You might have noticed that the Moon surface facing Earth seems to remain the same despite the change in lunar phase over a synodic month. This is because the Moon’s rotational speed is synchronised with its orbital speed around Earth, the Moon almost always shows the same side to Earth. However, the Moon’s appearance as viewed from Earth varies slightly indeed (figure 1). This variation is called Lunar Libration. Overall, 59% of the Moon’s surface is visible from Earth over time due to libration.

To understand the various causes of the Lunar Libration, let us first consider a simple toy model of orbital motion. In figure 2, a cube orbits about point O in a circular and counter-clockwise manner (as viewed from above), with period T. Notice that the cube always has its red face pointing towards the reader. Although the cube does not spin in space, due to its orbital motion, an observer at point O will perceive that the cube exhibits clockwise rotation (as viewed from above) with a period exactly equals T (see figure 3). Now suppose that during the circular motion the cube also rotates counter-clockwise with period T (synchronous rotation). As viewed from O, this real rotation of the cube will compensate for its apparent rotation due to the orbital motion, so that the cube appears to be non-rotating. This is as if the cube only shows one side to point O (in figure 4, an observer at O can only see the blue face of the cube), similar to the case for the Moon where it always shows the same side to Earth.

The Moon’s orbit around Earth, however, is not exactly circular. The Moon thus orbits faster when it is closer to Earth, slower when it is further away from Earth. Although the Moon’s rotational speed is fairly constant, the variation in its orbital speed causes its apparent rotation speed to fluctuate as viewed from the centre of Earth. The overall effect is that the Moon turns westward (eastward) when it is closer to (further away from) Earth than average. The Moon shows more of its eastern (western) surface to Earth on the way it is moving away from (towards) Earth. This is the longitudinal libration of the Moon.

The Moon has an axial tilt of about 6.7 degrees. As the Moon orbits around Earth, its north pole is sometimes oriented slightly towards Earth and sometimes away from it. The Moon reveals more of its surface in the northern (southern) polar region when its north (south) pole leans towards Earth. This is the latitudinal libration of the Moon. The combined effect of the longitudinal and latitudinal librations of the Moon on its appearance as viewed from Earth’s centre is illustrated in animation 1.

Due to the finite size and the rotation of Earth, an extra daily libration called diurnal libration may be observed from Earth, but the effect is less significant.

Besides the mentioned optical librations, there are still other physical librations — forced and free librations, due to the non-spherical shape and the non-uniform mass distribution of the Moon. The forced librations are primarily caused by the varying gravitational force on the Moon due to the relative motion between the Moon and other planetary objects including Earth, while the free librations are excited by seismic events such as meteoritic impact or by the forced librations. These physical librations can generally be ignored because their effects are tiny, interested readers may refer to the reference materials for further details.