How does the earth cast straight and reversed shadows on the moon?

Question

When the Earth regularly casts a shadow on the moon, why does the shadow progress from circular to a straight line and then to a reversed circle?

Since the earth is a sphere, shouldn't it cast round shadows only?w

I get how the first concave shadow (2nd image) would make sense, but I don't get how it evolves during the month to a straight line and then to a reversed, concave circular shadow (6th image).

Lunar phases, annotated from Wikimedia Commons

You should cite a source for the photo, those appear to just be the moon phases, not a lunar eclipse. But the Earth's shadow during an eclipse does appear non-intuitive sometimes. — Greg Miller, Jul 10 '22 at 03:28
It is not clear. Are you asking about a lunar eclipse, when the Earth casts a shadow on the moon. Or are you asking about the normal phases of the moon, which is what the image shows? Please clarify — James K, Jul 10 '22 at 10:33
related: https://astronomy.stackexchange.com/questions/38363/why-cant-we-see-saturns-phases-from-earth — Kai, Jul 10 '22 at 15:24
When the earth casts a shadow on the moon Those are not pictures of the earth casting a shadow. — John Gordon, Jul 10 '22 at 17:31
@JohnGordon They are in fact images of the Moon's phases, which indeed have nothing to do with the shadows cast on the Moon by the Earth. To make matters worse, this is a copyrighted image. Due to the combination of misinterpretation and misuse, I am voting to close. — David Hammen, Jul 10 '22 at 22:08
I’m voting to close this question because the question is a misinterpretation of a copyrighted ShutterStock image of the phases of the Moon. Since the OP added markups of the copyrighted image, I don't see a way to rescue the question. — David Hammen, Jul 10 '22 at 22:09
@DavidHammen "I don't see a way to rescue the question" Deleting the photo and replacing it with a description would be one way to rescue the question. Replacing the image with something that is not copyrighted would be another way. "Misinterpretation" alone is not a close reason. It's not a false premise so much as simply a misunderstanding, and "Answers to your question shall be prevented because you misunderstand" is absurd. — uhoh, Jul 11 '22 at 19:58
@DavidHammen I've made a simple edit along those lines. Looks "rescued" to me! — uhoh, Jul 11 '22 at 20:14

score 50 · Accepted Answer · answered Jul 10 '22 at 02:06

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Aha! I think you'll find that the answer is that those are not photos of Earth's shadow on the Moon at all!

Look at the photo of the Earth and the Moon seen from the spacecraft Voyager 1 as it was leaving our neighborhood in In this image taken by Voyager 1, which is closer: the earth or the moon?

Both the Earth and the Moon have the same crescent shapes, illuminated from the right side by the Sun.

What you're suggesting might be the shadow of the Earth is really just the pattern produced when a sphere is illuminated from one side by a narrow light source, like the 1/2 degree wide Sun.

You can see that both the Earth and the Moon have essentially the same illumination pattern.

answered Jul 10 '22 at 02:06

uhoh

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Can you clarify how the Sun is a "narrow" light source if it's actually bigger than the Earth or Moon? Or why that's relevant to how the sphere is lit up? – Romen Jul 11 '22 at 21:40
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@Romen - the answer states in what sense it's a narrow light source - it's 0.5 degrees wide in the sky (very far away, appears small), and thus it acts like small patch of sky that produces light rays - an apparently "small" light source situated much further away than the Earth-Moon distance, which is relevant because then the light rays hitting both the Earth and the Moon can be considered more or less parallel, which is why the illumination pattern is essentially the same. – Filip Milovanović Jul 11 '22 at 22:58
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@Romen the usual example is a globe or ball (even a ping-pong ball) in a dark room, illuminated from the side with an old style flashlight held at some distance away. The flashlight could be wider than the ball, but since the flashlight is far away it illuminates from a narrow cone of directions so that the light/dark transition of the shadow is fairly sharp. If you open a window or door and let a wide cone of light in, the shadow is no longer sharp. – uhoh Jul 12 '22 at 08:46

score 45 · Answer 2 · answered Jul 10 '22 at 13:12

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There is already a good and correct answer from @uhoh, but I thought I’d add another to show off some of my favorite teaching images, and to comment on what we do learn from lunar eclipses.

The reasoning in the question - a round Earth should only cast round shadows - is correct, and in fact has been used since ancient Greek times to argue that the Earth is round. (Again, I’ll emphasize that the pictures shown in the question are not eclipses, but just different views of the day vs. night sides of the Moon, which we call phases.)

In this diagram (from a 1683 geography text by Philipp Cluver, though possibly of earlier origin), the text (roughly translated) says, “This diagram shows that the Earth is round. If the Earth were triangular, its shadow would appear triangular in a lunar eclipse.” And so on for the square and hexagonal (!) Earths. It closes with “nevertheless, it appears round.”

The full shadow of the Earth is much larger than shown in this diagram, and can be recorded with successive images during a lunar eclipse, demonstrating not only that the Earth is round, but that it’s bigger than the Moon:

(Image by Anthony Ayiomamitis, via APOD.)

answered Jul 10 '22 at 13:12

Eric Jensen

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Exquisite and beautiful teaching images! No wonder they are some of your favorites. – uhoh Jul 10 '22 at 13:26
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yes... wonderous images. I cannot help but imagine that it might have been possible for a clever observer to construct a similar eclipse composite image well prior to the existence of cameras by making a series of quick individual sketches and integrating them into a unified whole. To anyone's knowledge was this done before photography? – BradV Jul 10 '22 at 18:32
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Note that the shadow's radius is smaller than that of the Earth. Radii of the Earth and the Moon have ratio of about 3.67, while one can fit less than 3 Moons across the shadow diameter (once the full circle is recovered from the photo). This is because the umbra has conical shape due to Sun's size being much larger than that of the Earth. – Ruslan Jul 10 '22 at 19:24
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Flamebait :-) -- this only shows the Earch is a disc! It's still flat, as anyone who has read Terry Pratchett knows. – Carl Witthoft Jul 11 '22 at 12:44
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@Ruslan: Unless I was told a myth or misremembering, an Ancient Greek (I forget who) made a reasonably close estimation of the Earth's diameter based on the shadow it throws on the moon. Given the size difference between the Earth and its shadow on the moon, I wonder if there is an intuitive way they could've accounted for that back in the day. – Flater Jul 11 '22 at 19:13
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@Flater it was Aristarchus, and he did estimate sizes of all three bodies. See On the Sizes and Distances. What's funny though, he still got Earth radius worth of 2.85 lunar radii (see Results section), which basically means ignored cone effect if other distances are taken with modern values. – Ruslan Jul 11 '22 at 19:19
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Thanks for the great answer, I would have also accepted it if I could accept multiple :) – chowder Jul 11 '22 at 23:48
@AlanBirtles the implication does work in this direction: since the Sun is larger than the Earth, umbra is a converging cone. If even diminished, the shadow still appears larger, then the Earth itself is at least not smaller than that. As for the Moon being farther, note that the shadow we observe on its surface also farther, by exactly the same amount. – Ruslan Jul 12 '22 at 15:40

How does the earth cast straight and reversed shadows on the moon?

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