Of Wax and Men

Last time, with a little help from our friends the Beatles, we used our powers of visual imagination to better understand the daily behavior of the Sun in the sky (and below it, at night).  As we discovered, the key is to think of the Sun’s motion as the product of the Earth spinning round and round and round on its axis.   This time out, we’re going to start to tackle the behavior of our nearest neighbor in space, the Moon.   First up will be the remarkable changes that take place in the Moon’s appearance, and position, over the course of each month.  What’s in this for you?  Suppose you went outside last night and casually noticed the Moon.  Could you have answered a companion’s questions about where the Moon would be in the sky tonight?  Where it will be tomorrow night?  And how its shape is going to alter?  Well, if you can get through the next two blogs with me, answering questions like that will become child’s play.  You’ll be able to effortlessly analyze the Moon’s appearance at any time of the month and know just where it is in its monthly cycle, why it appears the way it does, and where it is going.  Fun, right?  But not only that.  In the final installment of the Moon series, we’ll build on your newfound understanding to uncover and discuss a fascinating “secret” about our nearest neighbor and its behavior.

As you know already, the Moon’s monthly cycle starts and ends with the “New Moon” phase, when the Moon is completely invisible.  What hides it from our sight?  The answer rests with two simple facts.  First, the Moon is a big round ball.  Just like the Earth, exactly half of the Moon’s surface (one hemisphere’s worth) is always illuminated by the Sun, and the other half is always in darkness.  The figure below illustrates the second fact:  The Moon continuously circles (orbits) the Earth, completing one revolution every 27 days.   Notice from the figure that when the Moon is new, that corresponds to the point in the Moon’s orbit where the Earth, Moon, and Sun are perfectly aligned, and the Moon is between the Earth and the Sun.  See where the sun’s rays are hitting the Moon’s surface?  All the illumination is confined to the “far side”, the hemisphere that’s opposite the hemisphere that faces us (the near side).  In other words, when the Moon is new, the far side is experiencing daytime, and “our” side is experiencing night.

As I noted, the Moon takes 27 days to complete one orbit, and another two days before it again lines up with the Sun (the reason for the discrepancy is that the Earth is in constant motion around the Sun.  But that’s a topic for a future blog about, of all things,  astrology).  At an average distance from the Earth of about 239,000 miles, the Moon covers over 750,000 miles per orbit.   To go that far in just 27 days, the Moon has to be moving in excess of 1000 miles per hour.  That’s rather fast for an object that looks completely stationary when you view it in the night sky, wouldn’t you agree?  But I’m getting ahead of myself because, since we’re still talking about the new Moon, you can’t see it yet!

I know I said (and the figure gives the impression) that the new Moon is positioned directly between the Sun and us, but that’s not quite true.  Usually, the Moon’s path takes it just slightly above or below the Sun rather than directly in front of it.   On the rare occasions where the Moon does pass right in front, some lucky locations here on Earth experience a solar eclipse.  However, with that speed of 1000 miles an hour, the Moon doesn’t stay aligned with the Sun very long; very soon, and very quickly, it moves off to the left, and keeps on moving.

One of the primary tools in our “Moon visualization” arsenal is the simple fact that the Moon moves in an eastward direction, which means that it is always moving to the left through the sky.  An amateur astronomer took the photograph on the right immediately after sunset, scant hours after the moon was new.  That razor-thin crescent is, of course, the Moon, having traveled just a small way to the left (east) of the Sun and, since the orbit is curved, a small way “back” in our direction. 

The Moon assumes this form of crescent once every month.  You’d have to be really on your toes to see it, though, because it is very close to the Sun, and quickly follows the Sun below the horizon (that is, it quickly sets).  Even though the Moon is moving east, you’re viewing it from a vantage point that is itself spinning around in an easterly direction, and this rotation is “pushing” the Moon (and the Sun) down and to the right much faster than the Moon is moving to the left around its orbit.  Recall in the Beatle’s blog that I discussed how the Earth’s rotation controls the movement of the Sun after sunset, “pulling” it ever further down and to your left (if you’re looking south) until the Sun swings back into view along the Eastern horizon (dawn)?  That reminder should give you a sufficient basis to visualize what happens to the Moon after it sets on the heels of the Sun.  At any rate, I encourage you to try.   The first commenter who correctly identifies when the Moon “rises” in relation to the Sun gets today’s comment section prize!  

