An introductory review of ephemerides for lunar laser ranging

1977 ◽  
Vol 284 (1326) ◽  
pp. 461-466
Keyword(s):  
Numerical Integration ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
Fields Of Study ◽  
The Earth ◽  
Lunar Laser ◽  
Laser Systems ◽  
Orbital Data ◽  
Introductory Review

Precise predictions of the ranges of the retroreflectors on the Moon from the observing stations on the Earth are required to facilitate the making of observations and also to provide a sound basis for the analysis of the observations. The precision of observations is already such that the theories of the Moon’s motion and libration currently used for the ephemerides in the Astronomical Ephemeris are inadequate for the analysis, and so the orbital data are generated by numerical integration. New laser systems will give a further improvement in precision, and further factors will have to be taken into account in the predictions. The exploitation of the data will require the development of new analytical theories, but the results will be of value in many different fields of study.

Effect of non-tidal station loading on Lunar Laser Ranging observatories and on the estimation of Earth orientation parameters

2021 ◽  
Author(s):  
Vishwa Vijay Singh ◽  
Liliane Biskupek ◽  
Jürgen Müller ◽  
Mingyue Zhang
Keyword(s):  
Research Centre ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
Earth Orientation Parameters ◽  
Tidal Station ◽  
Earth Orientation ◽  
The Earth ◽  
Lunar Laser ◽  
Orientation Parameters

<p>The distance between the observatories on Earth and the retro-reflectors on the Moon has been regularly observed by the Lunar Laser Ranging (LLR) experiment since 1970. 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, and a higher number of LLR observations in total. Providing the longest time series of any space geodetic technique for studying the Earth-Moon dynamics, LLR can also support the estimation of Earth orientation parameters (EOP), like UT1. The increased number of highly accurate LLR observations enables a more accurate estimation of the EOP. In this study, we add the effect of non-tidal station loading (NTSL) in the analysis of the LLR data, and determine post-fit residuals and EOP. The non-tidal loading datasets provided by the German Research Centre for Geosciences (GFZ), the International Mass Loading Service (IMLS), and the EOST loading service of University of Strasbourg in France are included as corrections to the coordinates of the LLR observatories, in addition to the standard corrections suggested by the International Earth Rotation and Reference Systems Service (IERS) 2010 conventions. The Earth surface deforms up to the centimetre level due to the effect of NTSL. By considering this effect in the Institute of Geodesy (IfE) LLR model (called ‘LUNAR’), we obtain a change in the uncertainties of the estimated station coordinates resulting in an up to 1% improvement, an improvement in the post-fit LLR residuals of up to 9%, and a decrease in the power of the annual signal in the LLR post-fit residuals of up to 57%. In a second part of the study, we investigate whether the modelling of NTSL leads to an improvement in the determination of EOP from LLR data. Recent results will be presented.</p>

scholarly journals MILLIMETRE MOON MEASUREMENT: 50 YEARS OF LUNAR LASER RANGING SINCE APOLLO 11!

2020 ◽  
Vol XLIII-B3-2020 ◽  
pp. 1105-1110
Author(s):  
J. F. Brock
Keyword(s):  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Space Race ◽  
Lunar Laser ◽  
Space Star ◽  
Gravitational Influence ◽  
Tv Shows ◽  
Set Up

Abstract. Since the dawn of time the Moon has held fascination for the earliest humans who saw it as a natural navigational beacon, a heavenly body to be revered and a poetic inspiration. Ancient art features the Moon as a prominent subject from all epochs and genres. The name “lunatic” infers that it drives men insane. Giant tides and rapid recessions of water are all attributed to its gravitational influence. As a young boy I was thrilled by stories of Moon travel like Jules Verne’s “From the Earth to the Moon” plus TV shows and movies such as “Lost in Space”, “Star Trek” and “Dr. Who.”The Russian-American “Space Race” focussed on the exciting possibility of man landing on the Moon. I cannot forget the live telecast of the Apollo 11 astronauts on the Moon’s surface in 1969 when I was 13 years old. Four years later I decided to be a land boundary surveyor trained in precise measurement for land title creation. My curiosity was alerted to the Apollo 11 laser ranging aspect of the project when the US team set up a bank of retro-reflectors for measurements from powerful devices on the Earth in the same way we Earthly surveyors make our daily measurements using such EDM equipment.In this paper I will describe the techniques and equipment utilised during this accurate Moon positioning project. You will also see the Earth observatories still measuring to five sites on the Moon and some ancient admirable attempts to determine this distance.

scholarly journals LUNAR LASER RANGING TESTS OF THE EQUIVALENCE PRINCIPLE WITH THE EARTH AND MOON

