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From old weights and measures to the SI as a numerical standard for the world
Débarbat S., Passeron I. Institution of the first author: Observatoire de Paris/SYRTE/CNRS France After some unsuccessful attempts by Charlemagne, Picard was, most probably, the first in France to submit a proposal for a new system based on a unit relying length to time through the second-pendulum. Despite other proposals, during the 18th century, one century after PIcard came the Système métrique décimal, which fundamental standard was the Mètre. After almost one more century, by 1960, the SI was decided at the international level and, by 1983, a new realization of the meter was decided, relying length and time ! |
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Spin wave function associated to the young Universe, according to one polynomial solution for the Wheeler-DeWitt Equation
Echaurren J. Institution: Codelco Chile Chile Spin Wave Function Associated to the Young Universe, According to one Polynomial Solution for the Wheeler-DeWitt Equation. |
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An effect in satellite motion non-modeled by the current numerical standards
Kudryavtsev S. Institution: Sternberg Astronomical Institute of Moscow State University Russia Here we derive a theoretical effect in satellite motion, in particular non-modeled by the current IERS Conventions (McCarthy & Petit 2004). Numerical tests prove that, e.g., for LAGEOS and ETALON this effect may lead to periodic perturbations in the satellites coordinates of up to 10-20 cm (to be detectable by modern laser measurements). The respective excitations of the satellites eccentricity vector may reach the amplitude of a few tens of mas/year. This value is comparable to anomalous excitations observable in the satellites eccentricity vector (see, e.g., Tapley et al. 1993; Appleby 1998), that are still not completely explained. Research supported in part by the Russian Foundation for Basic Research under grant no.10-02-00234-a. References: Appleby, G.M. (1998): J. Geodesy, 72, 333-342. McCarthy, D.D., Petit,G. (2004): IERS Conventions (2003), IERS Tech. Note 32. Tapley, B.D. et. al. (1993): In: Contributions of Space Geodesy to Geodynamics: Earth Dynamics, AGU, 24, 147-173. |
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Motion of comet Tempel 1 before and after the collision with the impactor of Deep Impact space mission
Bondarenko Y. Institution: Institute of Applied Astronomy of Russian Academy of Sciences Russia The dynamics of comet Tempel 1 before and after its collision with the Deep Impact space mission impactor have been studied. The numerical theory of motion of the comet Tempel 1 is obtained using three different sets of parameters. The first solution assumed that on the considered interval non-gravitational parameters were unchanged. The second solution assumed that the collision with the impactor could lead to change in the non-gravitational acceleration. The instantaneous change of comet velocity due to collision with the impactor was assumed in the third solution. The perturbation in motion of the comet Tempel 1 due to collision with the impactor is estimated using the results of the Space mission Deep Impact. |
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Web Interface for Lunar Laser Ranging observations
Bouquillon S., Barache C., Carlucci T., Deleflie F., Feraudy D., Francou G., Manche H., Samain E., Torre J-M. Institution of the first author: Observatoire de Paris / SYRTE/CNRS France We report the current development of a web Interface for preparing and validating LLR observations. With this service, distant LLR Observers will be able to easily run some Paris Observatory tools dedicated to Lunar motion. It will allow them to compute predictions of Moon retro-reflectors topocentric coordinates and predictions of round-trip times of the laser-pulses. It will also allow them to compare their own LLR Data with Paris Observatory Lunar Ephemeris, in terms of rms, and with a real-time access. |
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A dynamical study of Phoebe's rotation
Cottereau L. Institution: Observatoire de Paris/SYRTE/CNRS France With a fast non synchronous rotation, Phoebe is a particular satellite in the Saturnian system(most of the satellites are subject a synchronous rotation)and must show a very different rotational evolution. We propose for the first time to determine the combined motion of the precession and nutation of Phoebe considered as a rigid body by numerical and analytical integration. We further compare our results with those obtain by Kinoshita for the Earth (1977), emphasizing their astonishing similarities (obliquity, value of the precession, nutation amplitudes and arguments).Moreover we show that a pure analytical accurate model of the nutation is not easy to construct due to the fact that the orbital motion of Phoebe is far from being keplerian. At last we present the prospect for future studies among which are the effect of the Sun , Titan and the dynamical ellipticity of Saturn on the precession-nutation motion. |
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New analytical planetary theories VSOP2010
Francou G., Simon J.L. Institution of the first author: Observatoire de Paris/SYRTE/CNRS France The planetary theories VSOP are essentially issued from Bretagnon’s research works. The precision of the last version, VSOP2000 (Bretagnon & Moisson) fitted to DE403, was 10 times better than the previous solutions VSOP82 and VSOP87, both fitted to DE200. Subsequently, Bretagnon began to make some improvements : better accuracy for the computation of series, simultaneous determination of the 8 major planets and the 5 big asteroids orbits, lunar perturbations taken into account for the motions of the major planets. We took up again this work introducing various changes and complements : fits to the numerical integrations DE405 (JPL) and INPOP08A (IMCCE) for VSOP2010A and VSOP2010B respectively, introduction of the perturbations coming from 298 asteroids, contribution of TOP theory (Simon), i.e., analytical theory of Pluto, perturbations due to Pluto, better accuracy for the orbits of Jupiter and Saturn. Over the time interval [1890,2000], the discrepancies between theories and numerical integrations are : < 0,04 mas for Mercury, Venus and Earth-Moon barycentre, <0,07 mas for Jupiter, <0,3 mas for Saturn and Neptune, <1,5 mas for Mars and Uranus. The precision is 3 to 10 times better than that of VSOP2000. Over the time interval [-4000,8000], the precision is a few 0.1” for Mercury, Venus and Earth-Moon barycentre and a few arc seconds for the other planets. Here, the gain in precision is 5 times better for the telluric planets and 10 to 50 times better for the major planets in comparison with VSOP2000. |
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Summary and Status of the Horizons Ephemeris System
