We’re all familiar with the fact that the Moon always turns the same side towards the Earth, meaning that we can only ever see one hemisphere, the so-called near side. It wasn’t until 1959 that we got a view of the far side, when the Soviet spacecraft Luna 3 sent back a few grainy black and white photographs.

And pretty much everyone understands that the reason for this is that the Moon takes the same time to turn on its axis as it does to revolve around the Earth. Like this:

The red side is the far side of my model Moon, and an observer on the blue Earth in the centre can only ever see the white near side.

Well, not quite. We can actually catch glimpses of the lunar far side, from here on Earth, because of a phenomenon called lunar libration. Which is what this post is about.

Libration is a rocking motion—the word comes from Latin libra, a set of balance scales. (Which should be familiar from the zodiacal constellation Libra, The Scales.) So to librate is to rock back and forth like a disturbed set of scales, and the Moon appears to do exactly that when viewed from the Earth, so we can glimpse a little rim of the far side from time to time.

The Moon’s rotation rate and axial inclination do vary a little, responding to the gravitational tug of the Sun and planets, but this physical libration accounts for very little of the apparent rocking motion we observe. Almost all of it is optical libration—arising from our changing angle of view as the Earth rotates and the Moon revolves around it.

The first category of optical libration I want to describe is diurnal libration, so-called because it is usually observed by a single observer during the course of a day. Or, to be more accurate, half a day, between moonrise and moonset. During that period, the Earth’s rotation carries a Moon-watcher through an arc that can span, at maximum, the entire width of the Earth. This change in vantage point allows us to peek a little way around the trailing hemisphere of the Moon, and then a little way around the leading hemisphere. Here’s a madly out-of-proportion diagram showing how that works:

This lets us see, at maximum, about three-quarters of a degree into the lunar far side. Here’s a little animation of how our perspective of the moon shifts during such conditions:

It looks fairly impressive, but remember that this is actually happening over the course of about twelve hours—and that for most observers (for instance, those at high latitudes), most of the time, the effect is considerably less than what’s shown.

While the animation shows our viewpoint shifting in lunar longitude, as it would appear for a single observer between moonrise and moonset, there’s also a two-observer form of diurnal libration that shifts in latitude. An observer in high northern latitudes can see a little way over the Moon’s north pole, while an observer in high southern latitudes can see a little way over the Moon’s south pole. They could take simultaneous photographs, compare them, and infer something like this:

But there are a couple of more significant effects contributing to lunar libration. The first is libration in longitude, which arises because the Moon’s orbit is not perfectly circular. It moves around the Earth in an ellipse, and moves faster when it is closest to the Earth.

Here’s the ideal situation, a circular orbit with constant angular velocity, as depicted earlier in this post:

I’ve shown my little diagrammatic Moon at four equally spaced times during its orbit, and added a couple of time-ticks between each of those stages. Each tick corresponds to a 30° rotation of the Moon, over about 2.3 days.

But here, in exaggerated form, is what really happens:

The Earth is no longer at the centre of a circular orbit, but rather at one focus of an ellipse. And while the Moon is rotating at constant velocity, it’s whooshing past the Earth at its closest approach, and dilly-dallying at its farthest excursion. The combination of these two facts means that we can see a little way into the Moon’s far side on its trailing hemisphere as it recedes from us, and a see a corresponding distance into the leading hemisphere as it approaches us.

Here’s an animation, 24 seconds long, of what we’d see in this scenario.

The centre of the white near side is marked with a red dot. My toy moon has no axial inclination (its equator is marked in red), and it’s in a strongly elliptical orbit. The orbital plane is also marked in red, spanning the field of view.

The animation starts with a full moon at closest approach (perigee), after which it initially recedes quickly, giving a good view into the eastern far side, before slowing down as it approaches its greatest distance (apogee). Then it accelerates towards us again, and we can see a little way into the western rim of the far side before it returns to perigee.

The Moon’s orbit is much less elliptical than my model above, but we can still see a little way into the far side as it moves from perigee to apogee and back again. The shape of the lunar ellipse varies, as I’ve described in detail in a previous post, but the maximum libration in longitude is about 8°, like this:

We also see libration in latitude, because the Moon’s rotation axis is tilted relative to its orbital plane. Here’s an exaggerated diagram of that situation, viewed from the side:

When the lunar north pole is tilted towards us, we can see a little way into the northern part of the far side. Half an orbit later, with the north pole tilted away from us, we can see into the southern part of the far side. Here’s another brief animation showing how that works:

The simulated Moon is in a circular orbit, but its axis is strongly tilted, as we can see from the angle of the equator in the opening frames. First, it nods its northern pole towards us, and then half an orbit later, its southern pole.

The real Moon is less strongly tilted, but we can nevertheless see almost seven degrees into the far side over its north and south poles during the course of one orbit, like this:

The real moon, of course, experiences libration in longitude and latitude simultaneously. Here’s a 52-second animation of what that looks like, using real orbital data:

This combination of libration in longitude and latitude, combined with diurnal libration, means that from here on Earth we can actually see 59% of the surface of the Moon, although some of that is seen only glancingly and occasionally.

You might think that’s a pretty gross and obvious behaviour, but bear in mind it happens over the course of an entire month, and that our naked-eye view of the Moon doesn’t let us see much detail, as I described in a previous post. So it seems that for most of human history these librations went entirely unnoticed. It wasn’t until the middle of the seventeenth century, when people started trying to map the Moon using the recently invented telescope, that they noticed that something odd was happening around the edges of the lunar disc, with features popping in and out of visibility. I’ll write more about that in another post.

If the Moon’s perigee and axial tilt remained fixed in space, the lolloping motion in the video above would repeat over and over again in the same pattern. But the Moon’s orbit is complicated. The perigee shifts continuously in one direction, and the lunar axis precesses constantly in the opposite direction. So libration in longitude has an oscillation period of 27.55 days (the length of an anomalistic month), while libration in latitude ticks along at a faster rate, completing a cycle in 27.21 days (the duration of the draconic month). So every month produces a slightly different, and steadily evolving, mix of longitude and latitude libration, until the pattern starts to repeat after 2190.35 days, or almost exactly six years. And I’ll write more about that, too, when I return to this topic later.