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I know that the full Moon appears when Sun, Moon and Earth are in a straight line, but if we consider that they are in straight line, why is the Moon illuminated?

I mean to say that Earth should block all the rays of the Sun and shouldn't allow any light ray to reach the Moon. In this case the moon should not get illuminated as no light has reached it which it can reflect back. Then why do we see a fully illuminated hemisphere of the Moon?

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    $\begingroup$ Possible duplicate: How can a full moon be seen south of an observer's location? $\endgroup$ – Ruslan Feb 17 '18 at 17:20
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    $\begingroup$ tldr, because the earth is 8000 miles across but the moon is 240,000 miles away. That 30:1 ratio means that the sun-Earth-moon line has to be dead-on to actually block the sunlight to the moon which only happens every year or two. $\endgroup$ – RBarryYoung Feb 18 '18 at 16:44
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    $\begingroup$ This should make it clear: xkcd.com/1878 $\endgroup$ – AstroRP Feb 18 '18 at 17:12
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    $\begingroup$ The real question should be, why do we call it "full" when in reality it isn't fully full. $\endgroup$ – Mr Lister Feb 19 '18 at 13:43
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    $\begingroup$ @AstroRP Cool, thanks, that makes it more cl... wait, what? $\endgroup$ – Michael Feb 19 '18 at 17:42
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One of the reasons people often have bad intuitions like yours about the relationship between the Earth and the Moon is because they've never seen an accurate picture. The distance from the Earth to the Moon is often pictured something like this:

enter image description here

The relative sizes of the Earth and the Moon are accurate but the distance is not. Given this picture it looks like the Moon ought to be almost always in the shadow of the Earth. A picture that accurately shows the relative sizes and distances is more like this:

enter image description here

And now it should be pretty clear that it would be really hard to get the Moon exactly in the shadow of the Earth from that far away. And if that's not clear, try it. Get a light bulb, a big grapefruit, a small orange, and a dark room and see if you can get the orange in the shadow of the grapefruit from twenty grapefruit-diameters away.

A fact that is missing from this diagram is: where exactly is the shadow of the Earth, and how large is it compared to the size and position of the moon?

I've edited the diagram above to give a rough idea of it.

The white lines on the left of the Earth, when extended, go to the "north" and "south" poles of the Sun, 150 million km away. The Sun is about 1.4 million km in diameter.

The white lines that continue on the right of the Earth indicate where the shadow of the Earth is; inside this region you can see neither the top nor the bottom of the sun. That region is about 1.5 thousand km long, or about four times the distance from the Earth to the Moon. Imagine those lines meet three or four screen widths to the right of your screen.

The Moon's orbit takes it both "north" and "south" of that shadow region; I've marked the approximate maximum positions of the Moon on the diagram.

So you can see, there's a pretty small region that the Moon has to hit in order to be in shadow on a full Moon. Most of the time the full Moon will be too far north or south of the shadowed region. enter image description here

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    $\begingroup$ To add to this answer, is something like universetoday.com/wp-content/uploads/2014/10/CLqdeKf.jpg, showing that there is room to line up every other planet in the solar system to fit between the earth and moon, with room to spare. $\endgroup$ – whatsisname Feb 19 '18 at 5:41
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    $\begingroup$ Brilliant explanation, I love how your diagram makes it so simple and intuitive. I'll have to remember this one for the next time I need to explain it. $\endgroup$ – Reinstate Monica Feb 19 '18 at 11:25
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    $\begingroup$ While this is true, if the lunar plane was identical to the Earth plane, then sure, there would be an eclipse every rotation. $\endgroup$ – Fattie Feb 19 '18 at 19:16
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    $\begingroup$ I think this is a poor explanation :) :) The answer to the question could not be simpler, the OP said "I know that the full moon appears when sun, moon and earth are in a straight line" - which is completely wrong. $\endgroup$ – Fattie Feb 19 '18 at 19:17
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    $\begingroup$ @Fattie: Then I encourage you to write your own answer that you like better; then we can all learn from your wisdom. $\endgroup$ – Eric Lippert Feb 19 '18 at 23:22
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The orbital plane of the Moon around the Earth is at an angle to the orbital plane of the Earth about the Sun.

This diagram was drawn to show why we do not have eclipses more often but is also shows how it is that a full Moon occurs.

enter image description here.

