scholarly journals Que pourra-t-on deduire des mesures de distance terre-lune par laser?

1974 ◽  
Vol 61 ◽  
pp. 269-274
Author(s):  
J. Kovalevsky
Keyword(s):  
Major Axis ◽  
Radio Interferometry ◽  
The Moon ◽  
Semi Major Axis ◽  
Lunar Laser Ranging ◽  
The Earth ◽  
Lunar Laser ◽  
Observational Errors ◽  
External Check

Although several lunar laser ranging stations exist, only one is now fully operational: the McDonald station with internal observational errors of less than 15 cm. The interpretation of the data involves a great number of parameters relative to the Earth and the Moon which are listed.The lunar laser is particularly fit for those parameters that pertain to the Moon, and with future lasers accurate to 2 or 3 cm, it may be expected that this accuracy will be projected into these parameters. The probable determination of the semi-major axis to 1 cm accuracy for a few months mean would imply a new means of determining the non conservative part of the motion of the Moon. A similar precision is to be expected for the rotation of the Moon. The situation for the Earth parameters (Earth rotation and polar motion) is not so good, because of a rather weak geometry of the problem and the monthly one week gap in the observations. Nevertheless, it will give a very useful external check on other competing methods (radio-interferometry, laser or radio-satellites).

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 The Shape of the Moon

1972 ◽  
Vol 47 ◽  
pp. 22-31 ◽  
Author(s):  
S. K. Runcorn ◽  
S. Hofmann
Keyword(s):  
Lunar Surface ◽  
Major Axis ◽  
Great Depth ◽  
The Moon ◽  
Method Of Least Squares ◽  
Global Shape ◽  
The Earth ◽  
Intrinsic Scatter ◽  
Simple Statistical Analysis

The determination of the heights of points on the lunar surface by Earth based astronomy using the geometrical librations, although individually of low accuracy, still provides our best method of obtaining the global shape of the Moon. The intrinsic scatter of the results arises from the effects of ‘seeing’ and simple statistical analysis is required to derive valid conclusions about the shape. Baldwin's method of fitting ellipsoidal surfaces to the points on the maria and uplands, separately by the method of least squares proves to be a valuable tool.Analyses of the ACIC points and of the Pic du Midi studies of G. A. Mills show that good first descriptions of the global shape of the Moon for both the maria and uplands are triaxial ellipsoids with their long axes within 10° of the Earth direction, the major axis of the maria being about 1.3 km smaller than that of the uplands. Of particular significance is that the ellipticity of these surfaces is about 2½ times greater than the dynamical ellipticity; thus the non-hydrostatic figure of the Moon is not simply the result of distortion from a uniform Moon during its early history. The angular variation in density within the Moon cannot be simply a phenomena within the crust but must extend to a great depth. Convection could provide an explanation.The departures of the lunar surface from the idealised ellipsoids are also of interest. The circular maria are systematically depressed relative to the maria ellipsoid: can the mascons have adjusted isostatically since their formation? Systematic differences in height between the western and eastern southern uplands are also noted.

scholarly journals Accretion of the Moon from non-canonical discs

2014 ◽  
Vol 372 (2024) ◽  
pp. 20130256 ◽  
Author(s):  
J. Salmon ◽  
R. M Canup
Keyword(s):  
Angular Momentum ◽  
Rotation Period ◽  
Major Axis ◽  
The Moon ◽  
Large Excess ◽  
Semi Major Axis ◽  
Earth’S Mantle ◽  
The Earth ◽  
Post Impact ◽  
Impact Simulations

Impacts that leave the Earth–Moon system with a large excess in angular momentum have recently been advocated as a means of generating a protolunar disc with a composition that is nearly identical to that of the Earth's mantle. We here investigate the accretion of the Moon from discs generated by such ‘non-canonical’ impacts, which are typically more compact than discs produced by canonical impacts and have a higher fraction of their mass initially located inside the Roche limit. Our model predicts a similar overall accretional history for both canonical and non-canonical discs, with the Moon forming in three consecutive steps over hundreds of years. However, we find that, to yield a lunar-mass Moon, the more compact non-canonical discs must initially be more massive than implied by prior estimates, and only a few of the discs produced by impact simulations to date appear to meet this condition. Non-canonical impacts require that capture of the Moon into the evection resonance with the Sun reduced the Earth–Moon angular momentum by a factor of 2 or more. We find that the Moon's semi-major axis at the end of its accretion is approximately 7 R ⊕ , which is comparable to the location of the evection resonance for a post-impact Earth with a 2.5 h rotation period in the absence of a disc. Thus, the dynamics of the Moon's assembly may directly affect its ability to be captured into the resonance.

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 Agreements and Disagreements between Theories of Rigid Earth Nutation

1997 ◽  
Vol 165 ◽  
pp. 319-324
Author(s):  
J. Souchay
Keyword(s):  
Very Long Baseline Interferometry ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Theoretical Determination ◽  
Long Baseline ◽  
The Earth ◽  
Lunar Laser ◽  
Rigid Earth ◽  
Good Agreement

AbstractThe necessity to elaborate a theory of nutation and precession matching the accuracy of very modern techniques as Very Long Baseline Interferometry and Lunar Laser Ranging led recently to various works. We discuss here the good agreement between those related to the nutation when considering the Earth as a solid body. In comparison we show the uncertainty concerning the modelisation of the transfer function leading to theoretical determination of the nutation coefficients when including dominant geophysical characteristics.

Determination of upper-atmosphere air-density profile from satellite observations

1959 ◽  
Vol 252 (1268) ◽  
pp. 28-34 ◽  
Keyword(s):  
Density Profile ◽  
Satellite Orbit ◽  
Major Axis ◽  
Scale Height ◽  
Semi Major Axis ◽  
Relative Variation ◽  
Air Density ◽  
The Earth ◽  
Point Data

The theory previously developed for the changes in the perigee distance and semi-major axis of a satellite orbit due to air drag is extended to enable the air-density profile (i. e. its relative variation with height) to be derived from the motion of the orbit’s perigee. The solution is first obtained in terms of the change in perigee distance and then in terms of the change in the radius of the earth at the sub-perigee point. Data are analyzed by the two methods, leading to 39 (± 9) and 36 (± 15) km for the scale height in the 180 and 220 km altitude regions.

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.

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.

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