# 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:** 18\ **Page:** 4
**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, 6:25pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/61 "2014-03-08T18:25:50Z")
> [@AncientHumanoid](#): > > Lunar eclipse shadow mentioned on first page I stand corrected. Always a risk when you come to a thread late. ---
**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, 6:47pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/62 "2014-03-08T18:47:11Z")
🆒 yeah, I do it all the time. Sometimes I remember the thread search tool. ---
**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 9, 2014, 4:04am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/63 "2014-03-09T04:04:19Z")
> [@jrepka](#): > > 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. Despite his guess-work, and being lucky Venus is just a hair smaller than earth, Venus at the time, IIRC, was really the only planet to make out its phases. Mars and Jupiter, if not full, are rarely observed anything less than gibbous. And Mercury was less than ideal for spying phases when you already have a Venus at your disposal. But, yeh, point noted. ---
**Author:** ![Ignotus](https://avatars.discourse-cdn.com/v4/letter/i/ecc23a/32.png) [@Ignotus](https://boards.straightdope.com/u/Ignotus)\ **Post date:** [March 9, 2014, 4:06am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/64 "2014-03-09T04:06:29Z")
Wait a minute. Before we start arguing from the shape of the lunar eclipse shadow, we must establish the shape of the lunar surface itself, _n’est-ce pas_? I see no explicit mentioning of it upthreads, but I take it we are all agreed upon that it must be a sphere? There is no alternative explanation for the lunar phases, right? (Well, I suppose it could be a half-sphere. But in this particular context it doesn’t matter.) ---
**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 9, 2014, 4:13am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/65 "2014-03-09T04:13:25Z")
> [@Ignotus](#): > > Wait a minute. > > Before we start arguing from the shape of the lunar eclipse shadow, we must establish the shape of the lunar surface itself, _n’est-ce pas_? I see no explicit mentioning of it upthreads, but I take it we are all agreed upon that it must be a sphere? There is no alternative explanation for the lunar phases, right? > > (Well, I suppose it could be a half-sphere. But in this particular context it doesn’t matter.) I believe that was one of the strongest/earliest arguments that the earth is probably a sphere too. But yes, anyone with a round stone and a candle in darkness would’ve noted the unmistakable correlation of the way the moon is lit by the sun. ---
**Author:** ![Ignotus](https://avatars.discourse-cdn.com/v4/letter/i/ecc23a/32.png) [@Ignotus](https://boards.straightdope.com/u/Ignotus)\ **Post date:** [March 9, 2014, 8:32am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/66 "2014-03-09T08:32:24Z")
So, squattin’ 'neath the camp-fire, the great sceptical chieftain grudgingly admits that the moon is most likely a ball, reflecting the light of the sun. That is certainly something to stand on! Now this next step may not be evident, and would perhaps take rather more than a stone and a candle, besides the mind of an Archimedes; but could one,( besides the general analogy in terms of shape), use the ashen glow as a corroborative, although not conclusive, evidence to show that something akin to the moon’s phases is happening with respect to the Earth? ---
**Author:** ![marshmallow](https://avatars.discourse-cdn.com/v4/letter/m/df705f/32.png) [@marshmallow](https://boards.straightdope.com/u/marshmallow)\ **Post date:** [March 9, 2014, 12:06pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/67 "2014-03-09T12:06:29Z")
Maybe I’m mathematically illiterate, but it seems a lot of the measurement experiments (and stuff like ships disappearing over the horizon) only disprove a naive perfectly flat Earth. But they’d be fooled if the flat Earth was misshapen and lumpy and we lived on a curved portion of it. ---
**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 9, 2014, 3:39pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/68 "2014-03-09T15:39:13Z")
> [@Ignotus](#): > > Wait a minute. > > Before we start arguing from the shape of the lunar eclipse shadow, we must establish the shape of the lunar surface itself, _n’est-ce pas_? I see no explicit mentioning of it upthreads, but I take it we are all agreed upon that it must be a sphere? There is no alternative explanation for the lunar phases, right? > > (Well, I suppose it could be a half-sphere. But in this particular context it doesn’t matter.) IIRC, and obviously YMMV, the shadow question was answered by the best fit for the shadow shape was a sphere casting a shadow on _another_ sphere. I wasn’t there, tho, so I can’t say for sure. ---
