Libration

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The lunar phases and librations in 2019 in the Northern Hemisphere at hourly intervals, with music, titles, and supplemental graphics
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 Earth. Lunar libration with phase Oct 2007 HD.gif
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 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. MoonVisibleLibration.jpg
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 due to the rotation of Earth over a few hours. Diurnal libration of the Moon (animated).gif
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 due to the rotation of Earth over a few hours.

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.

Contents

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

Lunar libration

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:

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

Forced physical libration

Full moon at opposite librations Libration des Vollmondes.jpg
Full moon at opposite librations

Cassini's laws state that:

  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 3 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 = (CA)/B and γ = (BA)/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.

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 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.

See also

Related Research Articles

<span class="mw-page-title-main">Ecliptic</span> Apparent path of the Sun on the celestial sphere

The ecliptic or ecliptic plane is the orbital plane of Earth around the Sun. From the perspective of an observer on Earth, the Sun's movement around the celestial sphere over the course of a year traces out a path along the ecliptic against the background of stars. The ecliptic is an important reference plane and is the basis of the ecliptic coordinate system.

<span class="mw-page-title-main">Lunar phase</span> Shape of the Moons sunlit portion as viewed from Earth

A lunar phase or Moon phase is the apparent shape of the Moon's directly sunlit portion as viewed from the Earth. In common usage, the four major phases are the new moon, the first quarter, the full moon and the last quarter; the four minor phases are waxing crescent, waxing gibbous, waning gibbous, and waning crescent. A lunar month is the time between successive recurrences of the same phase: due to the eccentricity of the Moon's orbit, this duration is not perfectly constant but averages about 29.5 days.

<span class="mw-page-title-main">Tidal acceleration</span> Natural phenomenon due to which tidal locking occurs

Tidal acceleration is an effect of the tidal forces between an orbiting natural satellite and the primary planet that it orbits. The acceleration causes a gradual recession of a satellite in a prograde orbit, and a corresponding slowdown of the primary's rotation. The process eventually leads to tidal locking, usually of the smaller body first, and later the larger body. The Earth–Moon system is the best-studied case.

<span class="mw-page-title-main">Orbital inclination</span> Angle between a reference plane and the plane of an orbit

Orbital inclination measures the tilt of an object's orbit around a celestial body. It is expressed as the angle between a reference plane and the orbital plane or axis of direction of the orbiting object.

<span class="mw-page-title-main">Axial precession</span> Change of rotational axis in an astronomical body

In astronomy, axial precession is a gravity-induced, slow, and continuous change in the orientation of an astronomical body's rotational axis. In the absence of precession, the astronomical body's orbit would show axial parallelism. In particular, axial precession can refer to the gradual shift in the orientation of Earth's axis of rotation in a cycle of approximately 26,000 years. This is similar to the precession of a spinning top, with the axis tracing out a pair of cones joined at their apices. The term "precession" typically refers only to this largest part of the motion; other changes in the alignment of Earth's axis—nutation and polar motion—are much smaller in magnitude.

<span class="mw-page-title-main">Axial tilt</span> Angle between the rotational axis and orbital axis of a body

In astronomy, axial tilt, also known as obliquity, is the angle between an object's rotational axis and its orbital axis, which is the line perpendicular to its orbital plane; equivalently, it is the angle between its equatorial plane and orbital plane. It differs from orbital inclination.

<span class="mw-page-title-main">Circle of latitude</span> Geographic notion

A circle of latitude or line of latitude on Earth is an abstract east–west small circle connecting all locations around Earth at a given latitude coordinate line.

<span class="mw-page-title-main">Lunar Laser Ranging experiments</span> Measuring the distance between the Earth and the Moon with laser light

Lunar Laser Ranging (LLR) is the practice of measuring the distance between the surfaces of the Earth and the Moon using laser ranging. The distance can be calculated from the round-trip time of laser light pulses travelling at the speed of light, which are reflected back to Earth by the Moon's surface or by one of several retroreflectors installed on the Moon. Three were placed by the United States' Apollo program, two by the Soviet Lunokhod 1 and 2 missions, and one by India's Chandrayaan-3 mission.

<span class="mw-page-title-main">Celestial equator</span> Projection of Earths equator out into space

The celestial equator is the great circle of the imaginary celestial sphere on the same plane as the equator of Earth. By extension, it is also a plane of reference in the equatorial coordinate system. In other words, the celestial equator is an abstract projection of the terrestrial equator into outer space. Due to Earth's axial tilt, the celestial equator is currently inclined by about 23.44° with respect to the ecliptic, but has varied from about 22.0° to 24.5° over the past 5 million years due to perturbation from other planets.

<span class="mw-page-title-main">Lunar node</span> Where the orbit of the Moon intersects the Earths ecliptic

A lunar node is either of the two orbital nodes of the Moon, that is, the two points at which the orbit of the Moon intersects the ecliptic. The ascending node is where the Moon moves into the northern ecliptic hemisphere, while the descending node is where the Moon enters the southern ecliptic hemisphere.

<span class="mw-page-title-main">Apache Point Observatory Lunar Laser-ranging Operation</span>

The Apache Point Observatory Lunar Laser-ranging Operation, or APOLLO, is a project at the Apache Point Observatory in New Mexico. It is an extension and advancement of previous Lunar Laser Ranging experiments, which use retroreflectors on the Moon to track changes in lunar orbital distance and motion.

