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NASA NTRS2010

Tests of gravity Using Lunar Laser Ranging

Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the pa~t four decades. The three retrorefiector arrays put on the Moon by the Apollo astronauts and the French built array on the second Soviet Lunokhod rover continue to be useful targets, and have provided the most stringent tests of the Strong Equivalence Principle and the time variation of Newton's gravitational constant. The relatively new ranging system at the Apache Point :3.5 meter telescope now routinely makes millimeter level range measurements. Incredibly. it has taken 40 years for ground station technology to advance to the point where characteristics of the lunar retrorefiectors are limiting the precision of the range measurements. In this article. we review the gravitational science and technology of lunar laser ranging and discuss prospects for the future.

Merkowitz, Stephen M.↗
NASA NTRS2020

Extending Science from Lunar Laser Ranging

The Lunar Laser Ranging (LLR) experiment has accumulated 50 years of range data of improving accuracy from ground stations to the laser retroreflector arrays (LRAs) on the lunar surface. The upcoming decade offers several opportunities to break new ground in data precision through the deployment of the next generation of single corner-cube lunar retroreflectors and active laser transponders. This is likely to expand the LLR station network. Lunar dynamical models and analysis tools have the potential to improve and fully exploit the long temporal baseline and precision allowed by millimetric LLR data. Some of the model limitations are outlined for future efforts. Differential observation techniques will help mitigate some of the primary limiting factors and reach unprecedented accuracy. Such observations and techniques may enable the detection of several subtle signatures required to understand the dynamics of the Earth- Moon system and the deep lunar interior. LLR model improvements would impact multi- disciplinary fields that include lunar and planetary science, Earth science, fundamental physics, celestial mechanics and ephemerides.

Vishnu Viswanathan↗
NASA NTRS2008

Precision Lunar Laser Ranging For Lunar and Gravitational Science

Laser ranging to retroreflector arrays placed on the lunar surface by the Apollo astronauts and the Soviet Lunar missions over the past 39 years have dramatically increased our understanding of gravitational physics along with Earth and Moon geophysics, geodesy, and dynamics. Significant advances in these areas will require placing modern retroreflectors and/or active laser ranging systems at new locations on the lunar surface. Ranging to new locations will enable better measurements of the lunar librations, aiding in our understanding of the interior structure of the moon. More precise range measurements will allow us to study effects that are too small to be observed by the current capabilities as well as enabling more stringent tests of Einstein's theory of General Relativity. Setting up retroreflectors was a key part of the Apollo missions so it is natural to ask if future lunar missions should include them as well. The Apollo retroreflectors are still being used today, and nearly 40 years of ranging data has been invaluable for scientific as well as other studies such as orbital dynamics. However, the available retroreflectors all lie within 26 degrees latitude of the equator, and the most useful ones within 24 degrees longitude of the sub-earth meridian. This clustering weakens their geometrical strength.

Merkowitz, S. M.↗
NASA NTRS1974

Operation and performance of a lunar laser ranging station

The Lunar Laser Ranging Experiment has been in continuous operation for about 4 years using the McDonald Observatory 2.7-m telescope. Occupying only a small percentage of the available telescope time, the system is now measuring 350 lunar ranges per year, each with an accuracy of from 10 to 15 cm. This article tabulates the observed signal strengths, the success ratios, and the major operating restrictions that have characterized the daily performance of the experiment. These empirical data can be used to optimize the design of such installations in the future.

Silverberg, E. C.↗
NASA NTRS1982

Results from lunar laser ranging data analysis

The lunar laser range data taken at McDonald Observatory between Aug. 1969 and May 1980 has been analyzed. The simple rms residual for the 2954 ranges is 31 cm. Results of the analysis include GM(earth) = 398600.45 cu km/sec sq within 0.02 cu km/sec sq and a secular acceleration of the lunar orbital mean longitude of -23.8 arcsec/sq century within 1.5 arcsec, which yields a Q of 12.3 at semidiurnal frequencies. The lunar harmonic C30 is -8.7/1,000,000 within 0.000001 and the lunar rotational dissipation of 0.0047 within 0.0005 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.

Dickey, J. O.↗
NASA NTRS1995

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.

