Theoretical topocentric distance of a lunar station

Summary Drawing on [1], the theoretical distance between two general points on the surface of the Earth and Moon is derived using ultraspherical polynomials, retaining terms of the order of 10^–11 .     

Force function of two general spheroids

¶rt;um ua u ¶rt; u m, a u an¶rt;u nm m ¶rt;mam uu u¶rt;a ma, m ¶rt; uu u ¶rt; u nmua numu ¶rt;m a u ¶rt;mam m. mau ¶rt;u uu m: m nm u m; a, n¶rt;u au umu u unu¶rt; uuu; amu m u a; amua ¶rt;uam ma a ¶rt; u m um ¶rt;m ma. u ¶rt;a ¶rt; u¶rt;, nuu ¶rt; a, ¶rt;a ¶rt;a ¶rt;o 4- n¶rt;a um.     

Magnetic variations excited by a radial magnetic dipole located in the earth's core

Summary Theoretical formulae are derived for computing a variable magnetic field, excited by a harmonically oscillating radial magnetic dipole (RMD), located eccentrically at the surface of the Earth's core. By numerical computations, using a three-layered conductivity model of the Earth, it is proved that the field due to this source, computed for the surface of the Earth, is relatively weak in comparison to the field of a stationary magnetic dipole, provided the period of the changes is less than 500 years. The zone of influence of the RMD at the Earth's surface is also determined and on its basis a number of conclusions were drawn with respect to representing the non-dipole part of the geomagnetic field by means of the RMD system in the Earth's core.Dedicated to RNDr. Jan Pícha, CSc., on his 60th Birthday     

The earth-moon-sun disturbing function in satellite orbit dynamics

am ¶rt; a uu u m nu uu n ¶rt;uu um nmua u aumau n m -a-. ¶rt;a ¶rt; 4- n¶rt;a um.     

Precession-nutation torque from the tidal potential

aam, m nu-mau m nuuau u m n¶rt;u ¶rt;a an¶rt;uu nmm . ¶rt; a u m nm u u nuua ma (, a) u naam, n¶rt;u au nu m u unu¶rt; uuu u u nuua ma.     

10Be accumulation in a soil chronosequence

We have measured the concentration of the cosmogenic isotope¹⁰Be in soil samples from various horizons at six sites, including three independently dated Rappahannock River terraces and a previously undated Piedmont soil to which we have assigned an age. All of the incident¹⁰Be can be accounted for in one of these soils and a second is within a factor of two. In three soils, whose concentrations vary widely with depth, a significant fraction of the incident¹⁰Be cannot be accounted for. Incomplete sampling, and enhanced Be mobility caused by organic components, are the probable reasons for the low inventory of Be from these three soils. Overall, the data from these six sites indicate that¹⁰Be accumulation could be used to assign ages to soils if Be is not mobilized and lost from the soil profile.     

Anomalous curvature of equipotential surfaces due to variations in the Earth's rotation

Summary The anomalies of the Gaussian curvature of geopotential equipotential surfaces due to variations in the Earth's rotation vector have been derived theoretically.

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am mmuu ¶rt; aau a uu nmunmuaa, a auauu ma au u.