# Curve of the shadow on the Moon **URL:** \ **Category:** Factual Questions\ **Created:** [October 19, 2003, 11:26am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343 "2003-10-19T11:26:14Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Shortie](https://avatars.discourse-cdn.com/v4/letter/s/ecd19e/32.png) [@Shortie](https://boards.straightdope.com/u/Shortie)\ **Post date:** [October 19, 2003, 11:26am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/1 "2003-10-19T11:26:14Z")
So I found this quote the other day: > [@](#): > > The church says the earth is flat, but I know that it is round, for I have seen the shadow on the moon, and I have more faith in a shadow than in the church. - Ferdinand Magellan And I can’t quite work out whether it makes sense. Yes the shadow on the moon is curved. But though that proves the Earth isn’t a flat square or a cube, does it prove the Earth isn’t a flat disc? If you take a disc and project it’s shadow onto a wall then as you rotate the disc the shape of the shadow will change to an oval. But will the curve projected onto a small area (i.e. the Moon) change so that it’s clearly not from a sphere? ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [October 19, 2003, 1:01pm UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/2 "2003-10-19T13:01:47Z")
If the earth were a flat disc, near sunset or sunrise the earth is lit edge-on by sunlight and the shadow is a thin ellipse. If a lunar eclipse happens just after sunset (which isn’t all that unusual), you should see a thin elliptical shadow on the moon. Instead the shadow is always circular regardless of when the eclipse happens. That’s a pretty convincing proof that the earth is spherical. ---
**Author:** ![RickJay](https://avatars.discourse-cdn.com/v4/letter/r/bb73d2/32.png) [@RickJay](https://boards.straightdope.com/u/RickJay)\ **Post date:** [October 19, 2003, 2:13pm UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/3 "2003-10-19T14:13:09Z")
Just to ensure nobody is confused, I assume we all understand Magellan was tlaking about a lunar eclipse, right? Anyway, scr4 nailed it. Take a disc - a dinner plate will do - and project its shadow while turning the disc around. When the plate is edge-on to the light source you’ll just get a flat line of a shadow. Now try the same experiment with a baseball. The shadow will always be round - just as the shadow of a lunar eclipse is. ---
**Author:** ![Hari\_Seldon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/hari_seldon/32/5173_2.png) [@Hari\_Seldon](https://boards.straightdope.com/u/Hari_Seldon)\ **Post date:** [October 19, 2003, 3:15pm UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/4 "2003-10-19T15:15:41Z")
The only thing I would wonder is that Magellan and any other sailor would have been familiar with the phenomenon of ships (or the shore) disappearing below the horizon and wouldn’t that have been even more convincing a demo? For one thing, how obvious is it that eclipses are caused by the earth’s shadow on the moon? You have to realize that the moon shines by reflected light, that the light comes from the sun, and that eclipses come only when the moon is on the ecliptic and that most of the time it is above or below it by a few degrees. All this seems clear enough to us today, but how obvious was it then? ---
**Author:** ![Shortie](https://avatars.discourse-cdn.com/v4/letter/s/ecd19e/32.png) [@Shortie](https://boards.straightdope.com/u/Shortie)\ **Post date:** [October 19, 2003, 10:05pm UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/5 "2003-10-19T22:05:02Z")
> [@](#): > > \*Originally posted by scr4 \* > \*\*If the earth were a flat disc, near sunset or sunrise the earth is lit edge-on by sunlight and the shadow is a thin ellipse. If a lunar eclipse happens just after sunset (which isn’t all that unusual), you should see a thin elliptical shadow on the moon. Instead the shadow is always circular regardless of when the eclipse happens. That’s a pretty convincing proof that the earth is spherical. \*\* Yeah, but what I can’t work out is whether hypothetically you could have a really big Earth, so that even when it’s nearly on edge the Moon takes up only a small part of the shadow. Thus meaning that you’d never see both sides of a thin shadow, and the curve might look pretty much the same on a distant object which isn’t obviously a sphere itself. Given that lunar exlipses aren’t that common, is the difference gonna be obvious? And **Hari Seldon** , yeah, but the whole shadow on the moon thing is a really nice phrase. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [October 20, 2003, 12:07am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/6 "2003-10-20T00:07:42Z")
