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IAA Transactions, No. 8, ``Celestial Mechanics'', 2002
Determination of UT0 from lunar laser ranging data
analysis
E. Yu. Aleshkina
Institute of Applied Astronomy, St. Petersburg, Russia
1. Introduction
Modern high­precision observations (VLBI, SLR, GPS and LLR) are used
for determination of parameters of the Earth's rotation, corrections to stations'
location and coordinates of extragalactic radio sources.
Analysis of LLR data permits to improve and to estimate a large set of seleno­
and geodynamical parameters. Essentially all modern selenodynamical researches
are based on LLR observations. These observations have been performed for more
than 30 years. Among the results stemming from the global fitting of LLR data
it should be noted the following ones: estimation of lunar dynamical flattening,
improvement of the selenocentric coordinate frame, detection of free libration
effect, construction of the numerical ephemerides of the Moon with high accuracy.
On the other hand, LLR analysis gives the useful geodynamical information about
the Earth's rotation parameters and permits to control estimations obtained from
VLBI.
2. Determination of UTO -- UTC and VOL
Using the modern lunar ephemerides the Moon's motion can be computed
with high accuracy and over short time--intervals a lunar reflector can be regarded
as a fiducial point. In this case the change in range can be assigned to the rotation
of the Earth. Our method of analysis consists of two steps. First, we use numerical
lunar ephemeris to estimate corrections to the set of global parameters [1].
After the global fitting of the whole set of LLR observations 1970--2000 the
post­fit residuals for 1995--2000 have been analyzed to determine diurnal correc­
tions to UT0 and the variations of latitude VOL caused by the polar motion.
The Earth orientation parameters UT1 and polar motion (x pol ; y pol
) are relat­
ed with the values of UT0 and VOL obtained from the LLR analysis for a station
with geocentric longitude and latitude (–; OE) by the following expression:
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UT0 \Gamma UTC = UT1 \Gamma UTC + (x pol sin – + y pol cos –) tan OE
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V OL = x pol cos – \Gamma y pol sin –
At least four normal points for each station--reflector pair at one day were
accepted for the diurnal UT0 estimations. Calculations were made with two lunar
ephemerides EM--2 [1] and LE403 [4]. All reductions were taken into account
according to the IERS Conventions 1996 [3] using the plate motion of ITRF96 [2]
for corrections to the station coordinates.
We obtained in total 492 UT0--UTC values from 4860 normal points for 1995--
2000, 328 from CERGA and 164 from McDonald. The estimations were derived
from post--fit residuals (O--C) by two ways:
1. Calculation of (O--C) was carried out using UT1--UTC, (x pol ; y pol
) being
provided by IERS EOP C04. From analysis of (O--C) we obtained corrections
\Delta(U T0 \Gamma UTC); \DeltaV OL to the corresponding IERS values.
2. Differences (UT1--UTC) were set equal to zero and not corrections but the
values of (UT0--UTC) themselves and VOL were determined.
References
1. Aleshkina E. Yu., Krasinsky G. A., Vasilyev M. V. Construction of the nu­
merical theory of rotation and orbital motion of the Moon taking into account
the tidal effects from LLR observation, in Abstract book of the Conference
``Astrometry, Geodynamics and Celestial Mechanics at the turn of XXIth
century'', 19--23 June, St. Petersburg, 2000, 235 (in Russian).
2. Boucher C., Altamimi Z., Sillard P. Results and analysis of the ITRF96,
IERS Technical Note 24, Observatoire de Paris, 1998.
3. McCarthy D. D. (ed.) IERS Conventions (1996), IERS Technical Note 21,
Observatoire de Paris, 1996.
4. Standish E. M., Newhall, XX, Williams J. G., Folkner W. M. JPL planetary
and lunar ephemerides, DE403/LE403, IOM 314, Publication Jet Propulsion
Laboratory, Pasadena, 1995, 10--127.
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