Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue

The new Earth Orientation Catalogue was recently derived, based mostly on the ARIHIP and Tycho-2 Catalogues that were combined with ground-based optical observations of latitude and Universal Time variations in the 20th century. The solution of Earth orientation parameters, based on this new star ca...

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Опубліковано в: :	Кинематика и физика небесных тел
Дата:	2005
Автори:	Vondrak, J., Ron, C.
Формат:	Стаття
Мова:	English
Опубліковано:	Головна астрономічна обсерваторія НАН України 2005
Теми:	MS4: Positional Astronomy and Global Geodynamics
Онлайн доступ:	https://nasplib.isofts.kiev.ua/handle/123456789/79664
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Назва журналу:	Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:	Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue / J., Ron C. Vondrak // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 305-310. — Бібліогр.: 15 назв. — англ.

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Digital Library of Periodicals of National Academy of Sciences of Ukraine

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spelling	Vondrak, J. Ron, C. 2015-04-03T18:10:23Z 2015-04-03T18:10:23Z 2005 Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue / J., Ron C. Vondrak // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 305-310. — Бібліогр.: 15 назв. — англ. 0233-7665 https://nasplib.isofts.kiev.ua/handle/123456789/79664 The new Earth Orientation Catalogue was recently derived, based mostly on the ARIHIP and Tycho-2 Catalogues that were combined with ground-based optical observations of latitude and Universal Time variations in the 20th century. The solution of Earth orientation parameters, based on this new star catalogue and the new IAU model of precession-nutation, is presented. This study was supported by grant No. IAA3003205, awarded by the Grant Agency of the Academy of Sciences of the Czech Republic. en Головна астрономічна обсерваторія НАН України Кинематика и физика небесных тел MS4: Positional Astronomy and Global Geodynamics Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue Article published earlier
institution	Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection	DSpace DC
title	Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue
spellingShingle	Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue Vondrak, J. Ron, C. MS4: Positional Astronomy and Global Geodynamics
title_short	Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue
title_full	Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue
title_fullStr	Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue
title_full_unstemmed	Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue
title_sort	solution of earth orientation parameters in the frame of new earth orientation catalogue
author	Vondrak, J. Ron, C.
author_facet	Vondrak, J. Ron, C.
topic	MS4: Positional Astronomy and Global Geodynamics
topic_facet	MS4: Positional Astronomy and Global Geodynamics
publishDate	2005
language	English
container_title	Кинематика и физика небесных тел
publisher	Головна астрономічна обсерваторія НАН України
format	Article
description	The new Earth Orientation Catalogue was recently derived, based mostly on the ARIHIP and Tycho-2 Catalogues that were combined with ground-based optical observations of latitude and Universal Time variations in the 20th century. The solution of Earth orientation parameters, based on this new star catalogue and the new IAU model of precession-nutation, is presented.
issn	0233-7665
url	https://nasplib.isofts.kiev.ua/handle/123456789/79664
citation_txt	Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue / J., Ron C. Vondrak // Кинематика и физика небесных тел. — 2005. — Т. 21, № 5-додаток. — С. 305-310. — Бібліогр.: 15 назв. — англ.
