Light does not just make one side bright and the other dark. On a round object there are always five parts, and the surprise is this: the darkest part is not the edge. It sits just before it, in a band called the core shadow — because the very edge catches light bouncing back up off the ground.
The other rule worth carrying around: a shadow always points straight away from the light, and it is darkest where the object touches the ground. The lower the sun, the longer the shadow — which is why your own shadow is enormous in the evening.