Lunar Laser Ranging Observations Research Articles

The 1970–1984 lunar laser ranging observations in the Crimean Astrophysical Observatory

The Lunar Laser Ranging (LLR) has been the main method of study of the dynamics of the Sun-Earth-Moon system since 1969 to present. Lunar parts of the three modern high-precision ephemerides of the Solar system bodies are based solely on LLR measurements: DE (USA), EPM (Russia), INPOP (France). LLR measurements allow to determine parameters of lunar orbital and rotational motion, as well as some parameters related to terrestrial and lunar tides, and also fundamental relativistic parameters. Those parameters were determined from LLR with high accuracy by different authors. In USSR, LLR measurements were performed in the Crimean Astrophysical Observatory (CrAO) in Nauchny, on the 2.6 m Shajn’s Zenith telescope (ZTSh) with an automated laser ranging system developed by the Russian Lebedev Physical Institute (LPI). Within the time span of 1969–1984, 1400 measurements were obtained. Unlike LLR measurements done in other observatories, they were eventually forgotten and have not made their way into the dataset that is used by scientists worldwide to build lunar ephemerides and conduct other lunar research. The main reason for writing this paper was the discovery by Tryapitsyn, a researcher at the Katziveli station of CrAO, of old printouts containing the 1970–1984 LLR observations made with the ZTSh 2.6 m telescope. Some details were missing from the printouts, which required careful restoration work. In this paper the history of those LLR observations with surrounding historical events is presented, and some details of the analysis these observations are described. Of particular interest is the finding related to the three normal points of Lunokhod-1 ranges obtained in 1974 that allowed Odile Calame to determine the rover’s position with a few kilometers accuracy. Unfortunately, the accuracy was not sufficient for other researchers to confirm and pin down the location of the rover.

Analyses of celestial pole offsets with VLBI, LLR, and optical observations

Aims. This work aims to explore the possibilities of determining the long-period part of the precession-nutation of the Earth with techniques other than very long baseline interferometry (VLBI). Lunar laser ranging (LLR) is chosen for its relatively high accuracy and long period. Results of previous studies could be updated using the latest data with generally higher quality, which would also add ten years to the total time span. Historical optical data are also analyzed for their rather long time-coverage to determine whether it is possible to improve the current Earth precession-nutation model. Methods. Celestial pole offsets (CPO) series were obtained from LLR and optical observations and were analyzed separately by weighted least-square fits of three empirical models, including a quadratic model, a linear term plus an 18.6-year nutation term, and a linear term plus two nutation terms with 18.6-year and 9.3-year periods. Joint analyses of VLBI and LLR data is also presented for further discussion. Results. We improved th determination of the nutation terms with both VLBI and LLR data. The VLBI data present a most reliable feature of the CPO series with the highest accuracy, and they are most important for determining the precession-nutation of the Earth. The standard errors of CPO obtained from the LLR technique have reached a level of several tens of microarcseconds after 2007, but they are probably underestimated because the models used in the calculation procedure are not perfect. Nevertheless, the poor time resolution of LLR CPO series is also a disadvantage. However, this indicates that LLR has the potential to determine celestial pole offsets with a comparably high accuracy with VLBI in the future and to serve as an independent check for the VLBI results. The current situation of LLR observations is also analyzed to provide suggestions of future improvement. The typical standard error of CPO series from historic optical observations is about two hundred times larger than that of the VLBI series and can therefore hardly contribute to the contemporary precession-nutation theory.

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 selenocentric coordinates of the lunar retro-reflectors. This paper presents the recent results from LLR data analysis at the Institut fur Erdmessung, Leibniz Universitat Hannover, based on all LLR data up to the end of 2016. The estimates of long-periodic nutation coefficients with periods between 13.6 days and 18.6 years are obtained with an accuracy in the order of 0.05–0.7 milliarcseconds (mas). Estimations of the Earth rotation phase $$\Delta $$ UT are accurate at the level of 0.032 ms if more than 14 normal points per night are included. The tie between the dynamical ephemeris frame to the kinematic celestial frame is estimated from pure LLR observations by two angles and their rates with an accuracy of 0.25 and 0.02 mas per year. The estimated station coordinates and velocities are compared to the ITRF2014 solution and the geometry of the retro-reflector network with the DE430 solution. The given accuracies represent 3 times formal errors of the parameter fit. The accuracy for $$\Delta $$ UT is based on the standard deviation of the estimates with respect to the reference C04 solution.