work_keys_str_mv	AT vondrakj solutionofearthorientationparametersintheframeofnewearthorientationcatalogue AT ronc solutionofearthorientationparametersintheframeofnewearthorientationcatalogue
first_indexed	2025-11-24T05:51:33Z
last_indexed	2025-11-24T05:51:33Z
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fulltext	SOLUTION OF EARTH ORIENTATION PARAMETERS IN THE FRAME OF NEW EARTH ORIENTATION CATALOGUE J. Vondrák, C. Ron Astronomical Institute, Academy of Sciences of the Czech Republic Bočńı II, 141 31 Prague 4, Czech Republic e-mail: vondrak@ig.cas.cz The new Earth Orientation Catalogue was recently derived, based mostly on the ARIHIP and Tycho-2 Catalogues that were combined with ground-based optical observations of latitude and Universal Time variations in the 20th century. The solution of Earth orientation parameters, based on this new star catalogue and the new IAU model of precession-nutation, is presented. INTRODUCTION We produced, in the past years, several solutions of Earth Orientation Parameters (EOP) in the frame of the Hipparcos Catalogue [2] that were based on optical astrometry observations of latitude / Universal Time variations made at up to 33 observatories in the years 1899.7–1992.0. All of them were referred to the “old” IAU 1976 precession [5] and IAU 1980 nutation [14] models. Three solutions, that differed in number of instruments, slightly different criteria for correcting positions / proper motions, and also in methods of merging observations with different instruments into series, were made (where OA stands for Optical Astrometry): • OA97 [12] that was based on observations made with 45 different instruments located at 31 observatories. 4.32 million individual observations in 48 series were used, and applied corrections to 11% of positions and / or proper motions of the observed Hipparcos stars. • OA99 [13] that was based on observations made with 47 instruments at 33 observatories. 4.45 million observations in 39 series were used, and 20% of positions and/ or proper motions of the observed stars were corrected. • OA00 [7] that was based on observations made with 47 instruments at 33 observatories. 4.45 million observations in 41 series were used, and 20% of star positions and / or proper motions were corrected. The reason why these corrections (mostly for double and multiple star systems) had to be applied was threefold: Firstly, the real motions of the observed objects are not linear – the reference point that was observed (either a component or a photocenter) exhibits, in addition to the linear drift, also a small periodic motion. Secondly, the Hipparcos mission was shorter than four years, i.e., usually much shorter that the orbital periods. As a result, the linear proper motion derived from Hipparcos observations is rather a tangential motion near the epoch of the Hipparcos mission (1991.25) than the mean motion over a longer time span (decades) that is required for deriving Earth orientation parameters. So, even if the amplitude of the periodic part is negligible, the extrapolated star’s position can have big error. Thirdly, it was sometimes not quite clear which object was observed: a component of a double star or its photocenter? This reference point was often different from the object listed in the Hipparcos Catalogue, and sometimes even different for different types of instruments (visual, photographic, photoelectric). Usually, the human eye proved to be a better detector than photography or photoelectric device, capable of distinguishing much closer objects. After these solutions were finished, several new star catalogues appeared as combination of Hipparcos /Tycho positions with ground-based catalogues with a much longer observational history. The result is the catalogues with much more reliable proper motions. The most important ones are Tycho-2 [3] (the combination of the Tycho Catalogue with additional 144 ground-based astrometric catalogues), and ARIHIP [15] (selection of the best stars from other combined catalogues FK6, GC+HIP, Tycho-2+HIP and Hipparcos itself). We decided to make use of these catalogues, and to combine them further with the rich observational material collected in Earth rotation