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NASA NTRS1986

Intercomparison of UT1 measurements during the MERIT campaign period

Universal time (UT1) measurements obtained using VLBI, lunar laser ranging (LLR), and BIH optical astronomy are compared. The JPL Kalman filter for the earth rotation and the polar motion is utilized to smooth one data set or combine data sets for intercomparison. The differences between raw UT1 data and independently smoothed data are employed to assess the accuracy of the measured series and the sufficiency of the error budget. Systematic errors in periodic signatures and length of day estimates are analyzed. The data reveal that the techniques of LLR and VLBI agree to within their formal errors. It is determined that the residual error for the LLR is too large and the residual error estimated for the BIH data is too small.

Spieth, M. A.↗

NASA NTRS1989

Investigating relativity using lunar laser ranging - Geodetic precession and the Nordtvedt effect

The emplacement of retroreflectors on the moon by Apollo astronauts and the Russian Lunakhod spacecraft marked the inception of lunar laser ranging (LLR) and provided a natural laboratory for the study of general relativity. Continuing acquisition of increasingly accurate LLR data has provided enhanced sensitivity to general relativity parameters. Two relativistic effects are investigated in this paper: (1) the Nordtvedt effect, yielding a test of the strong equivalence principle, would appear as a distortion of the geocentric lunar orbit in the direction of the sun. The inclusion of recent LLR data limits the size of any such effect to 3 + or - 4 cm. The sensitivities to the various PPN quantities are also highlighted. (2) the geodetic precession of the lunar perigee is predicted by general relativity as a consequence of the motion of the earth-moon system about the sun; its theoretical magnitude is 19.2 mas/yr. Analysis presented here confirms this value and determines this quality to a 2 percent level.

Dickey, J. O.↗

NASA NTRS1991

A survey of laser lightning rod techniques

The work done to create a laser lightning rod (LLR) is discussed. Some ongoing research which has the potential for achieving an operational laser lightning rod for use in the protection of missile launch sites, launch vehicles, and other property is discussed. Because of the ease with which a laser beam can be steered into any cloud overhead, an LLR could be used to ascertain if there exists enough charge in the clouds to discharge to the ground as triggered lightning. This leads to the possibility of using LLRs to test clouds prior to launching missiles through the clouds or prior to flying aircraft through the clouds. LLRs could also be used to probe and discharge clouds before or during any hazardous ground operations. Thus, an operational LLR may be able to both detect such sub-critical electrical fields and effectively neutralize them.

Barnes, Arnold A., Jr.↗

NASA NTRS2000

Jet Propulsion Laboratory

Analyses of laser ranges to the Moon are utilized for a broad range of investigations: lunar science, gravitational physics, geodesy, geodynamics and astronomy. Unique contributions from LLR include: detection of a molten lunar core; measurement of tidal dissipation in the Moon; an accurate test of the principle of equivalence for massive bodies (strong equivalence principle); and detection of lunar free librations. LLR analysis has provided tests of relativity, measurements of the Moon's tidal acceleration and the Earth s precession, and has provided orders-of-magnitude improvements in the accuracies of the lunar ephemeris and three-dimensional rotation. JPL has been active in all of these various LLR applications and supplies lunar and planetary ephemerides and lunar physical librations to the community.

Williams, Jim↗

NASA NTRS2003

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.↗

NASA NTRS2019

Observational Constraint on the Radius and Oblateness of the Lunar Core‐Mantle Boundary

Lunar laser ranging (LLR) data and Apollo seismic data analyses, revealed independent evidence for the presence of a fluid lunar core. However, the size of the lunar fluid core remained uncertain by _55 km (encompassing two contrasting 2011 Apollo seismic data analyses). Here we show that a new description of the lunar interior's dynamical model provides a determination of the radius and geometry of the lunar core-mantle boundary (CMB) from the LLR observations. We compare the present day lunar core oblateness obtained from LLR analysis with the expected hydrostatic model values, over a range of previously expected CMB radii. The findings suggest a core oblateness (f(c) = (2.2 ± 0.6) x 10(exp 14)) that satisfies the assumption of hydrostatic equilibrium over a tight range of lunar CMB radii (R(CMB) = 381 ± 12 km). Our estimates of a presently-relaxed lunar CMB translates to a core mass fraction in the range of 1.59 - 1.77% with a present-day Free Core Nutation (FCN) within (367±100) years.

Moon↗

NASA NTRS2008

Lunar Science from Laser Ranging - Present and Future

The interior properties of the Moon influence lunar tides and rotation. Three-axis rotation (physical librations) and tides are sensed by tracking lunar landers. The Lunar Laser Ranging (LLR) experiment has acquired 38 yr of increasingly accurate ranges from observatories on the Earth to four corner cube retroreflector arrays on the Moon. Lunar Laser Ranging is reviewed in [1]. Recent lunar science results are in [4,5]. In this abstract present LLR capabilities are described followed by future possibilities.

Lunar Laser Ranging (LLR)↗

NASA NTRS2013

Lunar Science from Lunar Laser Ranging

Love numbers↗

NASA NTRS1978

Estimability and simple dynamical analyses of range (range-rate range-difference) observations to artificial satellites

Non-Bayesian statistics were used in simulation studies centered around laser range observations to LAGEOS. The capabilities of satellite laser ranging especially in connection with relative station positioning are evaluated. The satellite measurement system under investigation may fall short in precise determinations of the earth's orientation (precession and nutation) and earth's rotation as opposed to systems as very long baseline interferometry (VLBI) and lunar laser ranging (LLR). Relative station positioning, determination of (differential) polar motion, positioning of stations with respect to the earth's center of mass and determination of the earth's gravity field should be easily realized by satellite laser ranging (SLR). The last two features should be considered as best (or solely) determinable by SLR in contrast to VLBI and LLR.

