In this Note we study perturbed isotropic harmonic oscillators in 1–1–1 resonance, which is one of the typical cases of galactic potential models. We focus on cubic and quartic axial symmetric potentials giving explicitly their normal form. The 3D normalized Hénon and Heiles case, which requires to reach fourth order, is studied showing its relative equilibria and bifurcations.

The motion of an artificial satellite in the Earth’s gravitational field is discussed in the post-Newtonian framework including the effect of weak gravitation waves using the perturbation technique of the canonical Lie-transformations. Two successive canonical transformations are used to derive analytical expressions for the short-period, long-period and secular perturbations of orbital elements. The solution is expressed in terms of the Delaunay variables.

Currently employed definitions of ephemeris astronomy and the system of astronomical constants are based on Newtonian mechanics with its absolute time and absolute space. To avoid any relativistic ambiguities in applying new IAU (1991) resolutions on reference systems (RS) and time scales one should specify the astronomical constructions and definitions of constants to make them consistent with general relativity (GRT). Such an approach is developed with the aid of the existing relativisting hierarchy of relativistic reference systems and time scales.

In the course of the Hipparcos data reduction, the system of coordinates obtained is the result of complicated and partly random processes. It is therefore an arbitrary system which could not be retained. It was decided to compute a rotation ϵ at epoch (1991.25) and a time-dependent rotation ω (or spin) such that, when applied, it would be a realisation of the IAU extragalactic reference system as defined in 1991 and implemented by IERS in 1995.

A working group was set up by the Hipparcos Science Team with the task to provide these rotations from all possible techniques. Actually eleven independent teams provided a solution. One can group them in four categories.

1. 1. Radio techniques included VLBI observations with the US Deep Space Network, VLBA and the European VLBI Network, and connected radio interferometers MERLIN and VLA. While VLBI provided a solution for both ϵ and ω, the other techniques allowed to get only ϵ.

2. 2. Medium and small field astrometry including the optical positions of compact sources (Hamburg and USNO), and observations with the HST which both provided solutions for ϵ only and comparisons of plates taken at large intervals of time (Bonn and Potsdam) which gave solutions for ω only.

3. 3. Star catalogues refered to galaxies: Lick Northern proper motion program, Yale Southern proper motion program, and KSZ catalogue. Yale University, ARI in Heidelberg and Kiev Observatory yielded solutions for ω.

4. 4. Comparison of Earth rotation parameters as obtained by VLBI and by a reduction of ground-based determinations with Hipparcos data (Prague Observatory) gave components of ϵ and ω in the equator.

Features of the systematic errors of the Carlsberg Automatic Meridian Circle (CAMC) reference frame are investigated using a secondary radio reference frame defined by a set of astrometric VLA, VLBI and submillimetric positions of radio stars, taken from the literature. The radio positions of 62 stars are compared against the corresponding CAMC positions. The systematic errors of the CAMC catalogue are found to be generally smaller than 005. The radio positions were also compared with the positions obtained with the Bordeaux Automatic Meridian Circle (BORD). It was found a good coincidence between (CAMC–Radio) and (BORD–Radio) systematic differences.

A good, working definition of what is required in a celestial reference frame is that it must provide observable fiducial points on the Celestial Sphere with internally consistent positions that are referred to coordinate axes of known direction. In reality, this statement gives the goals in the reverse order from that in which each must be achieved, the definition of the axes, or zero points of the system give orientation to the observationally defined set of primary objects whose coordinate relation to each other must give the frame rigidity. Finally, the primary objects are generally too sparse to define the frame within areas of less than tens of square degrees, and so additional objects must be related to the frame to increase the density. This last step is required to make the frame useful for most observational applications.

The paper presents a method to derive rotational angles between two reference frames from the systematic differences represented in terms of spherical functions – hereafter referred to as the ROTOR (ROTation by Orthogonal Representation). It is shown that the ROTOR is preferable over the least-squares technique since it (a) takes into account only the harmonics which correspond to rotation, (b) tests them for pure rotation, and (c) discovers the existence of quasirotational terms which may smear rotation. Due to these properties the ROTOR yields realistic results even in the case when the observational data contain not only noise but other systematic terms that have nothing to do with rotation. Numerical experiments with the FK5 and three catalogs of radio sources are described.

