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.     

The mean density of the earth

Résumé La densité moyenne de la Terre et la densité moyenne de la couche superficielle, jusqu'à1450 m, furent déterminées `a partir des observations du gradient vertical de la pesanteur, dans la mine Anna à Píbram. Les calculs furent effectués selon les formules(6) et(7), déduites sous la supposition que la Terre soit un ellipsoïde de révolution. Les résultats furent comparés aux valeurs déduites pour l'ellipsoïde astronomique et aux valeurs des densités obtenues des prises de roches dans la mine et on a constaté un bon accord.     

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

am mam ¶rt;a naam mmu u n a ¶rt;nmuaa u amua m uuu u, mmmu ¶rt;u au (2), (3).     

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

¶rt;am aum ua mm, m um aua m uuu u u amu n¶rt;u. aamuam m unau au au ma ¶rt; u nmm ¶rt; u. ¶rt;a u auu m uuu ¶rt;a, amuu u      

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

amu n¶rt;ma u ma mum au n¶rt;¶rt; m unu¶rt;a, amu n u amu uu, u n nmu ¶rt;a [2]; ¶rt;am nu uum, n m uum ¶rt;um au mau u ma ¶rt; muu¶rt;a.