Lost Lunar Librations

Lost Lunar Librations

The casual observer could anticipate that the Moon would display some irregular movements as its buffeted by the variable Solar Wind [and the associated Interplanetary Magnetic Field].

This should be especially true when its moving against the flow of the Solar Wind.

Moon - Fast and Slow cycle

The Clockwork Moon

The interplanetary magnetic field (IMF) is the solar magnetic field carried by the solar wind among the planets of the Solar System.


Unsurprisingly, the buffeting of the Moon has been clearly observed.

Over 100 years ago the mainstream was troubled because it could “not quite satisfactorily accounted for” the observed “small terms of much shorter period in the Moon’s motion”.

The problems of the Moon's motion

Some problems of astronomy – XV The problems of the Moon’s motion
E. W. Brown
Journal: The Observatory, Vol. 37, p. 206-211 (1914)

These troubles multiplied significantly in the 1960s when precise measurements [using Doppler Shift Radar techniques] identified “relatively large, variable, and unexplained discrepancy in radial acceleration” of the Moon that lasted for about a day.

Precise measurements of the Doppler shift of radar waves reflected from Moon disclose unexpectedly large discrepancies-averaging about 0.6 centimeter per second-between the radial velocities and the predictions based on the Eckert-Brown lunar ephemeris.

These residuals have a rapidly changing component corresponding to a relatively large, variable, and unexplained discrepancy in radial acceleration of about 10(-4) centimeter per second, per second, in magnitude and about 1 day in period.

Discrepancies between Radar Data and the Lunar Ephemeris.
Smith CR, Pettengill GH, Shapiro II, Weinstein FS.
Science. 1968 May 24;160(3830):876-8.

During the 1970s these troubles became really perturbing when the mainstream realised it had “no satisfactory explanations” for the “conspicuous effects of non-gravitational forces in the Earth-Moon system”.

The most conspicuous effects of non-gravitational forces in the Earth-Moon system are the accelerations of the Earth’s spin and of the Moon’s mean angular velocity.

Evidence indicates that the present acceleration of the Moon is between −20 and −52 s of arc per century per century and that the present average acceleration of the Earth is between −5 and −23 parts in 109 per century.

Over the past 2000 yr, the average for the Moon has been about −42 s per century per century and for the Earth has been about −28 parts in 109 per century; these values are probably correct within 10%.

There are no satisfactory explanations of the accelerations.

Existing theories of tidal friction are quite inadequate.

Astronomical evidence concerning non-gravitational forces in the Earth-Moon system
R. R. Newton
Astrophysics and Space Science – May 1972, Volume 16, Issue 2, pp 179-200

Therefore, it should come as no surprise that the mainstream is especially anxious to explain away these “non-gravitational forces” which cause perturbations in the orbit of the Moon.

In astronomy, perturbation is the complex motion of a massive body subject to forces other than the gravitational attraction of a single other massive body.

The other forces can include a third (fourth, fifth, etc.) body, resistance, as from an atmosphere, and the off-center attraction of an oblate or otherwise misshapen body.

In the Solar System, many of the disturbances of one planet by another are periodic, consisting of small impulses each time a planet passes another in its orbit.

This causes the bodies to follow motions that are periodic or quasi-periodic – such as the Moon in its strongly perturbed orbit, which is the subject of lunar theory.

The perturbing forces of the Sun on the Moon at two places in its orbit.

Because the perturbing force is different in direction and magnitude on opposite sides of the orbit, it produces a change in the shape of the orbit.


Diagram of perturbations by the Sun of the Moon in its orbit

The “largest lunar perturbations” have [at least] been named by Lunar Theory.

Several of the largest lunar perturbations in longitude (contributions to the difference in its true ecliptic longitude relative to its mean longitude) have been named.

Equation of the Center …
Evection …
Variation …
Annual Equation …
Parallactic Inequality …
Reduction to the Ecliptic …


However, the mainstream is overwhelmed by the smaller Lunar perturbations because “based on laser-ranging observations” there are “tens of thousands” perturbations they need to explain away.

The number of terms needed to express the Moon’s position with the accuracy sought at the beginning of the twentieth century was over 1400; and the number of terms needed to emulate the accuracy of modern numerical integrations based on laser-ranging observations is in the tens of thousands: there is no limit to the increase in number of terms needed as requirements of accuracy increase.


Consequently, Wikipedia prefers the casual reader to focus upon the “three types” of Lunar Librations that are purely observational artefacts.