programmes during the whole 20th century (latitude / Universal Time variations). The goal c© J. Vondrák, C. Ron, 2004 305 is to get a better and more stable celestial reference frame for long-period Earth rotation studies [10]. Thus, the idea of constructing the Earth Orientation Catalogue (EOC), containing all stars observed in Earth rotation programmes, appeared. A more detailed description of the combined catalogues, including EOC, can be found in [9]. Here follows an abbreviated outline of deriving the EOC. CONSTRUCTION OF THE NEW EOC CATALOGUE The idea is to use the observed data made by optical astrometry in Earth rotation programmes (instantaneous latitude /Universal Time / altitude difference) to improve the catalogue positions and proper motions. We have collected the data with 47 instruments located at 33 observatories, covering the interval 1899.7–2003.0. They can be divided into three groups according to the observables that they provide: 1. 10 Photographic Zenith Tubes that measured simultaneously latitude and Universal Time (3 at Washing- ton, DC; 2 at Richmond, Florida and Mizusawa, Japan; 1 at Mount Stromlo, Australia; Punta Indio, Argentina; Ondřejov, Czech Republic). 2. 7 Photoelectric Transit Instruments that measured only Universal Time (3 at Pulkovo and 1 at Irkutsk, Russia; Kharkiv and Mykolaiv, Ukraine; Wuhang, China). 3. 16 Visual Zenith-Telescopes and similar instruments that measured only latitude (7 Visual Zenith-Teles- copes at International Latitude Service stations – Carloforte, Italy; Cincinnati, Ohio; Gaithersburg, Vir- ginia; Kitab, Uzbekistan; Mizusawa, Japan; Tschardjui, Turkmenistan; Ukiah, California; 2 at Poltava, Ukraine; 1 at Belgrade, Serbia; Blagoveshchensk, Irkutsk, and Pulkovo, Russia; Józefoslaw, Poland; Float- ing Zenith Telescope at Mizusawa, Japan; Visual Zenith Tube at Tuorla-Turku, Finland). 4. 14 instruments for equal altitude method that measured the differences of stars’ altitude, i.e., the combina- tion of latitude and Universal Time (Danjon astrolabes at Paris, France; Santiago de Chile; Shanghai and Wuhang, China; Simeiz, Ukraine; 2 photoelectric astrolabes at Shaanxi, China; photoelectric astrolabes at Beijing, Shanghai, Yunnan, China, and Grasse, France; circumzenithals at Bratislava, Slovakia; Prague and Ondřejov, Czech Republic). The inspection of all observations made with these instruments showed that there were 4418 different objects observed (stars, double star components, photocenters). They were identified in different recent catalogues, and their positions, proper motions, parallaxes, and radial velocities taken over from them. Not all of them were found in the best one, ARIHIP, – we also had to use less precise Tycho-2, and the rest were found in the Hipparcos and PPM Catalogues [1, 8]. ARIHIP uses three types of solution, with slightly different positions / proper motions: single-star mode, short-term prediction mode and long-term prediction mode. To construct EOC, we used a “classical” single-star mode. The statistics is as follows: 2995 objects were taken over from ARIHIP, 1248 from Tycho-2, 144 from Hipparcos, and 28 from PPM; 3 objects were found in none of the above catalogues, and therefore, their initial entries were taken over from the catalogues used at the respective observatories. These entries formed the zero version of the catalogue, so-called EOC-0. The authors of ARIHIP introduced a classification of “astrometrical excellency” of each star – the number of asterisks (the larger is the number, the more reliable the position / proper motion). The stars with no asterisk are most probably double or multiple systems. There are 56% of such “non-excellent” stars in EOC-0 (including those originating from other catalogues than ARIHIP), so further improvement is still necessary and possible. Taking into account the number of observations and number of different objects observed, each of them was observed about a thousand times during long time interval, with precision of one observation of about 0.2′′. It means that proper motions can be determined with precision competing with recent catalogues, and the combination with EOC-0 should bring a significant improvement. The positions