Testing Lorentz Symmetry with Lunar Laser Ranging.

Lorentz symmetry violations can be parametrized by an effective field theory framework that contains both general relativity and the standard model of particle physics called the standard-model extension (SME). We present new constraints on pure gravity SME coefficients obtained by analyzing lunar laser ranging (LLR) observations. We use a new numerical lunar ephemeris computed in the SME framework and we perform a LLR data analysis using a set of 20 721 normal points covering the period of August, 1969 to December, 2013. We emphasize that linear combination of SME coefficients to which LLR data are sensitive and not the same as those fitted in previous postfit residuals analysis using LLR observations and based on theoretical grounds. We found no evidence for Lorentz violation at the level of 10^{-8} for s[over ¯]^{TX}, 10^{-12} for s[over ¯]^{XY} and s[over ¯]^{XZ}, 10^{-11} for s[over ¯]^{XX}-s[over ¯]^{YY} and s[over ¯]^{XX}+s[over ¯]^{YY}-2s[over ¯]^{ZZ}-4.5s[over ¯]^{YZ}, and 10^{-9} for s[over ¯]^{TY}+0.43s[over ¯]^{TZ}. We improve previous constraints on SME coefficient by a factor up to 5 and 800 compared to postfit residuals analysis of respectively binary pulsars and LLR observations.

Lunar laser ranging test of the Nordtvedt parameter and a possible variation in the gravitational constant

Context. Forty years of lunar laser ranging (LLR) data provide an excellent basis to determine various parameters of the Earth-Moon system as well as parameters related to gravitational physics. Aims. We update the Institut fur Erdmessung (IfE) LLR model taking the effect of a fluid lunar core into consideration. The temporal variation in the gravitational constant u G/G0 and the strong equivalence principle, parameterized by the Nordtvedt parameter η ,a re investigated. Methods. A set of LLR observations from 1970 to 2009 was analysed and the parameters were determined by a least squares adjustment in two runs. After solving for classical Newtonian parameters (e.g. initial conditions for the lunar orbit and rotation) in the first run, relativistic parameters were determined in the second run. Results. The upper limits to the gravitational constant and the Nordtvedt parameter were found to be u G/G0 = (−0.7 ± 3.8)×10 −13 yr −1 and η = (−0.6 ± 5.2) × 10 −4 .

Celestial pole offsets from lunar laser ranging and comparison with VLBI

Context. The analysis of lunar laser ranging (LLR) observations is based on determining the round- trip travel times of light pulses between stations on the Earth and reflectors on the surface of the Moon. Several works have demonstrated that this technique is powerful in various domains including astronomy, geodynamics and gravitational physics. Aims. In the field of geodynamics, LLR contributes to the realization of a dynamical celestial reference frame, in contrast to very long baseline interferometry (VLBI) that determines a kinematical celestial reference frame. In this paper, we have determined corrections to the celestial pole coordinates, denoted X, Y, using LLR observations. This determination is of particular interest for comparison with the one obtained from VLBI observations. The main purpose is to study the benefits of LLR for the determination of the celestial pole coordinates and second how to best combine the time series obtained from both techniques. Methods. For these determinations, data acquired by LLR tracking stations since 1969 were analyzed and corrections to the nutation terms estimated using a weighted least square fit. Finally, LLR data were combined with the IVS combined VLBI series of 23-year duration. Results. We have demonstrated the possibility of determining the celestial pole offsets from LLR data even though the results are not as accurate nor as dense as those obtained with VLBI. This work provides some external constraints to the celestial pole coordinates derived from VLBI observations. Moreover, the LLR determination of the long periodic nutation terms shows an improvement with respect to previous studies. The combination of LLR and VLBI series may indicate that the combined series reveal details that do not appear in the VLBI series alone.

