Libration

Source: Wikipedia, the free encyclopedia.
This article is about astronomical observations. For molecular motion, see libration (molecule). For orbital mechanics, see libration point orbit.
Not to be confused with liberation, libation, or vibration.
The lunar phases and librations in 2019 in the Northern Hemisphere at hourly intervals, with music, titles, and supplemental graphics
Over one lunar month more than half of the Moon's surface can be seen from the surface of the Earth.
Simulated views of the Moon over one month, demonstrating librations in latitude and longitude. Also visible are the different phases, and the variation in visual size caused by the variable distance from the Earth.
Theoretical extent of visible lunar surface (in green) due to libration, compared to the extent of the visible lunar surface without libration (in yellow). The projection is the Winkel Tripel projection. Mare Orientale, just outside the yellow region, is brought into visibility from Earth by libration.
Diurnal libration of the moon as actually observed from beginning to end of a single night. The two angles are created by the different position of the observer with respect to the Moon because of the rotation of the Earth over a few hours.

In lunar astronomy, libration is the cyclic variation in the apparent position of the

locked rotation
.

The quite different phenomenon of a

Lagrangian point
.

Lunar libration

Animation showing the changing position of the Moon due to libration, in relation to a fictitious red position on perfectly circular orbit.

The

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.[1]

Lunar libration arises from three changes in perspective because of 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 parallax, and the third physical libration. Each of these can be divided into two contributions.

The following are the three types of lunar libration:

Physical 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, and free libration represents oscillations that occur over longer time periods.

Forced physical libration

Full moon at opposite librations

Cassini's laws state the following:

  1. The Moon rotates uniformly about its polar axis keeping one side toward the Earth.
  2. The Moon's equator plane is tilted with respect to the ecliptic plane and it precesses uniformly along the ecliptic plane.
  3. 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.[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 three retroreflectors on the Moon by the

Lunar Laser Ranging experiment and two retroreflectors by Lunokhod
rovers allowed accurate measurement of the physical librations by laser ranging to the Moon.

Free physical libration

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:

  1. 1.3 seconds of arc with a 1056-day (2.9-year) period for rotation about the polar axis,
  2. a 74.6-year elliptical wobble of the pole of size 8.18 × 3.31 arcseconds, and
  3. an 81-year rotation of the pole in space that is 0.03 seconds of arc in size.[10]

The fluid core can cause a fourth mode with a period around four 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.

See also

References

  1. ^ Spudis, Paul D. (2004). "Moon". World Book at NASA. Archived from the original on July 3, 2013. Retrieved May 27, 2010.
  2. ^ a b c SVS, NASA's (2021-08-18). "SVS: Moon Phase and Libration, 2020". Home - NASA Scientific Visualization Studio. Retrieved 2022-06-01.
  3. ^
    ISBN 978-9401128285
    .
  4. ^ a b c Ratkowski, Rob; Foster, Jim (May 31, 2014). "Libration of the Moon". Earth Science Picture of the Day.
  5. ^ Stephen Pumfrey: Harriot's Maps of the Moon: New Interpretations. Notes Rec. R. Soc. 63, 2009, doi:10.1098/rsnr.2008.0062.
  6. S2CID 123650603
    .
  7. S2CID 7045590
    .
  8. Bibcode:1976CRASB.282..133C
    .
  9. S2CID 119505889
    .
  10. S2CID 45209988
    .
  11. S2CID 119508748
    .
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