Giorgini J. Institution: Jet Propulsion Laboratory/California Institute of Technology USA Since 1996, the Horizons system has provided searchable access to JPL ephemerides for all known solar system bodies, several dozen spacecraft, planetary system barycenters, and some libration points. Responding to 18,400,000 requests from 300,000 unique addresses, the system has recently averaged 420,000 ephemeris requests per month. Horizons is accessed and automated using three interfaces: interactive telnet, web-browser form, and e-mail command-file. Asteroid and comet ephemerides are numerically integrated from JPL's database of initial conditions. This small-body database is updated hourly by a separate process as new measurements and discoveries are reported by the Minor Planet Center and automatically incorporated into new JPL orbit solutions. Ephemerides for other objects are derived by interpolating previously developed solutions whose trajectories have been represented in a file. For asteroids and comets, such files may be dynamically created and transferred to users, effectively recording integrator output. These small-body SPK files may then be interpolated by user software to reproduce the trajectory without duplicating the numerically integrated n-body dynamical model or PPN equations of motion. Other Horizons output is numerical and in the form of plain-text observer, vector, osculating element, or close-approach tables, typically expected be read by other software as input. About one hundred quantities can be requested in various time-scales and coordinate systems. For JPL small-body solutions, this includes statistical uncertainties derived from measurement covariance and state transition matrices. With the exception of some natural satellites, Horizons is consistent with DE405/DE406, the IAU 1976 constants, ITRF93, and IAU2009 rotational models. |
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Propagation in time of errors for the mutual inclination of satellites
Marco F., Martínez M. J., López J. A. Institution of the first author: Universitat Jaume I Spain The theoretical and the observed values of the mutual inclination between natural satellites may be different due to physical or geometrical causes (or due to both of them). It is clear, for example, that a geometrical variation between the reference systems, for example the application of a infinitesimal rotation around an axis, implies a modification in the elements that determine the orbits. In addition, a bad determination of the mass of the body may imply false values in the integration of the elements. These errors in the initial elements propagate in time, so it may be useful to provide methods to analyse them and also to be able to discriminate the true source of the error, if possible. |
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Usage of asteroids to determine relations between ICRF and dynamical system
Medvedev Y. Institution: Institute of Applied Astronomy of Russian Academy of Sciences Russia Relation of dynamical coordinate system with ICRF is determined through VLBI observations of spacecraft orbiting around the major planets. Variability of gravitational fields of major planets because of tides makes construction of the theory of motion of spacecraft complicated. Possibility of usage of asteroids for determination of linkage between dynamical (and optical or stellar) coordinate system and ICRF is considered. With this aim in view we suggest to create on the orbits around specially selected asteroids several radio transmitters that makes it possible to fulfill VLBI observations. Small size of asteroids allows one to connect corresponding systems with significantly higher accuracy than it can be done with use of major planets. It is especially true with respect to optical observations. The problem of determining links between reference frames can be combined with solving tasks of counteraction against the asteroid-comet hazards for the Earth. The last problem is actively discussed during recent time, particularly in connection with very close approach of asteroid (99942) Apophis with the Earth. It would be desirable to combine solutions of mentioned problems, as an underling demand is the same: determination of precision of asteroid orbit with high accuracy. Errors of elements of Apophis orbit and those of a number of other asteroids have been estimated if their observations are made against quasar backgrounds. It has been also estimated what precision of linkage dynamical reference system and ICRF can be attained depending on interval and number of observations. |
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The ephemerides of Martian satellites Phobos and Deimos created by ERA system
Zamarashkina M. Institution: Institute of Applied Astronomy Russia The numerical theory of the motion of Martian satellites is constructed. The dynamical model of the satellite motion was realized in the framework of the universal programming system ERA (Ephemeris Research in Astronomy [1]) developed in IAA RAS. The initial coordinates of Phobos and Deimos were obtained by processing their astrometrical observations on the time interval 1877-2003. Comparison of the satellite ephemerides with analogous data obtained by other software ephemeris packages (ephemeris JPL [2], SSAI/IMCCE [3], IAM RAS [4]) is presented. It is shown that the divergence of all satellites’ trajectories on the time span 100 years has the same order. References: 1.Krasinsky G.A., Vasiliev M.V. ERA: knowledge base for ephemeris and dynamical astronomy // Proc. of IAU Coll.165.1996. P.239–244. 2.Jacobson, R.A. Ephemerides of the Martian Satellites - MAR080 // JPL IOM 343R-08-006, 2008. 3.Kudryavtsev S.M., Kolyuka Y.F., Tikhonov V.F. New Analytical Theory of Motion of Phobos and Deimos for Navigation Support of Mission to Mars // ESA SP-403: Proc. of the 12th International Symp.on Space Flight Dynamics. 1997. P. 377-382. 4. Shishov V.A. Determination of spacecraft and Phobos parameters of motion in the Phobos-Grunt project // Solar System Research. 2008. V. 42. P. 319-328. |
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Gaia Initial Quasar Catalogue – updates: morphology and variability
Andrei A. Institution: Observatorio Nacional/MCT Brasil The present version of the GAIA Initial QSO catalogue (GIQC_III) contains 174,744 sources, divided in 3 categories: defining (full reliability, 123,880 sources), candidate (lacking full confirmation of redshidft or magnitude or pointlikeness, 24,229 sources), and other (pending confirmation of two or more characteristis, 26,235 sources). The GIQC_III now includes morphological indexes, as derived from the study of the target's PSF from DSS R, B, and I plates, in comparison with at least 6 well imaged neighboor stars. A study was also made on the frelationship between optical flux long term variability and the centroid's random walk. For that, classes of objects most prone to exhibit such relationship are discussed. |
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The maoC08a combined catalogue of radio source positions created in the course of preparation for the ICRF2
Yatskiv Ya., Bolotin S., Lytvyn S. Institution of the first author: Main Astronomical Observatory NAS of Ukraine Ukraine Starting with 1991 the 12 combined radio source catalogues (RSC) were created at the Main Astronomical Observatory of the NAS of Ukraine (GAO UA acronym was used by the IERS) by using the so-called Kiev arc length method. In the course preparation for realization of the ICRF2 we created the new combined catalogue (designated as maoC08a) on the basis of data provided by the IVS WG. In this paper, the method for combining the individual RSC as well as the results of comparison of the maoC08a catalogue with other catalogues are briefly discussed. |
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On correlation between variations in Earth rotation and frequency of earthquakes
