Theory and Computation

The relations between geodesy and gravimetry are discussed in the monograph [Gravimetry and Geodesy, 2010, 570 p. In Russian] which is dedicated to the 90th birthday of Vsevolod V.Brovar, an outstanding Russian scientist in the domain of geodetic gravimetry and geodesy, and to the centenary of Mikhail S.Molodensky, a Russian geodesist and geophysicist, the founder of the contemporary Earth figure theory, who made geodesy free from hypotheses of the Earth internal structure and has transformed geodesy into an exact science.

The purpose of the book is to show fruitful interacted influences of gravimetry and geodesy, evolutions of their goals and tasks; to sum up the main theoretical,experimental and production work done at the verge of the 2nd an 3^rd millennia in the field of geodetic gravimetry (or physical geodesy), the transition from particular to system solutions of geodesy and gravimetry problems; to show the prospects for gravimetry development in the interests of geodesy.

The book is intended for the attention of geodesists, gravimetrists, astronomers,geophysicists, builders, navigators, ballisticians, designers, organizers of science and of all those who are interested in the development of geodesy and gravimetry [Gravimetry and Geodesy, 2010].

The determination of the motions of the Earth’s pole and the places of observations in XX century is reviewed in the paper [Tolchel’nikova S.A., 2010].

Information is given about the history of the spherical coordinate systems used by different international services monitoring the Earth rotation.

The principal possibility is shown to connect the mean coordinates of reference objects (stars, quasars) to the constant coordinates- λ, φ- of the one equatorial observatory which permits to exclude the usage of numerical (theoretical) models for precession and nutation to the obtained long periodic and secular motions under discussion. At the first step projections of mean polar places to the celestial sphere are considered.

In [Tolchel’nikova S.A., 2008] the transition is considered from studies of the motions of projections of objects in spherical coordinate systems to those of bodies in triads. The views of E.Mach and A.Einstein admitting only relative motion are not heuristic. As an example, the SRT formulae for stellar aberration are shown to be not adequate for the great velocity of an observer. Instead of their “improvement” using GRT corrections for space curvature, it is necessary to take into account the curvature of celestial sphere (a surface) in the case when the velocity of observer is not less than 0.01c and/or when the error of observation is less than 0.5ms of arc. For the latter case the formulae of stellar aberration were derived in Izvestija GAO (Pulkovo) № 213, 1998 and № 214, 2000.

In [Tolchel’nikova S.A., 2009] two periods are considered in the development of astronomy and geodesy which have been a single science, and were divided into two close cooperating departments in XIX century. After technical rearmament in both branches of science and the latest “revolution in astrometry” the differentiation in the two fields of activity has increased. Under discussion is the newest terminology, frequent changes in theoretical models implemented by IERS and reverberated in IAU Resolutions, the influence of cardinal changes in methods of establishing reference systems ICRF and ICRS on the studies of long periodic and secular problems in Earth’s rotation. The attention is paid to the actual idea of establishing International Earth’s Coordinate System advanced by the scientists of TsNIIGAiK.

In order to improve cooperation between scientists employing different methods for studies of motion, the method is considered used by Copernicus for simultaneous determination of secular and periodic components of the Earth’s orbital motion and rotation of its axis from the values of coordinates fixed in observations during 1500 years. In modern practice secular and periodic components are determined separately.

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