Transformations of spherical harmonics and applications to geodesy and satellite theory

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Invited Paper, 9^th Brazilian Congress in Cartography, Curitiba, Paraná, Brazil, February 4–9, 1979.     

Tri-axiality of the Earth,the Moon and Mars

Summary Parameters defining the tri-axiality of the Earth, the Moon and Mars are discussed and up-to-date values recommended, as recently computed and submitted to the XVIIth IAG General Assembly (Canberra, December 1979).     

On the rotational motion of deformable celestial bodies

¶rt;am au uu ¶rt; aam ¶rt;uu ¶rt;u ma; ¶rt;am am u ¶rt; a, ¶rt;a u¶rt; amua m uuu a; num n aaa auauu nm.     

On free nutation of the rotation vector of a rigid body

aam, m ¶rt;-mau ¶rt;uu a ma au am m¶rt; ma m unmuu m m. ¶rt;a, u a u unmuu annuuam, m am n una u 0,1 u a u ammuuu ¶rt;mau aa m m.     

Tilts due to the free nutation of the Earth's axis in the results of geodetic observations

Summary Simple expressions for the deformation of equipotential surfaces and changes of the deflections of the vertical are derived at points of the Earth's surface, which are due to the variations of the rotational component of the gravity potential under free nutation of the Earth's axis of rotation (pole wandering). The results of the solution of this problem given in[1] are discussed. The values of the tilts and the changes of geoid heights for extreme deviations of the poles are considered from the point of view of the effect on measuring tilts and on levelling. An elastically deformable Earth is assumed. It is concluded that reductions with respect to the mean Earth's pole are not realistic at the present degree of accuracy of levelling. The necessity to reduce long-term tilt observations, or the possibility of determining the time variations of the rotational axis from the analysis of these observations is pointed out.     

Possible differences between mean sea-levels from satellite altimetry

Summary The first attempt has been made at determining the differences between mean sea-levels, using the recent satellite altimetry data [1].     

On the problem of equal area block on a sphere

Summary A new untraditional way of dividing the sphere surface into an arbitrary number of equal area blocks by means of a spiral is proposed and its statistical properties are analysed.