Recent analyses of lunar ranging observations have revealed strong evidence of dissipation in the moon’s rotation (Ferrari et al. 1980; Cappallo et al. 1981). If interpreted as solid body friction, these results imply a tidal Q of about 25 (±5) at a frequency of one cycle per month. There is little evidence from other studies of the interior structure of the moon to support such a low solid-body Q. Yoder (1981) finds that turbulent fluid friction between the mantle and a core of radius ~300 km is a plausible mechanism to explain the observed dissipation. An iron or iron-sulfide core of this size is consistent with moment-of-inertia (Blackshear and Gapcynski 1977, Ferrari et al. 1980) and seismic (Goins et al. 1979) data, and is not excluded by conductivity data (Goldstein 1979). Stevenson and Yoder (1980) have proposed a model for formation of a solid iron inner core surrounded by a fluid iron sulfide layer of thickness 65 − 180 km.

Comparisons of numeric, semi-analytic and analytic lunar libration models indicate that the planetary and Earth figure perturbations used to supplement the semi-analytic and analytic models are inadequate. Using the ELP-2000 of Chapront and Chapront-Touzé, an improved solution of these perturbations is developed. For the libration in longitude there are numerous terms with periods near that of the free libration; their amplitudes remain ill-defined.

The effect of tidal friction in the lunar orbit is one of the classic examples of ad hoc modelling of an unknown physical phenomenon. The two basic calculational approaches in current use are developed in some detail, and numerical tests and comparisons are presented. Although attention is normally concentrated on the acceleration in orbital longitude produced as a result of terrestrial dissipation, it is shown that the variation in Earth-Moon distance due to Earth tides is far from negligible. A significant, though minor, fraction of this variation is supplied by the radial component of the acceleration, which would exist even in the absence of tidal friction. In fact, this represents almost all the difference in the predictions of the two models.

The question posed by the title is not yet conclusively resolved. Nonetheless, determinations of the lunar tidal acceleration based on dynamical time scales are now in reasonable accord with one another, whether based on the transits of Mercury, ancient eclipse observations, ocean tide models, or artificial satellite observations; these give a purely tidal component of −28.8 ± 1.5 “/cy2. Lunar occultations and laser ranging now give concordant results for the total anomalous acceleration of about −22.8 ± 1.5. The difference in these results gives an acceleration of possible cosmological origin of ṅ/n = +3.5 ± 1.2 × 10−11 per year, which is also consistent with very preliminary planetary radar studies. If interpreted in the scalar covariant cosmology of Canuto and Hsieh, this implies that Ġ/G = (−6.9 ± 2.4) × 10−11 per year, if measured in atomic time, but zero if measured in dynamical time. The implications for relativity and cosmology are discussed briefly in the paper, scheduled for the Astrophysical Journal issue of 1 September 1981.

The lunar laser range data taken at McDonald Observatory between August 1969 and May 1980 has been analyzed. The simple rms residual for the 2954 ranges is 31 cm. Results of the analysis include GMearth = 398600.45±0.02 km3/sec2 and a secular acceleration of the lunar orbital mean longitude of ṅ = −23.8±1.5“/century2 which yields a Q of 12.3 at semidiurnal frequencies. The lunar harmonic C30 is (−8.7 ± 1.1) × 10−6 and the lunar rotational dissipation k2mT = (4.7 ± 0.5) × 10−3 day. Also resulting from the solution are geocentric coordinates of McDonald accurate to 30 cm, including the first value for the longitude with the new IAU constants and a dynamical equinox.

In this contribution, a review of the calculation of the lunar orbit in the relativistic framework is drawn up. Then, the particular dependence of the lunar orbit motion upon the relativistic perturbations of the motions of the planets themselves is put forth.

Almost every aspect of the analytical theory of the motion of the Moon has been reinvestigated lately. This paper is a review of these investigations.

The improvement upon the I.L.E. (the best known earlier theory based upon the work of Brown) is spectacular, but it is still too early to assess the exact value of these theories with respect to numerical integration.

Until very recently the only available source of accurate positions for the Moon and planets were the american export ephemerides from JPL in particular DE86/LE40 which expired in May 1979 and then DE96/LE44 and DE102/LE51. Unfortunately, these ephemerides were constructed for various applications, but are not necessarily adapted for a purpose such as the EROLD program. Furthermore, these ephemerides are badly documented, which prevents having good homogeneity with the computations for the representation of the various motions of a lunar laser reflector with respect to a terrestrial station. Thus, in this framework, some other studies were useful.

