Lunar Retroreflectors Research Articles

Next-generation Laser Ranging at Lunar Geophysical Network and Commercial Lander Payload Service Sites

Five retroreflector arrays currently on the Moon reflect short laser pulses back to Earth, allowing range to be measured. Each array has multiple small corner cubes. Due to variable lunar optical librations of the direction to Earth, the tilted arrays spread return times of single photons in the returned laser pulse, degrading the synthesized multiphoton normal point range accuracy. The Next Generation Lunar Retroreflectors (NGLRs) and MoonLIGHT reflectors currently being fabricated are larger 10 cm single corner cubes that do not spread the pulse. The Lunar Geophysical Network (LGN) mission will place NGLRs at three separated sites on the lunar nearside. The Commercial Lander Payload Service (CLPS) and early Artemis missions will precede the LGN mission. Solutions that include 6 yr of simulated Lunar Laser Ranging (LLR) data to two sites in the north and two in the south show improvement in the uncertainties of many science parameters. Lunar solution parameters include displacement Love numbers h 2 and l 2, tidal dissipation at several frequencies, fluid-core/solid-mantle boundary (CMB) dissipation, and moment of inertia combinations (C–A)/B and (B–A)/C, with principal moments of inertia A < B < C. Submeter-accuracy coordinates of the new reflectors will result from the first month of well-distributed data. There are benefits other than lunar science: gravitational physics includes the equivalence principle; Earth science includes terrestrial tidal dissipation and ranging station positions and motions; and astronomical constants with GM(Earth+Moon) for the gravitational constant times the mass of the Earth–Moon system. Improvements are illustrated for h 2, l 2, (C–A)/B, (B–A)/C, equivalence principle, and GM(Earth+Moon).

Testing the Motion of Lunar Retroreflectors

AbstractThe Moon lacks recognizable plates moving with respect to each other, unlike the Earth. Analysis of Lunar Laser Ranging data does not find large Earth‐like (&gt;1 cm/year) relative motions for the five lunar retroreflectors. The distances between reflectors show few mm/year rates that are not statistically significant. Despite this lack of individual significance, curiously, all of the well determined distances have negative rates. There is an extra non‐synchronous lunar rotation rate of 1.0 ± 0.4 mas/yr that is suspected to arise from unmodeled very long period effects of physical libration in longitude.

Characterization in Dynamic Load Environment of COTS Synthetic Sapphire Bearings for Application in Magnetic Suspension in Space

The present research investigates the application of a cardan suspension making use of permanent magnet (PM) bearings employed to obtain high reliable/low-cost solutions for the permanent alignment of directional payloads such as laser reflectors for the Next Generation Lunar Retroreflector (NGLR) experiment or antennas to be deployed on the moon’s surface. According to Earnshaw’s Theorem, it is not possible to fully stabilize an object using only a stationary magnetic field. It is also necessary to provide axial control of the shaft since the PM bearings support the radial load but, they produce an unstable axial force when losing alignment between the stator and rotor magnets stack. In this work, the use of commercial off-the-shelf (COTS) sapphire as axial bearings in the cardan suspension has been investigated by testing their behavior in response to some of the dynamic loads experienced during the qualification tests for space missions. The work is innovative in the sense that COTS sapphire assembly has never been investigated for space mission qualification. As Artemis mission loads have not been yet provided for NGLR, test loads for this study are those used for the proto-qualification of the INFN INRRI payload for the ESA ExoMars EDM mission. Tests showed that, along the x and y directions, no damages were produced on the sapphire, while, unfortunately, on the z direction both sapphires were badly damaged at nominal loads.

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.

