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Since the discovery of the Y-Ba-Cu-O superconductors, their physical properties have been investigated by various methods. The chemical state of Cu in Y-Ba-Cu-O compounds la one of the greatest issues because the mechanism of superconductivity in Y-Ba-Cu-O is not understood theoretically. We are analyzing X-ray fluorescence spectra of Cu compounds including superconductors, intending to analyze the chemical state of Cu in Y-Ba-Cu-O. As for other 3d transition elements, structures due to unpaired electrons appear clearly on the lower energy side of the Kα1 line of the element. However there are little differences observed among Cu Kα spectra of Cu compounds even if they are measured by a high-resolution two-crystal spectrometer (see Fig. 1). Although Cu is a member of 3d transition elements, its Kα spectrum shows somewhat different behavior compared with other 3d transition elements. This point is one subject we are interested in.
We showed that it is feasible to measure the mass of a single star by observing the variation of gravitational deflection caused by the orbital motion of the Earth. When the distance of a star is less than 60 pc and some appropriate sources are within 1 arcsec. in its background, not only the distance but also the mass of the star may be determined by measuring the deflection with an accuracy of 10 μ arcsec. In the case of photometric microlensing by a MACHO, the observation of astrometric gravitational deflection is also useful. By measuring the separation between the primary image and the secondary image, the ratio of mass to distance of the MACHO will be obtained. Further, the orbital motion of the Earth modifying the light curve of the source is discussed.
The definition of the angular momentum of a finite body is given in the post-Newtonian framework. The non-rotating and the rigidly rotating proper reference frame(PRF)s attached to the body are introduced as the basic coordinate systems. The rigid body in the post-Newtonian framework is defined as the body resting in a rigidly rotating PRF of the body. The feasibility of this rigidity is assured by assuming suitable functional forms of the density and the stress tensor of the body. The evaluation of the time variation of the angular momentum in the above two coordinate systems leads to the post-Newtonian Euler's equation of motion of a rigid body. The distinctive feature of this equation is that both the moment of inertia and the torque are functions of the angular velocity and the angular acceleration. The obtained equation is solved for a homogeneous spheroid suffering no torque. The post-Newtonian correction to the Newtonian free precession is a linear combination of the second, fourth and sixth harmonics of the precessional frequency. The relative magnitude of the correction is so small as of order of 10−23 in the case of the Earth.
The relation between the units and the readings of time and space coordinates of the terrestrial and the barycentric frames is discussed from the viewpoint of general relativity. Attention is paid to the unit of space coordinates since the International Astronomical Union (IAU) regulates only the unit of time coordinate in the above two frames. Two definitions on unit of length are examined and their effects on the numerical expression of coordinate transformation, equations of planetary motions, and those for light propagation time are discussed. A clear conflict is found between the IAU(1976) recommendation on the definition of the time-scales in different frames and the statement that all constants in the IAU(1976) new system of astronomical constants are defined in terms of the international system of units (SI units). In order to dissolve this conflict, one of the two examined definitions on unit of length is proposed to be adopted, which requests the least alteration on the current procedures to analyze the astrometric observations such as radar/laser rangings, range and range-rate measurements, and very long baseline interferometric observations. An interpretation of numerical values in the IAU(1976) system of astronomical constants is also presented. It is stressed that the definition proposed in this paper requires that a slightly different formula from the current one be used in the numerical transformation of coordinates between the terrestrial and the barycentric frames.
The treatment of the coordinate systems is briefly reviewed in the Newtonian mechanics, in the special theory of relativity, and in the general relativistic theory, respectively. Some reference frames and coordinate systems proposed within the general relativistic framework are introduced. With use of the ideas on which these coordinate systems are based, the proper reference frame comoving with a system of mass-points is defined as a general relativistic extension of the relative coordinate system in the Newtonian mechanics. The coordinate transformation connecting this and the background coordinate systems is presented explicitly in the post-Newtonian formalism. The conversion formulas of some physical quantities caused by this coordirate transformation are discussed. The concept of the rotating coordinate system is reexamined within the relativistic framework. A modification of the introduced proper reference frame is proposed as the basic coordinate system in the astrometry. The relation between the solar system barycentric coordinate system and the terrestrial coordinate system is given explicitly.