and proper motions were first improved by means of combining EOC-0 with the observations made in local meridian (i.e., with only the first three groups of instruments shown above). This version, containing only 3784 objects, was denominated EOC-1 and described in detail in [11]. In further improvement of the catalogue we used all available observations (i.e., made with all four groups of instruments mentioned above) to determine relative positions of all stars with respect to those denoted as astrometrically excellent. The strategy, assuming that the latitude /Universal Time is constant only during a night, was chosen. Consequently, the method used was practically insensitive to any change of the terrestrial coordinates of the instruments during the time. We proceeded by following these steps: 1. The instantaneous observables (i.e., latitude /Universal Time / altitude difference) were transformed from original observations, using the entries from EOC-0 and the new model of precession-nutation IAU2000A [6]. 306 2. The deviations of these observables from the mean value of the night (calculated for astrometrically excellent stars only) were computed, and linear regression for these differences for the same star in different epochs was made. 3. Stars with statistically significant deviations were checked for multiplicity, using the information contained in the Hipparcos Catalogue. In positive case, the displacement of reference point from EOC-0 was esti- mated, and the respective position in EOC-0 was corrected. In this case, the procedure above (item 2) was repeated. 4. Combination of these deviations with EOC-0 was made. To this end, each entry of the star of the EOC-0 catalogue was represented by three virtual observations (of both right ascension and declination) in three epochs covering one century: t1 = t◦−90, t2 = t◦, t3 = t◦+10, where t◦ is the mean epoch of the catalogue. The values of these “observations” were implicitly set to zero. Their uncertainties were then calculated from catalogue standard errors of the position σ◦ and proper motion σμ as σ2 1 = 9000σ2 μ, σ2 2 = σ2 ◦/ [ 1 − (σ◦/σμ)2/900 ] , σ2 3 = 1000σ2 μ (1) that would reproduce exactly the catalogue entry if subject to linear regression. These values were then used to calculate the weights pi = (200/σi)2, if σi are given in milliarcseconds; all real observations (deviations calculated above) were assigned the weights 1. Then the weighted linear regression through all real and virtual observations was made to yield the combined position / proper motion. To this end, we used the following observation equations for the three types of observations (latitude ϕ, Universal Time UT, altitude h), respectively: vϕ = Δδ + Δμδ(t− t◦) − δϕ, vUT = Δα∗ + Δμ∗ α(t− t◦) − 15.041δUTcosϕ, (2) vh = Δα∗ sin q + Δμ∗ α(t− t◦) sin q + Δδ cos q + Δμδ(t− t◦) cos q − δh. Here Δα∗, Δμ∗ α stand for Δα cos δ, Δμα cos δ, and q is the parallactic angle of the star. First two of Eqs. (2) are used for virtual observations of declination and right ascension with their weights, respectively, and they are mixed with any of the three equations for real observations, according to their type. An illustrative example of combining declination is shown in Fig. 1; the observations at all ILS stations and the Floating Zenith Telescope at Mizusawa (MZL) are combined with Tycho-2 entry for star No. 36366, represented by three virtual observations whose weights are also depicted in the figure. year - 1900 )* 0 10 20 30 40 50 60 70 80 90 100 -2.5 -1.5 -0.5 0.5 1.5 2.5 ILS MZL 12 2377 111 Figure 1. Tycho-2 star No. 36366: observations at all ILS stations and Mizusawa FZT (MZL, crosses), virtual observa- tions (open circles with weights) and combined position (full line) The combination leads to the catalogue version EOC-2; the comparison of its standard errors (median values) with the Hipparcos is given in Table 1. A substantial improvement, especially of proper motions, is obvious. 