Charlot, P.↗
NASA NTRS2004

Lunar Laser Ranging Science: Gravitational Physics and Lunar Interior and Geodesy

Laser pulses fired at retroreflectors on the Moon provide very accurate ranges. Analysis yields information on Earth, Moon, and orbit. The highly accurate retroreflector positions have uncertainties less than a meter. Tides on the Moon show strong dissipation, with Q=33+/-4 at a month and a weak dependence on period. Lunar rotation depends on interior properties; a fluid core is indicated with radius approx.20% that of the Moon. Tests of relativistic gravity verify the equivalence principle to +/-1.4x10(exp -13), limit deviations from Einstein's general relativity, and show no rate for the gravitational constant G/G with uncertainty 9x10(exp -13)/yr.

relativity↗
NASA NTRS1978

Universal time - Results from lunar laser ranging

A least squares analysis of lunar laser ranging observations from the McDonald Observatory is used to estimate universal time. In addition to the ranging observations, the analysis simultaneously takes into account the parameters representing the locations of McDonald and the lunar retroreflectors, the orbits of the earth and the moon, and the moon's physical libration. The root-mean-square of the postfit range residuals for the 5-year period from October 1970 to November 1975 is 28 cm. The results are compared with those obtained by the Bureau International de l'Heure and by Stolz et al. (1976), and the reasons for discrepancies are discussed. It is suggested that problems in modeling the moon's motion make difficult the determination of UT with the accuracy inherent in the ranging observations.

King, R. W.↗
NASA NTRS1996

Relativity Parameters Determined from Lunar Laser Ranging

Analysis of 24 years of lunar laser ranging data is used to test the principle of equivalence, geodetic precession, the PPN parameters beta and gamma, and G/G. Recent data can be fitted with a rms scatter of 3 cm. (a) Using the Nordtvedt effect to test the principle of equivalence, it is found that the Moon and Earth accelerate alike in the Sun's field. The relative accelerations match to within 5 x 10(exp -13) . This limit, combined with an independent determination of y from planetary time delay, gives beta. Including the uncertainty due to compositional differences, the parameter beta differs from unity by no more than 0.0014; and, if the weak equivalence principle is satisfied, the difference is no more than 0.0006. (b) Geodetic precession matches its expected 19.2 marc sec/yr rate within 0.7%. This corresponds to a 1% test of gamma. (c) Apart from the Nordtvedt effect, beta and gamma can be tested from their influence on the lunar orbit. It is argued theoretically that the linear combination 0.8(beta) + 1.4(gamma) can be tested at the 1% level of accuracy. For solutions using numerically derived partial derivatives, higher sensitivity is found. Both 6 and y match the values of general relativity to within 0.005, and the linear combination beta+ gamma matches to within 0,003, but caution is advised due to the lack of theoretical understanding of these sensitivities. (d) No evidence for a changing gravitational constant is found, with absolute value of G/G less than or equal to 8 x lO(exp -12)/yr. There is significant sensitivity to G/G through solar perturbations on the lunar orbit.

Williams, J. G.↗
NASA NTRS1972

Single photon detection and timing in the Lunar Laser Ranging Experiment.

The goals of the Lunar Laser Ranging Experiment lead to the need for the measurement of a 2.5 sec time interval to an accuracy of a nanosecond or better. The systems analysis which included practical retroreflector arrays, available laser systems, and large telescopes led to the necessity of single photon detection. Operation under all background illumination conditions required auxiliary range gates and extremely narrow spectral and spatial filters in addition to the effective gate provided by the time resolution. Nanosecond timing precision at relatively high detection efficiency was obtained using the RCA C31000F photomultiplier and Ortec 270 constant fraction of pulse-height timing discriminator. The timing accuracy over the 2.5 sec interval was obtained using a digital interval with analog vernier ends. Both precision and accuracy are currently checked internally using a triggerable, nanosecond light pulser. Future measurements using sub-nanosecond laser pulses will be limited by the time resolution of single photon detectors.

Poultney, S. K.↗
NASA NTRS1980

Scientific achievements from ten years of lunar laser ranging

In the 10 years since lunar laser ranging became a reality the need to analyze the observations has motivated improvements in several aspects of the mathematical model of earth-moon dynamics. Application of the data to improved estimates of the physical parameters of the earth-moon system has yielded significant astronomical, selenophysical, geophysical, and cosmological results. The scientific impact, both in improved theories and in numerical applications, is surveyed. The underlying physics and major difficulties are discussed, as well as the scientific results.