The relative frequency stability and the accuracy of atomic time scales, like International Atomic Time TAI, is now of order 1 × 10-15 thanks to progresses in clock technology and in clock comparison techniques. Cold atom primary Cs standards have a stated accuracy of 1 × 10-15 and a stability in the 10-16 region. Other cold atom clocks provide even better prospects, as well as clocks based on trapped ions. Frequencies based on optical and microwave transitions can now be compared with a similar or even better uncertainty thanks to femtosecond comb technology. Clock comparison techniques based on GPS (see http://maia.usno.navy.mil/gpst.html), or on dedicated Two Way technology provide adequate performance when averaging data over one or a few days, and should be improved to accompany the progresses of clocks.
Since 1999, a number of organizations initiated a review on the future of the UTC system (insertion of leap seconds between TAI and UTC to keep |UT1 – UTC| < 0.9s). Several working groups have been initiated, notably by the International Telecommunications Union (Special Rapporteur Group (SRG) in the Working Party 7A), by the International Union of Radio Science, and by the IAU following Resolution B2(2000). No immediate conclusion may be foreseen but a consensus should be reached over the next triennium.
Research in Celestial Mechanics, for the past three years, has mainly focused on the understanding of Chaos on all its aspects. The always larger number of potential applications (meteors, KBO, NEA, asteroids of the main belt but also exoplanets or galactic motions) and the development of new efficient tools, like the symplectic integrators, have allowed the passage from QUALITATIVE models (for example the transfer mechanisms) to real QUANTITATIVE results (like the calculation of lifetimes). This important step has contributed to (re)create collaborations between theoreticians and observers (for example, in the prediction of catastrophic impacts) and to situate the Celestial Mechanics in a wider scientific context.
The CCTF (formerly named CCDS) held its 14th meeting on 20-22 April 1999. Following the discussions, seven Recommendations were adopted and submitted to the Comité International des Poids et Mesures (CIPM). The list is the following:
1. Recommendation S 1 (1999): Mise-en-pratique of the definition of the second.
2. Recommendation S 2 (1999): On stating uncertainty in comparisons involving primary frequency standards.
3. Recommendation S 3 (1999): On the comparison of primary frequency standards.
4. Recommendation S 4 (1999): On the use of multi-channel and multi-code GPS and GLONASS time receivers.
5. Recommendation S 5 (1999): Time and frequency comparisons using GPS phase and code measurements.
6. Recommendation S 6 (1999): Future global navigation satellite systems.
7. Recommendation S 7 (1999): On Two-Way Satellite Time and Frequency Transfer
Additionally discussed were the present form of UTC and mostly the interest of preserving the leap second. The advantages and disadvantages of several options regarding the future use of leap seconds were compared. The CCTF, however, felt that it did not have the authority to propose any action. Then CCTF decided to ask the BIPM Director to write to the relating international bodies including IAU so as to draw their attentions to this issue while recommending the usage of TAI in case a time scale without discontinuity is needed. Also it was decided, in order to make more expedite the process, to ask the opinions of the various Commissions of the Scientific Unions.
The projects LIGHT and MIRA are the space-borne and ground-based optical/Infrared-interferometer projects of the National Astronomical Observatory of Japan. The contents of each project are gradually developing, and the descriptions given below are the preliminary ones studied at the present time.