2009 ◽  
Vol 18 (07) ◽  
pp. 1129-1175 ◽  
Author(s):  
JAMES G. WILLIAMS ◽  
SLAVA G. TURYSHEV ◽  
DALE H. BOGGS
Keyword(s):  
Equivalence Principle ◽  
Primary Objective ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Wide Range ◽  
Near Term ◽  
Ppn Parameters

A primary objective of the lunar laser ranging (LLR) experiment is to provide precise observations of the lunar orbit that contribute to a wide range of science investigations. In particular, time series of the highly accurate measurements of the distance between the Earth and the Moon provide unique information used to determine whether, in accordance with the equivalence principle (EP), these two celestial bodies are falling toward the Sun at the same rate, despite their different masses, compositions, and gravitational self-energies. Thirty-five years since their initiation, analyses of precision laser ranges to the Moon continue to provide increasingly stringent limits on any violation of the EP. Current LLR solutions give (-1.0 ± 1.4) × 10-13 for any possible inequality in the ratios of the gravitational and inertial masses for the Earth and Moon, Δ(MG/MI). This result, in combination with laboratory experiments on the weak equivalence principle, yields a strong equivalence principle (SEP) test of Δ(MG/MI) SEP = (-2.0 ± 2.0) × 10-13. Such an accurate result allows other tests of gravitational theories. The result of the SEP test translates into a value for the corresponding SEP violation parameter η of (4.4 ± 4.5) × 10-4, where η = 4β - γ - 3 and both γ and β are parametrized post-Newtonian (PPN) parameters. Using the recent result for the parameter γ derived from the radiometric tracking data from the Cassini mission, the PPN parameter β (quantifying the nonlinearity of gravitational superposition) is determined to be β - 1 = (1.2 ± 1.1) × 10-4. We also present the history of the LLR effort and describe the technique that is being used. Focusing on the tests of the EP, we discuss the existing data, and characterize the modeling and data analysis techniques. The robustness of the LLR solutions is demonstrated with several different approaches that are presented in the text. We emphasize that near-term improvements in the LLR accuracy will further advance the research on relativistic gravity in the solar system and, most notably, will continue to provide highly accurate tests of the EP.

scholarly journals Dynamical Reference Frames in the Planetary and Earth-Moon Systems

1990 ◽  
Vol 141 ◽  
pp. 173-182
Author(s):  
E. M. Standish ◽  
J. G. Williams
Keyword(s):  
Reference Frame ◽  
Reference Frames ◽  
Optical Data ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Mariner 9 ◽  
Radar Ranging

We summarize our previous estimates of the accuracies of the ephemerides. Such accuracies determine how well one can establish the dynamical reference frame of the ephemerides. Ranging observations are the dominant data for the inner four planets and the Moon: radar-ranging for Mercury and Venus; Mariner 9 and Viking spacecraft-ranging for the Earth and Mars; lunar laser-ranging for the Moon. Optical data are significant for only the five outermost planets. Inertial mean motions for the Earth and Mars are determined to the level of 0.″003/cty during the time of the Viking mission; for Mars, this will deteriorate to 0.″01/cty or more after a decade or so; similarly, the inclination of the martian orbit upon the ecliptic was determined by Viking to the level of 0.″001. Corresponding uncertainties for Mercury and Venus are nearly two orders of magnitude larger. For the lunar mean motion with respect to inertial space, the present uncertainty is about 0.″04/cty; at times away from the present, the uncertainty of 1′/cty2 in the acceleration of longitude dominates. The mutual orientations of the equator, ecliptic and lunar orbit are known to 0.″002. The inner four planets and the Moon can now be aligned with respect to the dynamical equinox at a level of about 0.″005.

Lunar orbital theory

1977 ◽  
Vol 284 (1326) ◽  
pp. 565-571 ◽  
Keyword(s):  
Numerical Integration ◽  
Gravitational Theory ◽  
The State ◽  
Analytical Theory ◽  
Laser Ranging ◽  
The Moon ◽  
Orbital Theory ◽  
Lunar Laser Ranging ◽  
Lunar Laser ◽  
Better Than

The present and expected accuracies of lunar laser ranging imply that the gravitational theory of the motion of the Moon should be consistent with at least the same precision. It is therefore necessary to aim at internal relative consistencies better than 10 -11 or 10 -12 . Several theories based on numerical integration have been built and are currently being used in reducing the lunar laser ranging data. However, literal or semi-literal analytical theories have several im portant advantages over purely numerical ephemerides. This is why important programmes of building such theories are now in progress, particularly in the U. S. A. and in France. Characteristics and the state of advancement of these theories will be reviewed and the possibility of constructing an analytical theory with the above mentioned accuracy discussed.