Mulholland, J. D.↗
NASA NTRSDate not supplied

Lunar Laser Ranging in the Artemis Era

The retroreflector arrays placed on the lunar surface by the Apollo astronauts and the Soviet Luna missions continue to contribute to our understanding of gravitational physics, Earth and Moon geophysics, geodesy, and dynamics. The key science questions addressed by Lunar Laser Ranging remain very relevant today: What is the interior structure of the Moon? Is the Equivalence Principle exact? Does the strength of gravity vary with space and time? What is the nature of spacetime? Do extra dimensions or other new physics alter the inverse square law of gravity? The lunar retroreflectors are also an essential component of the realizations of the lunar reference frames. The half-century old lunar retroreflectors continue to provide excellent ranging targets but are showing signs of degradation and the measurement error associated with their physical size and varying tilt is becoming a limitation in the quest for more precise range measurements. In addition, the clustering of the arrays in the mid-latitudes of the Moon limits their geometrical strength and coverage. The south polar region planned for Artemis presents an ideal opportunity for improving the geometric distribution. Retroreflectors utilizing a large optical cross-section single cube corner do not have tilt error associated with the existing arrays making them good options for lunar deployment. Several new retroreflectors of this type are being prepared for upcoming Commercial Lunar Payload Services missions as well as Artemis. This presentation will discuss NASA’s plans for expanding the lunar laser ranging capabilities with a focus on the Artemis Lunar Laser Retroreflector.

Stephen Merkowitz↗
NASA NTRS1976

New test of the equivalence principle from lunar laser ranging

An analysis of six years of lunar-laser-ranging data gives a zero amplitude for the Nordtvedt term in the earth-moon distance yielding the Nordtvedt parameter eta = 0.00 plus or minus 0.03. Thus, earth's gravitational self-energy contributes equally, plus or minus 3%, to its inertial mass and passive gravitational mass. At the 70% confidence level this result is only consistent with the Brans-Dicke theory for omega greater than 29. We obtain the absolute value of beta - 1 less than about 0.02 to 0.05 for five-parameter parametrized post-Newtonian theories of gravitation with energy-momentum conservation.

Williams, J. G.↗
NASA NTRS1985

Earth orientation from lunar laser ranging and an error analysis of polar motion services

Lunar laser ranging (LLR) data are obtained on the basis of the timing of laser pulses travelling from observatories on earth to retroreflectors placed on the moon's surface during the Apollo program. The modeling and analysis of the LLR data can provide valuable insights into earth's dynamics. The feasibility to model accurately the lunar orbit over the full 13-year observation span makes it possible to conduct relatively long-term studies of variations in the earth's rotation. A description is provided of general analysis techniques, and the calculation of universal time (UT1) from LLR is discussed. Attention is also given to a summary of intercomparisons with different techniques, polar motion results and intercomparisons, and a polar motion error analysis.

Dickey, J. O.↗
NASA NTRS1973

Potentialities of lunar laser ranging for measuring tectonic motions.

The lunar laser-ranging system at McDonald Observatory, Texas, is currently attaining accuracies of plus or minus 15 cm, and plus or minus 3 cm appears feasible. Numerical error analyses containing 97 parameters (35 of them for error sources) indicate that the plus or minus 3 cm system would measure station motions to plus or minus 1 cm/year accuracy within a year for east-west motions and within about 3 years for north-south. Furthermore, the correlations of station motions with other parameters are low, so that it is unlikely that the estimate is too optimistic because of modeling inadequacies of the error analysis.

Kaula, W. M.↗
NASA NTRS1978

The McDonald Observatory lunar laser ranging project

A summary of the activities of the McDonald lunar laser ranging station at Fort Davis for the FY 77-78 fiscal year is presented. The lunar laser experiment uses the observatory 2.7m reflecting telescope on a thrice-per-day, 21-day-per-lunation schedule. Data are recorded on magnetic tapes and sent to the University of Texas at Austin where the data is processed. After processing, the data is distributed to interested analysis centers and later to the National Space Science Data Center where it is available for routine distribution. Detailed reports are published on the McDonald operations after every fourth lunation or approximately once every 115 days. These reports contain a day-by-day documentation of the ranging activity, detailed discussions of the equipment development efforts, and an abundance of other information as is needed to document and archive this important data type.

Silverberg, E. C.↗