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Libration is a term which is used to refer to small changes in the moves of satellites, as perceived from the perspective of a person standing on the celestial body being orbited. A well known example of libration is lunar libration, but libration also occurs with many other satellites in space. In the case of lunar libration, from the perspective of an observer on Earth, the moon appears to wobble slightly in its orbit, with the wobble being more or less pronounced at various points.
As many people on Earth are aware, the moon's orbit is tied to the Earth in such a way that the same part of the moon faces Earth at all times. This leads to the popular idea that we can only see 50% of the moon's surface from Earth. In fact, this isn't quite right: thanks to libration, observers on Earth can actually see around 59% of the moon's surface at various times. Not all of this 59% can be seen with equal clarity, because some features are hard to distinguish clearly since they are at the extreme edge of the area of the moon which is potentially visible from Earth.
Several phenomena account for lunar libration. The first is that the moon's orbit is irregular, and sometimes the rotation of the moon cannot keep up with its orbit, which means that small slivers on either side of the moon's face become visible. Another issue is the tilt of the moon as it orbits the Earth, which allows people to see different areas of the moon at different points. Finally, the position of an observer on Earth also changes which area of the moon can be seen.
If one views a series of time-lapse photographs illustrating the moon at various stages in its orbit, libration can clearly be seen, because the moon appears to shake or wobble. Each shake or wobble reveals a slightly different part of the moon's surface. For astronomers in the days before satellites could be launched to look at the moon from space, the realization that libration occurred was very important, as people could plan ahead so that they could have a chance of seeing features on the moon which are often hidden.
Understanding libration is also an important part of understanding the orbital paths of satellites. In addition to being of general scientific interest, this can also provide information which may be useful in the future, assuming that people are interested in navigating in space.