Fundamental geodetic parameters of the earth's figure and the structure of the earth's gravity field derived from satellite data

Summary Using the geocentric constant GM=398 601.3 × 10 ⁹ m ³s ^–2 , the known value of the angular velocity of the Earth's rotation , Stokes' constants J _n ^(k) and S _n ^(k) upto n=21 (zonal), n=16 (tesseral and sectorial) [2], the geocentric co-ordinates and heights above sea-level of SAO satellite stations [2], the following will be derived: the potential on the geoid W_o, the scale factor for lengths R_o=GM/W_o, the radius-vector of the surface W=W_o, the parameters of the best-fitting Earth tri-axial ellipsoid, and the components of the deflections of the vertical with respect to the geocentric rotational IAG ellipsoid (Lucerne 1967), as well as to the best-fitting geocentric tri-axial ellipsoid. Some of the differences in the structure of the gravity field over the Northern and Southern Hemispheres will be given, and the mean values of gravity over the equatorial zone, determined from the dynamics of satellite orbits, on the one hand, and from terrestrial gravity data, on the other, will be compared.Presented at the Fifteenth IUGG General Assembly, Moscow, July 30 — August 14, 1971.     

Comparison of satellite and terrestrial gravity data

Summary The integral mean values of gravity on the surface W=W ₀ , obtained from satellite observations with the use of harmonic coefficients[3, 7] and from terrestrial gravity measurements[12], are compared. The squares and products of the harmonic coefficients were neglected, with the exception of [J ₂ ⁽⁰⁾ ] ² , which was taken into account. The Potsdam correction and the geocentric constant are being discussed. The paper ties up with[13–15] and the symbols used are the same. The given problem was treated, e.g., in[2, 4, 6, 8–10]; in the present paper the values of gravity are compared directly.     

The differences in structure of the gravity field and the figure of the earth in the northern and southern hemispheres

Summary It was shown in [5] that the flattening of parallel sections of the geoid (ϕ=const.) differs in the northern and southern hemispheres. This leads up to the idea of studying further the size and shape of the Earth and the structure of the gravity field separately for the northern and for the southern hemispheres. In this paper attention is devoted especially to the mean values of the radius-vectors, to the best fitting ellipsoid parameters and to the mean values of gravity for the whole hemispheres, on the one hand, and for their ϕ=const. sections, on the other. The symbols used are the same as in [5,6]. Address: Politickych vězňů 12, Praha 1-Nové Město.     

Modern sediment yield compared to geologic rates of sediment production in a semi‐arid basin,New Mexico: assessing the human impact

An Erratum has been published for this article in Earth Surface Processes and Landforms 29(13) 2004, 1707. In the semi‐arid Arroyo Chavez basin of New Mexico, a 2·28 km² sub‐basin of the Rio Puerco, we contrasted short‐term rates (3 years) of sediment yield measured with sediment traps and dams with long‐term, geologic rates (～10 000 years) of sediment production measured using ¹⁰Be. Examination of erosion rates at different time‐scales provides the opportunity to contrast the human impact on erosion with background or geologic rates of sediment production. Arroyo Chavez is grazed and we were interested in whether differences in erosion rates observed at the two time‐scales are due to grazing. The geologic rate of sediment production, 0·27 kg m^?2 a^?1 is similar to the modern sediment yields measured for geomorphic surfaces including colluvial slopes, gently sloping hillslopes, and the mesa top which ranged from 0·12 to 1·03 kg m^?2 a^?1. The differences between modern sediment yield and geologic rates of sediment production were most noticeable for the alluvial valley ?oor, which had modern sediment yields as high as 3·35 kg m^?2 a^?1. The hydraulic state of the arroyo determines whether the alluvial valley ?oor is aggrading or degrading. Arroyo Chavez is incised and the alluvial valley ?oor is gullied and piped and is a source of sediment. The alluvial valley ?oor is also the portion of the basin most modi?ed by human disturbance including grazing and gas pipeline activity, both of which serve to increase erosion rates. Copyright © 2004 John Wiley & Sons, Ltd.     

Mean Earth'S Equipotential Surface From Topex/Poseidon Altimetry

The geopotential value of W ₀ = (62 636 855.611 ± 0.008) m ² s ^–2 which specifies the equipotential surface fitting the mean ocean surface best, was obtained from four years (1993 - 1996) of TOPEX/POSEIDON altimeter data (AVISO, 1995). The altimeter calibration error limits the actual accuracy of W ₀ to about (0.2 - 0.5) m ² s ^–2 (2 - 5) cm. The same accuracy limits also apply to the corresponding semimajor axis of the mean Earth's level ellipsoid a = 6 378 136.72 m (mean tide system), a = 6 378 136.62 m (zero tide system), a = 6 378 136.59 m (tide-free). The variations in the yearly mean values of the geopotential did not exceed ±0.025 m ² s ^–2 (±2.5 mm).     

Some Consequences of a Class of Gase0us Galactic Halo Models

If a significant fraction of QSO absorption line systems arises in halos of normal galaxies, absorber statistical data will tell us a lot about the structure of the gaseous envelopes of galaxies. Comparison of a class of density profile models for the metal-absorbing halos of luminous galaxies with the recent Lyα empirical data is presented. Cosmological mass fraction contained in such gas is also briefly discussed. It is shown that important constraints on the model parameters can be inferred in this way. This revised version was published online in August 2006 with corrections to the Cover Date.     

Decrease in the mechanical energy of the solar system due to tidal friction

Summary The total decrease in the mechanical energy of the Solar System due to the tidal friction during its whole history has been estimated at 1·7 × 10³³ kg m² s^–2 which is about 0·85% of its present energy integral. The main contributions come from Sun-Jupiter (63·4%), Sun-Saturn (26·6%), Sun-Neptune (5·9%), Sun-Uranus (3·7%), all satellite systems (0·2%), Sun-Venus (0·1%).     

Determination of tidal torques independently of densities

Summary The components of the tidal torques along the axes of the inertia ellipsoid of a perfectly elastic Earth have been derived quite independently of the density distribution of masses within the Earth. It has been demonstrated that not only the sectorial, but also the tesseral terms in the tidal forming potential are responsible for the tidal deceleration of the Earth's rotation.

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Triaxial level ellipsoids representing synchronously orbiting satellites

Summary The theory of determination of figures of synchronously orbiting satellites is presented based on equipotential level ellipsoids representing the given external equipotential surfaces. The theory has been applied to seven synchronously orbiting satellites in the solar System. The numerical values of the polar and equatorial flattenings of the level ellipsoids suggest the conclusion that tidal and rotational distortions are responsible for the actual figures of the seven synchronously orbiting satellites.Dedicated to the Memory of Professor Karel P