A few years ago, we decided that it would be desirable to support the Lunar Laser data reduction with the construction of a new ephemeris by numerical integration. This was considered valuable not only from the scientific point of view, but also as an operational tool for the EROLD and MERIT programs. Early in 1980, we adopted this ephemeris, called ECT 18, in the EROLD computations for the Annual Reports of BIH and for the needs of MERIT Operating Center and Analysis Center at CERGA.

SALE and ELP, analytical theories of the main problem of the Moon, are developed by Henrard (1979) and Chapront-Touzé (1980), respectively. Both theories are compared with numerical integration over one year, which covers about 13 revolutions of the Moon’s orbit. The root-mean-square residuals in the distance of SALE truncated at 10−5 arcsecond is about 10 cm for series truncated at 10−5 arcsecond and 1.2 cm for series truncated at 10−6 arcsecond. ELP is also compared with 20 years of numerical integration and the root-mean-square residuals in the distance is about 1.5 cm.

This contribution is an outline of the main results obtained by the authors in comparing their solution ELP-2000, to a JPL numerical integration, LE-51. A full paper containing discussions and comments on the results will be proposed to Astronomy ’ Astrophysics.

A solution for the orbital motion of the Moon has been built by the authors. It is named ELP-2000, the epoch of reference being J2000. It is a semi-analytical solution, its structure being quite similar to Brown-Eckert’s one, as it appears in the Improved Lunar Ephemeris, ILE, j=2, (Eckert et al., 1954). The main purpose of this work is to present the results of a comparison of a provisional but complete solution, to an external numerical integration, LE-51, built at JPL (Williams, 1980), and fitted to lunar laser rangings. The JPL numerical integration is regarded as an “observational model”. It is a first attempt to compare as a whole, a new lunar ephemeris, derived from a semi-analytical theory, to observations, via a numerical integration.

The aim of this paper is to present the principal features of a new evaluation of the direct perturbations of the planets on the Moon’s motion. Using the method already published in Celestial Mechanics (Standaert, 1980), we compute “a first-order theory” aiming at an accuracy of the order of the meter for all periodic terms of period less than 3 500 years.

From an external point of view, we mean by that:

1. a) keplerian orbits for the planets,

2. b) the ELP-2000 solution of the Main Problem proposed by Mrs. Chapront (Chapront-Touzë, 1980),

3. c) the first-order derivatives with respect to the constants of motion of the SALE theory of Henrard (Henrard, 1979).

On the other hand, from an internal point of view, the computations include:

1. d) the development in Legendre polynomials not only to the first-order in (a/a'), but also the following ones (up to the sixth-order for Venus, for example),

2. e) the contributions of the second-order in the Lie triangle,

3. f) second-order contributions coming from the corrections of the mean motions due to the planetary action.

The very great accuracy with which the motions of the Moon can now be monitored by laser ranging, differential VLBI and occultation observations, implies that the interpretation of the measurements is conditioned by the choice and the accurate knowledge of a selenocentric, a terrestrial and a celestial frames. Two different types of selenocentric reference frames can be envisioned. The present selenographic frames are discussed but the author proposes that one should introduce a system defined by a purely geometric means. Some consequences of such a choice are discussed. One feature of the future conventional terrestrial frame is very important for Earth-Moon dynamics. Its origin should coincide with the center of mass of the Earth as determined by lunar laser ranging. As far as the quasi-inertial reference systems are concerned, the liaisons between a purely lunar dynamical system, subject to some hardly modelable effects, and purely celestial systems are analysed. The reduction of observations made with various techniques implies the use of different systems, and several problems are stated that should be solved before a unique system for Earth-Moon dynamics might be used.

The selection of selenodetic reference coordinate system is an important problem in astronomy and selenodesy. For the purposes of reduction of observations, planning and executing space missions to the Moon, it is necessary, in any case, to know the orientation of the adopted selenodetic reference system in respect to the inertial coordinate system.

Let us introduce the following coordinate systems:

1. C(ξc, ηc, ζc), the Cassini system which is defined by the Cassini laws of the Moon rotation;

2. D(ξd, ηd, ζd), the dynamical coordinate system, whose axes coincide with the principal axes of inertia of the Moon;

3. Q(ξq, ηq, ζq), the quasi-dynamical coordinate system connected with the mean direction to the Earth, which is shifted by 254" West and 75" North from the longest axis of the dynamical system (Williams et al., 1973);

4. S(ξs, ηs, ζs), the selenodetic coordinate system, which is practically realized by the positions of the points on the Moon surface given in Catalogues;

5. I(X,Y,Z), the space-fixed (inertial) coordinate system. All the systems are selenocentric with the exception of S(ξs, ηs, ζs On the whole, the origin of this system does not coincide with the center of mass of the Moon.

