Editing Libration (section)

=== Forced physical libration ===
[[File:Libration des Vollmondes.jpg|thumb|Full moon at opposite librations]]
[[Cassini's laws]] state the following:

# The Moon rotates uniformly about its polar axis keeping one side toward the Earth.
# The Moon's equator plane is tilted with respect to the ecliptic plane and it precesses uniformly along the ecliptic plane. 
# The descending node of the equator on the ecliptic matches the ascending node of the orbit plane.

In addition to uniform rotation and uniform precession of the equator plane, the Moon has small oscillations of orientation in space about all three axes. These oscillations are called physical librations. Apart from the 1.5427° 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''.<ref>{{Cite journal|last=Eckhardt|first=Donald H.|date=1981|title=Theory of the libration of the moon|url=https://doi.org/10.1007/BF00911807|journal=The Moon and the Planets|language=en|volume=25|issue=1|pages=3–49|doi=10.1007/BF00911807|bibcode=1981M&P....25....3E|s2cid=123650603 |issn=1573-0794|url-access=subscription}}</ref> 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'' = {{val|6.31|e=-4}} and ''γ'' = {{val|2.28|e=-4}}.<ref>{{Cite journal|last1=Williams|first1=James G.|last2=Konopliv|first2=Alexander S.|last3=Boggs|first3=Dale H.|last4=Park|first4=Ryan S.|last5=Yuan|first5=Dah-Ning|last6=Lemoine|first6=Frank G.|last7=Goossens|first7=Sander|last8=Mazarico|first8=Erwan|last9=Nimmo|first9=Francis|last10=Weber|first10=Renee C.|last11=Asmar|first11=Sami W.|date=2014|title=Lunar interior properties from the GRAIL mission: Lunar Interior Properties|journal=Journal of Geophysical Research: Planets|language=en|volume=119|issue=7|pages=1546–1578|doi=10.1002/2013JE004559|s2cid=7045590 |doi-access=free}}</ref>

The placement of three retroreflectors on the Moon by the [[Lunar Laser Ranging experiment]] and two retroreflectors by [[Lunokhod programme|Lunokhod]] rovers allowed accurate measurement of the physical librations by laser ranging to the Moon.