I was under the impression that that quote from Magellan was thought to be a work of fiction. Lunar eclipses happen once or twice a year, pretty much. ---
**Author:** ![commasense](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/commasense/32/3017_2.png) [@commasense](https://boards.straightdope.com/u/commasense)\ **Post date:** [October 20, 2003, 12:20am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/7 "2003-10-20T00:20:08Z")
> [@](#): > > \*Originally posted by Hari Seldon \* > \*\*The only thing I would wonder is that Magellan and any other sailor would have been familiar with the phenomenon of ships (or the shore) disappearing below the horizon and wouldn’t that have been even more convincing a demo? For one thing, how obvious is it that eclipses are caused by the earth’s shadow on the moon? You have to realize that the moon shines by reflected light, that the light comes from the sun, and that eclipses come only when the moon is on the ecliptic and that most of the time it is above or below it by a few degrees. All this seems clear enough to us today, but how obvious was it then? \*\* Magellan is almost certainly referring to Aristotle’s argument in _[De Caelo](http://classics.mit.edu/Aristotle/heavens.2.ii.html) (On the Heavens)_ that the earth must be spherical. He refers to several forms of evidence of the earth’s shape, including the fact that **Hari** cites of ships disappearing over the horizon. However, he points out that this only proves that the earth’s surface is curved. On this evidence alone, the earth might be a hemisphere or some other portion of a sphere. He also refutes the possibilities of a flat disc, a cylinder and other shapes. As **scr4** points out, the evidence of a circular shadow on the moon regardless of the orientation of the earth is the only point that proves the spherical theory. The reasons for lunar eclipses were well known to the classical Greeks four or five centuries before the Common Era. And, therefore, to Magellan. ---
**Author:** ![RedDawgEsq](https://avatars.discourse-cdn.com/v4/letter/r/dbc845/32.png) [@RedDawgEsq](https://boards.straightdope.com/u/RedDawgEsq)\ **Post date:** [October 20, 2003, 12:45am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/8 "2003-10-20T00:45:47Z")
## quote: ## The church says the earth is flat, but I know that it is round, \*\* _for I have seen the shadow on the moon,_\*\* and I have more faith in a shadow than in the church. - Ferdinand Magellan To me, the above fragment is ambiguous. Is he speaking of the actual shadow cast (only) during a lunar eclipse or the apparent shadow (terminator) seen any evening except on the full or new moon? The two have entirely different explanations, of course. The curved terminator results from the angular difference between the earth and the sun, with the moon at the apex of the angle. The terminator can be either concave (as the phase approaches new) or convex (as the phase approaches full.) Is there evidence that these effects (eclipse vs. uneclipsed terminator) were well understood to have different causes? If Magellan (or whomever) thought it was always a true shadow, then a convex shadow could only be explained by a concave earth, which would have been a pretty unlikely theory, or at least one of which I have never heard. ---
**Author:** ![commasense](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/commasense/32/3017_2.png) [@commasense](https://boards.straightdope.com/u/commasense)\ **Post date:** [October 20, 2003, 12:56am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/9 "2003-10-20T00:56:01Z")
> [@](#): > > \*Originally posted by RedDawgEsq \* > \*\*The terminator can be either concave (as the phase approaches new) or convex (as the phase approaches full.) Is there evidence that these effects (eclipse vs. uneclipsed terminator) were well understood to have different causes? If Magellan (or whomever) thought it was always a true shadow, then a convex shadow could only be explained by a concave earth, which would have been a pretty unlikely theory, or at least one of which I have never heard. \*\* And at the quarter moon, the terminator is a straight line. The correct reasons for these effects (unrelated to the shadow of the earth) are mentioned by Aristotle in the same work I mentioned above. ---