Precession and nutation from joint analysis of radio interferometric and lunar laser ranging observations

24 years of Lunar Laser Ranging (LLR) observations and 16 years of Very Long Baseline Interferometry (VLBI) observations are combined in a global analysis to yield improved estimates of the Earth's precession and nutation. The correction to the International Astronomical Union (IAU) (1976) precession constant inferred from this joint VLBI/LLR analysis is -3.00 +/- 0.20 milliarcsec/yr (mas/yr). A significant obliquity rate correction of -0.20 +/- 0.08 mas/yr is also found. In all, 32 forced nutation coefficients are estimated. These coefficients confirm that the IAU (1980) nutation theory is in error by several mas. The estimated nutation coeficients are found to vary by as much as several tenths of mas, depending on the a priori nutation model used to analyze the VLBI and LLR data. Forced circular nutations derived from this analysis agree with the ZMOA-1990-2 nutation theory at the 0.2 mas level for the 18.6 yr terms, and at the 0.05 mas level for the other terms (periods less than or = 1 yr). A retrograde free core nutation with an amplitude of 0.20 mas is also detected. Its phase is found to be very sensitive to the precise value of the free core nutation period used in the solution. Separate analyses of four independent subsets of the LVBI data indicate no significant variations of the free core nutation since 1988. The pre-1988 estimates of the free core nutation are consistent with the post-1988 estimates but are not accurate enough to rule out possible variations of the free core nutation at these earlier epochs.

Dynamics of the Earth-Moon system

Lunar laser ranging (LLR) has been used to determine the precise orientation of the Earth since the early-1970's. Two observatories currently range with 2.5 centimeter accuracy to a constellation of four retroreflector targets. The quality and the 23 year span of the lunar data permit the determination of the constant of precession to an accuracy of 0.5 mas yr −1. The 18.6 year and 9 year nutation terms can be well separated from the precession constant and determined at the milliarcsecond level. The extreme altitude of the Moon, as an Earth satellite, prevents the stochastic effects of atmospheric drag. This allows estimation of the local components of Earth rotation (UTO, Df) to an accuracy of 2.5 milliarcseconds from as little as 1.5 hours of lunar data, with higher accuracies for longer spans of data. This near real time capability makes LLR a strong technique for the investigation of diurnal, and even sub-diurnal, variations in Earth rotation. The secular increase in the mean distance between the Earth and Moon is observed with an accuracy of 0.15 cm yr −1. LLR observations permit the determination of the obliquity of the ecliptic and the equinox with an accuracy of a few milliseconds of arc. The mass of the Earth-Moon system has been estimated from the lunar ranges to one part in 100 million.

Tidal deceleration of the Moon's mean motion

The secular change in the mean motion of the moon, n, caused by the tidal dissipation in the ocean and solid earth is due primarily to the effect of the diurnal and semidiurnal tides. The long-period ocean tides produce an increase in n, but the effects are only 1 percent of the diurnal and semidiurnal ocean tides. In this investigation, expressions for these effects are obtained by developing the tidal potential in the ecliptic reference system. The computation of the amplitude of equilibrium tide and the phase corrections is also discussed. The averaged tidal deceleration of the moon's mean motion, n, from the most recent satellite ocean tide solutions is -25.25 +/- 0.4 arcseconds/sq century. The value for n inferred from the satellite-determined ocean-tide solution is in good agreement with the value obtained from the analysis of 20 years of lunar laser-ranging observations.

Laser observations of the moon - Normal points for 1973

McDonald Observatory lunar laser-ranging observations for 1973 are presented in the form of compressed normal points, and amendments for the 1969-1972 data set are given. Observations of the reflector mounted on the Soviet roving vehicle Lunakhod 2 have also been included.