At the Seventeenth IAU General Assembly in Montreal, Canada, in 1979, the resolution was passed adopting the 1979 Nutation Series, which was based on: - the development of the rigid theory by Kinoshita (1977); - the modifications to this theory allowing for the effects of a fluid core and an elastic shell (Molodensky, 1961). The purpose of this action has been nothing but the adoption of a working Standard on Nutation. The details that follow are well known (Seidelmann, 1980). After a discussion at IAU Colloquium N°56 in Warsaw, Poland, in 1980, the Working Group on Nutation decided to recommend a change to the 1980 IAU Nutation Series, which is based on the theory developed by Wahr (1980). The differences between the above mentioned Series are within the limits of ±0002 and are not detectable with the present observational accuracy. As an example, we summarized in Table 1 the observed amplitudes of circular nutation component (2L☾−α) which were determined from astronomical observations with best accuracy. The effect of O1-tide on this component is taken into account by using the theoretical tide with Λ=1+k−1=1.2. The theoretical amplitudes of this component were reduced to the mean epochs of observations.

The new astronomical constants being introduced for 1984 affect the derived values of UT1 and terrestrial longitudes differently for the space techniques than for the optical techniques. The new sidereal time equation has been defined to avoid a discontinuity in UT1 as obtained by the established techniques. However, this definition does introduce a discontinuity in both the terrestrial longitude system and the UT1 rate derived by the space techniques which have an inertial celestial reference frame rather than a stellar catalog frame. The use of consistent expressions for precession and Greenwich Mean Sidereal Time will not eliminate differences between the inertial and classical optical techniques. Only improvements in the accuracy of the precession constant and equinox offset and drift will bring about consistency. Improvements in the precession constant can be expected in the next few years. The inertial techniques will exhibit shifts in the derived UT1 rate and terrestrial longitude system with each change in the precession constant if Greenwich Mean Sidereal Time is referenced to the mean equinox of date, as is the present practice, but would be stable if the reference is a fixed equinox. The latter choice is recommended.

Using models of the Earth-Moon system developed from analysis of 10 years of laser ranging observations from the McDonald Observatory, we have analyzed observations obtained by the Orroral Lunar Ranging Station since April 1978. Normal point residuals from many of the observations performed before April 1980 using a 20 ns, mi tiple-mode laser pulse are discreetly spaced, as multiples of 6 ns, and may have been corrupted by variations in pulse shape. Further evaluation is required before these observations are used in scientific analyses. Observations performed during the MERIT Short Campaign (August - October 1980) using a 6 ns, single-mode pulse are apparently reliable. Using 27 single photoelectron events, obtained on 7 nights during this period, we have estimated the coordinates of Orroral, with respect to McDonald, with uncertainties of 1-2 m in cylindrical radius and longitude and 5-10 m in z-axis distance.

Biases have been noted in pole positions computed from Doppler observations of different Navy Navigation Satellites. Studies show that the differences in the orbits of the Navy Navigation Satellites, although small, are large enough so that uncertainties in knowledge of the earth’s gravity field could produce the biases noted.

Results of VLBI measurement of 14 radio source positions at three U.S. stations during the MERIT short campaign is presented. Comparisons with other solutions are given, together with the comparisons between several radio source catalogues.

During the MERIT short campaign, several observatories cooperated in VLBI measurements organized jointly by the U.S. National Geodetic Survey (NGS) and the National Aeronautics and Space Administration (NASA). There were two 7-day observations arranged from Sept. 26 to Oct. 2 and from Oct. 16 to Oct. 22, with time span nearly 23 hours per day. Details of the observation and data reduction have been published elsewhere (1). This paper deals with radio source positions determined by three U.S. stations, the Haystack Observatory, the Harvard Radio Astronomy Station (HRAS) and the Owens Valley Radio Observatory (OVRO).

We present an expansion of the disturbing function for the third-body perturbations in the form , where ε is the ratio of semi-major axes (a/a’) and Xnm and Ynm depend only on the five elements e, i, ω, Ω, of the satellite while and depend on the corresponding elements of the perturbing body. Each one of the four functions X and Y is represented as a product of two factors as opposed to three factors in our previous publication of this subject (Broucke, 1981). We develop several relations for the construction of the X and Y-series. These series are relatively short and can be computed in advance and stored on magnetic tape, for instance.