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In lunar astronomy, libration is the cyclic variation in the apparent position of the Moon perceived by Earth-bound observers and caused by changes between the orbital and rotational planes of the moon. It causes an observer to see slightly different hemispheres of the surface at different times. It is similar in both cause and effect to the changes in the Moon's apparent size due to changes in distance. It is caused by three mechanisms detailed below, two of which cause a relatively tiny physical libration via tidal forces exerted by the Earth. Such true librations are known as well for other moons with locked rotation.
The quite different phenomenon of a trojan asteroid's movement has been called Trojan libration; and Trojan libration point means Lagrangian point.
The Moon keeps one hemisphere of itself facing the Earth, due to 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: over time, slightly more than half (about 59% in total) of the Moon's surface is seen from Earth due to libration.[1]
Lunar libration arises from three changes in perspective due to: the non-circular and inclined orbit, the finite size of the Earth, and the orientation of the Moon in space. The first of these is called optical libration, the second is called parallax, and the third is physical libration. Each of these can be divided into two contributions.
The following are the three types of lunar libration:
Also called real libration, as opposed to the optical libration of longitudinal, latitudinal and diurnal types, the orientation of the Moon exhibits small oscillations of the pole direction in space and rotation about the pole.
This libration can be differentiated between forced and free libration. Forced libration is caused by the forces exerted during the Moon's orbit around the Earth and the Sun, whereas free libration represents oscillations that occur over longer time periods.
Cassini's laws state that:
In addition to uniform rotation and uniform precession of the equator plane, the Moon has small oscillations of orientation in space about all 3 axes. These oscillations are called physical librations. Apart from the 1.5427º tilt between equator and ecliptic, the oscillations are approximately ±100 seconds of arc in size. These oscillations can be expressed with trigonometric series that depend on the lunar moments of inertia A < B < C.[6] The sensitive combinations are β = (C – A)/B and γ = (B – A)/C. The oscillation about the polar axis is most sensitive to γ and the 2-dimensional direction of the pole, including the 1.5427° tilt, is most sensitive to β. Consequently, accurate measurements of the physical librations provide accurate determinations of β = 6.31×10−4 and γ = 2.28×10−4.[7]
The placement of 3 retroreflectors on the Moon by the Lunar Laser Ranging experiment and 2 retroreflectors by Lunokhod rovers allowed accurate measurement of the physical librations by laser ranging to the Moon.
A free physical libration is similar to the solution of the reduced equation for linear differential equations. The periods of the free librations can be calculated, but their amplitudes must be measured. Lunar Laser Ranging provides the determinations. The two largest free librations were discovered by O. Calame.[8][9] Modern values are:
The fluid core can cause a fourth mode with a period around 4 centuries.[11] The free librations are expected to damp out in times very short compared to the age of the Moon. Consequently, their existence implies that there must be one or more stimulating mechanisms.