LIGHT (Light Interferometer satellite for the studies of Galactic Halo Tracers) is a scanning astrometric satellite for stellar and galactic astronomy planned to be launched between 2007 and 2010 by a M-V launcher of ISAS, Japan. Two sets of Fizeau-type 40cm-pupil interferometers with 1 m baseline are the basic structure of the satellite optics. The multi-color (U, B, V, R, I, and K) CCD arrays are planned to be used in the focal plane of the interferometer, optimized for detecting the precise locations of fringe patterns. LIGHT is expected to observe the parallaxes and proper motions of nearly a hundred million stars up to 18th visual (15thK-band) magnitude with the precision better than 0.1 milli-arcsecond (about 50 microarcsecond in V-band and 90 micro-arcsecond in K-band) in parallaxes and better than 0.1 milli-arcsecond per year in proper motions, as well as the precise photometric characteristics of the observed stars. Almost all of the giant and supergiant stars belonging to the disk and halo components of our Galaxy within 10 to 15 kpc from the sun will be observed by LIGHT to study the most fundamental structure and evolution of the Galaxy. LIGHT will become a precursor of a more sophisticated future astrometric interferometer satellite like GAIA (Lindegren and Perryman, 1996).
Long term integrations of highly eccentric orbits are necessary to study the orbital evolution of comets and some minor planets. We discovered that the KS regularization is effective not only in the sense the magnitude of local error is reduced in the close approach but in the sense it dramatically reduces the positional error growth. In fact, it is in proportion to the fictitious time s while the Cowell method, the usual integration in 3-dimensional space leads to the positional error growing as a quadratic function of time. This good property is independent of the type of the integrators, of the type of the perturbations or of the magnitude of the nominal eccentricity. This phenomenon is based on the fact that the equations of motion in the KS variables are those of perturbed harmonic oscillators. As the best numerical integrator, we recommend the predictor formula of symmetric linear multistep method because (1) it runs fast since only one functional evaluation is required at each step, (2) its error constants are close to the minimum among the class of linear multistep methods, (3) its numerical error of the conserved quantities remains almost constant with time, and (4) it shows no stepsize resonance/instability in integrating the KS regularized equation of motions and the harmonic oscillator potential is the only case where the step size instability does not appear. Therefore the KS regularization is useful to investigate the long term behavior of perturbed two body problems for studying comets, minor planets, Moon, and artificial satellites.
The location-independent part of TCB-TCG, the difference between the two new time scales adopted by the IAU (1992), was integrated numerically for three JPL planetary/lunar ephemerides; DE102, DE200, and DE245. The differences among these three integrations were mostly explained by the difference in the adopted constants of the ephemerides. It was shown that the post-Newtonian correction and the perturbation by asteroids are negligible except for the mean rate, LC. The comparison of these numerical integrations with the analytical formulas of Hirayama et al. (1987) and Fairhead and Bretagnon (1990) as well as their extended versions lead to the best estimate of LC as
Combining this with the recent value of the geoid potential in Bursa et al. (1992), we estimated the value of LB, the scale difference between TCB and TT, as
Table I summarizes these conclusions. These estimates of LC and LB are more reliable than the former values we gave (Fukushima et al. 1986). The new estimate of LB will be useful in converting the numerical values of some precisely determined astronomical constants such as AU measured in meter from those in TDB to those in TCB. Also the numerically integrated TCB-TCG, which are to be called Time Ephemeris, will be useful when converting between TCB and TDB, i.e. the time scales themselves. The full paper will be appeared in A & A with the title of Time Ephemeris.
