Recent Progress in Analytical Modeling of the Relativistic Effects in the Lunar Motion

1997 ◽  
Vol 165 ◽  
pp. 205-214
Author(s):  
Kenneth Nordtvedt ◽  
David Vokrouhlický
Keyword(s):  
Analytical Modeling ◽  
Relativistic Effects ◽  
Relativity Theory ◽  
Lunar Laser Ranging ◽  
Similar Treatment ◽  
Numerical Tests ◽  
Preferred Direction ◽  
Lunar Laser ◽  
Lunar Motion ◽  
Quantitative Results

AbstractLunar motion serves for a number of important tests of the relativity theory. Although the final quantitative results come out from the direct numerical treatment of the lunar laser ranging data, the analytical solutions yield important keys for understanding sensitivity of the lunar motion on diverse effects. In the last few years, important relativistic phenomena, notably the equivalence principle violation and the preferred direction effects, have been reexamined using detailed Hill-Brown type theories. Surprising amplification of the former effect, indicated also from the numerical tests, has been explained by intricate coupling with the tidal deformation of the lunar orbit. Similar treatment proved that the lunar motion hides potentially a high-quality test of the preferred frame effects. In both cases, fundamental resonances of the problem cause singular amplification of the effects for particular lunar-like orbits.

scholarly journals Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser Ranging

2010 ◽  
Vol 60 (4) ◽  
Author(s):  
Yi Xie ◽  
Sergei Kopeikin
Keyword(s):  
Solar System ◽  
Reference Frame ◽  
Reference Frames ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Local Frame ◽  
The Earth ◽  
Lunar Laser ◽  
Lunar Motion ◽  
New Generation

Post-Newtonian Reference Frames for Advanced Theory of the Lunar Motion and for a New Generation of Lunar Laser RangingWe overview a set of post-Newtonian reference frames for a comprehensive study of the orbital dynamics and rotational motion of Moon and Earth by means of lunar laser ranging (LLR). We employ a scalar-tensor theory of gravity depending on two post-Newtonian parameters, β and γ, and utilize the relativistic resolutions on reference frames adopted by the International Astronomical Union (IAU) in 2000. We assume that the solar system is isolated and space-time is asymptotically flat at infinity. The primary reference frame covers the entire space-time, has its origin at the solar-system barycenter (SSB) and spatial axes stretching up to infinity. The SSB frame is not rotating with respect to a set of distant quasars that are forming the International Celestial Reference Frame (ICRF). The secondary reference frame has its origin at the Earth-Moon barycenter (EMB). The EMB frame is locally-inertial and is not rotating dynamically in the sense that equation of motion of a test particle moving with respect to the EMB frame, does not contain the Coriolis and centripetal forces. Two other local frames - geocentric (GRF) and selenocentric (SRF) - have their origins at the center of mass of Earth and Moon respectively and do not rotate dynamically. Each local frame is subject to the geodetic precession both with respect to other local frames and with respect to the ICRF because of their relative motion with respect to each other. Theoretical advantage of the dynamically non-rotating local frames is in a more simple mathematical description. Each local frame can be aligned with the axes of ICRF after applying the matrix of the relativistic precession. The set of one global and three local frames is introduced in order to fully decouple the relative motion of Moon with respect to Earth from the orbital motion of the Earth-Moon barycenter as well as to connect the coordinate description of the lunar motion, an observer on Earth, and a retro-reflector on Moon to directly measurable quantities such as the proper time and the round-trip laser-light distance. We solve the gravity field equations and find out the metric tensor and the scalar field in all frames which description includes the post-Newtonian multipole moments of the gravitational field of Earth and Moon. We also derive the post-Newtonian coordinate transformations between the frames and analyze the residual gauge freedom.

scholarly journals A review of the lunar laser ranging technique and contribution of timing systems

2016 ◽  
Vol Volume 112 (Number 3/4) ◽  
Author(s):  
Cilence Munghemezulu ◽  
Ludwig Combrinck ◽  
Joel O. Botai ◽  
◽  
◽  
...  
Keyword(s):  
Reference Frames ◽  
Laser Pulses ◽  
Relativity Theory ◽  
Earth Tides ◽  
Laser Ranging ◽  
The Moon ◽  
Lunar Laser Ranging ◽  
Factors Affecting ◽  
Lunar Laser ◽  
Space Geodetic Techniques

Abstract The lunar laser ranging (LLR) technique is based on the two-way time-of-flight of laser pulses from an earth station to the retroreflectors that are located on the surface of the moon. We discuss the ranging technique and contribution of the timing systems and its significance in light of the new LLR station currently under development by the Hartebeesthoek Radio Astronomy Observatory (HartRAO). Firstly, developing the LLR station at HartRAO is an initiative that will improve the current geometrical network of the LLR stations which are presently concentrated in the northern hemisphere. Secondly, data products derived from the LLR experiments – such as accurate lunar orbit, tests of the general relativity theory, earth–moon dynamics, interior structure of the moon, reference frames, and station position and velocities – are important in better understanding the earth–moon system. We highlight factors affecting the measured range bias such as the effect of earth tides on station position and delays induced by timing systems, as these must be taken into account during the development of the LLR analysis software. HartRAO is collocated with other fundamental space geodetic techniques which makes it a true fiducial geodetic site in the southern hemisphere and a central point for further development of space-based techniques in Africa. Furthermore, the new LLR will complement the existing techniques by providing new niche areas of research both in Africa and internationally.

