Gravity field information from Gravity Probe-B

The Gravity Probe-B Mission will carry the Stanford Gyroscope relativity experiment into orbit in the mid 1990's, as well as a Global Positioning System (GPS) receiver whose tracking data will be used to study the earth gravity field. Estimates of the likely quality of a gravity field model to be derived from the GPS data are presented, and the significance of this experiment to geodesy and geophysics are discussed

Hierarchy of the Selberg zeta functions

We introduce a Selberg type zeta function of two variables which interpolates several higher Selberg zeta functions. The analytic continuation, the functional equation and the determinant expression of this function via the Laplacian on a Riemann surface are obtained.Comment: 14 page

Effect of altered loading conditions during haemodialysis on left ventricular filling pattern

Changes in the circulating volume associated with haemodialysis result in modification of left ventricular loading conditions. To determine the influence of haemodialysis on Doppler indices of left ventricular filling, 12 patients (mean age 40.8 ±2.7 (SEM) years) with renal insufficiency but without overt heart disease were studied by Doppler-echocardiography immediately before and after haemodialysis. Haemodialysis resulted in a decrease in body weight from 68.0±3.8 kg to 65.0 ±3.7 kg (P< 0.01). Heart rate and blood pressure did not change significantly during haemodialysis. Left ventricular diastolic dimension (M-mode) decreased from 53.5±1.1 mm to 49.5±1.9 mm (P < 0.05), whereas the shortening fraction did not change. Haemodialysis elicited marked changes in the early diastolic rapid filling wave (E wave) recorded by pulsed Doppler at the level of the mitral annulus. Peak velocity of the early rapid filling phase (peak E) decreased significantly from 95.3 ± 8.2 cm .s−1 to 63.0 ±5.7cm .s−1 (P< 0.001) and mid-diastolic deceleration of transmitral velocity decreased from 437.3 ±54.2 cm . s−2 to 239.7 ±54.4 cm . s−2 (P<0.01). The peak filling velocity during atrial contraction (peak A) did not change (79.7 ±6.3 cm .s−1 vs 74.1±4.7 cm.s−1;P=NS). The ratio peak E/peak A decreasedfrom 1.19±0.06 to 0.85 ± 0.04 (P < 0.01) during haemodialysis. The results provide further evidence for the pronounced preload-dependence of Doppler indices of left ventricular diastolic functio

The GEM-T2 gravitational model

The GEM-T2 is the latest in a series of Goddard Earth Models of the terrestrial field. It was designed to bring modeling capabilities one step closer towards ultimately determining the TOPEX/Poseidon satellite's radial position to an accuracy of 10-cm RMS (root mean square). It also improves models of the long wavelength geoid to support many oceanographic and geophysical applications. The GEM-T2 extends the spherical harmonic field to include more than 600 coefficients above degree 36 (which was the limit for its predecessor, GEM-T1). Like GEM-T1, it was produced entirely from satellite tracking data, but it now uses nearly twice as many satellites (31 vs. 17), contains four times the number of observations (2.4 million), has twice the number of data arcs (1132), and utilizes precise laser tracking from 11 satellites. The estimation technique for the solution has been augmented to include an optimum data weighting procedure with automatic error calibration for the gravitational parameters. Results for the GEM-T2 error calibration indicate significant improvement over previous satellite-only models. The error of commission in determining the geoid has been reduced from 155 cm in GEM-T1 to 105 cm for GEM-T2 for the 36 x 36 portion of the field, and 141 cm for the entire model. The orbital accuracies achieved using GEM-T2 are likewise improved. Also, the projected radial error on the TOPEX satellite orbit indicates 9.4 cm RMS for GEM-T2, compared to 24.1 cm for GEM-T1

Dynamic sea surface topography, gravity and improved orbit accuracies from the direct evaluation of SEASAT altimeter data

A method for the simultaneous solution of dynamic ocean topography, gravity and orbits using satellite altimeter data is described. A GEM-T1 based gravitational model called PGS-3337 that incorporates Seasat altimetry, surface gravimetry and satellite tracking data has been determined complete to degree and order 50. The altimeter data is utilized as a dynamic observation of the satellite's height above the sea surface with a degree 10 model of dynamic topography being recovered simultaneously with the orbit parameters, gravity and tidal terms in this model. PGS-3337 has a geoid uncertainty of 60 cm root-mean-square (RMS) globally, with the uncertainty over the altimeter tracked ocean being in the 25 cm range. Doppler determined orbits for Seasat, show large improvements, with the sub-30 cm radial accuracies being achieved. When altimeter data is used in orbit determination, radial orbital accuracies of 20 cm are achieved. The RMS of fit to the altimeter data directly gives 30 cm fits for Seasat when using PGS-3337 and its geoid and dynamic topography model. This performance level is two to three times better than that achieved with earlier Goddard earth models (GEM) using the dynamic topography from long-term oceanographic averages. The recovered dynamic topography reveals the global long wavelength circulation of the oceans with a resolution of 1500 km. The power in the dynamic topography recovery is now found to be closer to that of oceanographic studies than for previous satellite solutions. This is attributed primarily to the improved modeling of the geoid which has occurred. Study of the altimeter residuals reveals regions where tidal models are poor and sea state effects are major limitations