There are three types of lunar libration:

Libration in longitude results from the eccentricity of the Moon’s orbit around Earth; the Moon’s rotation sometimes leads and sometimes lags its orbital position.

Libration in latitude results from a slight inclination between the Moon’s axis of rotation and the normal to the plane of its orbit around Earth.
Its origin is analogous to how the seasons arise from Earth’s revolution about the Sun.

Diurnal libration is a small daily oscillation due to the Earth’s rotation, which carries an observer first to one side and then to the other side of the straight line joining Earth’s and the Moon’s centers, allowing the observer to look first around one side of the Moon and then around the other – because the observer is on the surface of the Earth, not at its center.


External links
Libration of the Moon from educational website From Stargazers to Starships


Wikipedia also prefers the casual reader to forget that their quoted external educational website actually admits there is a fourth category labelled “physical” librations of the Moon.

In addition to the preceding modes, there also exist “physical” librations, actual pendulum-like nodding and wobbling of the Moon around its equilibrium position, like the spring-attached head of one of those “bobblehead dolls” popular as souvenirs.

Libration of the Moon
Educational Web Sites on Astronomy, Physics, Spaceflight and the Earth’s Magnetism
Author and Curator: Dr. David P. Stern

The Lunar Laser Ranging experiment has been active since 1969 when Apollo astronauts placed the first retroreflector on the Moon.

The data accuracy of a few centimeters over recent decades, joined to a new numerically integrated ephemeris, DE421, encourages a new analysis of the lunar physical librations of that ephemeris, and especially the detection of three modes of free physical librations (longitude, latitude, and wobble modes).

This analysis was performed by iterating a frequency analysis and linear least-squares fit of the wide spectrum of DE421 lunar physical librations.

From this analysis we identified and estimated about 130–140 terms in the angular series of latitude librations and polar coordinates, and 89 terms in the longitude angle.

The Moon’s physical librations and determination of their free modes
N. Rambaux, J. G. Williams
Celestial Mechanics and Dynamical Astronomy – January 2011, Volume 109, Issue 1

Clearly, Wikipedia is perturbed by the buffeting [aka perturbations] of the Moon by the Solar Wind and prefers to avoid embarrassment by switching into Lost Down the Back of the Sofa [aka The Dog Ate My Homework] mode.

Quelle surprise!

Gallery | This entry was posted in Astrophysics, Atmospheric Science, Earth, Fluid Mechanics, Geomagnetism, Gravity, Moon, Science, Solar System, Vortices. Bookmark the permalink.

4 Responses to Lost Lunar Librations

  1. Ah, the embedded IMF in the solar wind is an error – Alven pointed this out in his Nobel Prize speech. Magnetic fields are not frozen in plasma, so the IMF is also not frozen in the solar wind as asserted by Wikipedia.

    I have also noticed a bit of confused thinking in this area, confusion that befuddles me as well. If we restrict our thinking to the plasma domain then gravity is irrelevant but then we can’t incorporate mass into those ideas either; mass is a gravitational factor.

    And it’s the anomalies in observed motion of bodies that are important.

    And while we can “see” the moon, we actually cannot “see” the solar wind directly so I wonder how we “know” that it’s comprised of electrons, protons and etc streaming from the sun. If protons are leaving the sun, then electrons must be arriving at the same time if we are dealing with an electric field.

    So if a plasma double layer explodes, this then implies it is some sort of object that has something happening to it, and here I wander into unknown territory where using the terminology of objects and Newtonian ideas may not be all that useful, yet it’s the tools we have for the moment.

    • malagabay says:

      I have changed “embedded” to read “associated”.
      Either way, neither of those words [in my lexicon] mean “frozen in plasma”.

      I wonder how we “know” that it’s comprised of electrons, protons and etc streaming from the sun.
      I definitely don’t “know”.
      I rely upon the Oracles and the Space Cadets [until I learn otherwise].
      Which is pretty much what this blog is all about i.e. learning otherwise 🙂

    • malagabay says:

      I guess we should add Subatomic particles [like the Neutrino] into the ingredient list for the Solar Wind.

      Neutrinos can be created in several ways, including in certain types of radioactive decay, in nuclear reactions such as those that take place in the Sun, in nuclear reactors, when cosmic rays hit atoms and in supernovae.

      The majority of neutrinos in the vicinity of the Earth are from nuclear reactions in the Sun.

      In fact, about 65 billion (6.5×1010) solar neutrinos per second pass through every square centimeter perpendicular to the direction of the Sun in the region of the Earth.


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