307 Table 1. Comparison of accuracy of EOC-2 with Hipparcos Catalogue No. Epα − 1900 σ∗ α σ∗ μα Epδ − 1900 σδ σμδ [mas] [mas/yr] [mas] [mas/yr] Hipparcos 117995 91.25 0.87 0.72 91.25 1.02 0.85 EOC-2 4418 91.16 0.70 0.47 91.03 0.60 0.35 NEW SOLUTION OF EOP IN THE FRAME OF EOC-2 The new solution of EOP consists in using virtually the same data as were used to improve the catalogue, but we did not go beyond 1992.0, when the number of active observatories and number of observations decreased substantially. The series of observations with 47 instruments were merged in cases when the instruments of similar type worked at the same observatory. The steps between them were estimated and removed beforehand. Namely, we merged the observations with the following instruments into a single series: the visual zenith- telescope and FZT at Mizusawa, Japan; two PZT’s at Mizusawa, Japan; two zenith-telescopes at Poltava, Ukraine; three photoelectric transit instruments at Pulkovo, Russia; two PZT’s at Richmond, Florida; two PZT’s at Washington, DC. On the other hand, the visual zenith-telescope at Pulkovo, Russia was treated as two different series, due to a long gap in the observations (and change of the instrument’s position) during the second world war. The same holds for circumzenithal in Prague, Czech Republic, that was moved to a distant location, and was treated as two different series. Thus, the total number of series used was 42. We followed more or less the same procedures as in our preceding solutions, with two exceptions: 1. New IAU2000A model of precession-nutation was used, which led to much smaller values of celestial pole offsets, and consequently 2. celestial pole offsets were represented by a constant plus linear trend for both coordinates, not by five- day individual points as before, in order to decrease the number of estimated parameters, and to make the solution more robust. The results of the solution, so-called OA04, are depicted in Figures 2 (polar motion) and 3 (Universal Time, only after 1956.0) for each five-day interval, where their mean errors σ are also shown. The latter are given in x F 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0 0.1 0.2 0.3 0.4 0.5 0.6 y F 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 Figure 2. Polar motion of the solution OA04 (in arcseconds) 308 F 1955 1960 1965 1970 1975 1980 1985 1990 -0.200 -0.150 -0.100 -0.050 0 0.050 0.100 0.150 0.200 0 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 F igure 3. R ed u ced U n iv ersa l T im e va ria tio n s o f th e so lu tio n O A 0 4 (in seco n d s o f tim e) enlarged scales – tw o tim es larger than the results for polar m otion,25-tim es larger for U niversalT im e. Instead of U T 1–T A I, the reduced values U T 1–T A X (w ith long-periodic part rem oved, in order to show the variations in m ore detail) are depicted. T he relation betw een T A I and T A X is given (in seconds of tim e) by the form ula T A X = T A I+ 2 .63− 0 .002047 t− 0 .236× 10 − 7t 2 + 0 .49× 10 − 1 2t 3− 0 .17 cos(2 π t/6000) + 0 .26 sin (2 π t/6000)− 1 .32 cos(2 π t/9000)+ 0 .16 sin (2 π t/9000), (3) w here t = M JD − 35300. T he form ula w as selected so that the difference U T 1–T A X never exceeds 0.2 s in the interval1956.0–1992.0. T he resulting celestialpole offsets (in m illiarcseconds) are given as Δ ψ sin ε = − 5 .7± 0 .3 2 + 28 .5± 1 .0 8 T , Δ ε = − 5 .5± 0 .3 2 + 6 .7± 1 .0 7 T , (4) w here T is given in centuries since 1956.0. T hese values represent a sum of a bias betw een IC R S and the new E O C catalogue w ith the correction of the new IA U precession. T hey are very sm all, and are quite com parable w ith the form aluncertainties of the link betw een the H ipparcos (to w hich E O C is linked) and IC R S (± 0 .6 m as at the epoch 1991.25 and ± 25 m as/cyr in rotation,according to [4]). C O N C L U S IO N S T he new star E O C catalogue (given in the IC R S) w as constructed,using about 4.5 m illion individualobserva- tions oflatitude / U niversalT im e / altitude difference,in com bination w ith recentcataloguessuch as the A R IH IP or T ycho-2. V ersion E O C -2 of the catalogue, in w hich m any double stars w ere detected and their posi- tions/ proper m otions referred to their reference points (either double star com ponents or photocenters) is m ore accurate and stable in long-periodic sense than the original catalogues based on the H ipparcos m ission (H ipparcos, T ycho, A R IH IP , ... ). T he