It's not only the Moon and Earth that “have” (or project) shadows, but also the other planets (and their moons), and every asteroid in the asteroid belt, etc. A shadow requires two things - a source of light and an opaque body to block it. read more
Every night the Moon passes in front of thousands of stars in the sky, blocking their light for about 90 minutes until they pop out behind it. During that time, you are in the Moon’s shadow from each of those stars. Cat Stevens was right, Moon shadows are everywhere. read more
The moon and the earth have shadows for the same reason that you have a shadow: they are solid and opaque, so they block sunlight thus casting a shadow. read more
A shadow is not the presence of darkness, but rather, the absence of light. Because an opaque object does not transmit light, and light tends to travel in straight lines, the area directly opposite an opaque object from a light source will not receive light directly from the light source. This absence of light appears as a shadow. read more