The Multidisciplinary Lunar Laser Ranging Experiment
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Lunar Laser Ranging Moon Earth relativity↗
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Stochastic Parameters in Lunar Laser Ranging
This oral presentation describes the techniques, algorithms, and results of incorporatng a Kalman-smoothing technique into the square-root information filter when estimating deterministic and stochastic parameters relating to Earth, the Moon, and the lunar and planetary ephemerides.
lunar laser ranging ephemerides stochastic paramet↗
Determination of the extragalactic-planetary frame tie from joint analysis of radio interferometric and lunar laser ranging measurements
Very Long Baseline Interferometry (VLBI) observations of extragalactic radio sources provide the basis for defining an accurate non-rotating reference frame in terms of angular positions of the sources. Measurements of the distance from the Earth to the Moon and to the inner planets provide the basis for defining an inertial planetary ephemeris reference frame. The relative orientation, or frame tie, between these two reference frames is of interest for combining Earth orientation measurements, for comparing Earth orientation results with theories referred to the mean equator and equinox, and for determining the positions of the planets with respect to the extragalactic reference frame. This work presents an indirect determination of the extragalactic-planetary frame tie from a combined reduction of VLBI and Lunar Laser Ranging (LLR) observations. For this determination, data acquired by LLR tracking stations since 1969 have been analyzed and combined with 14 years of VLBI data acquired by NASA's Deep Space Network since 1978. The frame tie derived from this joint analysis, with an accuracy of 0.003 sec, is the most accurate determination obtained so far. This result, combined with a determination of the mean ecliptic (defined in the rotating sense), shows that the mean equinox of epoch J2000 is offset from the x-axis of the extragalactic frame adopted by the International Earth Rotation Service for astrometric and geodetic applications by 0.078 sec +/- 0.010 sec along the y-direction and y 0.019 sec +/- 0.001 sec. along the z-direction.
Folkner, W. M.↗
Potential capabilities of lunar laser ranging for geodesy and relativity
Here, we review the LLR technique focusing on its impact on Geodesy and Relativity. We discuss the modem observational accuracy and the level of existing LLR modeling. We present the near-term objectives and emphasize improvements needed to fully utilize the scientific potential of LLR.
earth - moon dynamics↗
High precision lunar tracking for laser ranging
Laser ranging to lunar surface retroreflectors has provided a valuable source of data for the investigation of the lunar orbit, the earth's orientation in space, general relativity, and many other aspects of solar system dynamics. Due to the moon's relatively large distance, and the requirement to keep the beam from the relatively low-power laser very narrow, acquiring this data type requires very accurate telescope pointing and tracking capabilities. The nominal requirement is to keep the telescope on target within approximately 1 arcsec of its predicted location for at least several minutes. An expansion of this requirement and the methods used to accomplish this high precision pointing are presented. Difficulties encountered and a few future goals of automating the McDonald station are also discussed.
Ricklefs, Randall L.↗
Lunar Rotation and the Lunar Interior
Variations in rotation and orientation of the Moon are sensitive to solid-body tidal dissipation, dissipation due to relative motion at the fluid-core/ solid-mantle boundary, and tidal Love number k2. There is weaker sensitivity to flattening of the core-mantle boundary (CMB) and fluid core moment of inertia. Accurate Lunar Laser Ranging (LLR) measurements of the distance from observatories on the Earth to four retroreflector arrays on the Moon are sensitive to lunar rotation and orientation variations and tidal displacements. Past solutions using the LLR data have given results for dissipation due to solid-body tides and fluid core plus Love number. Past detection of CMB flattening has been marginal but is improving, while direct detection of the core moment has not yet been achieved. Three decades of Lunar Laser Ranging (LLR) data are analyzed using a weighted least-squares approach. The lunar solution parameters include dissipation at the fluid-core/solid-mantle boundary, tidal dissipation, dissipation-related coefficients for rotation and orientation terms, potential Love number k2, a correction to the constant term in the tilt of the equator to the ecliptic which is meant to approximate the influence of core-mantle boundary flattening, and displacement Love numbers h2 and l2. Several solutions, with different combinations of solution parameters and constraints, are considered.
Williams, J. G.↗
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.↗
Next generation lunar laser retroreflectors for fundamental physics and lunar science
Lunar Laser Ranging (LLR) data represent a powerful tool to understand the dynamics of the Earth-Moon system and the deep lunar interior. Over the past five decades, the ground station technology has significantly improved, whereas the lunar laser retroreflector arrays (LRAs) on the lunar surface did not. Current instrumental LLR error budget is dominated by the spread of the returning laser pulse due to the large size of the arrays. Next-generation single solid lunar Cube Corner Retroreflectors (CCRs) of large optical diameter (whose LLR performance is unaffected by that time spread) aim to fully exploit the current laser ranging station capabilities to attain LLR accuracy below current centimeter value down to the desired millimeter level and much higher data collection rates. Such improvements will have a significant impact, enabling more refined ephemerides, improved tests of General Relativity (GR) and of other theories of relativistic gravity in the Sun-Earth-Moon system and improved knowledge of the properties of the lunar interior.
L. Porcelli↗
Lunar Science from Lunar Laser Ranging
Variations in rotation and orientation of the Moon are sensitive to solid-body tidal dissipation, dissipation due to relative motion at the fluid-core/solid-mantle boundary, tidal Love number k2, and moment of inertia differences. There is weaker sensitivity to flattening of the core/mantle boundary (CMB) and fluid core moment of inertia. Accurate Lunar Laser Ranging (LLR) measurements of the distance from observatories on the Earth to four retroreflector arrays on the Moon are sensitive to variations in lunar rotation, orientation and tidal displacements. Past solutions using the LLR data have given results for Love numbers plus dissipation due to solid-body tides and fluid core. Detection of the fluid core polar minus equatorial moment of inertia difference due to CMB flattening is weakly significant. This strengthens the case for a fluid lunar core. Future approaches are considered to detect a solid inner core.