**Author:** ![Tim\_T-Bonham.net](https://avatars.discourse-cdn.com/v4/letter/t/46a35a/32.png) [@Tim\_T-Bonham.net](https://boards.straightdope.com/u/Tim_T-Bonham.net)\ **Post date:** [October 20, 2003, 4:00am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/10 "2003-10-20T04:00:12Z")
> [@](#): > > \*Originally posted by Shortie \* > **Yeah, but what I can’t work out is whether hypothetically you could have a really big Earth** Yes, but navigators of that time (like Magellan) DID have a fairly accurate knowledge of the actual size of the earth. (Actually, 2 sizes – the one Columbus used (without the American continent) and the rather more accurate post-Columbus one.) Any “really big Earth” that might have made this shadow shape possible would have to have been way bigger than they knew the earth to be. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [October 20, 2003, 9:16am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/11 "2003-10-20T09:16:12Z")
> [@](#): > > \*Originally posted by [t-bonham@scc.net](mailto:t-bonham@scc.net) \* > **Yes, but navigators of that time (like Magellan) DID have a fairly accurate knowledge of the actual size of the earth. (Actually, 2 sizes – the one Columbus used (without the American continent) and the rather more accurate post-Columbus one.)** Isn’t the rather more accurate one pre-Columbus? ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [October 20, 2003, 9:41am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/12 "2003-10-20T09:41:11Z")
> [@](#): > > \*Originally posted by [t-bonham@scc.net](mailto:t-bonham@scc.net) \* > \*\*Any “really big Earth” that might have made this shadow shape possible would have to have been way bigger than they knew the earth to be. \*\* Aren’t you assuming that they also knew the size and distance of the moon? > [@](#): > > _Originally posted by RM Mentock_ > **Lunar eclipses happen once or twice a year, pretty much.** There can be either two or three lunar eclipses in any given year. Each year has a total of seven eclipses, either five solar eclipses and two lunar eclipses, or four solar eclipses and three lunar eclipses. The lunar eclipses are visible from the entire hemisphere of the earth that’s facing the moon, whilst any particular solar eclipses is only visible from a narrow strip of the earth’s surface. Of course, not everyone on earth is going to _see_ all of the lunar eclipses that occur in any given year, so in a given year you might only see one or two, as you said, even though either two or three actually occurred. ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [October 20, 2003, 9:55am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/13 "2003-10-20T09:55:30Z")
> [@](#): > > \*Originally posted by Desmostylus \* > **Aren’t you assuming that they also knew the size and distance of the moon? There can be either two or three lunar eclipses in any given year.** A rough estimate would have been possible based on the fuzziness of the shadow (i.e. size of the umbra vs. penumbra). I don’ t know if they actually did it or not. What I’m wondering is, did the church in Magellan’s time still insist that the earth is flat? ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [October 20, 2003, 10:04am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/14 "2003-10-20T10:04:54Z")
> [@](#): > > \*Originally posted by scr4 \* > \*\*What I’m wondering is, did the church in Magellan’s time still insist that the earth is flat? \*\* I don’t think the church _ever_ insisted that the earth was flat. ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [October 20, 2003, 10:16am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/15 "2003-10-20T10:16:26Z")
And while I was looking for something to back up what I said to **scr4** , I found this, from **Cecil** : > [@](#): > > [You say the earth is round? Prove it](http://www.straightdope.com/classics/a2_087.html) > “The sphericity of the earth is proved by the evidence of … lunar eclipses,” **Aristotle** says. “For whereas in the monthly phases of the moon the segments are of all sorts–straight, gibbous [convex], crescent–in eclipses the dividing line is always rounded. Consequently, if the eclipse is due to the interposition of the earth, the rounded line results from its spherical shape” So it looks to me like someone took Aristotle’s quote, and falsely attributed it to Magellan, whilst confusing the Church’s position on heliocentrism (vis-a-vis Galileo) with some imaginary flat-earth position. 🙂 ---