McDonald observatory lunar laser ranging: Beginning the second 25 years

1996 ◽  
Vol 172 ◽  
pp. 409-414
Author(s):  
P.J. Shelus ◽  
R.L. Ricklefs ◽  
J.G. Ries ◽  
A.L. Whipple ◽  
J.R. Wiant
Keyword(s):  
Laser Pulse ◽  
Travel Time ◽  
Lunar Surface ◽  
Laser Ranging ◽  
The Moon ◽  
Round Trip ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Rich Spectrum

Lunar laser ranging (LLR) (Dickey et al., 1994) consists of measuring changes in the round-trip travel time for a laser pulse traveling between a transmitter on the Earth and a reflector on the Moon. The lunar surface reflectors are still operating normally after almost three decades of use. The ranging data exhibit a rich spectrum of change due to many effects.

scholarly journals WILL IT BE POSSIBLE TO MEASURE INTRINSIC GRAVITOMAGNETISM WITH LUNAR LASER RANGING?

2009 ◽  
Vol 18 (08) ◽  
pp. 1319-1326 ◽  
Author(s):  
LORENZO IORIO
Keyword(s):  
Orbital Motion ◽  
Radial Component ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Gravitomagnetic Field ◽  
Lunar Laser ◽  
Short Period ◽  
Orbital Revolution

In this paper we mainly explore the possibility of measuring the action of the intrinsic gravitomagnetic field of the rotating Earth on the orbital motion of the Moon with the lunar laser ranging (LLR) technique. Expected improvements in it should push the precision in measuring the Earth–Moon range to the mm level; the present-day root mean square (RMS) accuracy in reconstructing the radial component of the lunar orbit is about 2 cm; its harmonic terms can be determined at the mm level. The current uncertainty in measuring the lunar precession rates is about 10-1 milliarcseconds per year. The Lense–Thirring secular — i.e. averaged over one orbital period — precessions of the node and the perigee of the Moon induced by the Earth's spin angular momentum amount to 10-3 milliarcseconds per year, yielding transverse and normal shifts of 10-1-10-2 cm yr-1. In the radial direction there is only a short-period — i.e. nonaveraged over one orbital revolution — oscillation with an amplitude of 10-5 m. Major limitations come also from some systematic errors induced by orbital perturbations of classical origin, such as the secular precessions induced by the Sun and the oblateness of the Moon, whose mismodeled parts are several times larger than the Lense–Thirring signal. The present analysis holds also for the Lue–Starkman perigee precession due to the multidimensional braneworld model by Dvali, Gabadadze and Porrati (DGP); indeed, it amounts to about 5 × 10-3 milliarcseconds per year.

scholarly journals Relativistic rotational effects: application to the Earth-Moon system

1996 ◽  
Vol 172 ◽  
pp. 321-324 ◽  
Author(s):  
David Vokrouhlický
Keyword(s):  
Coordinate System ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Moon System ◽  
Geodetic Precession ◽  
Spin Effects ◽  
The Earth ◽  
Relativistic Spin ◽  
Lunar Laser

Relativistic spin effects involved in the Earth-Moon dynamics are reviewed. They enclose: (i) the coordinate system effects, and (ii) the relativistic physical librations. The geodetic precession is the only relativistic spin phenomenon which has been firmly detected so far. The best candidates of the effects which might be detected in the forthcoming period are the lunar physical librations and coordinate nutations. As for the latter, however, a fine cancellation between the geodetic and the Lense-Thirring coordinate effects results in decreasing their amplitude just below the possibility of the Lunar Laser Ranging technology.

scholarly journals Relations Between Celestial and Selenocentric Reference Frames

1981 ◽  
Vol 63 ◽  
pp. 268-280
Author(s):  
J. Kovalevsky
Keyword(s):  
Reference Frames ◽  
Center Of Mass ◽  
Great Accuracy ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Geometric Means ◽  
The Earth ◽  
Lunar Laser ◽  
Unique System ◽  
Different Types

AbstractThe very great accuracy with which the motions of the Moon can now be monitored by laser ranging, differential VLBI and occultation observations, implies that the interpretation of the measurements is conditioned by the choice and the accurate knowledge of a selenocentric, a terrestrial and a celestial frames. Two different types of selenocentric reference frames can be envisioned. The present selenographic frames are discussed but the author proposes that one should introduce a system defined by a purely geometric means. Some consequences of such a choice are discussed. One feature of the future conventional terrestrial frame is very important for Earth-Moon dynamics. Its origin should coincide with the center of mass of the Earth as determined by lunar laser ranging. As far as the quasi-inertial reference systems are concerned, the liaisons between a purely lunar dynamical system, subject to some hardly modelable effects, and purely celestial systems are analysed. The reduction of observations made with various techniques implies the use of different systems, and several problems are stated that should be solved before a unique system for Earth-Moon dynamics might be used.

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