**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 9, 2014, 4:19pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/69 "2014-03-09T16:19:14Z")
> [@marshmallow](#): > > Maybe I’m mathematically illiterate, but it seems a lot of the measurement experiments (and stuff like ships disappearing over the horizon) only disprove a naive perfectly flat Earth. But they’d be fooled if the flat Earth was misshapen and lumpy and we lived on a curved portion of it. Not if measured on the sea, or at least at opposite shores of a lake, since it has been understood since antiquity that water is level, no mater the topology beneath. ---
**Author:** ![Steve\_MB](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/steve_mb/32/5339_2.png) [@Steve\_MB](https://boards.straightdope.com/u/Steve_MB)\ **Post date:** [March 9, 2014, 4:44pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/70 "2014-03-09T16:44:26Z")
> [@Mangetout](#): > > A journey parallel to the arcs of those celestial objects, with an accurate clock, uncovers the notion of time zones - so the earth is rounded in an east-west direction, at least (but the Earth could still be a cylinder or cone or ovoid or something at this point). The problem is that accurate clocks (or the technology to actually build one even if you don’t have to figure out how to do so from scratch) didn’t come along until the sphericity of the earth had already been nailed down by other methods. ---
**Author:** ![jrepka](https://avatars.discourse-cdn.com/v4/letter/j/ee59a6/32.png) [@jrepka](https://boards.straightdope.com/u/jrepka)\ **Post date:** [March 9, 2014, 5:09pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/71 "2014-03-09T17:09:39Z")
> [@marshmallow](#): > > Maybe I’m mathematically illiterate, but it seems a lot of the measurement experiments (and stuff like ships disappearing over the horizon) only disprove a naive perfectly flat Earth. But they’d be fooled if the flat Earth was misshapen and lumpy and we lived on a curved portion of it. This is true. You can be as abstract and imaginative as you like in fitting a model to data (A seismologist buddy of mine once pointed out that you could make seismo data fit an earth model in which the core was made of butterscotch, if you were so inclined). But look at how round the moon and the sun are. (and how round earth looks from space. Kepler took years to accept an elliptical orbit for Mars because he was carrying over the ancient idea that an imperfect earth (with mountains and valleys and disease and sin) was in contrast to the perfect heavens, with spherical planets and circular orbits. So, for the people we’re talking about, the circular shadow of the earth means either (a) a spherical earth, or (b) a flat circular earth. And the horizon effect means a curved earth, which means a spherical earth. ---
**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 9, 2014, 5:41pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/72 "2014-03-09T17:41:35Z")
> [@jrepka](#): > > So, for the people we’re talking about, the circular shadow of the earth means either (a) a spherical earth, or (b) a flat circular earth. A flat circular Earth will _not_ cast a circular shadow at all angles. It will generally be an ellipse. The ancients used this very point in arguing a sphere as opposed to a disk. * * * As to “local topography” messing up things, a lot of things counter it. A _lot_. E.g., the length of day and the changes of length of day cannot be explained by anything on a local scale. The ancients knew that in the far north the Sun never rose above the horizon. And then understood this was because the Earth was round. A flat Earth has the same length of day everywhere. In fact, a late/early sunrise due to having a mountain range nearby is an inverse explanation. E.g., someone in Denver on a flat Earth would have an earlier, not later, sunset than someone in Kansas City. ---
**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 9, 2014, 8:41pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/73 "2014-03-09T20:41:03Z")
But I think the OP boils down to how do we prove the Earth is not flat given methods at the time they thought it was and so there is a certain assumption that it is local not global data that we can use. We have already dispensed with earlier sunrise at elevation and different angle of the sun at different latitudes. Those can easily be explained using a flat Earth model and anyone still claiming those work should reread my earlier posts. We have the ship at sea method but how would that work if you are not by the sea? We have measuring the angle of the Sun at various latitudes (at least three) but we have to account for how far the ancient could reasonably travel, the accuracy of the equipment and understanding trig. The Bedford Level looked interesting but again, do the local conditions have a flat canal/stream? Also interesting was how due to atmospheric refraction it was used to prove the Earth was flat. ---