Aleshkina E. Institution: Pulkovo observatory of RAS Russia Global geophysical phenomena such as powerful earthquakes make a significant contribution to the Earth rotation fluctuations. Catalogue CPE of powerful earthquakes with magnitudes greater then 7.5 for 450-years period are presented. The system of time-correction (TD-UT) characterized irregularities in Earth rotation for the time span 1700-1950 was obtained from analysis of the transits of Mercury and Venus and lunar observations. Changes in LOD for 250 years period were determined. Comparison of the frequency of earthquakes and secular and long-periodic changes in Earth rotation was carried out. |
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The source of the variable Chandler wobble
Bizouard C., Lambert S., Remus F., Seoane L., Gambis D. Institution of the first author: Observatoire de Paris/SYRTE/CNRS France We explain the variability of the Chandler wobble (CW) amplitude and phase along 1949--2009 by variations in atmospheric and oceanic excitations, as estimated from the NCEP/NCAR reanalysis project and the ECCO model, respectively. Unlike most of the studies related to this topic, the geophysical effects on polar motion are computed by a time integration of the Euler-Liouville equations. We show that the CW amplitude decreases between 1949 (250 mas) and 1970 (120 mas). Then, it slowly increases until the mid 1990's (200 mas) and finally decreases during the first decade of the 21st century (100 mas). The phase remains stable within $40^{circ}$. For the total atmospheric and oceanic contribution, the correlation between the observed and modeled amplitudes of the Chandler mode and the explained variance reach~80\% and 60\%, respectively. Though atmosphere and oceanic variations exhibit concomitant irregularities, the oceans are still dominant around 1990. |
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Motion of comet Tempel 1 before and after the collision with the impactor of Deep Impact space mission
Bondarenko Y., Kiselev, M., Filippova, A. Institution of the first author: nstitute of Applied Astronomy of Russian Academy of Sciences Russia The dynamics of comet Tempel 1 before and after its collision with the Deep Impact space mission impactor have been studied. The numerical theory of motion of the comet Tempel 1 is obtained using three different sets of parameters. The first solution assumed that on the considered interval non-gravitational parameters were unchanged. The second solution assumed that the collision with the impactor could lead to change in the non-gravitational acceleration. The instantaneous change of comet velocity due to collision with the impactor was assumed in the third solution. The perturbation in motion of the comet Tempel 1 due to collision with the impactor is estimated using the results of the Space mission Deep Impact. |
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Earth rotation based on the coordinates of the CIP in the GCRS: solution for a rigid Earth
Capitaine N., Folgueira, M. Institution of the first author: Observatoire de Paris/SYRTE/CNRS France We report on the continuation of the work devoted to the integration of the Earth's rotational motion in terms of the coordinates, X, Y of the celestial intermediate pole (CIP) in the Geocentric celestial reference system (GCRS) for an axially symmetric rigid Earth (Capitaine et al. 2006). Here, we discuss the method of integration in comparison with other methods used for the rigid Earth. We also analyse the semi-analytical solution for X and Y derived from the integration of these equations based on the external torque as computed from the theories ELP2000 for the Moon and VSOP87 for the Sun and planets. We compare different components of the obtained solution for the motion of the CIP in the GCRS with other solutions derived indirectly from the original SMART97 solutions for the Euler angles or the REN2000 solution for the classical precession and nutation variables. |
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Variations of the Earth main moments of inertia due to glacial cycles for the last 800Ka
Chapanov Y., Gambis D. Institution of the first author: Central Laboratory for Geodesy - BAS Bulgaria The Earth shape, gravity and rotation are highly affected by climatic variations associated with the glacial cycles in the late Pleistocene. The processes of glaciation, followed by ice melting, are connected with significant changes of the mean sea level. These processes redistribute great amount of water masses between oceans and ice sheets, which lead to changes of the main moments of inertia. The mean sea level data for the last 800Ka are composed by the reconstructed glacial sea level for the last 380Ka, determined by the sediments from the Red sea and sea level variations for the period 380Ka-800Ka before present, based on the temperature changes, determined by deuterium data from Antarctica ice core. The model of main moments of inertia variations is based on mean sea level changes and spatial and temporal variations of the continental ice sheets. The time series of the Earth main moments of inertia variations for the last 800Ka with step 500a are determined. |
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Combination of GPS and GLONASS in Precise Point Positioning algorithms and its effect on site coordinates determination
Hefty J., Lubomira Gerhatova, Juraj Burgan Institution of the first author: Slovak University of Technology Slovakia The Precise Point Positioning (PPP) adjustment using the un-differenced code and phase GPS observations, precise orbits and precise satellite clocks is recently an important alternative to the double differenced approach usually applied for geocentric coordinate determination. We introduce models for separate GPS and GLONASS PPP processing as well as for the combined solution. The procedures are examined by the software package ABSOLUTE developed at the Slovak University of Technology in Bratislava. Obtained site coordinates time series based on GPS and GLOANSSS observations processed at zero difference level are compared with GPS-only series resulting from application of other PPP packages. |
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The peculiarities in the change of the Earth's pole coordinates
Korsun A., Kurbasova G. Institution of the first author: Main Astronomical Observatory of Ukrainian Academy of Sciences Ukraine Traditional model of the polar motion of the Earth includes one secular component and two periodic ones: annual and free oscillation (the Chandler wobble). The deviation of the theoretical model of the polar motion from high-precision observations over the past decade raises some doubts about model completeness. The irregular rotation of the Earth due to the inluence of various external and internal factors should be taken into account. There is a general point of view that this task has not been solved yet. Therefore, the study of deviations of the pole coordinates from the model of the process as well as physical causes of these deviations are necessary for specifying the irregularities in the Earth rotation. The results of studies of Earth's polar motion based on the instantaneous coordinates X, Y for the period from 1962 to 2008 are discussed in this paper. Particular attention is paid to the analysis of features in the change of the coordinates of the instantaneous pole of the Earth. |
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Solution and an analysis of the general celestial body rotation problem
