The mean curvature of the external equipotential surface and the vertical gravity gradient as functions of stokes's constants

Summary The mean curvature of the equipotential surface and the vertical gradient of gravity are expressed in terms of a development into a series of spherical harmonics [1, 2, 4], neglecting terms of the order of 10^–8. The curvature anomalies have been computed using the satellite data [3]. The symbols used are the same as in [5].Dedicated to 90th Birthday of Professor Frantiek Fiala     

Über die Verteilung der aus Gezeitenbeobachtungen bestimmten gravimetrischen Faktoren in Europa

auamaumuu am, n u a¶rt;u nuu n ¶rt;a ₂, ₂, ₁ u ₁ (u. 1–4). na ¶rt;a ¶rt;am au ¶rt;um au an¶rt;u mu naam. a n¶rt;aam unam nu nuu nna m uu u u mmu mam ¶rt; uu u a a mau n.

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Vorgetragen am 2. Internationalen Symposium Geodäsie und Physik der Erde, Potsdam, Mai 1973.     

Differences between Mean Sea Levels for the Pacific,Atlantic and Indian Oceans From Topex/Poseidon Altimetry

Geopotential values W of the mean equipotential surfaces representing the mean ocean topography were computed on the basis of four years (1993 - 1996) TOPEX/POSEIDON altimeter data: W = 62 636 854.10m ² s ^–2 for the Pacific (P), W = 62 636 858.20m ² s ^–2 for the Atlantic (A), W = 62 636 856.28m ²s^–2 for the Indian (I) Oceans. The corresponding mean separations between the ocean levels were obtained as follows: A – P = – 42 cm, I– P = – 22 cm, I – A = 20 cm, the rms errors came out at about 0.3 cm. No sea surface topography model was used in the solution.     

Topex/Poseidon Altimetry and Dynamics of the Ocean-Atmosphere System

The T/P altimeter data 1993 – 1997 (cycles 11 – 194) has been analyzed with emphases on seasonal variations in sea surface topography (SST). The amplitude of the annual variations amounted to (5.9±0.3) mm when inverted barometer (IB) corrections were applied and (2.0±0.4) mm without any IB corrections. The amplitude of the semi-annual variations in SST was small with IB corrections applied: (0.6±0.3) mm. However, when no IB corrections were applied, it was (1.8±0.4) mm, i.e. the semiannual variations are at the same level as the annual variations with no IB corrections. The phase angle offset of the annual term has shifted by about 180° when IB correction was applied. The dynamics of the ocean-atmosphere system is discussed and it is concluded that it could, at least partly, be responsible for the above observed effects.     

Moments of the lunar disturbing force

Summary The components of the moments of the external force due to the gravitational effect of the Moon are derived, which causes disturbances in the motion of the Earth round its mass centre, taking into account the gravitational fields of both bodies in the form of a development in terms of harmonics upto degree n=4. This paper ties up with [3–5] and the notations are identical.     

Geoidal potential free of zero-frequency tidal distortion

It has been proved that the geoidal valueW ₀ is not dependent on the system used for defining the geoid surface. It is the same for the zero-frequency tidal system, mean system and tide-free system. It has been suggested,W ₀ be adopted as primary constant defining the length dimensions of celestial bodies.     

The Earth-Moon tidal force function

The concept “the tidal force function of the Earth-Moon system” is introduced and its exact determination based on the Stokes constants (harmonic coefficients) in the external gravitational potential of both bodies is outlined. The exact determination of the torque due to the Moon exerted on the Earth may be performed in terms of the Stokes constants of both bodies and the mutual position of both ellipsoids of inertia.     

Second Tesseral Harmonic Torque Due to the DynamicS of the Oceanic Surface Layer as Detected by TOPEX/POSEIDON Altimetry 1993-2000

Estimates of the second tesseral torque due to the variations in the radial space position of the mean ocean surface as monitored by TOPEX/POSEIDON altimeter system are derived. The magnitude of the studied torque may be compared to the tidal torque and to the tesseral torque caused by deformations due to the Earths rotation. However, such torque estimates strongly depend on the thickness of the ocean surface layer adopted in the spherical model of which the dynamics is believed to be responsible for the derived torque. The dependence on the thickness is discussed.     

Triaxiality of Halley's Comet

There are many aspects of observational evidence that cometary nuclei have irregular or nonspherical shape. The triaxial figure of the Halley's Comet nucleus is a well known fact. Therefore, the nucleus shape plays a significant role in consideration of the formation and evolution of comets and several attempts have been made to explain their nonsphericity. These studies were mainly based on the random-walk schemes for the aggregation processes. Although some results indeed lead to irregularities and deviation from sphericity, the spherical or irregular shape seem to be prevailing results. On the other hand the triaxial figure can be formed by the tidal and rotational forces. Thus, the assumption that the shape of the cometary nucleus due to some of these effects is in principle acceptable. In here assumed scenario already evolved cometary nucleus is situated as a satellite in the gravitation field of a planetary-like body. Since the rigidity of the nucleus is low, it may be easily transferred in the state of a synchronous satellite and in its shape could be imprinted the dynamical effects from this epoch. Here presented results indicate, that such a possibility should be seriously considered. The theory of this process is applied to the nucleus of comet Halley. It is shown, that the nucleus might be synchronously orbiting around a planetary-like hypothetical body with a period of 0.7 days. The minimal bulk tensile strength of the cometary material of about 10² N m^–2 is estimated.