One of the first tough things that we ask most astronomy students to understand is the phases of the moon. And most students never really grasp it. It's not easy -- understanding the moon's phases involves picturing a three-dimensional dance of the Sun, the Earth, and the moon. And most people visualize this wrong.
I was happy to get an email from a cousin asking about the phases of the moon. Yes, he had the basic idea wrong, but he was thinking about it, and he noticed some problems with his logic. And that made me very happy. So many of us are just content to believe what we are told without thinking any further about it.
So, here is his question and my answer. There are many websites that talk about the phases of the moon, many with spiffy Java animations, so you can search those out if you'd like. I'm going to stick to an analogy that seems to work for some people.
"The guys and I were trying to figure out how a half moon is possible, since the different phases of the moon are from the Earth's shadow and the last time I checked, the Earth isn't flat. So my question to you is, how is a half moon possible?"Before we think about the moon, let's imagine something completely different. Suppose you are in a movie, playing the role of an innocent man who is being framed for a murder by a rotten cop. The cop brings you in for interrogation. In the interrogation room, you have the stereotypical setup. You are in a lone chair; there is a bright light on a desk being shone into your eyes, and the dirty cop is pacing around you. He doesn't trust you, so as he walks around your chair, he turns his face so he can always keep a close eye on you. Suppose the cop is almost between the light on you. You'll be squinting into the light, and so not be able to see him well. But even if you could see him well, his face would be in shadow, because his back is to the lamp. The back of his head is in the full glare of the light, but his ugly mug blocks your view of the back of his head. Now the cop walks around to your left. You turn your head to look at him. He's still looking straight at you. The left side of his face will be lit up by the lamp, but the right side of his face will be in shadow -- that big ugly nose, the sunken eye sockets all cast big shadows across half of his face. Half of the back of his head is also lit up, but you can't see that, since you can't see through his face. Now the cop walks behind you. You crane your head to look at him. Now his full face is lit by the lamp, so you can see every hairy mole, every scar from the barroom brawls he's been in. No shadows at all. Of course, the back of his head is in full shadow, but you can't see that either. Finally, the cop walks around to your right. When you turn your head to look at him, you see that now the right side of his face is lit, the left side hidden by those ghastly shadows of his crooked nose. Can you picture that scene? The moon and the Earth work the same way, with the moon being the bad cop, and the Earth is the poor innocent man. And the sun is that awful desk lamp. At new moon, the moon is almost (but not quite exactly) between us and the sun. We can't see it because of the glare of the sun, and even if we could, the moon would be dark, hidden in the shadow of its far side. When the moon is half lit, it has moved to the left or the right of the Earth (it always moves counter-clockwise, as seen from above). Now, half the moon is shaded by the other half of the moon. Finally, at full moon, the moon is directly behind us. We can see the entire moon, as we are looking straight at the sunlit part of the moon. Like the bad cop in the story above, the moon happens to turn at exactly the same speed as its movement around the Earth, so we always see the same face of the moon. We never see the back of it. Why it turns at the same speed can be explained by physics, but it doesn't have any thing to do with the phases we see. And, lastly, on some occasions the moon does come directly between us and the sun -- that's when we see an eclipse of the sun. An eclipse of the moon (such as one that will be visible late this month!) is when the moon passes into Earth's shadow. So it is only during eclipses that the Earth's shadow comes into play. The ancient Greeks used these eclipses of the moon as their proof that the Earth was round. If the Earth was any other shape, then the shadow of the Earth on the moon would be different. But the Earth's shadow during an eclipse is always round. I hope this clears things up a little. Understanding the phases of the moon is all trying to understand the three little spheres that are the Earth, the sun, and the moon, and picturing how they line up with each other. That makes it hard. But I think the story of the interrogation room can help people to visualize what's going on a little bit.