Bad moon rising
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In reading picture books to my young son, I have come across several pictures like these:
From Sandra Boynton's Pajama Time, copyright Workman Publishing, Inc.
From Maurice Sendak's Where the Wild Things Are, Harper and Row, ©1963.
In looking at these “moon shadows,” you should get a feeling that they are not right. Why? Because at any time other than a lunar eclipse, only half the the moon’s surface has a direct path to the sun. If you look at a ball, you always see half and you don’t see half. If a light looks at a ball, it lights half directly and doesn’t light half directly. Spheres are self-shadowing, so the half away from the light source is in a shadow cast by the half near the light source, with the halves separated by a plane.
Exactly and only half the moon's surface is directly illuminated by the sun.
In the picture books, the shadows are less than half, smaller than a hemisphere. This means they can’t be self-shadows. Nor can they be Earth’s shadows cast on the moon during a lunar Eclipse, because Earth projects a shadow bigger than the moon. These shadows are simply not physically plausible. At least these books contain other implausible things, like singing pigs and rooms that turn into wild woods.
To illustrate what moon shadows are physically plausible, I have whipped up a proof-by-construction WebGL-renderer of a lit sphere. If you’re in the children’s book publishing market, give it a run before picking up your brush.
Just use a modern non-Internet Explorer browser, click on the canvas, and use the W, A, S, and D keys to move the light source.