Until 1972, astrometry based on a network of optical instruments was the only technique able to monitor the Earth orientation (polar motion, Universal Time and nutation). Since various techniques have shown their capability to give all or a part of these parameters: Doppler observations of navigation satellites, laser ranging to the Moon and to dedicated artificial satellites, Very Long Baseline Interferometry (VLBI) and more recently GPS and DORIS. The different Earth Orientation Parameters (EOP) series obtained by the individual techniques are inhomogeneous in time span, quality, time resolution – which supports the concept of combined solutions taking advantage of the various contributions.

The main task of IERS is the maintenance of both a conventional terrestrial reference system based on observing stations and a conventional celestial reference system based on extragalactic radio sources and also the matrix product allowing the transformation between these two systems which takes into account precession-nutation, polar motion and Earth rotation.

The objective of this paper is to present the evolution, the state of the art and future prospectives concerning the multi-technique EOP combined solution made at IERS/CB.

The celestial pole offsets (CPO) in provisional HIPPARCOS reference frame determined from the optical astrometry observations since 1899.7 until 1992.0 (Vondrák et al., 1996) and CPO determined from VLBI observations since 1980.0 until 1996.0 (Ma et al., 1996) are combined to get amplitudes of the long periodic nutation terms 18.6 and 9.3 years, respectively. The amplitudes are compared with previous solution based only on VLBI observations (Souchay et al., 1995).

Since 1953 regular observations have been carried out with the polar photographic tube (PT) of A. A. Mikhailov at Pulkovo, a fixed astrograph (D = 200 cm, F = 600 cm) which can take photographs of a circumpolar zone of 60′radius. An analysis of measured polar distances of the same 30 stars on each plate gives corrections to the adopted values of coefficients of the nutation and precession constant. Though several papers have appeared during the last decade in which VLBI and LLR observations were used for the determination of the nutation coefficients and precession constant, the results from a 40-year series of observations with the PT are of interest, because of its two-times period of the principal nutation term. The method is fully independent.

The Astrographic Catalogue (AC) measures are being reduced at the U.S. Naval Observatory to provide early epoch positions for approximately 5 million stars. The data, when combined with recent observations, provide a baseline of about 100 years with which to compute proper motions. Due to the inhomogeneity of telescopes and measuring techniques used in the AC program, each of the 22 zones is being reduced independently with the Astrographic Catalog Reference Stars (ACRS). The data are analyzed and corrected for radial distortions, tilt, magnitude-dependent terms, coma, and distortions based on reseaux and measuring apparatus. To date, eleven zones have been reduced and are available on the WWW (http://aries.usno.navy.mil/ad/ac.html) or the international data centers. Mean errors of the positional data vary from zone to zone, but are generally in the 190-320 mas range per each image.

The newly reduced AC data are being combined with the USNO’s Twin Astrograph Catalog (TAC) in support of the Sloan Digital Sky Survey. This catalog should be available by the end of 1996. When the Tycho data are released, the AC positions will be used to improve the proper motions of the Tycho stars. In order to aid this work, the AC zones released by USNO have Tycho identifications, where applicable.

The main task of this work was to construct a new catalogue of positions and proper motions of stars in the north polar cap, and using the results obtained to study the systematic features of the source catalogues as well as the reference system in the polar region. To achieve the goal, thirteen source catalogues, both meridian and photographic, covering an epoch span near one and a half century, were collected. Most of them were not involved in the process of both the PPM and the ACRS constructions. The new combined catalogue of positions and proper motions, named North Polar Catalogue (NPC), lists 4272 stars on the FK5 system, J2000.0. The catalogue was constructed using the method of infinitely overlapping circles. It represents the second use of this procedure to construct a star catalogue. External rms accuracy of positions for the epoch of 2000 is equal to 015 and 025 for the centennial proper motions, respectively. The internal rms errors of positions at the mean catalogue epoch, near 1940, are equal to 018 and 015 for right ascension and declination correspondingly, while external rms position errors for that epoch are of the order of 005. Comparisons were made between the NPC and three modern catalogues, the FK5, PPM, and ACRS. The systematic differences between the new catalogue and PPM one for the epoch of 2000 are valuable, especially in the case of errors depending on right ascension. The authors consider as an essential part of the systematic differences that, which is caused by some shortcomings of the PPM in the polar zone. For the mean epoch of the new catalogue positions the systematic differences are smaller.

