scholarly journals The Orientation of the Dynamical Reference Frame

1991 ◽  
Vol 127 ◽  
pp. 146-152
Author(s):  
J.G. Williams ◽  
J.O. Dickey ◽  
X X Newhall ◽  
E.M. Standish
Keyword(s):  
Reference Frame ◽  
Current Status ◽  
Laser Ranging ◽  
Reference Systems ◽  
Data Types ◽  
Lunar Laser Ranging ◽  
Accurate Knowledge ◽  
Lunar Laser ◽  
The Impact ◽  
Precession Constant

AbstractWe summarize the current status of the JPL ephemerides, focusing on the various data types utilized, especially the impact of the modern ranging data, and the resulting accuracies obtained. The dynamical equinox, as determined from the analysis of Lunar Laser Ranging data, is determined with an accuracy of 5 mas and the obliquity to a 2 mas level in ~1983, the weighted center of data. Knowledge of the lunar and planetary positions with respect to the dynamical equinox degrades to 10 mas at J2000. Twenty years of LLR data allow for the separation of the 18.6 yr nutation terms from the precession constant. The correction to IAU precession is found to be −2.7 ± 0.4 mas/yr, while the 18.6 yr nutation of the pole is 3.0 ± 1.5 mas larger in magnitude than the 1980 IAU series. The necessity of different reference systems and the accurate knowledge of the interconnections between frames is addressed.

scholarly journals Geocentric Terrestrial Reference Frame Accuracy: DSN Spacecraft Tracking and VLBI/Lunar Laser Ranging

1988 ◽  
Vol 128 ◽  
pp. 115-120 ◽  
Author(s):  
A. E. Niell
Keyword(s):  
Reference Frame ◽  
Terrestrial Reference Frame ◽  
Spin Axis ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Deep Space Network ◽  
Long Baseline ◽  
Lunar Laser ◽  
Spacecraft Tracking ◽  
Geocentric Coordinates

From a combination of 1) the location of McDonald Observatory from Lunar Laser Ranging, 2) relative station locations obtained from Very Long Baseline Interferometry (VLBI) measurements, and 3) a short tie by traditional geodesy, the geocentric coordinates of the 64 m antennas of the NASA/JPL Deep Space Network are obtained with an orientation which is related to the planetary ephemerides and to the celestial radio reference frame. Comparison with the geocentric positions of the same antennas obtained from tracking of interplanetary spacecraft shows that the two methods agree to 20 cm in distance off the spin axis and in relative longitude. The orientation difference of a 1 meter rotation about the spin axis is consistent with the error introduced into the tracking station locations due to an error in the ephemeris of Jupiter.

scholarly journals Observations of Luni-Solar Precession

1995 ◽  
Vol 10 ◽  
pp. 198-198
Author(s):  
D.D. McCarthy ◽  
B.J. Luzum
Keyword(s):  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Lunar Laser ◽  
Made In ◽  
Precession Constant

The observations of dψ and dε used in this analysis were taken from the combination solution of the IERS Sub-Bureau for Rapid Service and Precition (McCarthy and Luzum 1991a). Besides corrections to the coefficients determined from VLBI, additional estimates can be derived from lunar laser ranging (LLR) observations (Williams et al. 1991; Whipple 1993). Table ?? shows a comparison of the estimates of the change in longitude and obliquity derived in this analysis with corresponding terms from analyses by other authors using different observations. The theoretical value of obliquity by Williams (1994) is also included for comparison. There are significant unexplained discrepancies among the rate estimates. Difference in the methods of the analyses such as the procesure for the estimation of the nutation coefficients and correlations within the solutions probably account for the greater part of these discrepancies. In considering the adoption of changes in the IAU model for nutation, it is important to recall that changes must also be made in the precession constant. Introduction of changes in nutation without corresponding changes in precession will not improve the agreement between observations and theory.

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 Introduction of JD 19: Nutation

1995 ◽  
Vol 10 ◽  
pp. 209-213
Author(s):  
V. Dehant
Keyword(s):  
Global Positioning System ◽  
Laser Ranging ◽  
Lunar Laser Ranging ◽  
Long Baseline ◽  
Lunar Laser ◽  
Global Positioning ◽  
Nutation Series ◽  
Precise Time ◽  
Better Than ◽  
Precession Constant

Due to both precise time measurements and precise geodetic positioning methods (like Very Long Baseline Interferometry (VLBI), Lunar Laser Ranging (LLR), Satellite Laser Ranging (SLR) and Global Positioning System (GPS)), the position of the instantaneous axis of the Earth’s rotation in space is measured with a precision better than a tenth of milliarcsecond. Simultaneously the amplitudes of the nutations of the Celestial Ephemeris Pole (CEP) deduced from the observations, i.e. the periodic motions in space of the CEP due to the luni-solar attraction or to other planetary attractions, have also been improved. However, these observed nutation amplitudes differ with respect to the computated ones based on an elliptical, uniformly rotating and deformable Earth responding to the lunar and solar attractions, as adopted by the IAU in 1980. The first session on “Observations and data reduction” dealt with Earth’s orientation observations and data analysis for deriving precession and nutations, as well as the associated residuals with respect to the adopted precession constant and nutation series. Comparisons between the different results have been presented including in-phase and out-of-phase components of the prograde and retrograde nutations or of nutations in longitude and in obliquity (see Session 1 of our JD: Newhall et al., McCarthy and Luzum, Herring, and Session 2: Gross). These differences “observed - adopted” nutations achieve several milliarcseconds and exhibit periodic as well as secular characteristics.

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.

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 An Accurate Model of Mercury’s Spin-Orbit Motion

2005 ◽  
Vol 13 ◽  
pp. 64-66
Author(s):  
Nicolas Rambaux ◽  
Eric Bois
Keyword(s):  
Laser Ranging ◽  
Spin Orbit ◽  
Relativistic Model ◽  
Lunar Laser Ranging ◽  
Secular Resonance ◽  
Observational Accuracy ◽  
Lunar Laser ◽  
The Mean ◽  
The Impact

AbstractOur work deals with the physical and dynamical causes that induce librations of Mercury around an equilibrium state defined by the 3:2 spin-orbit resonance. In order to integrate the spin-orbit motion of Mercury, we have used our gravitational model of the solar system including the Moon’s spin-orbit motion. This model, called SONYR (acronym of Spin-Orbit N-bodY Relativistic model), was previously built by Bois, Journet and Vokrouhlicky in accordance with the requirements of the Lunar Laser Ranging observational accuracy.Using the model, we have identified the main perturbations acting on the spin-orbit motion of Mercury such as the planetary interactions or the dynamical figure of the planet. Moreover, the complete rotation of Mercury exhibits two proper frequencies, namely 15.847 and 1066 years, and in addition one spin-orbit secular resonance (298 898 years). A new determination of the mean obliquity of Mercury has been proposed. Besides, we have identified in the Hermean librations the impact of the uncertainty of the greatest principal moment of inertia (C/MR2) on the obliquity as well as on the libration in longitude (2.3 mas and 0.45 as respectively for an increase of 1% on the C/MR2 value). These accurate relations have to be taken into account in the context of the two upcoming missions BepiColombo and MESSENGER.

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