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Analysis of Global Positioning System (GPS) data from two sites separated by a horizontal distance of only ∼2.2 m yielded phase residuals exhibiting a systematic elevation angle dependence. One of the two GPS antennas was mounted on an ∼1‐m‐high concrete pillar, and the other was mounted on a standard wooden tripod. We performed elevation angle cutoff tests with these data and established that the estimate of the vertical coordinate of site position was sensitive to the minimum elevation angle (elevation cutoff) of the data analyzed. For example, the estimate of the vertical coordinate of site position changed by 9.7±0.8 mm when the minimum elevation angle was increased from 10° to 25°. We performed simulations based on a simple (ray tracing) multipath model with a single horizontal reflector which demonstrated that the results from the elevation angle cutoff tests and the pattern of the residuals versus elevation angle could be qualitatively reproduced if the reflector were located 0.1–0.2 m beneath the antenna phase center. We therefore hypothesized that the elevation‐angle‐dependent error was caused by scattering from the horizontal surface of the pillar, located a distance of ∼0.2 m beneath the antenna phase center. We tested this hypothesis by placing microwave absorbing material between the antenna and the pillar in a number of configurations and by analyzing the changes in apparent position of the antenna. The results indicate that (1) the horizontal surface of the pillar is indeed the main scatterer, (2) both the concrete and the metal plate embedded in the pillar are significant sources of scattering, and (3) the scattering can be reduced greatly by the use of microwave absorbing materials. These results have significant implications for the accuracy of global GPS geodetic tracking networks which use pillar‐antenna configurations identical or similar to the one used for this study at the Westford WFRD GPS site.

An important source of error in very‐long‐baseline interferometry (VLBI) estimates of baseline length is unmodeled variations of the refractivity of the neutral atmosphere along the propagation path of the radio signals. We present and discuss the method of using data from a water vapor radiometer (WVR) to correct for the propagation delay caused by atmospheric water vapor, the major cause of these variations. Data from different WVRs are compared with estimated propagation delays obtained by Kalman filtering of the VLBI data themselves. The consequences of using either WVR data or Kalman filtering to correct for atmospheric propagation delay at the Onsala VLBI site are investigated by studying the repeatability of estimated baseline lengths from Onsala to several other sites. The lengths of the baselines range from 919 to 7941 km. The repeatability obtained for baseline length estimates shows that the methods of water vapor radiometry and Kalman filtering offer comparable accuracies when applied to VLBI observations obtained in the climate of the Swedish west coast. For the most frequently measured baseline in this study, the use of WVR data yielded a 13% smaller weighted‐root‐mean‐square (WRMS) scatter of the baseline length estimates compared to the use of a Kalman filter. It is also clear that the “best” minimum elevation angle for VLBI observations depends on the accuracy of the determinations of the total propagation delay to be used, since the error in this delay increases with increasing air mass. For use of WVR data along with accurate determinations of total surface pressure, the best minimum is about 20°; for use of a model for the wet delay based on the humidity and temperature at the ground, the best minimum is about 35°.

We studied the growth of the shell-like radio structure of supernova SN 1993J in M 81 from September 1993 to October 2003 with very-long-baseline interferometry (VLBI) observations at the wavelengths of 3.6, 6, and 18 cm. We developed a method to accurately determine the outer radius (R) of any circularly symmetric compact radio structure such as SN 1993J. The source structure of SN 1993J remains circularly symmetric (with deviations from circularity under 2%) over almost 4000 days. We characterize the decelerated expansion of SN 1993J until approximately day 1500 after explosion with an expansion parameter m = 0.845 ± 0.005 (R ∝ t m ). However, from that day onwards the expansion differs when observed at 6 and 18 cm. Indeed, at 18 cm, the expansion can be well characterized by the same m as before day 1500, while at 6 cm the expansion appears more decelerated, and is characterized by another expansion parameter, m 6 = 0.788 ± 0.015. Therefore, since about day 1500 onwards, the radio source size has been progressively smaller at 6 cm than at 18 cm. These findings differ significantly from those of other authors in the details of the expansion. In our interpretation, the supernova expands with a single expansion parameter, m = 0.845 ± 0.005, and the 6 cm results beyond day 1500 are caused by physical effects, perhaps also coupled to instrumental limitations. Two physical effects may be involved: (a) a changing opacity of the ejecta to the 6 cm radiation; and (b) a radial decrease of the magnetic field in the emitting region. We also found that at 6 cm about 80% of the radio emission from the backside of the shell behind the ejecta is absorbed (our average estimate, since we cannot determine any possible evolution of the opacity), and the width of the radio shell is (31 ± 2)% of the outer radius. The shell width at 18 cm depends on the degree of assumed absorption. For 80% absorption, the width is (33.5 ± 1.7)%, and for 100% absorption, it is (37.8 ± 1.3)%. A comparison of our VLBI results with optical spectral line velocities shows that the deceleration is more pronounced in the radio than in the optical. This difference might be due to a progressive penetration of ejecta instabilities into the shocked circumstellar medium, as also suggested by other authors.

The Gravity Probe B mission provided two new quantitative tests of Einstein’s theory of gravity, general relativity (GR), by cryogenic gyroscopes in Earth’s orbit. Data from four gyroscopes gave a geodetic drift-rate of −6601.8 ± 18.3 marc-s yr−1 and a frame-dragging of −37.2 ± 7.2 marc-s yr−1, to be compared with GR predictions of −6606.1 and −39.2 marc-s yr−1 (1 marc-s = 4.848 × 10−9 radians). The present paper introduces the science, engineering, data analysis, and heritage of Gravity Probe B, detailed in the accompanying 20 CQG papers.

Source and a laser-heating system s~milar to one reported prevousy [C S. Yooetal , Phys. Rev B 48. 15529 (1993)l The x-ray beam slze, 20 k m by 20 k m , was comparable to the slze of laser-heat~ng spot, which varied from 30 to 100 k m , dependng on the temperature (For the later pari of ths study, we reduced the sze of x-ray beam to 5 I l m by 20 k m by focusng the 75 I l m by 20 krn beam n the vertcal drecton with an x-ray focusng reflector ) Therefore. the temperature gradents could be large n both the r a d a and axal directons of the sample beng xrayed, we estmated that t h s could be as much as 103k of the value repolted here The x-ray dffracton of Iron was collected at 2 0 = 19' or 21 ' for 1 to 10 min to obtan the spectra presented here The microscope system contans an achromatc objective lens that can cause some chromatic abberat~on and thereby, the uncertanty in temperature Ths uncertanty could be significant n the case where the temperature IS measured from a heat~ng spot smaller than a few to several mcrometers However, consderlng the relat~vely large heating spot used n t h s study, we estmate that t 1s a mnor effect The det a s regardng the setup w I be presented elsewhere [C S Yoo e? a/ , in preparaton]. 16. H. K Mao e? a/ , J k p p l Phys. 49, 3276 (1 978). 17 A P Jephcoat, R J Hemey, H K Mao, Physica B 150, 1 15 (1 988) 18 The d spacng of the new diffraction line, 2.229 A.