Libration

The quite different phenomenon of a trojan asteroid's oscillation has been called Trojan libration, and Trojan libration point means Lagrangian point.

Lunar libration

The Moon keeps one of its hemispheres facing the Earth because of tidal locking. Therefore, the first view of the far side of the Moon was not possible until the Soviet probe Luna 3 reached the Moon on October 7, 1959, and further lunar exploration by the United States and the Soviet Union. This simple picture is only approximately true since over time, slightly more than half (about 59% in total) of the Moon's surface is seen from Earth because of libration.

Lunar librations arise in broadly two ways—firstly, geometrical librations comprising changes in observational perspective because of the non-circular inclined orbit of the Moon around Earth as well as the Moon's own orientation in orbit and secondly, physical librations which involve actual pendulum-like nodding and wobbling of the Moon around its equilibrium position. Geometrical libration includes optical, parallax and diurnal types, while physical libration includes forced and free types.

The following are the three types of lunar geometrical libration:

1. Optical libration, observed from a point on Earth, it is the combination of longitudinal and latitudinal libration producing a movement of the sub-Earth point and a wobbling view between the temporarily visible parts of the Moon during a lunar orbit. The sub-Earth point is the apparent center of the Moon's disk and the location on the Moon where the Earth is directly overhead. This type of libration is because the orbiting motion of the Moon is not steady—at some times it advances faster than average and some times it is slower. This is not to be confused with the change of Moon's apparent size because of changing distance between Moon and the Earth during the Moon's elliptic orbit, or with the "parallax" type—caused by change of positional angle because of change in position of the Moon's tilted axis, or with the "diurnal" type observed swinging motion of the Moon because of relative position of the Earth's tilted axis vis-a-vis an orbit of the Moon.
   • Libration in longitude results from the eccentricity of the orbit of the Moon around the Earth; the Moon's rotation sometimes leads and sometimes lags its orbital position. The lunar libration in longitude was discovered by Johannes Hevelius in 1648. It can reach 7°54′ in amplitude. Longitudinal libration allows an observer on Earth to view at times further into the Moon's west and east respectively at different phases of the Moon's orbit.
   • Libration in latitude results from the Moon's axial tilt (about 6.7°) between its rotation axis and orbital axis around Earth. This is analogous to how Earth's seasons arise from its axial tilt (about 23.4°) between its rotation axis and orbital axis about the Sun. Galileo Galilei is sometimes credited with the discovery of the lunar libration in latitude in 1632 although Thomas Harriot or William Gilbert might have done so before. Note Cassini's laws. It can reach 6°50′ in amplitude. The 6.7° depends on the orbit inclination of 5.15° and the negative equatorial tilt of 1.54°. Latitudinal libration allows an observer on Earth to view beyond the Moon's north pole and south pole at different phases of the Moon's orbit.
2. Parallax libration are the differences observed when viewing from different locations at the same time; it depends on both the longitude and latitude of the locations on Earth from which the Moon is observed.
3. Diurnal libration is the small daily libration and oscillation observed due to Earth's rotation, because during the time when the Moon is visible on any day, the rotation of the Earth carries an observer from one side (dusk) to the other side (dawn) allowing the observer to look first around one side of the Moon and then around the other—since the observer is on the Earth's surface, and not at its center, which shifts the line of view and slightly increases the observable area, though, this reaches less than 1° in amplitude.

Physical libration is the oscillation of orientation in space about uniform rotation and precession. There are physical librations about all three axes. The sizes are roughly 100 seconds of arc. As seen from the Earth, this amounts to less than 1 second of arc. Forced physical librations can be predicted given the orbit and shape of the Moon. The periods of free physical librations can also be predicted, but their amplitudes and phases cannot be predicted.