by John P. Pratt
The moon is something that is so familiar that one might think that an artist could draw it easily in a painting without having an advanced degree in astronomy. But there are many subtle implications when the moon is included in a picture, which the trained eye notices. It turns out that the most information is implied by the thin crescent moon, which artists often include so that people will definitely recognize it as the moon. If the location of the scene is known, then the crescent not only indicates the time of day, but also the direction and the season of the year. Let's see just how, by considering three kinds of mistakes artists unwittingly make.
One can determine where the sun must be by looking at where the ends of the crescent are. The sun must be lighting up those two sides of the crescent equally, so it must be on a line that is perpendicular to the line connecting the two points on the crescent, as shown in the illustration. Now astronomy can tell us just how far away the sun should be from the moon, but for this first kind of mistake, all that is necessary is to know that, very often, the picture implies that the sun is above the horizon, and so it must be daytime and not night time.
For example, in the B.C. cartoon, the sun would have to left to the left of the moon and nearly as high above the horizon, as shown in this illustration. But if the sun were that high above the horizon, it would have to be daytime! So by merely considering the lighting, we can see that we have an impossible picture here.
So how common is this mistake? Is it only in cartoons? Consider the following picture, which was taken from Sky and Telescope Magazine (for shame!). It appears to be a beautiful night on the beach. But what about that moon? Where must the sun be for the crescent to be that shape? That's right, it's almost identical to the cartoon. The sun would have to be about as high as the moon above the horizon. That saddest thing to me, is that after this mistake appeared in an astronomy magazine, no one wrote in to point out the error.
What about the B.C. cartoon which specifically addresses the issue that the moon is often seen in the daytime. Is the moon right in this picture? As far as this first test is concerned, yes, the sun is almost exactly on the line perpendicular to the horns of the crescent.
1. The crescent moon is seen at night only shortly after sunset or shortly before sunrise. The amount of time depends on how thin the crescent is. If it is only a sliver, the it is very shortly before of after sunrise. Thus, a very thin crescent usually implies an hour after sunset and can only be seen very near the horizon. A standard sized crescent is usually chosen by artists simply to indicate the "moon at night." If it is fairly high in the sky, then it is shortly after sunset. If it is nearly setting, then it indicates two-three hours after sunset. But one must be cautious here because it can also be the same amount of time before sunrise. See the direction and seasons below to know for sure.
2. The first quarter moon (right side lit) is seen highest in the sky at sunset. It then gets lower, and sets about midnight. So a first quarter moon very near the horizon implies it is midnight.
3. The full moon rises at sunset and sets at sunrise. That is because it must be completely opposite from the sun in order to be fully lit. Thus, a full moon shown only slightly above the horizon implies that the time of night is shortly after sunset (or shortly before sunrise). If it is high, then it is a few hours after (or before) sunset. It is highest in the sky at midnight.
4. The last quarter moon (left side lit) rises at midnight and is highest in the sky at sunrise. Note that when it is near the horizon that one cannot easily tell whether it is the right side or left side of a quarter moon which is lit in the picture because it is necessarily the bottom. But for the timing, it doesn't matter because either way it indicates midnight. That is, if it is a first quarter moon it is setting at midnight, and if it is a last quarter moon it is rising at midnight.
So for example, in the B.C. cartoon here, we first do the day-night test and see that this time the cartoon passes with flying colors. That is, drawing a line perpendicular to the horns shows that the sun is most likely below the horizon, so it is indeed nighttime as indicated. But how late at night? Using Rule 1, we see a standard crescent fairly high in the sky, so it is probably an hour or two after sunset, which is mostly likely just what the artist wished to imply. But we are not done with this cartoon because whether or not it indicates after sunrise or before sunset is also indicated.
The other thing you need to know is that all during the year, the sun and moon never stray more than 30 degrees from the celestial equator. That means they tend to rise and set on an angle of about some 50 degrees to the horizon, which is the angle at the celestial equator. At sun or moon rise the angle is toward the south, at setting it is toward the north. And the directions of north and south are also implied because in an illustration, if the 50 degrees angle is to the right, then one must be facing east (rising) and if the angle opens to the left we must be facing west (setting).
Now let us apply this newfound information to the last B.C. cartoon. We have found both the sun
and the moon in this picture. Assuming both are near the equator, then the equator is about 50
degrees as expected. But the angle is opening to the right, so the moon is in the EAST, and hence
must be rising. That means it is about two hours BEFORE SUNRISE rather than after sunset.
Actually, in this cartoon that is even better, because it implies that B.C. was waiting all night for
his girlfriend to show up, rather that merely an hour or so. But in many cases, it is clearly a
mistake. One example is the cover of a nursery rhyme book which shows big sister reading to little
brother. Through the window the moon shines just as in the B.C. cartoon, implying that these kids
have been reading all night, and it is now about 4 a.m.!
The sun travels in a great circle (the ecliptic) through the sky each year which is tipped some 23 degrees to the celestial equator. In the spring and fall, it is very close to the points where the equator and ecliptic intersect, which are called the equinoxes. Hence the sun rises nearly due east and sets due west. In the summer it rises in the northeast and sets in the northwest, and in the winter it rises in the southeast and sets in the southwest.
The moon's orbit is only tipped 5 degrees from the suns, so for our purposes, let's approximate by saying it also follows the ecliptic circle like the sun. I'll give an example of how this affects the setting crescent moon, which is so commonly drawn. If the season is spring (March), then the ecliptic forms a 23 degree angle ABOVE the celestial equator. Hence the moon tends to be shaped like a "U." On the other hand, in September, the ecliptic is BELOW the equator, and hence the crescent looks like a "D." In summer and winter, it is in between. So presumably, B.C. in the above cartoon is in the summer because the crescent is neither D nor U.
Isn't it amazing how much information is implied in the simple shape of a crescent moon?