Kudlay O. Institution: Main Astronomical Observatory of NAS Ukraine One performed numerical integration of general 3-axis solid body rotation problem to compare with commonly used linear system of Munk & Macdonald. Been calibrated on analytical Euler solution it provided the accuracy better than 1 microsecond of arc for wobble and 1 nanosecond for spin. This enabled to investigate the effect of as ever neglected small terms and find out the new phenomena. Wobble period variation under atmospheric forcing is studed as example of nonlinearity influence and compared with observations. |
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Determination of nutation offsets by combining VLBI/GPS-produced normal equations
M. Kudryashova, S. Lambert, P. Defraigne, V. Dehant, C. Bruyninx Institution of the first author: Royal Observatory of Belgium Belgium Long standing routing operation of individual geodetic space- and ground-based techniques (like, for instance, VLBI, GNSS, LLR, etc.) revealed their strong and weak aspects. More effective use of these strengths as well as reduction of their weaknesses is possible by incorporating of the information collected by each individual technique into combined products. Such a consistent combination can be performed either by combination at the observational level or at the level of normal equations. We concentrate on the combination of normal equations gathered during VLBI/GPS-data processing. The main goal of this combination is to construct a time series of nutation offsets in the most consistent way. The objective of this presentation is to describe the developed strategy of combination and to present the current status of its implementation and first results. Combination presented here is based on the normal equations stemmed from the processing of VLBI and GPS observations during a continuous VLBI campaign CONT08. Earth orientation parameter determination will, in our procedure, benefit from angle and rate observation for a unique estimation. |
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Operational and research activity at the Paris Observatory VLBI analysis center
Lambert S., Gontier A.-M., Barache C. Institution of the first author: Observatoire de Paris/SYRTE/CNRS France The Paris Observatory IVS analysis center (OPAR) renewed its activities after 2007. It is now fully operational for processing of diurnal and intensive VLBI sessions scheduled by the IVS, with a latency optimized by an automated analysis scheme. A number of other tasks are regulary achieved: quarterly solution providing up-to-date reference frames and Earth orientation parameters, time series of site coordinates, and time series of radio source coordinates. Publication and availability of the products are ensured by the maintenance of one of the primary IVS data center and by a web site. After a large participation to the construction of the ICRF2, future developments include software improvement, new operational products, and new axes of research mainly oriented towards astrometry of quasars. |
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Using modified Allan variance for time series analysis
Malkin Z. Institution: Pulkovo Observatory Russia Allan variance (AVAR) was first introduced more than 40 years ago as a estimator of the stability of frequency standards, and now it is actively used for investigations of time series in astronomy, geodesy and geodynamics. However, unlike time and frequency measurements, astronomical and geodetic time series consist, as a rule, of data points with associated uncertainties, which are used for data weighting during statistical processing. Moreover, some kinds of time series we deal with in practice are in fact physically connected components of multidimensional vectors, e. g. Cartesian station coordinates with respect to the station position vector. Unfortunately, originally defined AVAR definition does not allow us to process unevenly weighted and multidimensional data. To overcome this deficiency, AVAR modifications are proposed (Malkin, J. of Geodesy, 82, 325, 2008). In this paper, several examples are given of processing of various time series making use the classical and modified AVAR approaches, and a comparison of results is made. |
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Phase variations of the Chandler wobble from 163-yr polar motion series
Malkin Z., Miller N. Institution of the first author: Pulkovo Observatory Russia Investigations of the anomalies in the Earth rotation, in particular, the polar motion components, play an important role in our understanding of the processes that drive changes in the Earth's surface, interior, atmosphere, and ocean. This paper is primarily aimed at investigation of the Chandler wobble (CW) at the whole available 164-year interval to search for the major CW amplitude and phase variations. First, the CW signal was extracted from the IERS (International Earth Rotation and Reference Systems Service) pole coordinates time series using two digital filters: the singular spectrum analysis and Fourier transform. The CW amplitude and phase variations were examined by means of the wavelet transform and Hilbert transform. Results of our analysis have shown that, besides the well-known CW phase jump in the 1920s, two other large phase jumps have been found in the 1850s and 2000s. As in the 1920s, these phase jumps occurred contemporarily with a sharp decrease in the CW amplitude. |
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Method for prediction of deltaT based on long-periodic terms in the Earth's rate of rotation
Marceta D., Segan S. Institution of the first author: Faculty of Mathematics of Belgrade Serbia Both external and internal mechanisms are responsible for variations in the Earth’s rate of rotation. Seasonal and annual fluctuations have been mapped in detail only since the introduction of atomic time. Decadal variations in the length of day (LOD) can be traced over the last four centuries i.e. over the telescopic period, mainly using occultations of stars by the Moon. However, any trend is difficult to detect over such a relatively short period. Regardless of choice of expression used to extrapolate DeltaT in pretelescopic period or to the future, still there is an inherent uncertainty of about +-20s due to indeterminate behavior of decade fluctuations. As we know, for very near future the uncertainty will be much smaller than this because in the next few years mathematical modeling can be used to predict value of DeltaT with more confidence (Kalarus M. at all,2010, in press). By using parabolic long term approximation (Stephenson and Morrison, 1995) of LOD changes in pretelescopic period, we have modified expression for DeltaT by adding some long-periodic terms to gain inner uncertainty less than +-5s for whole period. |
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Applications of simultaneous ground-based and satellite observations
Marco F., Martinez M. Institution of the first author: Universitat Jaume I Spain Simultaneous ground-based and satellite observations either of a body in the solar system or an external source, together with mutual observations between satellite and Earth observational site could be used to monitorize differents reference systems. |
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Dynamical regression and filtering models of the Earth pole oscillations
