Re: How is it possible to see a crescent moon and the sun in the same sky?

The sun always illuminates the half of the moon which is facing it. This means that an entire hemisphere is lit up. However, depending on where the moon is in its orbit about Earth, we don't see all of the lit part. When the side which is lit is facing directly toward us, we see full moon; when it is facing away and only the dark side faces Earth, we see a new moon. When the dividing line between dark and light (on the moon) is directly aimed at us (in other words, half the moon is lit and the other half dark as seen from Earth) we see a 1st or 3rd Quarter phase. These are a little easier to understand since we can get the geometry intuitively just using two dimensions (flat, like paper).

To see the crescent phases, and the gibbous phases, we need to remember that the Moon is approximately a sphere. This is what causes the night/day line (called the "terminator") to look curved. There are a few ways to demonstrate this to yourself (alas, I haven't found any good 3-D demonstrations on the web). Since the sunlight is reflected from the moon's surface, the terminator must lie on the surface of the sphere. Two demonstrations of why this causes the terminator to appear curved are as follows:

Take a ball, preferrably one large enough to work with easily, such as a small beach ball or soccer ball. Take some masking tape (or other easily seen tape, such as colored electrical tape) and make a "great circle" (like longitude) around the ball - be sure to get it around the whole diameter so that it looks like a straight line if viewed directly down on it. This represents the dividing line between night and day on the moon, and looking directly down on it is like seeing 1st or 3rd quarter phase. Now, turn the ball slowly so that your "terminator" line moves toward what you see as the "edge" of the ball. As you turn the ball, you should be able to see that the line - which is really part of a circle - begins to look curved. (Remember we "see" the moon as "flat" because it's far away and our eyes can't see that it is a sphere)

Now, keeping that in mind, take a look at this animation showing the phases of the moon: http://www.ac.wwu.edu/~stephan/phases.html See how the moon phases look like the "terminator" circle on the spherical ball?

It is because the moon is a sphere that the crescent and gibbous phases have curved terminators. But, it is also confusing because our eyes can't tell that the moon is a sphere just by looking at it. Interestingly, it was the fact that the terminator appears curved that led the Greeks to argue that the moon must be a sphere!

Another quick demonstration can be shown with your ball and a flashlight in a dark room. This is similar to the above experiment, only using your flashlight to represent the "sun". You want your flashlight to be as far from the ball as possible, so turn it on and set it on something facing you, and move away from it. Be sure you can still see its reflection off your ball! Then make the ball "orbit" you. You will see that the ball is half lit all the time (facing the flashlight, also see this demonstration: http://www.uwlax.edu/faculty/sallmen/phy155/lecs/nitsky/phases_of_the_moon.htm ) but that the lit side is not always facing you. Again, the fact that the ball is spherical makes the crescent and gibbous phases have curved terminators.

A quick note on the second website above - you can click and drag the mooon to any part of its orbit, and then click on "Earth View" to see what phase it looks like from Earth.