scholarly journals Comparison of ELP-2000 to a JPL Numerical Integration

1981 ◽  
Vol 63 ◽  
pp. 257-264
Author(s):  
Jean Chapront ◽  
Michelle Chapront-Touzé
Keyword(s):  
Analytical Solution ◽  
Numerical Integration ◽  
Orbital Motion ◽  
Complete Solution ◽  
Analytical Theory ◽  
The Moon ◽  
Full Paper ◽  
Lunar Laser ◽  
Lunar Ephemeris

This contribution is an outline of the main results obtained by the authors in comparing their solution ELP-2000, to a JPL numerical integration, LE-51. A full paper containing discussions and comments on the results will be proposed to Astronomy ’ Astrophysics.A solution for the orbital motion of the Moon has been built by the authors. It is named ELP-2000, the epoch of reference being J2000. It is a semi-analytical solution, its structure being quite similar to Brown-Eckert’s one, as it appears in the Improved Lunar Ephemeris, ILE, j=2, (Eckert et al., 1954). The main purpose of this work is to present the results of a comparison of a provisional but complete solution, to an external numerical integration, LE-51, built at JPL (Williams, 1980), and fitted to lunar laser rangings. The JPL numerical integration is regarded as an “observational model”. It is a first attempt to compare as a whole, a new lunar ephemeris, derived from a semi-analytical theory, to observations, via a numerical integration.

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.

scholarly journals Analytical Theories of the Motion of the Moon

1981 ◽  
Vol 63 ◽  
pp. 227-232
Author(s):  
Jacques Henrard
Keyword(s):  
Numerical Integration ◽  
Analytical Theory ◽  
The Moon

AbstractAlmost every aspect of the analytical theory of the motion of the Moon has been reinvestigated lately. This paper is a review of these investigations.The improvement upon the I.L.E. (the best known earlier theory based upon the work of Brown) is spectacular, but it is still too early to assess the exact value of these theories with respect to numerical integration.

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 Expected Use of Lunar Range Data to Determine Modified Nutation Terms

1980 ◽  
Vol 78 ◽  
pp. 127-128
Author(s):  
P. L. Bender
Keyword(s):  
Angular Position ◽  
Gravitational Theory ◽  
Range Data ◽  
The Moon ◽  
Lunar Laser Range ◽  
Laser Range ◽  
Lunar Laser ◽  
Lunar Ephemeris ◽  
The Mean

The lunar laser range data from the McDonald Observatory in Texas have been used so far to determine major improvements in the lunar ephemeris and librations, to provide a new test of gravitational theory, and to determine single-day UT0 values on about 200 days during the period 1970-1974. The mean uncertainty in the UT0 values is 0.5 msec, and the smallest uncertainty is 0.2 msec (Stolz et al. 1976). The changes in the angular position of the moon with time are believed to be well enough known so that their uncertainty does not substantially degrade the accuracy of the UT0 values.

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 Planetary Ephemerides

1974 ◽  
Vol 3 ◽  
pp. 223-227
Author(s):  
R. L. Duncombe ◽  
P. K. Seidelmann ◽  
P. M. Janiczek
Keyword(s):  
Numerical Integration ◽  
The Moon ◽  
Outer Planets ◽  
Lunar Ephemeris ◽  
Empirical Corrections ◽  
Nautical Almanac ◽  
Astronomical Constants

At the present time the planetary ephemerides in the Astronomical Ephemeris and in the American Ephemeris and Nautical Almanac (both hereinafter referred to as the AE), the Astronomical Ephemeris of the U.S.S.R. and most other national almanacs have the following basis: For Mercury, Venus, Earth, and Mars the general theories of Simon Newcomb (1898a), the ephemeris of Mars including the empirical corrections determined by Ross (1917); for the five outer planets, the numerical integration of Eckert et al. (1951); the Connaissance de Temps publishes ephemerides of Mercury, Venus, Earth, and Mars based on the theories of Leverrier (1858, 1859, 1861a, b); for Jupiter, Saturn, Uranus, and Neptune the ephemerides are based on Leverrier’s (1876a, b, 1877a, b) expressions as modified by Gaillot (1904,1910, 1913). The ephemeris of Pluto is based on the numerical integration of Eckert et al. In all of the above publications the ephemeris of the Moon is now based on the Improved Lunar Ephemeris which is derived from the theory of Brown (1919). Newcomb’s theories and the numerical integration of the orbits of the five outer planets all rest primarily on the system of astronomical constants and planetary masses adopted at the Paris conferences of 1896 and 1911 {Monthly Notices Roy. Astron. Soc., 1912).

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 Role of Occultations in the Improvement of the Lunar Ephemeris

1972 ◽  
Vol 47 ◽  
pp. 395-401
Author(s):  
L. V. Morrison
Keyword(s):  
Time Scale ◽  
The Moon ◽  
Secular Acceleration ◽  
Lunar Ephemeris ◽  
Occultation Data ◽  
Correction Terms ◽  
Empirical Constants ◽  
Atomic Time

Analyses of occultation timings show that periodic correction terms with semi-amplitude as great as 0.″18 arise from corrections required to the empirical constants of the Brown/Eckert theory. Using the atomic time-scale, some of the occultation data have been used to determine a correction of – 30 ± 16″/cy2 to Spencer Jones' value for the secular acceleration of the Moon. In the light of this correction, and previous determinations, attention is drawn to the possible weakness of Spencer Jones' value, which is not reflected in his quoted error of ± 1″/cy2. Further analyses of 50000 occultations observed since 1943 promise to reveal more accurately-determined corrections.

An analytical theory of distributed axisymmetric barotropic vortices on the β-plane

1994 ◽  
Vol 269 ◽  
pp. 301-321 ◽  
Author(s):  
G. M. Reznik ◽  
W. K. Dewar
Keyword(s):  
Radiation Effects ◽  
Planetary Wave ◽  
Complete Solution ◽  
Asymptotic Series ◽  
Vortex Motion ◽  
Present Theory ◽  
Analytical Theory ◽  
Wave Radiation ◽  
Initial Value ◽  
Numerical Predictions

An analytical theory of barotropic β-plane vortices is presented in the form of an asymptotic series based on the inverse of vortex nonlinearity. In particular, a solution of the initial value problem is given, in which the vortex is idealized as a radially symmetric function of arbitrary structure. Motion of the vortex is initiated by its interaction with the so-called ‘β-gyres’ which, in turn, are generated by the vortex circulation. Comparisons of analytical and numerical predictions for vortex motion are presented and demonstrate the utility of the present theory for times comparable to the ‘wave’ timescale. The latter exceeds the temporal limit derived from formal considerations. The properties of the far-field planetary wave radiation are also computed.This theory differs from previous calculations by considering more general initial vortex profiles and by obtaining a more complete solution for the perturbation fields. Vortex trajectory predictions accrue error systematically by integrating vortex propagation rates which are too strong. This appears to be connected to higher-order planetary wave radiation effects.

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