual shape might be a sphere or a cylinder or an ellipsoid, etc. Why should it ? A flat Earth with the Sun sinking below its horizon is the same as, say, a die dropping from a table as observed with your eyes at table level. Lift your head and hey, you can see the die over the edge ! Same with the Sun and the cherry-picker, if we assume it to be (apparently) rotating around a flat-ish disc. Possibly supported by four elephants, themselves standing on the shell of a turtle. ---
**Author:** ![randompattern](https://avatars.discourse-cdn.com/v4/letter/r/7993a0/32.png) [@randompattern](https://boards.straightdope.com/u/randompattern)\ **Post date:** [March 8, 2014, 4:46am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/56 "2014-03-08T04:46:09Z")
This is pretty well covered by Carl Sagan in the first episode of Cosmos. ---
**Author:** ![tonyfop](https://avatars.discourse-cdn.com/v4/letter/t/85f322/32.png) [@tonyfop](https://boards.straightdope.com/u/tonyfop)\ **Post date:** [March 8, 2014, 5:02am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/57 "2014-03-08T05:02:25Z")
> [@Napier](#): > > I got interested in the method that observes sailboats sink below the horizon as they get further away. We spend a week every summer at an ocean beach, and I’ve been looking for a nice example of this happening, and in over 25 years I’ve never been able to observe it. The horizon is always too indistinct and hazy for this to work. It sounds like it should work, but I don’t think it does. I used to see a different version of this when i was in the Navy. When I was onboard a carrier, I could use the height difference between the flight deck and the lower decks to change the angle of viewing another ship on the horizon. I could see the whole ship from the flight deck, but only the tops of the stacks from lower decks. Unfortunately, digital cameras didn’t exist then, so i could not get good shots of it. ---
**Author:** ![jrepka](https://avatars.discourse-cdn.com/v4/letter/j/ee59a6/32.png) [@jrepka](https://boards.straightdope.com/u/jrepka)\ **Post date:** [March 8, 2014, 5:53pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/58 "2014-03-08T17:53:27Z")
> [@cmyk](#): > > I described a setting sun. The person on the ground would see the sunset before the person at the peak, and therefore wave their flag before the person at the top. > > It would, of course, be opposite for a sunrise. You recognise of course, that you don’t need people with flags for this demonstration. Standing at the western base of any tall structure, you can easily observe that the top of the structure remains in sunlight well after the sun is below your own horizon. Of course this doesn’t demonstrate that the horizon is different for the base and the top. You would need to locate your two observers, with their flags, as far away from you as possible to the west and to the east on a very flat plain. If you can demonstrate that the horizon varies for two observers _at the same elevation_ you have demonstrated the curvature of the earth. What no one has mentioned here (at least in my cursory scanning of the posts) is the observation (credited to Pythagoras, but who knows) that, during a lunar eclipse, the earth’s shadow is round. Again, this leaves the possibility open that the earth is a flat disk, but we’ve at least made it a flat circular disk. I’ve always contended that the spherical earth is a concept that quickly becomes obvious to anyone who has regularly traveled more than 5-10 miles from their place of birth. It does require the propensity to make careful observations and to draw conclusions that differ from one’s own preconceptions. ---
**Author:** ![AncientHumanoid](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ancienthumanoid/32/278_2.png) [@AncientHumanoid](https://boards.straightdope.com/u/AncientHumanoid)\ **Post date:** [March 8, 2014, 6:20pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/59 "2014-03-08T18:20:47Z")
Lunar eclipse shadow mentioned on first page ---
**Author:** ![jrepka](https://avatars.discourse-cdn.com/v4/letter/j/ee59a6/32.png) [@jrepka](https://boards.straightdope.com/u/jrepka)\ **Post date:** [March 8, 2014, 6:24pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/60 "2014-03-08T18:24:43Z")
> [@cmyk](#): > > [Also, here’s Huygens’s method.](http://www.space.com/17081-how-far-is-earth-from-the-sun.html) Huygens method, as described above, makes several assumptions that are untestable. The primary reason he is not usually given credit for measuring the value of an AU (though his value is close to the true one) is that his errors cancelled each other out. For instance, he assumed that Venus was the same size as earth to determine its actual distance. As it happens Venus is the only planet whose radius is close to the earth’s, so, lucky he didn’t use Mars or Jupiter. Cassini and Richter measured the parallax of Mars from different latitudes, which didn’t require assuming the physical size of the planet, and came up with an measurement that was not as accurate as Huygens, but was limited only by measurement precision. The first accurate and precise measurement had to wait until data was available from the 1761 & 1769 transits of Venus, and was credited to Jerome Lalande. Since the 17th and 18th centuries all measurements have improved only as technology has allowed us to add decimal point to already accurate measurements. [Previous page](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819.md?page=2) [Next page](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819.md?page=4)