# Facing the Earth

#### Why the man in the moon never turns his back

Someone recently asked me: Why do we only see one face of the moon?

The short answer is that the moon rotates very slowly, in precisely the same amount of time that it takes to revolve around the earth. It is not the case, as has often been stated, that the moon does not rotate at all! If it did, we would see different faces as it revolved around the earth. You can verify this easily by pretending to be the moon and walking around, say, your dining room table, and facing north at all times (i.e., not rotating).

This leads one to ask, how did things get to be this way? After all, it would be one big colossal coincidence if the moon's rotation period and revolution period just happened to be the same. It's no coincidence, as it turns out: the moon rotates that slowly because it is tidally locked by the earth.

The moon creates tides on the earth. The oceans can be raised by meters or so because of the gravitational pull of the moon (and to a lesser degree, the sun). The tides not only create better surfing situations, they also slow down the earth.

This is kind of tricky. What happens is that the tidal bulges raised by the moon would be directly under the moon (and directly opposite it, on the other side of the earth), except that the earth rotates, and friction with the ocean floor carries the tidal bulges ahead of the moon. This bulge then pulls the moon and gives it extra energy, raising it into a higher orbit. If you've read that the moon is gradually receding from the earth (by about an inch every year), that's why—tidal forces.

Meanwhile, in that same interaction, the moon is pulling back on the tidal bulges, and friction with the ocean floor slows the earth down, so that angular momentum is in this way conserved (the earth loses it, the moon gains it). If you've read that the earth's rotation is gradually slowing down (by about a millisecond every century), that's why—tidal forces.

If left alone sufficiently long, the moon would slow the earth down until it rotated once every month. At that point, the earth's rotation would no longer rotate ahead of the moon, and the drag effect would cease, for all intents and purposes. The earth would then be said to be "tidally locked" to the moon, and it would keep one face to the moon, just as the moon now keeps one face to the earth. It turns out that this effect would also occur if the earth had no oceans—the solid crust of the earth also bulges in response to the moon's pull. The ocean is simply much more efficient at dragging the earth down.

What about the moon? If the moon, being 81 times less massive than the earth, can create such effects on the earth, then shouldn't the earth, which is so much larger, create that much more effect on the moon? The moon is smaller by diameter, to be sure, by about a factor of 4, but the tidal effect of the earth on the moon is still about 20 times larger than the corresponding effect of the moon on the earth.

In fact, the earth is so much stronger than the moon that its influence has already tidally locked the moon. What's more, the moon is slightly lopsided, and its heavy part is forever facing the earth, so it has even less reason to escape its tidal lock than it would otherwise. That is supposed to be one reason why the near face has so many maria; they are apparently areas of higher mass concentrations—mascons for short.

The moon's tidal influence, as noticeable as it is, is still too slow to tidally lock the earth before the sun expands and toasts them both. The same cannot be said for Pluto and Charon, which hold the distinction as the only planet-satellite pair in which both objects are tidally locked to each other. They rotate approximately once every 6 days, and keep the same face toward each other at all times. There is an entire half of the planet which never sees its moon.

Incidentally, the moon's motion is not completely regular—its orbit is noticeably eccentric and inclined, it's perturbed by the sun and other planets, etc. For these reasons, the moon's rotation rate, which is relatively constant, is not perfectly matched to its revolution rate, which varies throughout the month. As a result, the moon's rotation alternately falls behind and overtakes its revolution, allowing us to see "around the edge of the moon" to the far side. This effect is called libration, and it is mapped out in issues of Sky and Telescope. Because of libration, we can actually see something like 55 percent of the moon's surface area from the earth.