Markov Y., Rychlova L., Sinitsyn I. Institution of the first author: Moscow Aviation Institute Russia Astrometry data measurements [1] testify that the mechanism of exciting oscillations of the Earth’s pole has celestial-mechanic nature. Local geophysical factors (atmospheric, oceanal, seasonal etc) are of small influence. Hydrosphere (oceans and atmosphere) is subjected to the essential gravitational and tidal disturbances and influences on the yearly oscillations of the Earth Pole. This circumstance is the basis of sinphase dynamical variations of hydrosphere and the Earth mantle. For high-precision data measurements the linear dynamic regression models (DRM) for the Earth pole parameters (trend and yearly and Chandler oscillations) for estimation (identification, interpolation and extrapolation) based on the IERS measurements [1] are developed in [2]. For astrometry measurements with stochastic dynamical errors in the Earth’s pole parameters the linear and quasilinear dynamical filtering models (DFM) for the on-line estimation are presented in [3, 4]. Software tools for modeling and estimation based on Kalman and Pugachev filters are given in [5]. DRM and DFM modeling results for 1995-2010 years are demonstrated. Perspectives of DRM and DFM development based on new signal processing information technologies are considered. References 1. IERS Annual Reports, http//hpiers.obspm.fr/eop-pc. 2. Akylenko L.D. Kumakshev S.A., Markov Yu. G., Rychlova L.V. High-precision prognosis of the Earth pole movement // Astron. J., 2006, V.83, №4, pp. 376-384. 3. Sinitsyn I.N. Hereditary informational model building methods in the Earth stochastical dynamics // Informatika I Ee Primenenie, 2009, V.3, №3, pp. 2-11 (in Russian). 4. Sinitsyn I.N. Kalman and Pugachev filters (2nd edition). M.: Logos, 2007 (in Russian). 5. Sinitsyn I.N., Sinitsyn V.I., Korepanov E.R., Beloysov V.V., Semendyaev N.N. On-line informational model building of the Earth Pole by linear and linearized filters // Informatika i Ee Primenenie, 2010, V.4, №1, pp.2-11. (in Russian). |
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Earth pole coordinates prediction and precision assessment within a short-time interval
Markov Y., Akulenko L., Barkin M., Kiselev M. Institution of the first author: Moscow Aviation Institute Russia The fundamental astrometric problem of high-accuracy interpolation and forecasting of the Earth’s polar motion on short time scales from 1-2 to 10-30 days is studied [1]. Hierarchies of interval length and parameter accuracy are established using appropriate models for the process. We can reach the required interpolation and forecast accuracy for the polar motion for very long (several years), moderately long (about a year), and comparatively short (10-30 days) time intervals by modifying and adjusting the filtering procedure used. The probability of high-precision short-term (1-2 days) prediction of the Earth’s pole motion when solving practical key navigation problems applying the polynomial filter obtained by the Least-Square Method ignoring small scale variations. The theoretical accuracy reaches milliarcsecond (centimeter) levels, which are comparable to the effects of irregular geophysical perturbations. References 1. Akulenko L.D., Markov Yu.G., Perepelkin V.V., Rykhlova L.V. Short-Time-Scale Features of the Earth’s Polar Motion// Astron. J., 2009, V. 53, №11, pp.1070-1077. |
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Applications of simultaneous ground-based and satellite observations
Marco F., Martinez M. Institution of the first author: Universitat Jaume I Spain Simultaneous ground-based and satellite observations either of a body in the solar system or an external source, together with mutual observations between satellite and Earth observational site could be used to monitorize differents reference systems. |
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Dynamical regression and filtering models of the Earth pole oscillations
Markov Y., Rychlova L., Sinitsyn I. Institution of the first author: Moscow Aviation Institute Russia Astrometry data measurements [1] testify that the mechanism of exciting oscillations of the Earth’s pole has celestial-mechanic nature. Local geophysical factors (atmospheric, oceanal, seasonal etc) are of small influence. Hydrosphere (oceans and atmosphere) is subjected to the essential gravitational and tidal disturbances and influences on the yearly oscillations of the Earth Pole. This circumstance is the basis of sinphase dynamical variations of hydrosphere and the Earth mantle. For high-precision data measurements the linear dynamic regression models (DRM) for the Earth pole parameters (trend and yearly and Chandler oscillations) for estimation (identification, interpolation and extrapolation) based on the IERS measurements [1] are developed in [2]. For astrometry measurements with stochastic dynamical errors in the Earth’s pole parameters the linear and quasilinear dynamical filtering models (DFM) for the on-line estimation are presented in [3, 4]. Software tools for modeling and estimation based on Kalman and Pugachev filters are given in [5]. DRM and DFM modeling results for 1995-2010 years are demonstrated. Perspectives of DRM and DFM development based on new signal processing information technologies are considered. References 1. IERS Annual Reports, http//hpiers.obspm.fr/eop-pc. 2. Akylenko L.D. Kumakshev S.A., Markov Yu. G., Rychlova L.V. High-precision prognosis of the Earth pole movement // Astron. J., 2006, V.83, №4, pp. 376-384. 3. Sinitsyn I.N. Hereditary informational model building methods in the Earth stochastical dynamics // Informatika I Ee Primenenie, 2009, V.3, №3, pp. 2-11 (in Russian). 4. Sinitsyn I.N. Kalman and Pugachev filters (2nd edition). M.: Logos, 2007 (in Russian). 5. Sinitsyn I.N., Sinitsyn V.I., Korepanov E.R., Beloysov V.V., Semendyaev N.N. On-line informational model building of the Earth Pole by linear and linearized filters // Informatika i Ee Primenenie, 2010, V.4, №1, pp.2-11. (in Russian). |
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Earth pole coordinates prediction and precision assessment within a short-time interval
Markov Y., Akulenko L., Barkin M., Kiselev M. Institution of the first author: Moscow Aviation Institute Russia The fundamental astrometric problem of high-accuracy interpolation and forecasting of the Earth’s polar motion on short time scales from 1-2 to 10-30 days is studied [1]. Hierarchies of interval length and parameter accuracy are established using appropriate models for the process. We can reach the required interpolation and forecast accuracy for the polar motion for very long (several years), moderately long (about a year), and comparatively short (10-30 days) time intervals by modifying and adjusting the filtering procedure used. The probability of high-precision short-term (1-2 days) prediction of the Earth’s pole motion when solving practical key navigation problems applying the polynomial filter obtained by the Least-Square Method ignoring small scale variations. The theoretical accuracy reaches milliarcsecond (centimeter) levels, which are comparable to the effects of irregular geophysical perturbations. References 1. Akulenko L.D., Markov Yu.G., Perepelkin V.V., Rykhlova L.V. Short-Time-Scale Features of the Earth’s Polar Motion// Astron. J., 2009, V. 53, №11, pp.1070-1077. |
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About the configuration of the geoid undulations and their kinematics