The next order of business is to understand why a sliver of the near side is now illuminated.  Looking back at the “phases of the Moon” figure, fast-forward about two weeks, to the point when the Moon has traveled exactly half way around its circular orbit.  You see from the illustration that the Sun, Moon, and Earth are once again lined up, but this time, with the Moon furthest from the Sun and the Earth in the middle.

See what happens now?  The Sun’s rays are falling directly on the near side, lighting it up fully, and it’s the far side that’s shivering in darkness (by the way, this illustration helps you see why lunar eclipses, which occur when the Moon passes through the Earth’s shadow, only happen when the Moon is full). 

Now, turn the clock back two weeks, when the Moon was still a thin crescent near the Sun.  Every day, the Moon travels about 25,000 miles along it’s orbit, so every day, it draws a little closer to the position that it’s eventually going to occupy when full.   Moving ever closer to that position causes us to be able to see a little bit more of the sunlit hemisphere each night; a good way to think about this is to imagine the moon moving, not only out and to the left of the Earth, but also a little more “along side” the Earth, thus revealing a bigger and bigger piece or fraction of the sunlit hemisphere that used to be hidden behind the right limb.  After about a week, the Moon is at the top of the figure, and forms a right angle triangle with the Earth and the Sun.  At this point, exactly half of the illuminated hemisphere is visible to us, and we say the Moon is “half full”. Where is the other half? On the far side, of course, meaning exactly half of the far side is illuminated too.

But there’s something else that’s important to glean from the figure.  Take a look at the little circle in the middle representing the Earth, half of which is lit, and half of which is not.  You’re seeing the Earth as it would look if you were directly above the North Pole.   Now imagine the little circle rotating in its counterclockwise (Eastward) direction around the pole.  Now change your perspective, and pretend to move  from your “eagle eye”, way above the North Pole, to your present location on the Earth’s surface, right on the line between the dark side and the light side.  That position corresponds to sunrise, of course; the Sun is coming into view on the eastern horizon.  As the day wears on, you continue to rotate in a counterclockwise direction.  Although the half-full Moon starts out below the horizon, the Earth’s spin pulls it closer and closer to your eastern horizon, until, right at local noon, the Moon swings into view.  Yes, when the Moon is half full, it rises right around local noon (and is clearly visible, even thought it’s broad daylight).  Your day progresses, the Earth continues to spin, and the Sun slowly sinks into the West.  Meanwhile, the Moon continues to climb higher into the sky.  At local sunset, you are now positioned right at the very top of the little Earth ball in the figure, and the Moon is now directly overhead. With nightfall, the Moon blazes brightly in the sky.  Over the evening hours, though, it follows the sun into the west, until finally setting half-way through the night.

As the Moon proceeds towards full, her thousand mile-per-hour orbital speed opens up more and more distance between her and the Sun.  If you visualize the relative locations of the Sun and Moon near sunrise, (i.e., below your feet and off to your left if you are outside facing south), you’ll see that the increasing Sun-Moon distance is creating a longer and longer delay between sunrise and moonrise.  The increase also means that the Moon is visible in the night sky for a longer and longer period after sunset. 

Eventually, the Sun-Moon gap gets big enough that the Moon is both full, and rises just as the Sun is setting.  Again, the figure shows why this is the case:  The Moon is only full when it is on the other side of the Earth from the Sun, as far away from the Sun as it can get.

OK.  We’ve covered things up to the full moon phase.  In the next blog, we’re going to tackle the other half of the cycle, when the Moon starts waning.  If you’re like most people, and like me before I started to pay attention to these things, the waning Moon is much less familiar than the waxing Moon.   This is because most people stay up after sunset, so they gain plenty of experience with seeing the Moon when it is visible in the early nighttime sky.  In the waning phase, though, the constant leftward movement of the Moon in its orbit causes it to move back in the Sun’s direction, on a trajectory that has it approaching the Sun from the right-hand side.  As we’ll see next time, this geometry means that the Moon rises later and later each night, after we’ve typically gone to bed, and remains visible longer and longer in the morning.  However, since we much more naturally associate the Moon with a nighttime object, we almost never look for (or see) it in the morning, and our nearest neighbor completely exits our consciousness.

But more on that next time.