Gravitational model improvement at the Goddard Space Flight Center

Major new computations of terrestrial gravitational field models were performed by the Geodynamics Branch of Goddard Space Flight Center (GSFC). This development has incorporated the present state of the art results in satellite geodesy and have relied upon a more consistent set of reference constants than was heretofore utilized in GSFC's GEM models. The solutions are complete in spherical harmonic coefficients out to degree 50 for the gravity field parameters. These models include adjustment for a subset of 66 ocean tidal coefficients for the long wavelength components of 12 major ocean tides. This tidal adjustment was made in the presence of 550 other fixed ocean tidal terms representing 32 major and minor ocean tides and the Wahr frequency dependent solid earth tidal model. In addition 5-day averaged values for Earth rotation and polar motion were derived for the time period of 1980 onward. Two types of models were computed. These are satellite only models relying exclusively on tracking data and combination models which have incorporated satellite altimetry and surface gravity data. The satellite observational data base consists of over 1100 orbital arcs of data on 31 satellites. A large percentage of these observations were provided by third generation laser stations (less than 5 cm). A calibration of the model accuracy of the GEM-T2 satellite only solution indicated that it was a significant improvement over previous models based solely upon tracking data. The rms geoid error for this field is 110 cm to degree and order 36. This is a major advancement over GEM-T1 whose errors were estimated to be 160 cm. An error propagation using the covariances of the GEM-T2 model for the TOPEX radial orbit component indicates that the rms radial errors are expected to be 12 cm. The combination solution, PGS-3337, is a preliminary effort leading to the development of GEM-T3. PGS-3337 has incorporated global sets of surface gravity data and the Seasat altimetry to produce a model complete to (50,50). A solution for the dynamic ocean topography to degree and order 10 was included as part of this adjustment

Wear Behavior of Low-Cost, Lightweight TiC/Ti-6Al-4V Composite Under Fretting: Effectiveness of Solid-Film Lubricant Counterparts

The wear behavior of low-cost, lightweight 10-wt% TiC-particulate-reinforced Ti-6Al-4V matrix composite (TiC/Ti- 6Al-4V) was examined under fretting at 296, 423, and 523 K in air. Bare 10-wt% TiC/Ti-6Al-4V hemispherical pins were used in contact with dispersed multiwalled carbon nanotubes (MWNTs), magnetron-sputtered diamondlike carbon/chromium (DLC/Cr), magnetron-sputtered graphite-like carbon/chromium (GLC/Cr), and magnetron-sputtered molybdenum disulphide/titanium (MoS2/Ti) deposited on Ti-6Al-4V, Ti-48Al-2Cr-2Nb, and nickel-based superalloy 718. When TiC/Ti-6Al-4V was brought into contact with bare Ti-6Al-4V, bare Ti-48Al-2Cr-2Nb, and bare nickel-based superalloy 718, strong adhesion, severe galling, and severe wear occurred. However, when TiC/Ti-6Al-4V was brought into contact with MWNT, DLC/Cr, GLC/Cr, and MoS2/Ti coatings, no galling occurred in the contact, and relatively minor wear was observed regardless of the coating. All the solid-film lubricants were effective from 296 to 523 K, but the effectiveness of the MWNT, DLC/Cr, GLC/Cr, and MoS2/Ti coatings decreased as temperature increased

Conservative evaluation of the uncertainty in the LAGEOS-LAGEOS II Lense-Thirring test

We deal with the test of the general relativistic gravitomagnetic Lense-Thirring effect currently ongoing in the Earth's gravitational field with the combined nodes \Omega of the laser-ranged geodetic satellites LAGEOS and LAGEOS II. One of the most important source of systematic uncertainty on the orbits of the LAGEOS satellites, with respect to the Lense-Thirring signature, is the bias due to the even zonal harmonic coefficients J_L of the multipolar expansion of the Earth's geopotential which account for the departures from sphericity of the terrestrial gravitational potential induced by the centrifugal effects of its diurnal rotation. The issue addressed here is: are the so far published evaluations of such a systematic error reliable and realistic? The answer is negative. Indeed, if the difference \Delta J_L among the even zonals estimated in different global solutions (EIGEN-GRACE02S, EIGEN-CG03C, GGM02S, GGM03S, ITG-Grace02, ITG-Grace03s, JEM01-RL03B, EGM2008, AIUB-GRACE01S) is assumed for the uncertainties \delta J_L instead of using their more or less calibrated covariance sigmas \sigma_{J_L}, it turns out that the systematic error \delta\mu in the Lense-Thirring measurement is about 3 to 4 times larger than in the evaluations so far published based on the use of the sigmas of one model at a time separately, amounting up to 37% for the pair EIGEN-GRACE02S/ITG-Grace03s. The comparison among the other recent GRACE-based models yields bias as large as about 25-30%. The major discrepancies still occur for J_4, J_6 and J_8, which are just the zonals the combined LAGEOS/LAGOES II nodes are most sensitive to.Comment: LaTex, 12 pages, 12 tables, no figures, 64 references. To appear in Central European Journal of Physics (CEJP