Algorithm for solving 3-D problems of em induction by means of a vector integral equation

Summary An algorithm is presented for solving the problem of electromagnetic induction in a halspace with a 3-D perturbing body under a harmonically variable exciting field. There are analysed properties of the Green's tensor function elements as well as their integrals in elementary prismatic volumes into which the body is divided. The results, obtained from numerical computations, are given for a long highly conducting prism, which is one of the models in the COMMEMI project.

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Variations of the earth's gravity field due to the free nutation

Summary Expressions for the time variation of gravity and for deformations of equipotential surfaces due to the free nutation of the Earth have been derived. The possibility has been shown of determining the polar motion by means of accurate gravity observations under the assumption that the other effects, particularly tidal, may be expressed with sufficient accuracy theoretically. The necessity of introducing gravity corrections due to the polar motion has been pointed out in investigating the secular variations of gravity and in accurate gravity measurements (standard error of the order of 0.01 mgal and less), in general.     

Single-layer density as function of Stokes' constants

Summary A relation between Stokes' constants (harmonic coefficients) J _n ^(k) , S _n ^(k) has been derived in the development for the external geopotential and the coefficients in the development for the single-layer density distributed over the surface of the external ellipsoid, the external equipotential surface, as well as the smoothed physical surface of the actual Earth. Terms of the 2nd order, (J ₂ ⁽⁰⁾ ) ² , were taken into account, terms of the 3rd and lower orders were neglected.     

Parameters of the normal gravity field deduced from satellite observations

Summary The parameters of the normal gravity field were deduced from the harmonic coefficients[3, 4] upto n=6 and compared with the parameters used hitherto. The symbols used are the same as in papers[5, 6, 8] with which this paper connects up.     

Determination of the parameters of a selenocentric reference system and the deflections of the vertical at the lunar surface

Summary Stokes' constants and, the selenocentric constant, and the angular velocity of the rotation of the Moon define the shape of the external equiselenopotential surfaces, generalized in dependence on the degree N of the harmonics preserved. The scale factor for lengths was computed on the basis of absolute gravity measurement made by the first lunarlanding mission Apollo11 at the landing site[1] under the assumption of a sufficient accuracy of the Stokes' constants used[2, 15]. Anyway, the numerical solution here is only to be considered as an example of the application of the outlined theoretical method, inclusive of the parameters of the lunar reference system, which will be made considerably more accurate when gravity measurements at more points of the lunar surface are available.Presented at the XVth IUGG General Assembly, Moscow, July 30 – August 14, 1971.     

Equatorial flattening and principal moments of inertia of the earth

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Luni-solar precession constant and accuracy of the Earth's principal moments of inertia

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Deflections of the vertical on the territory of Europe from satellite data

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