Why Does the Moon Change Shape?

The moon is always a sphere. It never changes shape. What changes is how much of its sunlit side you can see from Earth. The sun always illuminates half the moon, and the moon's orbit changes the viewing angle. When the moon is between Earth and the sun, its lit side faces away from us. That is a new moon. As it moves around Earth, we see a growing sliver, then a half-lit quarter moon, then a fully lit full moon when it is opposite the sun. The cycle from new moon to new moon takes about 29.5 days. The phases are not caused by Earth's shadow. Earth's shadow causes lunar eclipses, which are separate events and require much more exact alignment.