The given mission of the subgroup on Standard Procedures (SGSP) of IAUWGon Astronomical Standards (IAU/WGAS) is to prepare report “on standard procedures needed in fundamental astronomy, which a) should have a maximum degree of compatibility with the IERS Standards, b) should include the implementations of procedures in the form of tested software and/or test cases, c) should be available not only in written form, but also in machine-readable form” as described in the third item of Recommendation VIII of the IAU Resolution A4 (1991). After some general discussions, in 1992 we issued a questionnaire on the image and mechanism on the supposed set of standard procedures (IAU/WGAS Circulrar 51.2.1) and sent it to over 200 scientists in the world. Within a few months, 16 answers were sent back. The detailed answers and the questionnaire was distributed (IAU/WGAS Circular 54.2.1). As a simulation of supposed mechanism, in 1993 we did a test campaign to collect computational procedure(s) to compute the present IAU precession formula (Lieske et al., 1979) in FORTRAN (IAU/WGAS Circular 59.2.1). Within a few months, 5 submissions from 5 countires (Japan, China, USA, Russia, and UK) reached. The analysis of submitted routines was circulated (IAU/WGAS Circular 65.2.1). Based on these responses, we concluded that the establishment of a mechanism to provide such procedures to the community of astronomy is quite useful. To realize this, we will recommend some action items to the IAU as is described in the next Section. Its main purpose is to establish a mechanism by the combination of a comiittee of board and a center, which are to operate within a year after the recommendations are adopted by the IAU. Section 3 will describe some guidelines for the committee and center to perform the tasks to create and maintain standard procedures. Of course, these are to be consulted if necessary and are not to restrict or regulate the activity of the committee and the center.
Equilibria of rigidly rotating polytropic gas with small compressibilities are computed in order to investigate the relation between the incompressible and compressible equilibria. The equilibrium figure varies from a spheroid-like shape to a concave hamburger as the angular velocity increases. This result is supported by the fact that a concave hamburger equilibrium is obtained even in the complete incompressible case. Thus the Maclaurin spheroid does not represent the incompressible limit of the rotating polytropic gas because of its restriction of the figure. The computed sequence of equilibria clarifies the relation between the Maclaurin spheroid and the Dyson-Wong toroid. Moreover it is the sequence of minimum-energy configuration. These results suggest that our solutions are more physical and probably stabler than any other equilibrium of incompressible fluids.
Due to the adoption of the new International Celestial Reference Frame (ICRF), the Earth’s Ori-entation Parameters (EOP) will be revised and their definitions will need to be re-examined and clarified. This implies that precession/nutation formulation will be also revised in the future.
The precession/nutation theories for a non-rigid Earth suffer from a lack of dissipation in the core and from a mismodeling of the ocean and of the atmospheric effects. The scientific community is examining these questions. The IAU community is consequently not yet ready to adopt a new precession/nutation geophysical model but the users may use the International Earth Rotation Service (IERS) empirical series.
In order to review those questions and prepare the future research, the Scientific Organizing Committee (SOC: P. Bretagnon, V.A. Brumberg, N. Capitaine, V. Dehant (Chair), T. Fukushima, E. Groten, H. Kinoshitä, B. Kolaczek, D.D. McCarthy, P.K. Seidelmann and P.T. Wallace) has proposed invited talks on the current situation concerning:
(1)the formulation of precession/nutation (N. Capitaine, see paper 1),
(2)the planetary theories and their relation to precession/nutation (P. Bretagnon, see paper 2),
(3)the precession/nutation for a rigid Earth (J. Souchay and H. Kinoshita, see paper 3),
(4)the DExxx JPL ephemerides precision and accuracy (E.M. Standish, see paper 4),
(5)the observations of the Celestial Ephemeris Pole (CEP) and in particular the pole offset from which precession/nutation corrections can be derived (M. Feissel and A.M. Gontier, see paper 5),
RCMA SWG was appointed by the IAU WGAS (Working Group on Astronomical Standards) in accordance with IAU Resolution C6 (1994) with the aim ‘to provide definitions of the astronomical units, of the quantities linking these astronomical units to the units of the International System (SI), and of other astronomical quantities, compatible with the theory of General Relativity’. It is evident that the relativistic aspects of units of measurement cannot be isolated from the more general problem of astronomical constants and fundamental astronomy concepts in the relativistic framework. Therefore, along with the problem of units the main topics of discussion of RCMA SWG concerned also the IAU (1991) Resolutions on References Systems (RSs) and Time Scales (TSs) and their interpretation in IERS Standards (1992) and IERS Conventions (1996). In what follows we tried to summarize the results of these discussions.