**Author:** ![Desmostylus](https://avatars.discourse-cdn.com/v4/letter/d/c57346/32.png) [@Desmostylus](https://boards.straightdope.com/u/Desmostylus)\ **Post date:** [October 20, 2003, 11:13am UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/16 "2003-10-20T11:13:36Z")
My apologies to **commasense** , for not noticing that **commasense** had already posted the stuff about Aristotle. :smack: ---
**Author:** ![CurtC](https://avatars.discourse-cdn.com/v4/letter/c/ce73a5/32.png) [@CurtC](https://boards.straightdope.com/u/CurtC)\ **Post date:** [October 20, 2003, 2:10pm UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/17 "2003-10-20T14:10:02Z")
> [@](#): > > _scr4 wrote:_ > A rough estimate [of the size/distance of the Moon] would have been possible based on the fuzziness of the shadow (i.e. size of the umbra vs. penumbra). I don’ t know if they actually did it or not. Could you work out the size/distance of the Moon based on the shadow and penumbra, if you didn’t already know the size/distance of the Sun? They knew the size of the Earth, and the angular sizes of the Sun and Moon, but I can’t figure out how to then calculate the absolute distance/size of the Moon or Sun from there based on shadows. ---
**Author:** ![RM\_Mentock](https://avatars.discourse-cdn.com/v4/letter/r/e274bd/32.png) [@RM\_Mentock](https://boards.straightdope.com/u/RM_Mentock)\ **Post date:** [October 20, 2003, 3:20pm UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/18 "2003-10-20T15:20:33Z")
> [@](#): > > \*Originally posted by Desmostylus \* > **There can be either two or three lunar eclipses in any given year.** 0, 1, 2, or 3 according to [Mr. Eclipse](http://www.mreclipse.com/Special/LEprimer.html) > [@](#): > > \*\* > Each year has a total of seven eclipses, either five solar eclipses and two lunar eclipses, or four solar eclipses and three lunar eclipses. The lunar eclipses are visible from the entire hemisphere of the earth that’s facing the moon, whilst any particular solar eclipses is only visible from a narrow strip of the earth’s surface. \*\* [Mr. Eclipse](http://www.mreclipse.com/Special/SEprimer.html) says that there will have been 14,263 solar eclipses during the 6000 years from 2000BC to 4000AD, a little more than two per year on average. [2003](http://sunearth.gsfc.nasa.gov/eclipse/OH/OH2003.html) only has two lunar eclipses, both total, and two solar eclipses, one total, one annular. Same numbers for [2004](http://sunearth.gsfc.nasa.gov/eclipse/OH/OH2004.html) except both solar eclipses are partial. > [@](#): > > \*\* > Of course, not everyone on earth is going to _see_ all of the lunar eclipses that occur in any given year, so in a given year you might only see one or two, as you said, even though either two or three actually occurred. \*\* Yes, I was responding to Shortie’s comment that lunar eclipses weren’t that common, with respect to European viewing. ---
**Author:** ![JRDelirious](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/jrdelirious/32/9531_2.png) [@JRDelirious](https://boards.straightdope.com/u/JRDelirious)\ **Post date:** [October 20, 2003, 3:24pm UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/19 "2003-10-20T15:24:19Z")
> [@](#): > > \*Originally posted by RM Mentock \* > \*\*Isn’t the rather more accurate one pre-Columbus? \*\* The one from Greek times was indeed the better estimate. What happened was that once they figured that was a whole continent and TWO oceans between Spain and China, everyone ditched the Columbus estimate and went back to the older one. (In fairness to Chris, if as it is suspected he had intelligence sources about the existence of lands around where our East Coast is, he must have figured that must be Asia, and if so then the Earth has to be smaller than the Greeks said or else it would be 5 times as far, so let’s fudge the computations so that it squares…) ---
**Author:** ![scr4](https://avatars.discourse-cdn.com/v4/letter/s/59ef9b/32.png) [@scr4](https://boards.straightdope.com/u/scr4)\ **Post date:** [October 20, 2003, 3:51pm UTC](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343/20 "2003-10-20T15:51:47Z")
> [@](#): > > \*Originally posted by CurtC \* > **Could you work out the size/distance of the Moon based on the shadow and penumbra, if you didn’t already know the size/distance of the Sun?** You just need to know the angular (apparent) size of the sun as seen from the earth, which you can measure by simply looking up. That angle is equal to the angle between the edge of the umbra and the edge of the penumbra. Again, I don’t know if this method was used, or whether they had more accurate methods. [Next page](https://boards.straightdope.com/t/curve-of-the-shadow-on-the-moon/208343.md?page=2)