Vangelder, B. H. W.↗

NASA NTRS1982

Intercomparison of lunar laser and traditional determinations of earth rotation

Since August, 1969, ranges to one or more retroreflector arrays on the lunar surface have been measured by means of a laser procedure. Analysis of these measurements improves determination, not only of the orbit and librations of the moon, but also of the rotational parameters of the earth, including the X and Y coordinates of the terrestrial pole, and the true rotational angle of the earth with respect to atomic or to broadcast time. The considered approach for deriving the Universal Time 1 (UT1) involves two steps. During the first step the parameters of the lunar orbit and librations are solved along with the coordinates of the retroreflectors on the moon and of the observatory. Improved values of the Universal Time 0 (UT0) and range corrections at the observatory are obtained in the second step. Attention is given to lunar laser ranging (LLR), raw data in UT1, an harmonic analysis of the LLR UT1 data, and data obtained in 1980. The results provide UT1 with an accuracy of a factor of 2 or more better than was previously available from conventional astrometric data.

Fliegel, H. F.↗

NASA NTRS1983

Earth rotation from lunar laser ranging

The rotational orientation (Universal Time and the variation of latitude at McDonald Observatory, Texas) of the earth has been determined between mid 1970 and mid 1982 from McDonald Observatory lunar laser ranging (LLR) data. Universal Time, UT1, is calculated and supplied in three forms, the raw daily decomposition values, the Gaussian filtered values and the Fourier smoothed values. Formal error estimates are available for all three types. LLR can calculate corrections to one component of polar motion, the variation of latitude at McDonald Observatory. Modelling improvements have been applied here and a significant drop is seen in the residuals. The rms weighted residual for the entire thirteen year data span (3,326 'normal' points acquired between August 1969 and May 1982) is 18.7 cm.

Dickey, J. O.↗

NASA NTRS1993

Poisson filtering of laser ranging data

The filtering of data in a high noise, low signal strength environment is a situation encountered routinely in lunar laser ranging (LLR) and, to a lesser extent, in artificial satellite laser ranging (SLR). The use of Poisson statistics as one of the tools for filtering LLR data is described first in a historical context. The more recent application of this statistical technique to noisy SLR data is also described.

Ricklefs, Randall L.↗

NASA NTRS1994

A Planar Approximation for the Least Reliable Bit Log-likelihood Ratio of 8-PSK Modulation

The optimum decoding of component codes in block coded modulation (BCM) schemes requires the use of the log-likelihood ratio (LLR) as the signal metric. An approximation to the LLR for the least reliable bit (LRB) in an 8-PSK modulation based on planar equations with fixed point arithmetic is developed that is both accurate and easily realizable for practical BCM schemes. Through an error power analysis and an example simulation it is shown that the approximation results in 0.06 dB in degradation over the exact expression at an E(sub s)/N(sub o) of 10 dB. It is also shown that the approximation can be realized in combinatorial logic using roughly 7300 transistors. This compares favorably to a look up table approach in typical systems.

Thesling, William H.↗

NASA NTRS1994

Cosmic acceleration of Earth and the Moon by dark matter

In order to test the hypothesis that the gravitational interaction between our Galaxy's dark matter and the ordinary matter in Earth and the Moon might not fulfill the equivalence principle (universality of free fall), we consider the pertinent perturbation of the lunar orbit -- a sidereal month period range oscillation resulting from a spatially fixed polarization of the orbit. Lunar laser ranging (LLR) data can measure this sidereal perturbation to an accuracy equal to or better than its existing measurement of the synodic month period range oscillation amplitude (+/- 3 cm) which has been used for testing whether Earth and the Moon accelerate at equal rates toward the Sun. Because of the slow precession rate of the Moon's perigree (8.9 yr period), the lunar orbit is particularly sensitive to a cosmic acceleration; the LLR fit of the orbit places an upper limit of 10(exp -13) cm/sq. s for any cosmic differential acceleration between Earth (Fe) and the Moon (silicates). This is 10(exp -5) of the total galactic acceleration of the solar system, of which, it has been suggested, a large portion is produced by dark matter.

Nordtvedt, Kenneth L.↗

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 NTRS1994

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.↗

NASA NTRS1997

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↗

NASA NTRS1998

The Moon's Molten Core and Tidal Q

The rotation of the Moon is influenced by solid-body tides and interaction at a liquid-core/solid-mantle boundary. The Lunar Laser Ranging (LLR) data are sensitive to variations in lunar rotation. Analysis of those ranges reveals four dissipation periodicities in the rotation. These signatures can be explained with the combined effects of tide plus core, but not with either alone. The fluid core detection exceeds three times its uncertainty. The inferred core radius has a 1 -sigma upper limit of 352 km for iron and up to 374 km if sulfur is present. The tidal dissipation is strong, Q at one month is 37 +/- 5 .Q increases for longer periods and is 60 (-15, +40) at one year.Dynamical evidence for a fluid lunar core has previously been presented. These-earlier solutions included three dissipation parameters. New solutions benefit from additional LLR data and an improved gravity field from Doppler tracking of Lunar Prospector. Five dissipation parameters are now solved for. There are several options for dissipation parameters: a core coupling parameter, a time delay for tidal distortion of the moments of inertia, and five periodic terms in the rotation angles. Solutions with different combinations of these are compatible (a theory relates K/C and time delay to a series of periodic terms). The solutions used K/C, time delay, and one periodic term. When dissipation signatures at five rotation frequencies are solved for, four amplitudes (4 to 263 milliarcseconds) are detected above the noise. Attempts to explain these results using either tides alone or core alone fail (less than 3(sigma) discrepancy for the former and 9(sigma), for the latter). A combination of tides and liquid core matches the results well.

Williams, J. G.↗