catalogue is used in the new solution of E arth orientation param eters from optical astrom etry in the interval 1899.7–1992.0. T he present solution, O A 04, has a better precision of five-day values than our preceding solutions based on the H ipparcos, w hich is dem onstrated by the statistics show n in T able 2. T able 2. C o m p a riso n o f so m e ch a ra cteristics o f th e so lu tio n O A 0 4 w ith O A 0 0 S o lu tio n n o b s n p a r a m σ◦ σ x σ y σ U T 1 [ ′′] [m a s] [m a s] [m s] O A 0 0 4 4 4 7 4 0 0 2 9 8 0 9 0 .1 8 8 2 0 .5 1 8 .3 0 .8 7 O A 0 4 4 5 3 8 6 9 4 1 6 4 4 3 0 .1 9 0 1 7 .4 1 5 .7 0 .7 2 T hanks to the better star catalogue,m ore observations (n o bs ) could be used in the solution O A 04 than before, because less observations w ere rejected due to large residuals. T he num ber of estim ated param eters (n p a r a m ) 309 decreased, because a better precession-nutation model was used, and it became unnecessary to estimate five- day values of celestial pole offsets. Thus, the solution is made more robust. Although the mean error of one observation (σ◦) slightly increased, the median mean errors of the unknowns representing five-day values of pole position and Universal Time (σx, σy, σUT1) decreased substantially, by almost 20%. Acknowledgements. This study was supported by grant No. IAA3003205, awarded by the Grant Agency of the Academy of Sciences of the Czech Republic. [1] Bastian U., Röser S. Positions and proper motions – South.–Astron. Rechen-Inst. Heidelberg, 1993. [2] ESA The Hipparcos and Tycho Catalogues.–ESA SP-1200, 1997. [3] Høg E., Fabricius C., Makarov V. V., et al. The Tycho-2 catalogue of the 2.5 million brightest stars // Astron. and Astrophys.–2000.–355.–P. L27–L30. [4] Kovalevsky J., Lindegren L., Perryman M. A. C., et al. The Hipparcos Catalogue as a realization of the extragalactic reference system // Astron. and Astrophys.–1997.–323–P. 620–633. [5] Lieske J. H., Lederle T., Fricke W., Morando B. Expressions for the precession quantities based upon the IAU (1976) system of astronomical constants // Astron. and Astrophys.–1977.–58–P. 1–16. [6] Mathews P. M., Herring T. A., Buffet B. A. Modeling of nutation and precession: New nutation series for nonrigid Earth and insights into the Earth’s interior // J. Geophys. Res.–2002.–107, N B4.–P. ETG 3-1–3-26. [7] Ron C., Vondrák J. On the celestial pole offsets from optical astrometry in 1899–1992 // Journées 2000 Systèmes de référence spatio-temporels / Ed. N. Capitaine.–Obs. de Paris, 2001.–P. 201–202. [8] Röser S., Bastian U. Positions and proper motions – North // Astron. Rechen-Inst. Heidelberg.–1991. [9] Vondrák J. Astrometric star catalogues as combination of Hipparcos/Tycho catalogues with ground-based obser- vations // Serb. Astron. J.–2004.–N 168.–P. 1–8. [10] Vondrák J., Ron C. An improved reference frame for long-term Earth rotation studies // Journées 2002 Systèmes de référence spatio-temporels / Eds N. Capitaine, M. Stavinschi.–Obs. de Paris, 2003.–P. 49–55. [11] Vondrák J., Ron C. Earth Orientation Catalogue – An improved reference frame // The ICRS maintenance and future realizations: Proc. IAU XXV Joint Discussion 16 / Eds R. Gaume, D. McCarthy, J. Souchay.–USNO Washington, 2004. [12] Vondrák J., Pešek I., Ron C., Čepek A. Earth orientation parameters 1899.7–1992.0 in the ICRS based on the Hip- parcos reference frame // Publ. Astron. Inst. Acad. Sci. Czech Rep.–1998.–87.–P. 1–56. [13] Vondrák J., Ron C., Pešek I. Survey of observational techniques and Hipparcos re-analysis // Polar motion: His- torical and scientific problems / Eds S. Dick, D. D. McCarthy, B. Luzum.–ASP Conf. Ser.–2000.–208.–P. 206–213. [14] Wahr J. M. The forced nutations of an elliptical, rotating, elastic and oceanless Earth // Geophys. J. Roy. Astron. Soc.–1981.–64.–P. 705–727. [15] Wielen R., Schwan H., Dettbarn C., et al. Astrometric Catalogue ARIHIP containing stellar data selected from the combination catalogues FK6, GC+HIP, TYC2+HIP and from the Hipparcos Catalogue // Veröff. Astron. Rechen-Inst. Heidelberg.–2001.–N 40.–P. 1–36. 310

Solution of Earth orientation parameters in the frame of new Earth orientation Catalogue

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