A Staff Report from the Straight Dope Science Advisory Board

# Why does the same side of the moon always face the earth?

January 30, 2003

Dear Straight Dope:

As every fourth grader (at least of my generation) is or was taught, the moon revolves once on its axis for every orbit around the earth. Thus, the same side of the moon is seen from earth at all times. OK, fine. But it recently struck me that it's gotta be EXACTLY one r.p.o.; if it's off by even half a footprint, before long we'll be able to see the dark side of the moon for ourselves, rather that depending on Pink Floyd's description. My question: Is this a cosmic coincidence? Or is there something regulating Luna's spin?  My first reaction is that maybe the moon's mass is off center, and the earth's gravity is holding the heavy side down. But then wouldn't the moon revolve around its center of mass (rather than its center of volume) and thus appear to wobble?

After I got done writing this up I discovered Cecil had already answered the question. But my feeling is that celestial mechanics is a topic of enduring interest. It's not like because Shakespeare wrote sonnets on the subject we don't get to write any more about love.

Anyway, Tim, your intuition is on the money. Yes, the moon's rotation is perfectly synchronized with its orbit; no, it's not coincidence; yes, it has to do with the moon's mass distribution, and yes, the moon does wobble. But let's take this one point at a time. First, we're going to have to talk about tidal forces for a bit.

An orbit can be considered as a balance between gravity and centrifugal force. Yes, I said centrifugal force: It's a perfectly valid way to describe the physics, and in this case, it happens to be the simplest. Centrifugal force is pulling the moon out, and gravity is pulling it in. But these forces aren't uniform: Centrifugal force gets stronger as you get further from the center, while gravity gets weaker as you get further from the center. What this means is that the balance is only perfect at the center of the moon: For a piece of moon closer to the earth, the earth's gravity is stronger than the centrifugal force, and for a piece of moon on the far side, the centrifugal force is stronger than the earth's gravity. This effect is referred to as tidal force, and it has the effect of slightly elongating the moon--that is, pulling it into a football shape pointing toward the earth. (I exaggerate, of course.) Tides on the earth work in the same way, which is why there are two tidal bulges on the oceans, one on the side of earth directly beneath the moon, the other on the earth's far side. (Cecil has written about this, too.) Of course, the tides on earth are mostly noticeable on the oceans, since water stretches a lot more easily than rock, but even rock on the moon can be pulled out of place to some extent.

Now let's picture a moon that's not perfectly synchronized. It's always trying to stretch out on a line pointing towards and away from the earth, but that line isn't always in the same place. So the distortion is constantly changing as it tries to keep up. This constantly-changing distortion heats up the rock and causes energy to be lost from the rotation. So the moon slows down until it's synchronized. It still feels the effects of tidal distortion, but now the distortion is constant and permanent: The moon is slightly elongated, with its long axis pointing towards and away from the earth. In fact, this is the situation of moons in general: All of the moons in the solar system are synchronized, or tidally locked, with their primary planet, and in the case of Pluto and its moon Charon, the planet is locked to its moon as well. For an even more interesting case, the planet Mercury has what's called a harmonic lock with the sun: Mercury's rotational period is exactly two thirds of its orbital period. This is because Mercury's orbit is very elliptical, as planets go, and a 2/3 ratio lets its permanent elongation line up every orbit when it's closest and the tides are strongest.

Lunar motion has a few additional subtleties to it. The period of rotation does exactly match the period of revolution, but that doesn't mean the two are perfectly synchronized. To put it another way, over the course of a month, the speed of the moon's rotation can be considered constant, but its orbital speed can't be. That's because the orbit is slightly elliptical rather than circular, and an orbiting object moves faster the closer it is to the center. So sometimes the rotation leads the revolution by a bit, and sometimes it lags a bit, and the moon appears to wobble by a few degrees in the sky. This may seem like no great shakes, but in fact it results in shakes of fairly substantial proportions: Due to the wobble, called libration, the tidal distortion is still changing and energy is still going into heat in the moon, occasionally causing moonquakes. Currently, this energy is coming from the orbital energy of the moon in such a manner that the orbit is becoming more circular. On our moon, this just causes occasional minor quakes, but it can be much more significant: Because of tidal heating, Jupiter's moon Io is the most volcanically active world in the solar system.

Staff Reports are written by the Straight Dope Science Advisory Board, Cecil's online auxiliary. Though the SDSAB does its best, these columns are edited by Ed Zotti, not Cecil, so accuracywise you'd better keep your fingers crossed.

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