The accurate positions of extragalactic radio sources are in use to link the radio and fundamental reference frames and contribute to determining relative orientation of HIPPARCOS and the radio reference frames as well as HIPPARCOS and FK5. Catalogues of intermediate stars chosen in the vicinity of extragalactic radio sources are an important part of the link and can be used for extension and densification of the HIPPARCOS frame. The description of main catalogues of intermediate stars is given. Results of investigation and comparison beetween CAMC, RRS2, PIRS and CRIS are presented.

A classical task of cross-identification of stars taken from different catalogs becomes a non-trivial one in a case of very big catalogs with significant epoch difference and without proper motions. Some new concepts for this problem solution are proposed here. The method discussed was applied for the Guide Star Catalog with the Astrographic Catalogue identification. About 4.3 million stars were identified in both catalogs.

Only the Hubble Space Telescope (HST) can detect about 20 of the faint satellites discovered with the two Voyager spacecraft. We describe here the techniques used in obtaining astrometric positions of the inner satellites of Uranus with the Wide Field Planetary Camera 2 (WFPC2) of HST, and those planned for our scheduled observations of the inner Neptunian satellites.

We present observations of Saturnian inner satellites, Janus, Epimetheus, Pandora and the new objects 1995S5 and 1995S6. Data were obtained with the COME-ON+ adaptive optics system mounted on the 3.6-m telescope of the European Southern Observatory, during the 10 August 1995 Earth crossing. During this time, the usually bright rings become faint, an ideal time to study the small inner satellites. Two unresolved objects have been detected. They have been identified with the objects 1995S5 and 1995S6, which have been detected on frames obtained with the Hubble Space Telescope, more than one day later. Astrometric reductions relative to the brighter satellites and the Cassini division yield planetocentric positions with accuracies of 015 and 026, respectively. These measurements, combined with the HST data, and the NIR photometric parameters point to the possible transient character of these objects, and provide a more accurate solution for the 1995S5 orbital parameters.

From 1992 to 1999, the satellites of Saturn are involved in several phenomena: eclipses or occultations by the planet, transits in front of Saturn, or transits of their umbra. These phenomena occur thanks to the geometrical circumstances in 1995 when the Earth and the Sun went through the plane of the Saturnian ring and consequently through the orbital planes of the main satellites. These circumstances are also favorable to the observation of mutual phenomena occurring when the satellites eclipse or occult each other. These mutual phenomena and the eclipses by Saturn are rare as they occur only every 15 years. But, they are very useful to get highly accurate astrometric observations and they allowed us to estimate some physical parameters. We have organized the PHESAT95 campaign to observe these phenomena and a special effort was made to observe as many events as possible. At the present time, the observations are still being collected from different teams and different countries; this paper shows the first results which have been obtained in several sites, and the first comparison with the theory of the motions.

This paper describes the methods used with the Flagstaff 20–cm CCD transit telescope for determining the positions of planets and asteroids directly in the extragalactic reference frame. As a result, the observations are not affected by (optical – radio) zonal errors, which can be ±0.1 arcsec or greater in catalogs based on traditional fundamental observations. The telescope can observe objects as faint as V ~ 17.5 mag with an accuracy of σ ~ ±0.16 arcsec in each coordinate. As a result, a large number of asteroids and the planets Uranus, Neptune, and Pluto are being routinely observed so that their ephemerides can be improved, masses determined, and accurate predictions made for occultation events. These observations are considerably more accurate than most previous results.

The Carlsberg meridian telescope has made nearly 20 000 observations of outer Solar System objects since it began operation in 1984. A preliminary version of the Hipparcos catalogue has been used to refer the positions to the International Celestial Reference Frame (ICRF). The observed positions of the major planets are compared with JPL DE403 which is also referred to the ICRF. The agreement with DE403 is good, except for the declination of Jupiter where there is a systematic difference reaching 015 in 1995. The cause of this discrepancy is being investigated at JPL with recent VLBI observations of Galileo.

We present results of CCD observations for 85 quasars with −80° ≤ δ ≤ +20° declination, belonging to the International Celestial Reference System (ICRS). The positions are referred to the Carlsberg Series (CAMC) and PPM catalogues. We discuss a method which allows one to obtain precise positions based only on CCD observations, on the use of the Digitized Sky Survey of ST ScI and on the Guide Star Catalogue. The results are compared with the VLBI positions.