Benefit of New High-Precision LLR Data for the Determination of Relativistic Parameters

Since 1969, Lunar Laser Ranging (LLR) data have been collected by various observatories and analysed by different analysis groups. In the recent years, observations with bigger telescopes (APOLLO) and at infra-red wavelength (OCA) are carried out, resulting in a better distribution of precise LLR data over the lunar orbit and the observed retro-reflectors on the Moon. This is a great advantage for various investigations in the LLR analysis. The aim of this study is to evaluate the benefit of the new LLR data for the determination of relativistic parameters. Here, we show current results for relativistic parameters like a possible temporal variation of the gravitational constant G˙/G0=(−5.0±9.6)×10−15yr−1, the equivalence principle with Δmg/miEM=(−2.1±2.4)×10−14, and the PPN parameters β−1=(6.2±7.2)×10−5 and γ−1=(1.7±1.6)×10−4. The results show a significant improvement in the accuracy of the various parameters, mainly due to better coverage of the lunar orbit, better distribution of measurements over the lunar retro-reflectors, and last but not least, higher accuracy of the data. Within the estimated accuracies, no violation of Einstein’s theory is found and the results set improved limits for the different effects.

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.

Lunar laser ranging in infrared at the Grasse laser station

For many years, lunar laser ranging (LLR) observations using a green wavelength have suffered an inhomogeneity problem both temporally and spatially. This paper reports on the implementation of a new infrared detection at the Grasse LLR station and describes how infrared telemetry improves this situation. Our first results show that infrared detection permits us to densify the observations and allows measurements during the new and the full Moon periods. The link budget improvement leads to homogeneous telemetric measurements on each lunar retro-reflector. Finally, a surprising result is obtained on the Lunokhod 2 array which attains the same efficiency as Lunokhod 1 with an infrared laser link, although those two targets exhibit a differential efficiency of six with a green laser link.

Tests of Gravity Using Lunar Laser Ranging.

Lunar laser ranging (LLR) has been a workhorse for testing general relativity over the past four decades. The three retroreflector arrays put on the Moon by the Apollo astronauts and the French built arrays on the Soviet Lunokhod rovers 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 retroreflectors 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.

Lunar Laser Ranging: Glorious Past And A Bright Future

Lunar Laser Ranging (LLR), a part of the NASA Apollo program, has beenon-going for more than 30 years. It provides the grist for a multi-disciplinarydata analysis mill. Results exist for solid Earth sciences, geodesy and geodynamics,solar system ephemerides, terrestrial and celestial reference frames, lunar physics,general relativity and gravitational theory. Combined with other data, it treatsprecession of the Earth's spin axis, lunar induced nutation, polar motion/Earthrotation, Earth orbit obliquity to the ecliptic, intersection of the celestial equatorwith the ecliptic, luni-solar solid body tides, lunar tidal deceleration, lunar physicaland free librations, structure of the moon and energy dissipation in the lunar interior.LLR provides input to lunar surface cartography and surveying, Earth station and lunar retroreflector location and motion, mass of the Earth-moon system, lunar and terrestrial gravity harmonics and Love numbers, relativistic geodesic precession, and the equivalence principle of general relativity. With the passive nature of the reflectors and steady improvement in observing equipment and data analysis, LLR continues to provide state-of-the-art results. Gains are steady as the data-base expands. After more than 30 years, LLR remains the only active Apollo experiment. It is important to recognize examples of efficient and cost effective progress of research. LLR is just such an example.

Lunar moments, tides, orientation, and coordinate frames

To determine the lunar moments of inertia ( A < B < C) it is necessary to determine three quantities. (C − A) B and (B − A) C come from Lunar Laser Ranging (LLR) measurement of the lunar orientation Spacecraft or lunar orbit perturbations provide J 2 Combining five reported J 2 results gives a normalized polar moment of inertia C MR 2 = 0.3929 ± 0.0009 Solid-body tides displace the surface about 0.1 m, but can perturb the orbit of a Moon-orbiting spacecraft. The selenocentric coordinates of four lunar retroreflectors are accurately known and can serve as reference points. The orientation and orbit of the Moon are very well known for the time span of the LLR data.