<span class="mw-page-title-main">Astronomy on Mars</span> Astronomical phenomena viewed from the planet Mars

Many astronomical phenomena viewed from the planet Mars are the same as or similar to those seen from Earth; but some are quite different. For example, because the atmosphere of Mars does not contain an ozone layer, it is also possible to make UV observations from the surface of Mars.

Cassini's laws provide a compact description of the motion of the Moon. They were established in 1693 by Giovanni Domenico Cassini, a prominent scientist of his time.

<span class="mw-page-title-main">Lunar standstill</span> Moon stops moving north or south

A lunar standstill or lunistice is when the Moon reaches its furthest north or furthest south point during the course of a month. The declination at lunar standstill varies in a cycle 18.6 years long between 18.134° and 28.725°, due to lunar precession. These extremes are called the minor and major lunar standstills.

<span class="mw-page-title-main">Orbit of the Moon</span> The Moons circuit around Earth

The Moon orbits Earth in the prograde direction and completes one revolution relative to the Vernal Equinox and the stars in about 27.32 days and one revolution relative to the Sun in about 29.53 days. Earth and the Moon orbit about their barycentre, which lies about 4,670 km from Earth's centre, forming a satellite system called the Earth–Moon system. On average, the distance to the Moon is about 384,400 km (238,900 mi) from Earth's centre, which corresponds to about 60 Earth radii or 1.282 light-seconds.

Earth tide is the displacement of the solid earth's surface caused by the gravity of the Moon and Sun. Its main component has meter-level amplitude at periods of about 12 hours and longer. The largest body tide constituents are semi-diurnal, but there are also significant diurnal, semi-annual, and fortnightly contributions. Though the gravitational force causing earth tides and ocean tides is the same, the responses are quite different.

The poles of astronomical bodies are determined based on their axis of rotation in relation to the celestial poles of the celestial sphere. Astronomical bodies include stars, planets, dwarf planets and small Solar System bodies such as comets and minor planets, as well as natural satellites and minor-planet moons.

<span class="mw-page-title-main">Earth-centered inertial</span> Coordinate frames

Earth-centered inertial (ECI) coordinate frames have their origins at the center of mass of Earth and are fixed with respect to the stars. "I" in "ECI" stands for inertial, in contrast to the "Earth-centered – Earth-fixed" (ECEF) frames, which remains fixed with respect to Earth's surface in its rotation, and then rotates with respect to stars.

This glossary of astronomy is a list of definitions of terms and concepts relevant to astronomy and cosmology, their sub-disciplines, and related fields. Astronomy is concerned with the study of celestial objects and phenomena that originate outside the atmosphere of Earth. The field of astronomy features an extensive vocabulary and a significant amount of jargon.

<span class="mw-page-title-main">Planetary coordinate system</span> Coordinate system for planets

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References

  1. Spudis, Paul D. (2004). "Moon". World Book at NASA. Archived from the original on July 3, 2013. Retrieved May 27, 2010.
  2. 1 2 3 SVS, NASA's (2021-08-18). "SVS: Moon Phase and Libration, 2020". Home - NASA Scientific Visualization Studio. Retrieved 2022-06-01.
  3. 1 2 Jacqueline Bergeron, ed. (2013). Highlights of Astronomy: As Presented at the XXIst General Assembly of the IAU, 1991. Springer Science & Business Media. p. 521. ISBN   978-9401128285.
  4. 1 2 3 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. Eckhardt, Donald H. (1981). "Theory of the libration of the moon". The Moon and the Planets. 25 (1): 3–49. Bibcode:1981M&P....25....3E. doi:10.1007/BF00911807. ISSN   1573-0794. S2CID   123650603.
  7. Williams, James G.; Konopliv, Alexander S.; Boggs, Dale H.; Park, Ryan S.; Yuan, Dah-Ning; Lemoine, Frank G.; Goossens, Sander; Mazarico, Erwan; Nimmo, Francis; Weber, Renee C.; Asmar, Sami W. (2014). "Lunar interior properties from the GRAIL mission: Lunar Interior Properties". Journal of Geophysical Research: Planets. 119 (7): 1546–1578. doi: 10.1002/2013JE004559 . S2CID   7045590.
  8. Calame, O. (1976). "Determination des librations libres de la Lune, de l'analyse des mesures de distances par laser". Comptes Rendus de l'Académie des Sciences, Série B (in French). 282 (5): 133–135. Bibcode:1976CRASB.282..133C.
  9. Calame, O. (1976). "Free librations of the Moon determined by an analysis of laser range measurements". The Moon. 15 (3–4): 343–352. Bibcode: 1976Moon...15..343C . doi: 10.1007/BF00562246 . S2CID   119505889.
  10. Rambaux, N; Williams, J. G. (2011). "The Moon's physical librations and determination of their free modes" (PDF). Celestial Mechanics and Dynamical Astronomy. 109 (1): 85–100. Bibcode:2011CeMDA.109...85R. doi:10.1007/s10569-010-9314-2. S2CID   45209988.
  11. Viswanathan, V.; Rambaux, N; Fienga, A.; Laskar, J.; Gastineau, M. (2019). "Observational constraint on the radius and oblateness of the lunar core-mantle boundary". Geophysical Research Letters. 46 (13): 7295–7303. arXiv: 1903.07205 . Bibcode:2019GeoRL..46.7295V. doi:10.1029/2019GL082677. S2CID   119508748.