Morcov G. Institution: Technical University of Civil Engineering of Bucharest Romania The paper will cover the following: Purpose: - Highlight the continuity of certain positions of the same frequency undulations on the equipotential surface, due to possible differential movements of these undulations in relation to the Earth's rotation Method: Creating the undulations configuration in some sections, at the same scale, resulting in specific figures. Kinematic running (animation) of these figures in order to determine if there is: - a continuity of the same frequency undulations from a section to another - kinematic vectors of the undulations in certain directions Results: By kinematic unfolding of the undulation’s configuration is found that: - There is a continuity of the same frequency undulations from a parallel to another - there are kinematic vectors in two directions: a) in east-west direction b) in north-south direction in the Boreal Hemisphere and in south-north direction in the Southern Hemisphere. - There is an advance of the same frequency undulations in equatorial section, in progressively relation with the undulations placed in the parallels sections. Conclusions: Using the undulations animation globally highlights the Coriolis effect, emphasizing possible progressive stages in undulation’s translation from west to east and from the equator to the poles. If the apparent path of the undulations in some directions, can be explained as a product of continental drift, there may be clarifications, for the principle of the terrestrial reference frame, no net rotation (NNR) with regard to the Earth’s lithosphere. |
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Delta T and tidal acceleration values from three european medieval eclipses
Martinez M., Marco F. Institution of the first author: Universidad Politécnica de Valencia Spain Deta T value is strongly related with occultations and eclipses because it is necessary not only for the calculation of exact times of an eclipse, but also for determining the position of the central line or the zone of visibility. The eclipse of AD1239 June 3 was observed at no less than ten sites in Europe. The one of AD1241 October 6 was reported from two European places and possibly one or two other sites in North Africa, while the one from AD1354 September 17 was observed from two European sites. The conjunct analysis of these astronomical phenomena is useful for determining a range of Delta T in function of the variations for he tidal acceletation of the moon. |
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Nonlinear sea level variations in the equatorial Pacific due to ENSO
Niedzielski T., Kosek W. Institution of the first author: Space Research Centre, Polish Academy of Sciences Poland Gridded sea level anomaly time series from TOPEX/Poseidon and Jason-1 satellite altimetry have been processed in order to detect nonlinearity of sea level change. Basic statistics, such as standard deviation, skewness and kurtosis, along with testing hypothesis served well the purpose of statistical evaluation. The data span has been fixed to be 10.01.1993-14.07.2003. The data obtained by both satellites have been merged by applying the offset between two time series, separately for each location grid. In order to infer nonlinear features of sea level variation, four specific terms (linear trend, annual oscillation, semiannual component and alias-type 62-days oscillation) have been removed from merged time series at every grid. It has been shown that the particularly meaningful departures from the normal distribution of sea level change are present within the equatorial zone in the Pacific and Indian Oceans. This finding has been associated with the asymmetry between strengths of El Niño and La Niña episodes. The interpretation of the results has been based on the geophysics of Kelvin and Rossby ocean waves which drive the ocean part of the ocean-atmosphere coupling in the El Niño/Southern Oscillation (ENSO). It has been argued that the local nonlinear heating occurring only during strong ENSO episodes can be responsible for the local nonlinear sea level change during such considerable ENSO events. |
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Mathematical modeling of subdiurnal variation in the Earth's rotation
Perepelkin V. Institution: Moscow Aviation Institute Russia Methods of celestial mechanics are used to refine a mathematical model for irregularity in the axial rotation of the Earth proposed earlier [1]. This refinement [2] applies corrections (residuals) introduced by perturbations of zonal tides. Numerical modeling (interpolation and forecasting) confirms the improvement in the model accuracy. We have used the meteorological NCEP/NCAR data to compare the model of the tidal irregularity in the Earth’s rotation with oscillations in the axial atmospheric angular momentum. Fluctuations in the velocity of the Earth’s axial rotation can successfully be used to forecast the overall angular momentum of the atmosphere [2]. References 1. Akulenko L.D., Markov Yu.G., Perepelkin V.V. A celestial mechanics model of the Earth’s rotation irregularity // Cosmic Research, 2009, V. 47, №5, pp.417-425. 2. Akulenko L.D., Markov Yu.G., Perepelkin V.V., Rykhlova L.V. Irregularities in the Earth’s Rotation and the Overall Angular Momentum of the Atmosphere// Astron. J., 2010, V. 54, №3, pp.260-268. |
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Model of Earth rotation irregularity and forecast of the axial atmospheric angular momentum
Perepelkin V., Barkin M., Skorobogatyh I. Institution of the first author: Moscow Aviation Institute Russia Methods of celestial mechanics are used to refine a mathematical model for irregularity in the axial rotation of the Earth proposed earlier [1]. This refinement [2] applies corrections (residuals) introduced by perturbations of zonal tides. Numerical modeling (interpolation and forecasting) confirms the improvement in the model accuracy. We have used the meteorological NCEP/NCAR data to compare the model of the tidal irregularity in the Earth’s rotation with oscillations in the axial atmospheric angular momentum. Fluctuations in the velocity of the Earth’s axial rotation can successfully be used to forecast the overall angular momentum of the atmosphere [2]. References 1. Akulenko L.D., Markov Yu.G., Perepelkin V.V. A celestial mechanics model of the Earth’s rotation irregularity // Cosmic Research, 2009, V. 47, №5, pp.417-425. 2. Akulenko L.D., Markov Yu.G., Perepelkin V.V., Rykhlova L.V. Irregularities in the Earth’s Rotation and the Overall Angular Momentum of the Atmosphere// Astron. J., 2010, V. 54, №3, pp.260-268. |
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Earth rotation parameters determined over CONT08 VLBI campaign by the GRGS from the combination of space geodetic techniques
Richard J.Y., Gambis D., Bizouard C. Institution of the first author: Observatoire de Paris/SYRTE/CNRS Spain An IERS Working Group on Combination at the Observation Level (COL) was created in the course of 2009. Its main objective is to review the interest in combining techniques at the observation level for EOP and reference frames and to bring together groups capable to do such combinations. The first action taken by COL was to select a benchmark period to make inter comparisons between the different groups involved. The continuous VLBI campaign CONT08 period extending from 10 to 30th August 2008 was a good opportunity for such analyses We present the first analyses performed in the frame of the GRGS before results be compared in the future to those obtained by the other institutes taking part of the project. |
