The 142-year series of pole coordinates in the system of mean pole of epoch of observation are used for the investigation of the Chandler period. The method of the best approximation of the initial data with the step of 1.5 years by means of quasi-polynomials is used.

Since 1953 regular observations have been carried out with the Polar photographic tube at Pulkovo [1, 2, 3]. A detailed description of the observational procedure, the data reduction technique, and error sources were given by Potter [4].

The nutation of the Earth with slightly nonelliptical liquid core is investigated by the perturbation theory method. It is shown that first-order terms affect the core ellipticity and its triaxiality. The most sensitive nutation terms in the second approximation were found to be retrograde 18.6-year term and retrograde annual term. The observed nutation amplitude values can be satisfied by special core-mantle boundary form.

The problem of calculation of low frequency oscillations of an ideal rotating compressible fluid is investigated. An original method of solving such a problem, based on using characteristic functions of the Poincaré operator is proposed. An efficient scheme of calculating the characteristic numbers and functions of the Poincaré operator is worked out. The high speed of convergence of the method is shown. An essential influence of compressibility on the theoretical nutation amplitude is found.

One of the fundamental problems of lunar astronomy is the reduction of the coordinates of the Moon's surface, found by astronomical methods, to its mean pole. The instantaneous poles of the rotation axis and the instantaneous equator move in the Moon's body. The unstable position of this equator does not allow one to use in selenodesy the instantaneous spherical coordinates which have not been preliminarily transformed into some unified system of coordinates. Such a reduction can be made to the system of coordinates connected with the mean pole—to be definite, we shall speak about the Moon's North pole.

In this paper some problems are discussed concerning the connection between the highly accurate optical and radio observations in the case when the waves propagate in an anisotropic medium.

For connecting the inertial coordinate system with the non-inertial planetocentric one we need to know values of the fundamental astronomical constants as well as global figure parameters of the planet. We distinguish among planetary figures a dynamical, a level, and hypsometric figures.

In this paper possible contributions of classical instrument of time and latitude determinations in the study of geoscience is discussed. Some research results indicate that the observations of the classical instruments contain rich information on geoscience study. They can play a certain role in research of crust structure, plate motion, vertical variation, topography of core-mantle boundary, and in study of seismicity and major earthquake forecasting. It is important that a stable reference system is established and maintained and a relevant observed programme is formulated upon a star catalogue with good quality for geoscience and astro-geodynamics. Some instruments with high precision, especially located in seismic regions, would be continuously operated after the end of their task in ERP determination.

We summarize our previous estimates of the accuracies of the ephemerides. Such accuracies determine how well one can establish the dynamical reference frame of the ephemerides. Ranging observations are the dominant data for the inner four planets and the Moon: radar-ranging for Mercury and Venus; Mariner 9 and Viking spacecraft-ranging for the Earth and Mars; lunar laser-ranging for the Moon. Optical data are significant for only the five outermost planets. Inertial mean motions for the Earth and Mars are determined to the level of 0.″003/cty during the time of the Viking mission; for Mars, this will deteriorate to 0.″01/cty or more after a decade or so; similarly, the inclination of the martian orbit upon the ecliptic was determined by Viking to the level of 0.″001. Corresponding uncertainties for Mercury and Venus are nearly two orders of magnitude larger. For the lunar mean motion with respect to inertial space, the present uncertainty is about 0.″04/cty; at times away from the present, the uncertainty of 1′/cty2 in the acceleration of longitude dominates. The mutual orientations of the equator, ecliptic and lunar orbit are known to 0.″002. The inner four planets and the Moon can now be aligned with respect to the dynamical equinox at a level of about 0.″005.

The realization of theoretical and applied researches in the domain of ephemeris astronomy, connected with analysis of precision of existing planetary and lunar theories, the construction of an inertial coordinate system and investigation of physical properties of space-time, necessitated the elaboration in ITA of the numerical theory of the motion of heavenly bodies suitable for calculation of high-precision ephemerides at large time-spans, and fit also for the maintenance of space experiments.

