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There's no way around it: when I look at the full moon at night it looks like a mostly flat disc, with at most a bit convexity in the middle. Phases of moon look like a full moon seen through a cut-out.

Why is that the case? I recall, when I was really young, looking at it through what at the time seemed to be a very strong telescope, and it appeared not only a lot more textured but also a lot rounder. A similar thing can be seen in a video I saw a couple months ago, at 2:05: https://www.youtube.com/watch?v=XCrJ3NflOpE . So it's clearly a naked eye thing.

I presume it's related to the optics, which made me hesitant to post it on this stack exchange (thinking it might be more suited to the physics one), but chose against it presuming people here would have more experience with celestial bodies and "large" distances.

I have a hunch that the answer is very simple, but I really don't know what that might be, especially since it's done over what I view as large distances.

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It is an optical illusion.

We perceive nearby objects in 3d because we have two eyes. As we see objects from two different viewpoints, our brain can put the images together to make a 3d image.

Objects that are more distant perceived as 3d if they are moving fast enough for us to see them change appearance. Again it is not in the eyes but in the brain that the perception of depth occurs

The moon is a long way away, far too far for any 3d from our two eyes, and doesn't change fast enough for to see any motion. It is too small for us to see shadows or any other clues that we could interpret as 3d structure, so it looks like a small flat shape.

Telescopes can make shadows visible, and time-lapse can make the motion of the moon apparent, and so add to the perception of a solid.

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  • $\begingroup$ Phases of the moon, where it has a distinct horned shape, reveal its not just some flat disk. $\endgroup$ – Wayfaring Stranger Mar 16 at 1:12
  • $\begingroup$ Why would shadows be more visible through a telescope? $\endgroup$ – VienLa Mar 16 at 5:22
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    $\begingroup$ The shadows are too small to be visible with the naked eye. $\endgroup$ – James K Mar 16 at 6:53
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In addition to James K's perception methods, one can make a stereo pair of images by taking photos at different times in the Moon's libration as explained in Stereoscopic Pictures of the Moon.

Newportts has a nice modern example:

enter image description here If you can do the eye-crossing trick you can see a 3D Moon. It is more impressive if you open the image in a browser window and fullscreen it.

(The pairs in "Stereoscopic Pictures of the Moon" are meant to be viewed left image with left eye and right image with right eye, so if you use the eye-crossing trick you will see a concave Moon.)

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    $\begingroup$ I can do the eye-crossing trick. Good one Keith. $\endgroup$ – John Duffield Mar 16 at 11:40
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    $\begingroup$ Wow the magic eye on this is spectacular. It’s literally a ball $\endgroup$ – Autodidact Mar 16 at 11:53
  • $\begingroup$ Why I do interprete each single image as 3D? Just because I know that the moon is a sphere or bacuse the features it displays? If I try the cross eyes I see three inmges. $\endgroup$ – Alchimista Mar 16 at 13:02
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    $\begingroup$ @Alchimista Try holding your hands a few cm from your face so the L eye can only see the R image and vice versa. $\endgroup$ – Keith McClary Mar 16 at 16:05
  • $\begingroup$ @alchimista - just concentrate on the middle one of those three images. Once you have it right your brain will tube the others out a bit $\endgroup$ – Rory Alsop Mar 17 at 11:50
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Our brains rely on a variety of clues to determine depth. The most powerful clue is binocular vision but that only works at short distances, it's irrelevent here.

Other clues include the relative brightness of different parts of the image, the size and shape of shadows and the curving of linear features, the brain puts these clues together and sees a ball.

When you look at the moon with the naked eye at night it's difficult to see much detail because of it's small size and high brightness (compared to the rest of the night sky). So your brain can't see the clues that tell it the moon is not flat.

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