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Comparison of the various atmospheric and oceanic angular momentum series
Ron C., Vondrák J., Stefka V. Institution of the first author: Astronomical Institute AS CR Czech Republic Two approaches are used for studying the impact of the atmosperic and oceanic excitations on the motion of Earth's spin axis in space. One way consists in the integration of the Brzezinski broad band Liouville equation and second way in the spectral analysis of both the geodesic and geophysical excitation functions. We applied both approaches to the latest series of the atmospheric (NCEP/NCAR, ERA40) and oceanic (ECCO, OMCT) angular momentum excitation functions. The comparison of the methods and series is discussed. |
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Impact of climate change scenarios on angular momentum and related EOP parameters
Salstein D., Quinn K., Abarca del Rio R. Institution of the first author: Atmospheric and Environmental Research, Inc. USA Changes to greenhouse gas concentration are expected to impact the Earth’s climate system, and indeed have already done so. However, part of the uncertainty in estimating such future effects depends on how climate forcing scenarios are formulated. The coupled ocean-atmosphere models simulate the consequences of the various scenarios as well as over the 20th century using modeled forcings from possible future scenarios. Using outputs from certain coupled models, we note how they are related to the overall atmospheric angular momentum (AAM) can lead to changes in the Earth rotation parameters over this century and beyond. For the axial component, we examine variations and trends in zonal AAM by latitude band and height from several models. Particularly strong increases in zonal winds can occur in the upper troposphere subtropics/lower stratosphere in both hemispheres, strengthening the zonal jets there, having an overall impact on the angular momentum balance, and especially on length-of-day changes. |
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The recent results of non-rigorous combination method of results of space geodetic techniques
Stefka V. Institution: Astronomical Institute of the Czech Republic Czech Republic The non-rigorous method is based on combining station position vectors in the celestial reference frame using the transformation from ITRF to GCRS, which is function of known and solved parameters. The new terrestrial reference frame (ITRF 2008) was recently published with revised collocation ties, which play key role in combination of different techniques because they give necessary information about spatial relation between geodetic instruments located on particular collocation site. By using the revised ties, some discontinuities in coordinate series at particular stations were corrected so that they could then be used in the combination to compute EOPs and station coordinate vectors. All results were compared with the ones published by ITRF 2008. Additionally, computed EOPs were compared with C04 2005 (IAU2000A). |
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The interpretation of the high frequency signals in the G-ring laser gyroscope
Tian W, Brzezinski, A. Institution of the first author: TU Dresden, Lohrmann-Observatory Germany As a promising geodetic instrument, G-ring laser gyroscope in Wettzell has been improved over last several years. its current sensitivity is around 10^{-9} which makes it possible to detect the variations of the instantaneous rotation pole directly and precisely. In this paper,concerning its long stability, we only consider the high-frequency (diurnal and semi-diurnal) signals existing in the raw data. There are two main sources contributing the diurnal and semi-diurnal signals in ring laser gyroscope. one is the orientation variations of the platform which are reduced by the tilt meters nearby, another one is the variations of Earth rotation (Retrograde diurnal polar motion) modeled by Brzezinski (1986) using the transfer function of Wahr which is consistent with the nutation model IAU 1980. After these reductions there are still some diurnal and semi-diurnal signals remaining in the reduced data. So in this paper our aim focuses on interpreting these unknown high-frequency signals by extending our Earth rotation models according to the IERS convention 2003. |
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Modelling of the Earth orientation and high precision astrometric observation techniques
Yao K., Capitaine, N. Institution of the first author: Observatoire de Paris/SYRTE/CNRS France After a short description of the characteristics of each technique contributing to observations of Earth's rotation, we investigate their potentiality to determine the various components of precession-nutation. |
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2PN light propagation and measurement in the solar system
Deng X.-M., Huang T.-Y. Institution: Purple Mountain Observatory,China China The second post-Newtonian (2PN) framework for light propagation is developed with two additional parameters varsigma and eta besides the two parameterized post-Newtonian (PPN) parameters gamma and beta. For a precision level of a few microacrsecond for space astrometry missions in the near future, we consider the effects of monopole and quadrupole moments of the gravitating bodies in the Solar System and their gravitomagnetic fields on light propagation. Besides, the expression for the influence of the second zonal harmonic coefficient on light propagation is presented. After the light trajectory is obtained, the light time equation is given. Started from the definition of a measurable quantity, a gauge-invariant angle between the directions of two incoming photons for a differential measurement in astrometric observation is discussed and its formula is derived in detail. |
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Perturbation of a Planetary Orbit by the Lambda-Term ("Dark Energy") in Einstein Equations
Dumin Y. Institution: IZMIRAN, Russian Academy of Sciences Russia The problem of cosmological influences at small (e.g. interplanetary) scales is discussed for many decades, starting from the early 1930's, but still remains unsolved definitively by now [W.B.Bonnor. Gen. Rel. Grav., v.32, p.1005 (2000)]. It became especially topical in the context of the "dark-energy"-dominated cosmology, because the commonly-used arguments against the local Hubble expansion (such as Einstein-Straus theorem [Rev. Mod. Phys., v.1 , p.120 (1945)]) are no longer applicable when the most contribution to the energy density of the Universe comes from the perfectly-uniform dark energy (Lambda term). Moreover, there are some empirical evidences in favor of the local cosmological influences. For example, assumption of the local Hubble expansion in the dynamics of the Earth-Moon system enabled us to resolve a long-standing discrepancy in the rates of secular increase of the lunar semi-major axis measured by the lunar laser ranging, on the one hand, and derived from the astrometric observations of the Earth's rotation deceleration, on the other hand [Yu.V.Dumin. Adv. Space Res., v.31, p.2461 (2003); Proc. 11th Marcel Grossmann Meeting on Gen. Rel., p.1752 (2008)]. The aim of the present report is to provide a rigorous mathematical treatment of the planetary motion against the cosmological background, which is based on the Kottler metric reduced to the Robertson-Walker cosmological coordinates, as outlined in our earlier work [Yu.V.Dumin. Phys. Rev. Lett., v.98, p.059001 (2007)]. As follows from our numerical computation, under certain circumstances (depending on the ratio between the radius of the orbit, Schwarzschild, and de Sitter radii) the perturbed orbit becomes a spiral. This points to the potential importance of the Hubble effect for the local planetary dynamics. |
