In my most recent article for Scientific American, I may have lied to you.
In my defense, I didn’t so much lie as maybe oversimplify a tiny bit. I wrote that because of the effects of the tidal force from Earth, “the moon always shows one face to Earth.” That turns out to be only mostly true. We actually see more like 59 percent of the moon’s total surface from Earth, not strictly half, as you might expect. What I didn’t get into last week was the slow rocking and nodding motion our satellite makes with respect to Earth, which together we call libration. (That shouldn’t be confused with libations, which can cause similar motions in people.)
As I explained in that article, the moon spins once for every one time it orbits Earth. This is the outcome of the inexorable force of our planet’s gravity, which has slowed the moon’s spin and moved our satellite farther and farther from Earth until both angular rates matched. (We sometimes call this spin-orbit resonance, if you want to get technical.)
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Some people have a misconception that the moon doesn’t spin at all, but this is easily debunked: Take a spherical object such as an orange and place it on a table—this will be our model moon—and put some small object near it to represent Earth. Now move the orange around the other object. If you don’t spin the orange, you’ll find that someone on the ersatz Earth will see the entire surface of the orange over the course of one orbit. You have to carefully spin the orange once per revolution to ensure only one side is seen, thus proving that the moon does indeed spin and that this rotation takes the same amount of time as its orbital period.
The overall effect is that the moon is apparently split into two halves: the hemisphere that always faces Earth, which we call the near side, and the half that always points away, known as the far side. Another misconception is that the far side is literally the dark side, but the sun shines for half the time on the lunar far side, giving it two weeks of light and two of darkness, just as on the near side. I’m willing to give some metaphorical ground here because “dark” can mean unknown or unexplored; most of the moon’s far side is forever hidden from Earth, so the metaphor is apt. It wasn’t until the former Soviet Union sent the spacecraft Luna 3 around the moon in 1959 that the first images of the far side were ever seen by human eyes.
Libration is the reason this near- and far-side dichotomy isn’t quite so clear-cut. The phenomenon chiefly arises because the moon’s orbit isn’t a perfect circle but is instead quite elliptical (oval-shaped). Perigee, the closest point in the moon’s orbit to Earth, is about 356,000 kilometers distant, while apogee, its farthest point, is 407,000 km, a difference of roughly 13 percent. This means that from Earth, the moon can appear about 13 percent larger at perigee than apogee—but this also has orbital implications as well.
The speed at which, say, a moon orbits a planet depends on its distance from that planet. The farther out it is, the slower it moves along its trajectory, and conversely, the closer it is, the faster it moves. Because the moon is a huge, massive object, however, its spin doesn’t change at all; it always rotates at the same rate.
This means that when the moon is at apogee, its spin rate is a bit faster than its actual orbital rate, and vice versa at perigee. At apogee it rotates its western side a little bit more into our view, and at perigee we see a little bit more of its eastern side. The amount of extra lunar territory we see is about 7.5 degrees on each side.
So we can, in effect, peek over the edges of the moon’s near side—but only a little. An odd geometric effect makes this difficult to discern: on the moon’s edge, that extra rotation is mostly in a direction straight toward Earth, so the actual extra surface we see is hugely foreshortened and difficult to spot. The effect is greatest for landmarks near the meridian, the moon’s central line that divides east from west. There we see features rock back and forth by 15 degrees, which is quite easy to spot in photographs. When I was in high school, I shot a lot of photographs of the moon using my telescope and camera, and I remember seeing Mare Crisium, a dark impact feature near the moon’s eastern limb, clearly closer to the moon’s edge in one shot than the other. I had discovered libration!
And I found it only 330 years after astronomer Johannes Hevelius first explained it. I will accept partial credit.
This effect is called longitudinal libration, the libration seen east to west. But there’s also latitudinal libration north to south as well. This is because the moon’s orbit is not directly above Earth’s equator but is instead tilted by about five degrees. (The technical term for this is inclination.) When the moon is at the northernmost point in its orbit, we can see a little bit more surface past its south pole, and at its southernmost orbital point we can see farther into the far side at the north.
Together this means we can see 59 percent more moon than if the orbit were perfectly circular and aligned with Earth’s equator. Over the course of the monthlong lunar orbit, the moon appears to wobble east to west and nod north to south. This effect can be seen quite clearly in a video NASA puts out every year showing the moon’s physical motion and phase; the resulting animation is quite mesmerizing.
I’ve known about libration a long time, but it can still surprise me. I’ve always heard that from the moon, spin-orbit resonance means Earth never moves in the sky, as if nailed to a single spot. But libration means that can’t be true: the effect, in fact, makes Earth move in the moon’s sky up to 15 degrees! That would be very noticeable if you were at the extreme eastern or western moon edge of the moon; you could actually see Earth slowly rise and sink back down below the horizon over the course of a few hours every month. That wouldn’t be a bad place to set up a tourist spot. How much would you pay for a cozy spot from which to watch earthrise?
In astronomy—in everything—we take mental shortcuts, such as saying we only see half of the moon, to simplify situations. In general these are fine; they help us grasp what can be complex situations. But we need to be careful not to let these be oversimplifications because there can be very cool science, and poetic beauty, in discovering the details.