Once in while I hear someone insist that the expression "half moon" is incorrect, that one should say either "first quarter" or "third quarter." But "half moon" is established usage and very descriptive, and the terms "first quarter" and "third quarter" refer not to the appearance of the moon in the sky but to how far along the moon is in its cycle of phases, a cycle that averages a bit over 29 1/2 days.
The first quarter is the moment halfway between a new moon and a full moon, when we see a half-illuminated moon in the sky. The third quarter is halfway between a full moon and the next new moon, when we see the opposite half lit.
It strikes me a perverse to insist that a half-illuminated moon not be called a "half moon." The expression is obvious, commonplace, and very descriptive. Besides, no one insists on calling a fully illuminated moon anything but a "full moon."
Out of curiosity, do you happen to know the current phase of the moon? I have to admit I don't. For most of us city dwellers it's not something we need to keep up with unless we happen to be astronomers or werewolves. For our ancestors it was of considerably more practical importance, and they not only knew the phase of the moon, they could tell you whether it was waxing or waning and that moonrise and moonset happened about 50 minutes earlier each night.
The reasons for this are surprisingly simple to understand. In an earlier draft of this post I rambled on rather too long about it until I realized that it would be a lot easier to explain with pictures, preferably animated ones. Maybe I'll even get around to doing a YouTube video about it, though you should probably not hold your breath while waiting.
But in the meantime, if you're interested, you can figure out a remarkable amount in just a few minutes. The key is to keep it simple, at least as a first pass. Don't worry about orbital inclination or eccentricity or axial tilt or any of that stuff. You don't even need to think about the fact that the Earth orbits the Sun, since all you really care about is the Moon's position in its orbit relative to the direction of the Sun. You can pretend that a window or floor lamp on the other side of the room is the Sun, and you can represent the Earth by any convenient object sitting on a table. The Moon can then be a coffee cup or a tennis ball or whatever else is handy, and the Moon is the only piece you actually need to move in your model.
It helps to know that the Moon orbits the Earth in the same direction that the Earth rotates on its axis, and that the Earth rotates on its axis a little less than 30 times while the Moon completes one orbit of the Earth relative to the Sun. From that knowledge and playing around with that little table-top model of the Earth-Moon system you should be able to answer these questions:
- What does the Moon look like for someone standing on the Earth when the Moon is at the point in its orbit closest to the Sun -- how much of it do we see illuminated, for example?
- What does the Moon look like a day or two later? Where is it in the sky just past sunset (i.e, from the viewpoint of someone who has just been carried by the Earth's rotation from sunlight into shadow)?
- How does it look a week or so later at the time of the first quarter -- that is, when the Moon is 1/4 of the way through its orbit of the Earth? What about halfway through its orbit, when it's on the opposite side of the Earth from the Sun? What about at the third quarter?
- Does moonrise and moonset happen earlier or later each night? By how many minutes? (That last question is easier to answer than you'd probably expect.)
- Often when we see a narrow crescent Moon we can see the rest of the lunar surface weakly illuminated. Where does that light come from. (Hint: It's light reflected from something.)
- Some paintings show a crescent moon with its "horns" (the pointy bits) angled more or less downward, toward some point on the horizon. Is that actually possible?