**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 9, 2014, 9:54pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/74 "2014-03-09T21:54:35Z")
> [@Saint\_Cad](#): > > We have already dispensed with earlier sunrise at elevation and different angle of the sun at different latitudes. Those can easily be explained using a flat Earth model and anyone still claiming those work should reread my earlier posts. I have checked all your posts in this thread and _not a single one_ actually “dispensed with” any such thing. Yes, elevation will change the time of sunrise, a _very_ little bit. In order to explain the vast differences in time of day the elevation has to be really, really big, i.e, on the scale of the curvature of the Earth! I.e., your alleged elevation argument is in fact a curvature argument. And how does elevation (on the scale of mountains, not Earth’s curvature) change why the Sun never rises on the solstice in far northern climes? The incredible absurdity of this argument is explaining why the elevation is mainly a north-south effect. Someone on a mountain top and someone down at the base will experience fairly similar length of days. But someone on a mountain top a thousand miles north will experience a much shorter day in the winter than someone at sea level in the south. Something is uniformly bent, it’s the Earth. Get used to it. ---
**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 10, 2014, 5:38am UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/75 "2014-03-10T05:38:19Z")
> [@ftg](#): > > I have checked all your posts in this thread and _not a single one_ actually “dispensed with” any such thing. Yes, elevation will change the time of sunrise, a _very_ little bit. In order to explain the vast differences in time of day the elevation has to be really, really big, i.e, on the scale of the curvature of the Earth! I.e., your alleged elevation argument is in fact a curvature argument. The argument that was dispensed with was: an earlier sunrise/later sunset can ONLY occur on a curved Earth. And I don’t know how you think elevation creates a “vast difference” in time of day. Assuming a radius of 8000 mi., at 10’ the angle of depression to the horizon is 0.0394 degrees. At a 1000’ the angle of depression is 0.39425. The Sun travels approximately 0.0042 degrees every second yielding a sunrise just under 1 min 15 seconds earlier or a total of 2.5 minutes more daylight for that 1000’ elevation. Did the OP allow us to take two precise watches back in time? Now what I will admit is that those angles and elevations give a distance to the edge of the Earth 10 times larger at 1000’ than 10’ - but that “proving” the Earth is curved means having a device capable of precision of at least hundredth of a degree and keeping with the OP, did such a device exist back when the Earth was believed flat and would that civilization understand the trig involved. So your point is that in the modern world with modern equipment and modern mathematics we can with local measurements prove the Earth is curved? Well OK but I don’t see how that answers the OP. ---
**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 10, 2014, 3:59pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/76 "2014-03-10T15:59:08Z")
I really don’t know what’s going on with **Saint Cad**. Apparently logic isn’t going to work here. Look, precision is _not needed_ to tell that the length of day at two places at the same latitude but different elevations are fairly similar. While length of day at places at different latitudes can vary greatly. You don’t need a stopwatch to notice that the sun barely goes down in summer and barely comes up in winter in northern Europe. Meanwhile the difference between day and night is modest in southern Egypt regardless of time of year. “Precise watches” my foot. If **SC** can’t understand something so simple and straightforward, then I give up. ---
**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 10, 2014, 5:15pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/77 "2014-03-10T17:15:14Z")
The radius of the earth is ~4,000 miles, not 8,000. ---
**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 13, 2014, 4:40pm UTC](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819/78 "2014-03-13T16:40:56Z")
> [@ftg](#): > > Look, precision is _not needed_ to tell that the length of day at two places at the same latitude but different elevations are fairly similar. While length of day at places at different latitudes can vary greatly. You don’t need a stopwatch to notice that the sun barely goes down in summer and barely comes up in winter in northern Europe. Meanwhile the difference between day and night is modest in southern Egypt regardless of time of year. > > “Precise watches” my foot. > > If **SC** can’t understand something so simple and straightforward, then I give up. Umm why don’t you understand I didn’t discuss daylight at different latitudes but SAME latitude DIFFERENT elevation and that more daylight at elevation at the same latitude can occur on the flat Earth. I also pointed out that while the curvature of the Earth is provable using measurements at different latitudes, would the distance needed to travel vs. the precision of instruments be ruled out by the ground rules in the OP. [Previous page](https://boards.straightdope.com/t/how-to-prove-the-earth-and-moon-isnt-flat/682819.md?page=3)