Indian calendars follow a sidereal system of astronomy taking a fixed initial point on the ecliptic as the origin from which the longitudes are measured. Its position for the official Indian Calendar has been defined by the Calendar Reform Committee (1955) as the point on the ecliptic whose true tropical longitude was 23°15′00″ as on 21 March 1956, 0h UT. Its position was determined upto the year 1984 in accordance with Newcomb's value for general precession using the relation

where T is in centuries of 36525 ephemeris days from 1900 January 0.5 ET. Recent changes in the location and the motion of the equinox with reference to the epoch J2000.0 have necessitated corresponding changes to be included in the determination of the mean and true positions of the above initial point. The new algorithm worked out is

where T is in Julian centuries of 36525 days from J2000.0.

A definition of the initium-method of spherical arcs is proposed. Theoretical and operational aspects of the method are discussed. Geometrical homogeneity is achieved by measuring arc distances between vertices of the octant (a right-angle spherical triangle) and the object in question. The measurements are made with the use of the standard angle γ on board a satellite with rotation rate reconstructions with splines. The chosen standard angle is discussed. The accuracy estimations are given.

A brief summary of results obtained by the authors for investigations of the efficiency of numerical prediction algorithms for natural and artificial minor bodies using regularizing and stabilizing transformations is given.

On the basis of about 40 000 optical observations of the Sun and major planets obtained with 33 meridian and photographic instruments during last 3 decades a comparative consistency analysis of old and new ephemerides with these observations has been made.

For the inner planets significant improvement in RA is confirmed while in DEC it is less apparent. For outer planets the improvement is strongly marked in DEC for Jupiter and Saturn and espesially for Neptune in both coordinates. Significant systematic differences between meridian and photographic observations are detected.

The possibility of using precise astrometric observations of Martian satellites in 1988 for improving the mutual orientation of the dynamic and stellar reference frames is discussed. The results obtained lead to the conclusion that the stellar reference frame is rotated about the X axis of the dynamic one. However, the value of this rotation (∼2.″5) proves to be unrealistically large and repetitions of precise observations of Martian satellites are needed in the future for verifying this result.

Based on extragalactic radio sources, a new high precision extragalactic radio reference frame can be established from radio interferometric measurements. To link the optical fundamental reference frame presently represented by the FK4/5 to the extragalactic radio frame, the optical counterparts of extragalactic radio sources (quasars, BL Lac objects etc.) and radio stars are the most important classes of objects. Besides these two classes of objects, are there any other objects which can be used to link the optical and radio frames? A posible answer is that artificial satellites could be a candidate class of objects contributing to this subject.

Ancient Chinese astronomers had special interest to measure positions of celestial bodies. “Shishi Xingjing” including at least 115 stars was produced in the 4th century BC. By the 11th century, the measure of stellar coordinates was in full swing and 5 detailed measures were carried on in only 100 years. So several ancient stellar catalogs have been retained up to now. As an ancient reference system, many astronomical phenomena have been recorded on it. This is meaningful for modern astronomers to do some modern research.

In ancient societies the Sun was the natural time marker in daytime and base for the calendar. At night, however, the stars, their movements, risings and settings, disappearence and reappearence served quite obviously as time-keepers, and people were not always conscious that they measured time using two slightly but fundamentally different clockworks.

As was pointed out by IAU in 1976, an important problem in fundamental astronomy is the improvement of the vernal equinox and equator positions. To this aim, it is necessary to know the accurate values of minor planets orbital elements. The classical methods of orbital elements differential corrections are based on linking the observations at different epochs considering equal derivatives respect to the initial and osculating elements.

In this paper we present an improved method in which the least squares matrix coefficients is calculated from the integration of the Lagrange planetary equations and its derivatives.

The secular quadratic term in the expression of the Moon's longitude has been introduced empirically after the conclusion that its mean motion is not constant (Halley, 1695).

But, the explanation of this term and also of its numerical evaluation presented and still presents in our time great difficulties. All efforts, namely, to obtain an exact agreement between observed and theoretical value of Moon's secular acceleration were unsuccessful: the first of these two values exceeds always the second one by a very large amount. This discordance and unexplained residuals (O – C) in the mean longitude of the Moon gave rise finally to the statement that these are due to a retardation and irregularity in the Earth's rotation. But, after hardly a fifty years, this hypothesis revealed even more new difficulties and questions concerning also the problem of stability of the Earth-Moon system. It seems that there is a true reason for which this problem occurs as one of the unsolved problems of Celestial Mechanics (Brumberg and Kovalevsky, 1986; Seidelmann, 1986).