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Millisecond pulsars and planetary ephemerides: frame ties and other considerations
Fienga A., Desvignes G., Cognard I., Theureau G. Institution: IMCCE - observatoire de Besancon France We have used pulsar timing (obtained at NRT) and pulsar VLBI observations to link reference frames: planetary ephemerides to each others (DE200,DE405,INPOP08 and DE421) and to ICRF. The obtained rotation matrices will be presented here. |
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Development of the TWSTFT Carrier–Phase technique at LNE-SYRTE
Kanj A., Achkar, J. Institution of the first author: Observatoire de Paris/SYRTE/CNRS France The Two-Way Satellite Time and Frequency Transfer (TWSTFT) method [ITU-R TF.1153-3 recommendation, 2010] permits to compare two remote atomic clocks by using a microwave link through a geostationary satellite. The best performance reachable today is achieved on the Ku band link with a frequency stability of 8.10-16 at one day [Zhang et al., PTTI meeting, 2009]. Our aim is to improve this value and to obtain a high performance comparison system of remote primary frequency standards with uncertainties in order of sub-nanoseconds. In this case, the TWSTFT carrier-phase is the most appropriate method to improve the short-term stability of the two-way links. The work proposed here is limited to the development of the TWSTFT carrier-phase method. The main idea is to calculate the offset between the frequencies of the two clocks located each one in a different station. The Doppler’s effect is taken into consideration regarding the spread of the signal between each station and the satellite and vice versa. We establish the equation system of the TWSTFT carrier-phase technique composed by four nonlinear equations with four unknowns: the first Doppler coefficients, the satellite’s local oscillator frequency and the frequency offset of the distant clocks. This system cannot be solved directly [Fonville et al., PPTTI meeting, 2004]. As a first approach, we use the Newton-Raphson method to transform the nonlinear system to a linear one. Then, the singular value decomposition technique is used to solve the resulting linear system. Scientific and technical details will be presented at the conference. |
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Light time calculations for deep space navigation
Le Poncin-Lafitte C., Bertone S. Institution of the first author: Observatoire de Paris/SYRTE/CNRS France With the recent discovery of several astrometric anomalies derived from tracking of spacecrafts, such as Pioneer 10/11 and Earth Flyby, we propose to reconsider the relativistic formulation of Deep Space Navigation. We show in particular that some traditional approximations can lead to neglect tiny terms that may produce instability in the orbit determination of probe during Earth flyby. |
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Propagation in time of errors for the mutual inclination of satellites
Marco F., Martínez M. J., López J. A. Institution of the first author: Universitat Jaume I Spain The theoretical and the observed values of the mutual inclination between natural satellites may be different due to physical or geometrical causes (or due to both of them). It is clear, for example, that a geometrical variation between the reference systems, for example the application of a infinitesimal rotation around an axis, implies a modification in the elements that determine the orbits. In addition, a bad determination of the mass of the body may imply false values in the integration of the elements. These errors in the initial elements propagate in time, so it may be useful to provide methods to analyse them and also to be able to discriminate the true source of the error, if possible. |
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Usage of asteroids to determine relations between ICRF and dynamical system
Medvedev Y. Institution: Institute of Applied Astronomy of Russian Academy of Sciences Russia Relation of dynamical coordinate system with ICRF is determined through VLBI observations of spacecraft orbiting around the major planets. Variability of gravitational fields of major planets because of tides makes construction of the theory of motion of spacecraft complicated. Possibility of usage of asteroids for determination of linkage between dynamical (and optical or stellar) coordinate system and ICRF is considered. With this aim in view we suggest to create on the orbits around specially selected asteroids several radio transmitters that makes it possible to fulfill VLBI observations. Small size of asteroids allows one to connect corresponding systems with significantly higher accuracy than it can be done with use of major planets. It is especially true with respect to optical observations. The problem of determining links between reference frames can be combined with solving tasks of counteraction against the asteroid-comet hazards for the Earth. The last problem is actively discussed during recent time, particularly in connection with very close approach of asteroid (99942) Apophis with the Earth. It would be desirable to combine solutions of mentioned problems, as an underling demand is the same: determination of precision of asteroid orbit with high accuracy. Errors of elements of Apophis orbit and those of a number of other asteroids have been estimated if their observations are made against quasar backgrounds. It has been also estimated what precision of linkage dynamical reference system and ICRF can be attained depending on interval and number of observations. |
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The ephemerides of Martian satellites Phobos and Deimos created by ERA system
Zamarashkina M. Institution: Institute of Applied Astronomy Russia The numerical theory of the motion of Martian satellites is constructed. The dynamical model of the satellite motion was realized in the framework of the universal programming system ERA (Ephemeris Research in Astronomy [1]) developed in IAA RAS. The initial coordinates of Phobos and Deimos were obtained by processing their astrometrical observations on the time interval 1877-2003. Comparison of the satellite ephemerides with analogous data obtained by other software ephemeris packages (ephemeris JPL [2], SSAI/IMCCE [3], IAM RAS [4]) is presented. It is shown that the divergence of all satellites’ trajectories on the time span 100 years has the same order. References: 1.Krasinsky G.A., Vasiliev M.V. ERA: knowledge base for ephemeris and dynamical astronomy // Proc. of IAU Coll.165.1996. P.239–244. 2.Jacobson, R.A. Ephemerides of the Martian Satellites - MAR080 // JPL IOM 343R-08-006, 2008. 3.Kudryavtsev S.M., Kolyuka Y.F., Tikhonov V.F. New Analytical Theory of Motion of Phobos and Deimos for Navigation Support of Mission to Mars // ESA SP-403: Proc. of the 12th International Symp.on Space Flight Dynamics. 1997. P. 377-382. 4. Shishov V.A. Determination of spacecraft and Phobos parameters of motion in the Phobos-Grunt project // Solar System Research. 2008. V. 42. P. 319-328. |