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I know this sounds like (and probably is) a stupid question, but I can't figure it out.

As far as I know, the crescent shape of the moon is when the moon is on the sunny side of the Earth, but that wouldn't explain how it can be seen from the night.

Horrible, not-to-scale and probably completely wrong diagram of what I think here:

diagram

How is it that we can see clear to the other side of the Earth?

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    $\begingroup$ Something you may never have noticed is that the moon rises at a different time each day. The night of the full moon the moon rises at sunset, and then it rises 50 minutes later every day for the next 29 days, at which point it has fallen behind 24 hours, so it is full at sunset again. From that information you can reason about when the moon will be visible and what it's phase will be, from where you are on the surface of the Earth. $\endgroup$ – Eric Lippert Nov 23 '15 at 15:36
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    $\begingroup$ It also might help to get an orange, a light bulb, and a dark room. You be the earth, the orange is the moon, and the bulb is the sun. Move the orange around at arm's length and you'll figure out how it looks at various positions, and therefore how the earth-moon-sun must be during various phases. $\endgroup$ – Eric Lippert Nov 23 '15 at 15:39
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Here's a slightly more accurate diagram:

Diagram of crescent moon visible from the night side of Earth

It's still not quite to scale — the Moon is actually a lot further away from the Earth than shown here — but it should suffice to demonstrate that the moon can indeed be seen from the night side of the Earth even when it's nearly between the Earth and the Sun. Note how, in the orientation shown in the diagram, the side of the Moon visible to Earth is almost completely dark, with only a thin crescent lit by the Sun.

The diagram also illustrates some notable properties of the Sun-Earth-Moon geometry:

  • The crescent Moon is only visible (at night) shortly after sunset or before sunrise. Indeed, for the Moon to be visible at midnight, it must be at least (approximately) half full. There's some fuzziness here due to the fact that the Earth's axis of rotation doesn't perfectly match the axis of the Moon's orbit, but even so, you can never see a thin crescent Moon at midnight — unless you're close enough to the Earth's poles that you can see the Moon over the pole.

  • The lit side of the Moon's disk at night always faces (more or less) downwards, towards the Sun. At the equator, it faces (almost, again due to axial tilt) straight down; the further north or south you go, the more the Moon's crescent is tilted, but even so, it never faces upwards while the Sun is below the horizon.

Of course, another reason why we can see the crescent Moon is that the Moon is actually quite visible even during the day:

Daytime Moon and Clouds by Alana Sise
Daytime Moon and Clouds by Alana Sise @ Flickr, used under the CC-By 2.0 license.

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    $\begingroup$ Look, I have read a bazillion books on the subject, with my toddler. And all of them -- goodnight moon, the going to bed book, etc -- all clearly indicate that the moon arrives when you go to sleep, at night. "You can see the moon during the day" is photoshopped, I can tell from the pixels! $\endgroup$ – Yakk Nov 23 '15 at 15:28
  • $\begingroup$ I look upon Venus on the blue, Yakk. $\endgroup$ – Joshua Nov 23 '15 at 19:37
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Your diagram is not quite to scale, and the errors are important. Notice that only the hemisphere of the moon which points toward the sun is illuminated, rather than what your drawing shows. This has the following implications.

1) When the moon is new, it rises and sets at the same time as the sun, and is not (mostly) visible at night. The extreme example of this occurs when there is a solar eclipse.

2) When the moon is full, it rises at sunset and sets at sunrise, and is visible during the entire night.

3) When the moon is at half-illumination, it is only visible for half the night.

So the answer to your title question is "We can't."

The dark portion of the moon is not actually dark, since it is illuminated by light reflected by the earth. When the sky is dark, you can see the dimly-illuminated portion fairly clearly, but during daylight hours the sky is brighter than the dark portion of the moon, and that portion is invisible against the sky. That's why you can't see the moon just before and after a solar eclipse.

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  • $\begingroup$ Ah, okay. So at what position is the moon when it's in the crescent phase? I was always taught it was almost between the Earth and Sun, which never made sense to me. $\endgroup$ – imyxh Nov 23 '15 at 6:56
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    $\begingroup$ Well, for a very narrow crescent, it is almost in line with the sun. The result is that it is only visible at sunrise or sunset (depending on whether it's waxing or waning). If it is actually in line with the sun it's a new moon and a solar eclipse. $\endgroup$ – WhatRoughBeast Nov 23 '15 at 7:05
  • $\begingroup$ @WhatRoughBeast Stop slouching. $\endgroup$ – temporary_user_name Nov 23 '15 at 18:02
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How can we see the moon while it's between the Earth and the Sun?

This phenomenon is called "Solar Eclipse". You do not really see the moon, you simply do not see the sun because of the moon which block the sunlight.

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    $\begingroup$ You misunderstood the question. He's not asking about when the moon is directly on the line between the earth and the sun, he's asking about when the moon is closer to the sun than the earth is. $\endgroup$ – GreenAsJade Nov 23 '15 at 10:49

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