From the Earth to the Moon

Several blogs ago, we engaged in a visualization exercise to help understand the apparent movement of the Sun in our sky.  In today’s blog, I want to continue the fun by visualizing the Sun’s behavior again, but this time from the point of view of a tourist (you! you!) on the surface of the Moon.  The purpose?  To illuminate one of the Moon’s best-kept secrets!

Before boarding your spacecraft, I’ll briefly review how the Moon behaves from our vantage point here on Earth.  As you know, the Moon is constantly moving in an easterly (leftward) direction, circling the Earth every 27 days or so.  The cycle starts with a small crescent that grows a little fatter every night until, about two weeks later, the Moon has the appearance of a big round ball.  Then, the pattern reverses itself; each night, darkness steals more and more of the ball from our sight until it disappears completely, and we say that the Moon is “New”.

Through the last two blogs, we’ve discovered that these changes in appearance are completely explained by the change in the relative positions of the Sun, Moon, and Earth due to the movement of the Moon around the Earth.  When the Moon is new, it is between us and the Sun; when the Moon is full, we are between it and the Sun.  But although the Moon’s constantly shifting position fully explains its phases, a mystery remains. Imagine the Moon in its “New” position, between the Sun and the Earth.  The “far side” is fully illuminated by the Sun, and the “near side” is in darkness.  If there was a small city on the near side, we’d be able the lights of the city twinkling in the lunar night.

Now, using your powers of visualization, imagine just picking the Moon up and moving it to the position it occupies when full.  Where is our hypothetical city now?  By rights, it should now be on the “far side”, the side invisible to us.  The side that is completely illuminated, and the side we actually see, should be what was the Moon’s far side (the side facing the Sun) when the Moon was new.  But that’s not the case.  What you see, instead, is the same side that faced you when the Moon was new: The so-called near side, the side containing our hypothetical city.  Assuming the city were big enough, you could see the buildings with a telescope.

How can this be the case, when the Moon has traveled all the way around the Earth?  You are on your way to the Moon’s surface to answer this question.

Flash forward a couple of days, and you’ve arrived at your destination. Your spacecraft has deliberately landed smack dab on the Moon’s equator (half way between the “top” and the “bottom” of the Moon as seen from Earth), and smack dab along the extreme right edge of the disk, as viewed from here (we want to be able to see you, so you’re just barely inside the edge).  In addition, you’ve timed your arrival so that it coincides exactly with new Moon.

Imagine getting out of your spacecraft and lying flat on the ground with your head closer to the North Pole and your feet closer to the South Pole (so that if you look down at your feet, you’re looking south). From our perspective here on Earth, your feet would be toward the “bottom” of the moon, and your head toward the top.  Now, stretch your arms out so that your left arm is pointing due East, and your right arm is pointing due West.

Having positioned yourself in exactly the right configuration, all you have to do now is wait, and tell me, back here on Earth, what you experience during the next two weeks.   The goal is to connect your experience with the changes I will see in the Moon’s appearance.   For a short time after you lie down, you’d be in pitch darkness; your particular location along the right limb is still in darkness.  But not for long.  Just a short time past new Moon, I see the Moon as the thin crescent, as in the photograph below that you’ve seen before.  From my perspective, the area around the right limb (the area around you) has transitioned from being in darkness to being in sunlight.  The area off to your west (your right) has not yet undergone this transition, and is still shrouded in darkness.

What causes this transition from darkness to light?  Sunrise, of course: The same event that transforms night into day here on Earth.   You’ve been right on the dividing line between night and day, and now the Sun has risen right at the location along the eastern horizon that you are pointing to with your outstretched left arm.

24 hours now pass. Viewing the Moon from my vantage point here on Earth, the crescent has grown a little fatter, which means that a larger area of the Moon’s surface beyond the limb (off to your right) has become illuminated. I’ve captured this situation in the photograph of the Moon above.  From where you are located, the only way that areas to the west of you can have transitioned into daytime is if the Sun has climbed higher in the sky over to your east, exactly the track it takes across the sky after sunrise here on Earth.

Over the two weeks that the Moon waxes, you stay completely still, and we compare notes every night.  At “half full” from my perspective here on Earth, where is the Sun located for you?  Straight overhead.  It’s high noon on the limb of the Moon, and the temperature is approaching the boiling point of water!  Skip ahead anther week, to when I report seeing a full Moon.  For you, the Sun has moved all the way across the sky and down to the western horizon, where it is now poised to set.  The very next night, I report that the Moon is just past full; the right limb of the Moon has fallen into darkness.  That’s entirely consistent with your report, which is that the Sun has now set, and the temperature is plunging.  Your long lunar night has begun. 