An analysis of MLRS Near-Real-Time Earth orientation results

In this paper a comparison is presented between near-real-time earth orientation parameters, produced on-site by the McDonald Laser Ranging System (MLRS) at McDonald Observatory, using observations to the Apollo 15 lunar retroreflector, and those results which are obtained after the fact at the University of Texas at Austin and elsewhere, as well as the results obtained from other techniques. The MLRS data set which is included in this study spans the interval from the commencement of on-site earth orientation solutions at MLRS in February 1985, through the present time, September 1986. This research is supported by the National Aeronautics and Space Administration under Grant NAG5-754 and Contract NAS5-29404 to McDonald Observatory and the University of Texas at Austin from the Goddard Space Flight Center in Greenbelt, Maryland.

Constants related to the Moon

Determinations of constants related to the Moon obtained from Doppler tracking data from Lunar Orbiter 4 combined with laser ranging data from lunar retroreflectors are compared with those obtained previously by classical methods.

Geophysical parameters of the Earth‐Moon System

Doppler tracking data from Lunar Orbiter 4 have been combined with laser ranging data from lunar retroreflectors to yield a number of geophysical and geodetic parameters for the earth and moon. This joint solution gives values of (1) the lunar principal polar moment C/MR2 = 0.3905 ± 0.0023, (2) GME = 398600.461 ± 0.026 km3/s2, and (3) an earth/moon mass ratio at 81.300587±0.000049. Also determined are the harmonics of a complete lunar gravity field through degree and order 5, the obliquity of the lunar pole, selenocentric coordinates of the lunar retroreflectors, geocentric coordinates of the McDonald Observatory, and the lunar secular acceleration. The lunar potential Love number is weakly determined at 0.022±0.013, and a surprisingly large dissipation of rotational energy is inferred, though either solid body tidal dissipation or liquid core mantle interactions could be causes.

Universal time: Results from lunar laser ranging

Lunar laser ranging observations from the McDonald Observatory have been analyzed by least squares to estimate universal time (UT) simultaneously with 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 (rms) of the postfit range residuals for the 5‐year period from October 1970 to November 1975 is 28 cm. The rms of the differences between our determinations of UT and those of the Bureau International de l'Heure is 2.1 ms, after removal of the mean difference. The differences between our determinations and those of Stolz et al. (1976), who analyzed most of the same ranging data with a different approach, have an rms of 0.8 ms and, in addition to high‐frequency ‘noise,’ exhibit low‐frequency variations of ≲ 1 ms in magnitude which result at least in part from differences in models used for the lunar orbit. Thus problems in modeling the moon's motions, especially those of long period, make difficult the determination of UT with the accuracy inherent in the ranging observations.

Lunar dynamics and selenodesy: Results from analysis of VLBI and laser data

Very-long-baseline interferometry (VLBI) observations of lunar radio transmitters have been combined with data from laser ranging to lunar retroreflectors to estimate simultaneously (i) parameters in models of the lunar orbit and libration; and (ii) the selenodetic coordinates of the radio transmitters and retroreflectors. For the ratio of the mass of the sun to that of the earth plus moon, we obtain 328,900.50 ± 0.03. For the lunar moment-of-inertia ratios we find β[Ξ(C-A)/B] = (631.27 ± 0.03) x 10-6 and ϒ[Ξ(B-A)/C] = (227.7 ± 0.7) x 10-6. The value implied for C/MR2 is 0.392 ± 0.003, with the uncertainty being dominated by that of the coefficient, J2, of the second zonal gravity harmonic, obtained by Gapcynski et al. from analysis of Explorer spacecraft orbital data. The values and most of the uncertainties that we obtain for the third-degree harmonics of the moon’s gravity field are comparable to those which have been obtained by others from observations of lunar-orbiting spacecraft. However, our determination of β appears to be the best available, and our results for two third-degree gravity coefficients, C31 = (26 ± 4) x 10-6 and C33 = (2 ± 2) x 10-6, have much less uncertainty than determinations based on laser data alone. For the relative-position vectors of both the lunar radio transmitters and the retroreflectors our estimates have uncertainties of about 30 m along the earth-moon direction and about 10 m in each of the two transverse coordinates.