Phases of the Moon

“”—‘’
In my previous post, I made the error of assuming that most readers would know how the phases of the Moon work, which is by no means an understanding that can be taken for granted.  I wonder why this bit of information is presented to kids when they’re so young.  Understanding the geometry of the Sun, the Earth and the Moon, and the kinematics—which means the geometry in motion— is not easy for a young person who is still struggling with the thought that the Earth is not flat.

Anyone who understands the phases of the Moon perfectly well may feel free to skip this post; it is entirely educational, and doesn’t have all the opinions that people are accustomed to seeing here.

First of all, the phases of the moon are not things that really happen to the Moon in quite the same way as one might think.  Let’s try to visualize the phases of the Earth first.  We know perfectly well that half the Earth is lit up at any given time of day.  If we were flying around the Earth in a rocket or Space Shuttle, depending on where we’re looking from, we would see the Earth completely lit up by the Sun, partially lit up, or we might be looking at the night side, and the Earth would not be lit up at all.

To make things even clearer, suppose we’re in a room with a bright floodlight at the far end of the room, and someone is walking about the room holding a tennis ball.  At any time, exactly half the tennis ball will be illuminated.  Suppose we call the line that separates the lighted side from the dark side the Night/Day line, if we make the person holding the tennis ball to just stand still for a minute, and stand right opposite the Night/Day line (which is actually a circle that goes round the ball), we should see something that looks like a half-moon.  If we move by 45 degrees (centered at the tennis-ball, of course) away from the lamp, we would see a ‘quarter-moon;’ if we move 45 degrees towards the lamp, we would see a three-quarter moon.  If we look at the tennis ball from the side of the lamp (being careful not to let our shadow interfere with the scene), we would see a full moon, and so on.

Now, if we were to observe the Earth, the Moon and the Sun from outer space, ideally from up, way above the North Pole, what we would notice is that the relative positions of the Earth, the Moon and the Sun do not change very much.  In fact, you could watch for a couple of days, and not notice much motion.  But you will notice that the Earth is spinning.  That is by far the fastest thing that is happenning.  It will appear to go around one complete rotation in roughly 24 hours, not surprisingly.  This means that the point of view of the Moon from anyone on the Earth doesn’t change much for a day or two.  If we could keep running round the Earth to keep the Moon always in sight, it will appear to have the same phase for a day or two.  Actually, if we wait until the Moon is directly overhead, and then start running, it will be the same time of day wherever we are, because the Sun will also appear to be motionless.  (This happened to me on New Year’s Eve of 2000; I took a plane out from London, and when I arrived in New York, it was still New Year’s Eve.)

Let’s represent the Sun, the Earth and the Moon by points, and call them S, E, and M respectively.  Over a week, the angle SEM will change about 90 degrees, and in a little less than a month, the angle will be back where it was.  This period of time is called a Lunar Month for this very reason.  Whatever the phase of the moon was at any given moment, the phase is exactly the same one Lunar Month later.

If you’re comfortable with the idea that the phase of the Moon depends on only the angle SEM, which slowly goes from 0 to 360 degrees over a Lunar Month—which is about 28 days—we can now connect the dots.

If the Moon is exactly overhead at 6:00 PM, it has to be a half moon, because it is being illuminated squarely from one side.

If the Moon is exactly overhead at 12:00 Midnight, it has to be a full moon, because it will be illuminated from ‘behind our heads,’ the Sun being on the opposite side of the Earth from us (and the Moon), and the Sun is “looking” at the Moon in exactly the same direction as we are.  (This is why all eclipses of the Moon take place when there is a full moon.)

If the Moon is exactly overhead at, er, let’s see: at 9:00 PM, it will be a 3/4 -moon.

If the Moon is exactly overhead at Noon, it will be a new moon, which is a moon which is all black, or rather, in shadow.

If the Moon is exactly overhead at 3:00 AM, it is essentially the same as if it were overhead at 9:00 PM; if the Moon is exactly overhead at 3:00 PM, it is essentially the same as if it were exactly overhead at 9:00 AM: a quarter-moon.  The two phases are called First Quarter or Last Quarter, I’m not sure which is which.

The figures I’m providing are not as clear as I had planned, mostly because I’m squeezing in so much detail into each diagram, to save space.  (Ha ha; there is so much of it, it seems unnecessary...)

In the first diagram, the angle between the line to the Moon and the line to the Sun is about 90 degrees,

In the second diagram, the angle between the line to the Moon and the line to the Sun is about 135 degrees, which is about 3/4 of one hundred and eighty degrees.

In the last diagram, the angle is 180 degrees, which is when you get a Full Moon.  When the Sun is behind the Moon, you get a New Moon, which is a dark moon, illuminated from behind.  (We still see it, lit by Earthlight, light reflected out to the Moon from us, the Earth.  Astronauts say that Earthlight is very beautiful, and of a bluish cast.)

Arch