scholarly journals On the dominant relativistic terms in the lunar theory

1986 ◽  
Vol 114 ◽  
pp. 53-57
Author(s):  
M. Soffel ◽  
H. Ruder ◽  
M. Schneider
Keyword(s):  
Reference Frame ◽  
Lunar Theory ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Mean Motion ◽  
Lunar Laser ◽  
Lunar Motion ◽  
Jacobi Equations

For a simplified 3-body (Earth, Moon, Sun) problem it is shown how the usual Einstein-Infeld-Hoffmann equations for the lunar motion reduce to the Jacobi-equations after the transformation to the proper reference frame. The dominant relativistic contributions to the lunar laser ranging observables are then obtained in a Hill-Brown calculation. It is argued that in the proper reference frame all post-Newtonian variational terms are proportional to m = n′/(n-n′) [n(n′) = mean motion of Moon (Sun)].

scholarly journals Relativistic Reduction of Astronomical Measurements and Reference Frames

1980 ◽  
Vol 56 ◽  
pp. 283-294
Author(s):  
V. A. Brumberg
Keyword(s):  
Light Propagation ◽  
Reference Frames ◽  
Relativistic Effects ◽  
Propagation Characteristics ◽  
Lunar Laser Ranging ◽  
Schwarzschild Metric ◽  
The Earth ◽  
Lunar Laser ◽  
Relativistic Treatment ◽  
Relativistic Reduction

AbstractWith the accuracy of modern observations the relativistic treatment of the basic astronomical reference frames only requires the consideration of comparatively simple types of metrics such as heliocentric Schwarzschild metric, geocentric Schwarzschild metric and metric of the Earth-Sun system. Dynamical (related to the motion of the bodies) and kinematical (related to the light propagation) characteristics of these metrics enable one to perform the accurate relativistic reduction of astronomical measurements. In this reduction, the choice of specific quasi-Galilean coordinates may remain arbitrary. This paper presents expressions for the main relativistic terms in coordinates of the principal planets and Moon using the PPN formalism parameters β, γ and coordinate parameter α. General formulae for the reduction of radar, radio-interferometric and astrometric observations of planets and for the interpretation of lunar laser ranging are given. For estimating the actual magnitude of relativistic effects, the ephemeris data should be expressed in terms of physically measurable quantities.

scholarly journals Varying Physical Constants, Astrometric Anomalies, Redshift and Hubble Units

Galaxies ◽  
2019 ◽  
Vol 7 (2) ◽  
pp. 55 ◽  
Author(s):  
Rajendra P. Gupta
Keyword(s):  
Hubble Constant ◽  
Astronomical Unit ◽  
Lunar Laser Ranging ◽  
Current Time ◽  
Physical Constants ◽  
Lunar Laser ◽  
Walker Metric ◽  
The One ◽  
Two Parameters ◽  
Secular Increase

We have developed a cosmological model by allowing the speed of light c, gravitational constant G and cosmological constant Λ in the Einstein filed equation to vary in time, and solved them for Robertson-Walker metric. Assuming the universe is flat and matter dominant at present, we obtain a simple model that can fit the supernovae 1a data with a single parameter almost as well as the standard ΛCDM model with two parameters, and which has the predictive capability superior to the latter. The model, together with the null results for the variation of G from the analysis of lunar laser ranging data determines that at the current time G and c both increase as dG/dt = 5.4GH0 and dc/dt = 1.8cH0 with H0 as the Hubble constant, and Λ decreases as dΛ/dt = −1.2ΛH0. This variation of G and c is all what is needed to account for the Pioneer anomaly, the anomalous secular increase of the moon eccentricity, and the anomalous secular increase of the astronomical unit. We also show that the Planck’s constant ħ increases as dħ/dt = 1.8ħH0 and the ratio D of any Hubble unit to the corresponding Planck unit increases as dD/dt = 1.5DH0. We have shown that it is essential to consider the variation of all the physical constants that may be involved directly or indirectly in a measurement rather than only the one whose variation is of interest.

Lunar Laser Ranging at CERGA for the ruby period (1981–1986)

1993 ◽  
pp. 189-193 ◽  
Author(s):  
C. Veillet ◽  
J. F. Mangin ◽  
J. E. Chabaubie ◽  
C. Dumolin ◽  
D. Feraudy ◽  
...  
Keyword(s):  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Lunar Laser

scholarly journals CONSTRAINT ON INTERMEDIATE-RANGE GRAVITY FROM EARTH–SATELLITE AND LUNAR ORBITER MEASUREMENTS, AND LUNAR LASER RANGING

2005 ◽  
Vol 14 (10) ◽  
pp. 1657-1666 ◽  
Author(s):  
GUANGYU LI ◽  
HAIBIN ZHAO
Keyword(s):  
Experimental Tests ◽  
Earth Satellite ◽  
Laser Ranging ◽  
Satellite Measurement ◽  
Lunar Orbiter ◽  
Lunar Laser Ranging ◽  
Intermediate Range ◽  
Earth Gravity ◽  
Lunar Laser ◽  
Order Of Magnitude

In the experimental tests of gravity, there have been considerable interests in the possibility of intermediate-range gravity. In this paper, we use the earth–satellite measurement of earth gravity, the lunar orbiter measurement of lunar gravity, and lunar laser ranging measurement to constrain the intermediate-range gravity from λ = 1.2 × 107 m –3.8 × 108 m . The limits for this range are α = 10-8–5 × 10-8, which improve previous limits by about one order of magnitude in the range λ = 1.2 × 107 m –3.8 × 108 m .

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>

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