Analytical extension of lunar libration tables

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. In this determination, we found the non-negligible amplitudes of the three modes of free physical libration. The determined amplitudes reach 1.296 in longitude (after correction of two close forcing terms), 0.032 in latitude and 8.183 × 3.306 for the wobble, with the respective periods of 1056.13 days, 8822.88 days (referred to the moving node), and 27257.27 days. The presence of such terms despite damping suggests the existence of some source of stimulation acting in geologically recent times. Electronic supplementary materialThe online version of this article (

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“…7) and are often described in the analytical theories (see e.g. Eckhardt 1981;Moons 1982;Petrova 1996).…”

Section: Geometry Of the Physical Librationsmentioning

confidence: 99%

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

Rambaux

Williams

2010

Celest Mech Dyn Astr

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“…Usually, σ is multiplied by I to be comparable to ρ, ρ and Iσ, which are referred to as the latitude librations and τ is referred to as the longitude libration. The pole position of the ecliptic of date on the lunar equator coordinate system is denoted by (P 1 , P 2 ) (Eckhardt 1981;Petrova 1996), which is…”

Section: Libration Modelmentioning

confidence: 99%

Determination of the free lunar libration modes from ephemeris DE430

Yang

Ping

et al. 2017

Res. Astron. Astrophys.

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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 Planetary and Lunar Ephemeris DE430 by JPL/NASA, which was created in April 2013, and is reported to be the most accurate lunar ephemeris today using the data from Gravity Recovery and Interior Laboratory (GRAIL). Therefore, the residuals after fitting the model have reduced owing to improvement in the libration models, and the free librations embedded in the Euler angles have also improved. We use Fourier analysis to extract the approximate frequencies from DE430 and then a quadratic interpolation method is used to determine higher accuracy frequencies. With the frequencies, the linear least-squares fitting method is employed to fit the lunar physical librations to DE430. From this analysis we identified the three modes of free physical librations, and estimated the amplitudes as 1.471 ′′ in longitude, 0.025 ′′ in latitude and 8.19 ′′ × 3.31 ′′ for the wobble, with the respective periods of 1056.16, 8806.9 and 27262.99 d. Since the free librations damp with time, they require recent excitation or a continuous stimulating mechanism in order to sustain.

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“…XYZ is the uniformly rotating ecliptical coordinate system; the angle XoX is equal to the mean lunar longitude L; xyz is the dynamical coordinate system, x is directed towards the minimal moment of inertia A, and z towards the maximal moment C; fi, v, v are libration angles. Eckhardt (1981aEckhardt ( , 1981b, the analytical tables of Migus (1980) and Moons (1982aMoons ( , 1982bMoons ( , 1984aMoons ( , 1984b, and of Petrova (1996). Although the analytical solutions are less accurate than numerical solutions, they have some advantage (see Eckhardt, 1981a).…”

Section: X(t)mentioning

confidence: 99%

“…The analytical tables of Petrova (1996) are constructed for variables of physical libration fi,i/,w. These variables are the angles defining the position of the Dynamical System of Coordinates (DSC) determined by the lunar principal axes of inertia in the uniformly rotating ecliptical coordinate system.…”

Section: Characteristics Of Analytical Libration Tables C O N S T R U C T E D For Libration a N G L E S /I V Izmentioning

confidence: 99%

Lunar Libration Tables and Determination of Crater Coordinates

Petrova

1997

International Astronomical Union Colloquium

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The study of lunar rotation has attracted considerable interest with the advent of the epoch of exploration of the Solar system by space technology. A series of works on an investigation of the lunar gravitational field carried out with the help of artificial lunar satellites have greatly advanced our possibility for that study. The problem concerning the landing on the lunar surface of spacecraft, and the creation of durable lunar bases, impose heavy demands on the accuracy of theoretical description of orbital and rotational motion of the Moon.The development of the observational technology with the help of radio-and laser ranging (LLR) provides at the present time measurements of the distance to a given point on the Moon with an accuracy of about 2 cm, probably improved in the future to about 5mm (Banerdt, 1995). By using differential VLBI measurement with extragalactic radio sources angularly near the Moon, it should be possible to obtain routine estimates of angular position of the beacon to 0.1 mas from each observation (Baudry, 1995). Therefore, combining VLBI and LLR techniques will provide a means of achieving new objectives, and that calls for the development of the theories adequate to an accuracy for observations.

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Analytical extension of lunar libration tables

Cited by 22 publications

References 11 publications

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

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

Determination of the free lunar libration modes from ephemeris DE430

Lunar Libration Tables and Determination of Crater Coordinates

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