Image downloaded from Taylor Science Geeks website

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    $\begingroup$ @Awesome boy. In a straight line is too much. When "Earth is between Sun and Moon " is more appropriate as condition to have a full M. $\endgroup$ – Alchimista Feb 17 '18 at 14:18
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    $\begingroup$ @Nat Thanks for you comment. I was in a hurry so did not notice the background which I have now changed. $\endgroup$ – Farcher Feb 17 '18 at 21:05
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    $\begingroup$ @Awesomeboy. It makes a big difference, since they are so far apart. The moon is more than 60 Earth radii away. At 5 degrees that means the Moon is more than 6 Earth radii (more than 3 diameters) out of the ecliptic plane. $\endgroup$ – Jens Feb 18 '18 at 10:37
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    $\begingroup$ So, if we could just find some way to shift the orbital plane of the moon to be in the orbital plane of the Earth around the sun, we could have an eclipse every month! I'll file that away with my idea for speeding up the rotation of the Earth to get rid of the need for those pesky leap years... $\endgroup$ – Michael Feb 19 '18 at 17:44
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    $\begingroup$ @Michael While you're at it, could we also get more "medium tides", I'm a bit sick of having to constantly move my sun lounger up and down the beach. $\endgroup$ – Bilkokuya Feb 20 '18 at 12:09
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If the moon was exactly behind the Earth then yes, it would be in shadow. This happens sometimes: it's called a Lunar Eclipse.

This is pretty unlikely though because the Earth's shadow is small and space is big, so it doesn't happen often. Normally, when there's a full moon the moon is behind the Earth, but not exactly. It's close enough that you can't tell the difference looking at it.

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I know that the full moon appears when sun, moon and earth are in a straight line

It doesn't; it can't, as you described.

The full moon appears when the sun, moon and Earth are almost in a straight line. :)

Lunar eclipses happen reasonably frequently because, as you'd expect, it becomes a completely straight line reasonably often... or, at least, more often than never.

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  • $\begingroup$ There's always “some particular vantage point” (in fact a whole plane of vantage points) for which the Sun-Earth-Moon line appears to be straight. Eclipses happen when it is straight, regardless of viewpoint. $\endgroup$ – Anton Sherwood Feb 17 '18 at 21:36
  • $\begingroup$ @AntonSherwood: lol good point $\endgroup$ – Lightness Races with Monica Feb 17 '18 at 21:40
  • $\begingroup$ The only correct answer here. Good grief! $\endgroup$ – Fattie Feb 19 '18 at 19:18
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    $\begingroup$ @AntonSherwood - that's totally incorrect. The English sentence "in a straight line" means and can only mean they are all in a straight line. (ie: "in" a straight line, part of a line.) $\endgroup$ – Fattie Feb 19 '18 at 19:21
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    $\begingroup$ @Fattie: That's true, but Anton was referring to a previous edit which was subtly wrong $\endgroup$ – Lightness Races with Monica Feb 19 '18 at 20:02
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Projecting the Moon's path onto the plane of the Earth's orbit (plane of the ecliptic), the full moon is when the Sun, Earth, and projected position of the Moon are in alignment. But, as stated in the other answers, the Moon's orbital plane is slightly tilted relative to the ecliptic, so at the full Moon, it is usually passes either north or south of Earth's shadow. Occasionally, things line up so that at the full moon it does pass through Earth's shadow, resulting in a lunar eclipse.

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  • $\begingroup$ This is precisely: incorrect. When "viewed from above" (i.e. , what you mean is projected on a plane - flattened to 2D) they are often in a 2D-line, but very specifically they are on those cases usually not actually in a real line (because the lunar plane is tilted), which is exactly what the OP is asking. $\endgroup$ – Fattie Feb 19 '18 at 19:23
  • $\begingroup$ @Fattie I couldn't quite find the right wording. You've helped. $\endgroup$ – Anthony X Feb 19 '18 at 19:32
  • $\begingroup$ Now you're answer is the best one here :) $\endgroup$ – Fattie Feb 19 '18 at 19:39
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    $\begingroup$ @Fattie if you believe this answer is now correct, you should remove your original comment - the one that claims it's wrong. Otherwise you are misleading people into believing it's still wrong (or at least that you think it is). $\endgroup$ – Dawood says reinstate Monica Feb 20 '18 at 10:05
  • $\begingroup$ hi @DawoodibnKareem, welcome to the site. The three comments are right there before one's eyes, and it's totally clear what has happened. I actually do usually go around and delete all old comments, but it's really not the norm on SO sites. Usually you just leave the whole tedious comment chain there! (For example, if I deleted my comment, Anthony's and yours would be rather confusing! :) ) $\endgroup$ – Fattie Feb 20 '18 at 14:54
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The moon is not always in the Earth-Sun plane. The moon has an orbital tilt of about 5 degrees, so usually the Earth's shadow misses the moon, and therefore we have a full moon instead of a lunar eclipse.

