The Moon’s physical librations and determination of their free modes

  title={The Moon’s physical librations and determination of their free modes},
  author={N. Rambaux and James G. Williams},
  journal={Celestial Mechanics and Dynamical Astronomy},
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… 

Determination of the free lunar libration modes from ephemeris DE430

The Moon’s physical librations have been extensively studied, and elaborate researches have been developed for the purpose of deriving accurate modes of free librations. Our motivation comes from the

Estimation of the lunar free libration modes based on the recent ephemerides

The accuracy of lunar laser ranging (LLR) experiment has already increased to about 1 cm in recent years. When the LLR data joined to the lunar dynamical model updated from DE430, three independent

Use of an Analytical Theory for the Physical Libration of the Moon to Detect Free Nutation of the Lunar Core

A brief review of modern observational achievements and the theoretical basis of physical libration of the Moon is presented. Special attention is given to the inferred existence of a lunar core and

Contributions to reference systems from Lunar Laser Ranging using the IfE analysis model

Lunar Laser Ranging (LLR) provides various quantities related to reference frames like Earth orientation parameters, coordinates and velocities of ground stations in the Earth-fixed frame and

The effect of the Earth’s oblateness on the Moon’s physical libration in latitude

The Moon’s physical libration in latitude generated by gravitational forces caused by the Earth’s oblateness has been examined by a vector analytical method. Libration oscillations are described by a

Effects of a physical librations of the moon caused by a liquid core, and determination of the fourth mode of a free libration

An analytical theory of lunar physical librations based on its two-layer model consisting of a non-spherical solid mantle and ellipsoidal liquid core is developed. The Moon moves on a high-precision

Lunar Laser Ranging: a tool for general relativity, lunar geophysics and Earth science

Only a few sites on Earth are technically equipped to carry out Lunar Laser Ranging (LLR) to retroreflector arrays on the surface of the Moon. Despite the weak signal, they have successfully provided

Comparison of Two Methods on Lunar Free Librations Considering Two-Layer Model

Introduction: Lunar librations have been researched for decades. We tried to compare the numerical and analytic methods on periods of lunar free librations. Furthermore, the layer structure has been

Influence of the layered Moon and Earth’s orientation on lunar rotation

One of the most efficient ways to probe the lunar inner structure at present is through the study of its rotation. Range and range rate (Doppler) data between the Chang’E-3 lander and station on the



Free librations of the moon determined by an analysis of laser range measurements

Among the lunar laser range measurements obtained during the past six years at McDonald Observatory, those available cover the period August 1969-November 1974, being 1377 normal observations made on

Free librations of the moon from lunar laser ranging.

Analyses of the lunar laser ranging measures, performed at the McDonald Observatory during these last six years, has permitted the improvement of a number of parameters relative to the Earth-Moon

A new determination of lunar orbital parameters, precession constant and tidal acceleration from LLR measurements

An analysis of Lunar Laser Ranging (LLR) observations from January 1972 until April 2001 has been performed, and a new solution for the lunar orbital motion and librations has been constructed that

Lunar Laser Ranging: A Continuing Legacy of the Apollo Program

Laser ranging analysis has provided measurements of the Earth's precession, the moon's tidal acceleration, and lunar rotational dissipation, and the verification of the principle of equivalence for massive bodies with unprecedented accuracy.

Dynamical consequences of meteorite impacts on the Moon

The magnitudes of the excitation of free precession of the lunar spin axis about the position defined by Cassini's laws, free libration in longitude, and free wobble are determined as a function of

Passing through resonance: The excitation and dissipation of the lunar free libration in longitude

The acceleration of the mean lunar longitude has a small effect on the periods of most terms in a Fourier expansion of the longitude. There are several planetary perturbation terms that have small

Estimation of the lunar physical librations

The recent long-term integration of JPL ephemeris DE403/LE403 yielded lunar physical librations covering 6000 years. A Fourier analysis of a 718-year subset of this span produced estimates of the

The free librations of a dissipative Moon

  • C. F. Yoder
  • Physics
    Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences
  • 1981
Dissipation in the Moon produces a small offset, ca. 0.23", of the Moon's rotation axis from the plane defined by the ecliptic and lunar orbit normals. Both solid body tidal friction and viscous

Planetary perturbations on the Libration of the Moon

A theory of the libration of the Moon, completely analytical with respect to the harmonic coefficients of the lunar gravity field, was recently built (Moons, 1982). The Lie transforms method was used