The moon is a sphere. So this os not a shadow of something else. The sphere is being lit by the sun from the "left" in this picture (where the sun is). So you only see half of the sphere in the light.

Imagine a ball that is being lot by a torchlight and you're looking from the side.

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Yes, I can get behind that, as Super Phat Arrow said. It just doesn't seem to fit. In my limited scope. Also, I can make out the underside of the moon, with the naked eye anyway. That suggests some light is being reflected towards my eye. Where is that coming from if the sphere explanation is correct?

That is the light that's reflected from the earth to the moon, it's called eartshine.

Very good observation and even better question!

I feel like this is getting somewhere, thanks. So, at night we are not facing the sun, where is the "earthshine" coming from (in that photo)? Are you saying from other parts of the earth not in shade? Would that mean, at the zenith of night, let's call it midnight, we would not be able to see any reflected "earthshine"?

If the moon was at this zenith position, it would have to be on the exact opposite side of the sun. But then we see the moon as a full moon (the dark side is invisible).

Cheers ears. I can understand that. For everyone else, I am open minded for a different opinion but Chris and others here have a good explanation

This video may help (not to scale):

https://m.youtube.com/watch?v=J4IlzZKWyYQ