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

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.