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    $\begingroup$ Would have to be one of the best answers on the site :) $\endgroup$ – Fattie Feb 20 '18 at 14:43
  • $\begingroup$ I am learning about astronomy in my science class. I am currently an eighth grader. Thank you very much!! $\endgroup$ – Famous Michael Wang Feb 21 '18 at 3:25
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    $\begingroup$ Congratulations on your clear writing and good understanding. $\endgroup$ – Fattie Feb 21 '18 at 14:08
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To chime in on the issue. The overwhelming point here is:

1. It's commonplace that writing on the internet is just plain wrong.

The entire, total confusion here is that (as the OP rightly points out), clowns writing on the internet often refer to the Earth-Moon-Sun as being "in a line".

All the various confusion flows from that.

Note that even in the more-better article referred to in the top answer (with the excellent diagram), the same mistake is again made causing even more confusion.

enter image description here

2. "In a line" means "in" "a line" and can mean nothing else. Casual writers are unfamiliar with phrasing such as "a projection", etc.

In the example below the three blue objects are of course not in a line.

"A line" is indicated by the yellow ... line.

It would be not unreasonable - but totally incorrect - to casually refer to them as being "in a line", particularly when the final one is spinning around. Of course, what you really mean is something like "it's come to the 'outside' of the 'circle'" or whatever. Quite simply, you're saying that "as seen from the top" they've become aligned.

Exactly as the OP enquires, when they are actually in a line - bingo, eclipse!

Other than that, extremely simply they are not in a line: bad writing.

enter image description here

enter image description here

To once again summarize, the OP points out that you can see stated, on the internet, in a zillion places that: "... the full moon appears when sun, moon and earth are in a straight line ..." but that sentence is, simply, wrong!

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  • $\begingroup$ If the yellow spheres have the same dimensions, seen from above one would know they are not "in a line" because the areas of the first two circles (nearer to the viewer) would be greater than that of the third (further from the viewer). $\endgroup$ – camden_kid Feb 20 '18 at 15:42
  • $\begingroup$ hi @camden_kid - true, but only in a perspective projection. if it is an isomorphic projection they're the same; also just to avoid further confusion, they simply represent "points" in the diagram! :) $\endgroup$ – Fattie Feb 20 '18 at 16:49
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    $\begingroup$ Your example is misleading, first because it is massively out of scale, and second, because the Sun, Earth and Moon are not points; the Sun is enormous compared to the deviation of the Moon from the plane of the Earth's rotation. Try drawing your diagram with the Sun, Earth and Moon to scale in both their distances and the maximum deviation from "straight line", instead of this misleading diagram where we have three balls the same size and the same distance apart. $\endgroup$ – Eric Lippert Feb 20 '18 at 18:32
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    $\begingroup$ Put another way: the deviation of the Sun-Earth-Moon from a straight line is maximum on the order of 30 thousand kilometers. But the Sun is about 1400 thousand kilometers in diameter. It would be reasonable for the original poster to ask why then, if the Moon is "above" the straight line between the centers of the Earth and Sun, that it is not on a straight line between some two points inside the Earth and Sun, since the Sun is so huge. It is not on such a straight line, but explaining why requires a more detailed explanation. $\endgroup$ – Eric Lippert Feb 20 '18 at 18:56
  • $\begingroup$ hi @EricLippert - nah, it's a pedagogic issue. Let me put it this way, you (Eric) are "too smart to understand the confusion at hand." Let us say this: the basic confusion at hand can be stated in a sentence: OP has often read that "sun, moon and earth are in a straight line". This is - and I wish I could use red lettering because bold, italics are not enough - simply wrong. $\endgroup$ – Fattie Feb 20 '18 at 19:45

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