Love numbers↗
Solar-System Tests of Gravitational Theories
We are engaged in testing gravitational theory by means of observations of objects in the solar system. These tests include an examination of the Principle Of Equivalence (POE), the Shapiro delay, the advances of planetary perihelia, the possibility of a secular variation G in the "gravitational constant" G, and the rate of the de Sitter (geodetic) precession of the Earth-Moon system. These results are consistent with our preliminary results focusing on the contribution of Lunar Laser Ranging (LLR), which were presented at the seventh Marcel Grossmann meeting on general relativity. The largest improvement over previous results comes in the uncertainty for (eta): a factor of five better than our previous value. This improvement reflects the increasing strength of the LLR data. A similar analysis presented at the same meeting by a group at the Jet Propulsion Laboratory gave a similar result for (eta). Our value for (beta) represents our first such result determined simultaneously with the solar quadrupole moment from the dynamical data set. These results are being prepared for publication. We have shown how positions determined from different planetary ephemerides can be compared and how the combination of VLBI and pulse timing information can yield a direct tie between planetary and radio frames. We have continued to include new data in our analysis as they became available. Finally, we have made improvement in our analysis software (PEP) and ported it to a network of modern workstations from its former home on a "mainframe" computer.
Shapiro, Irwin↗
Lunar Fluid Core and Solid-Body Tides
Variations in rotation and orientation of the Moon are sensitive to solid-body tidal dissipation, dissipation due to relative motion at the fluid-core/solid-mantle boundary, and tidal Love number k2 [1,2]. There is weaker sensitivity to flattening of the core-mantle boundary (CMB) [2-5] and fluid core moment of inertia [1]. Accurate Lunar Laser Ranging (LLR) measurements of the distance from observatories on the Earth to four retroreflector arrays on the Moon are sensitive to lunar rotation and orientation variations and tidal displacements. Past solutions using the LLR data have given results for dissipation due to solid-body tides and fluid core [1] plus Love number [1-5]. Detection of CMB flattening has been improving [3,5] and now seems significant. This strengthens the case for a fluid lunar core.
Williams, J. G.↗
Lunar Core and Tides
Variations in rotation and orientation of the Moon are sensitive to solid-body tidal dissipation, dissipation due to relative motion at the fluid-core/solid-mantle boundary, and tidal Love number k2 [1,2]. There is weaker sensitivity to flattening of the core-mantle boundary (CMB) [2,3,4] and fluid core moment of inertia [1]. Accurate Lunar Laser Ranging (LLR) measurements of the distance from observatories on the Earth to four retroreflector arrays on the Moon are sensitive to lunar rotation and orientation variations and tidal displacements. Past solutions using the LLR data have given results for dissipation due to solid-body tides and fluid core [1] plus Love number [1-5]. Detection of CMB flattening, which in the past has been marginal but improving [3,4,5], now seems significant. Direct detection of the core moment has not yet been achieved.
Williams, J. G.↗
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↗
Earth rotation and polar motion from laser ranging to the moon and artificial satellites
Earth-based laser ranging to artificial satellites and to the moon is considered as a technique for monitoring the Earth's polar motion and diurnal rotation. The kinematics of Earth rotation as related to laser ranging is outlined. The current status of laser ranging as regards its measuring capabilities is reviewed. The relative merits of artificial satellite and lunar laser ranging are pointed out. It appears that multistation combined artificial satellite and lunar laser ranging is likely to ultimately meet a 0.002 arcseconds in pole position and 0.1 msec in UT1 daily precision requirement.
Aardoom, L.↗
Eighth International Workshop on Laser Ranging Instrumentation
The Eighth International Workshop for Laser Ranging Instrumentation was held in Annapolis, Maryland in May 1992, and was sponsored by the NASA Goddard Space Flight Center in Greenbelt, Maryland. The workshop is held once every 2 to 3 years under differing institutional sponsorship and provides a forum for participants to exchange information on the latest developments in satellite and lunar laser ranging hardware, software, science applications, and data analysis techniques. The satellite laser ranging (SLR) technique provides sub-centimeter precision range measurements to artificial satellites and the Moon. The data has application to a wide range of Earth and lunar science issues including precise orbit determination, terrestrial reference frames, geodesy, geodynamics, oceanography, time transfer, lunar dynamics, gravity and relativity.
Degnan, John J.↗
The gravity and shape of the moon
This review discusses the current knowledge of the gravity and geometry of the moon, and their implications as to lunar structure. Measurements pertaining to the gravity field are, first and foremost, Doppler tracking of spacecraft that have orbited the moon, but also the laser ranging from the earth to the moon and the gravity meters and accelerometers landed with the Apollo spacecraft. Measurements pertaining to the geometry include (1) those related to the shape: the metric photography and laser altimeters on Apollo 15, 16, and 17; the electromagnetic sounder on Apollo 17; the landmark tracking from earlier Apollo orbiters; and occupations, plus (2) measurements related to the orientation: the laser ranging and interferometry from the earth. The review does not cover determinations of topography from photography taken for geologic or landing reconnaissance purposes. The discussion of tectonic implications is limited to inferences of a quantitative nature. The emphasis is on work since 1970; see Kaula [1969, 1971] for reviews of earlier work.
William M. Kaula↗
Lunar laser tests of gravitational physics
Analyses of laser ranges from Earth to Moon yield several tests of interest to gravitational physics. Examined are the equivalence principle, geodetic precesssion, and invariance of the gravitational constant G.
Moon relativity gravity range↗
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.↗