Okay.  You’ve been describing how the position of the Sun has changed every day, rising in the East and setting in the West, just the way the Sun behaves for us here on Earth.  We know that the Sun’s apparent movement across our sky is an illusion, brought on by the Earth’s counterclockwise rotation.  Is the similarity between the Sun’s behavior here and on the surface of the Moon just a lucky coincidence? Hardly.  The only way that the Sun can behave in the same way from your vantage point on the Moon, as it does here on Earth, is if the Moon, too, is spinning on its axis in an easterly direction (or to the left, from your perspective on the Moon’s surface).  

How can the Moon’s rotation be reconciled with the fact that the same side of the Moon always faces the Earth?  At first, this seems rather difficult.  If the Moon spins in a counterclockwise direction, like the Earth does, over time, shouldn't new regions of the Moon’s surface become visible to us? Specifically, why doesn't new lunar territory constantly spin into view along the left limb of the disk (as viewed from Earth), and constantly disappear from view along the right limb?  Why, in other words, don’t you disappear behind the right limb?

The reason is simple, but subtle. Let's shift perspective for just a moment and pose a different question.  If the Moon didn't rotate on its axis the way we’ve established it does, what parts of its surface would we see during the two-week period that it moves from new (barely visible as a crescent) to fully illuminated? Well, since the Moon moves continuously in a leftward direction along its orbital track around the Earth, our viewpoint should be constantly shifting "around" the moon in a rightward direction.  We should be seeing new territory appearing constantly on the right side of the Moon's disk (right limb), where you are, while territory constantly disappears from the left limb.  This fact is a little easier to visualize with our old friend, the phases of the Moon figure, so I'm including it again below.

Let’s pause and summarize these points.  Considering the Moon’s movement around the Earth, the sides of the Moon’s disk where territory should be becoming visible and invisible are exactly opposite the sides where territory should be becoming visible and invisible, given the Moon's own rotation.  That’s a big conceptual mouthful to swallow, so it’s worth kind of savoring it, if you have the time and patience.

Are you still with me, patient Whabbloggers? I hope so, because if you are, you have all the conceptual ingredients needed to put the big picture together.  A key to the entire issue is the speed at which the Sun moves across the lunar sky from your perspective on the surface.  Recall that, approximately one week after your sunrise, the Sun was directly overhead (it was locally noon)?  That means that what takes approximately 6 hours to happen on the Earth (the time needed for the Sun to move from it’s position on the eastern horizon at sunrise to fully overhead at noon) has taken a full week on the Moon.  A week after that, when the Moon is full, the Moon's rotation has pushed the Sun all the way to "sunset position” off to your right.  A day on the Moon is two weeks long, and following sunset, two weeks will pass before the sun once again peeks above your eastern horizon.

It takes exactly one month for the moon to rotate once around on its axis. It also takes exactly the same amount of time for the Moon to complete one revolution around the Earth.  Consider: During the time it takes the Moon to revolve from the position it occupies when it is new (right in front of the Sun) to when it is half full (so its position forms a right angle with the Sun and the Earth), it has moved through 90 degrees, exactly one quarter of its orbital circle.  If the Moon wasn’t spinning on its axis, exactly one quarter of the far side would have swung into view along the right side of the disk.   But, in the week it takes to reach that “half moon” position, the Moon has also rotated, in a counterclockwise direction, exactly one quarter of the way around on its axis, effectively blocking any new territory from appearing.  The two motions completely cancel each other out, leaving the same side of the moon permanently turned toward the Earth! 

There’s just one loose end to wrap up.  For the Earth to complete a day in a scant 24 hours, it has to be rotating at an extremely fast clip, reaching a thousand miles an hour at the equator.  What about the moon, where a day lasts a month?  It turns out that even at the Equator, the Moon only rotates at about 10 miles an hour!  As you move away from the Equator, toward one of the lunar poles, the rotation rate slows down all the way to walking speed and below.  Yes: There are places on the moon where you could walk toward the west and keep the Sun permanently fixed at one position in the sky.  Someday, I can imagine moon settlers living in specially designed double-wide boxcars on a railroad track that completely circumnavigates the Moon.  With the boxcar moving along the track at just walking speed, the residents would live in perpetual daylight, with the Sun permanently frozen in a position low enough in the sky (shortly enough after sunrise) that the ambient temperature would always be a balmy 72 degrees!   Yes, you could construct things on the Moon so you lived your life in permanent daylight, and endless summer!

And with that, it’s time for both of us to leave the Moon.  Next blog, I will tackle the behavior of another compelling object in our sky, the planet Venus, the Evening and the Morning Star.  The question is, how can it be both?