Mass detection by means of measuring gravity gradients.
Mass detection by measuring gravity gradients with cruciform mass sensor
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Mass detection by measuring gravity gradients with cruciform mass sensor
Repeated absolute gravity measurements have been made at 12 sites in California between 1984.3 and 1989.7. As determined in laboratory tests, the instrument used has an estimated accuracy of 10 microgal (approximately 10 to the -8th g). The repeatability of the measurements is consistent with this accuracy assessment. No gravity changes above the limits set by instrumental uncertainty and environmental noise are observed during this period; the field observations provide upper limits on the rates of secular gravity changes which could be attributed to crustal deformation with a resolution corresponding to vertical displacement rates of 1-2 cm/yr.
This paper addresses the problem of redundant gravity measurements for reduction of measurement errors. The approach exploits constraints imposed upon the components of the gravity gradient tensor by the conditions of integrability needed for reconstruction of the gravity potential. It has been demonstrated that the total error of noisy measurements can be reduced by 25% using the best fit into the integrability constraints.
The gravity at the Apollo 14 landing site has been determined from the accelerometer data that were telemetered from the lunar module. The values for the lunar gravity measured at the Apollo 11, 12, and 14 sites were reduced to a common elevation and were then compared between sites. A theoretical gravity, based on the assumption of a spherical moon, was computed for each landing site and compared with the observed value. The observed gravity was also used to compute the lunar radius at each landing site.
A methodology for improving gravity-gradient measurement data exploits the constraints imposed upon the components of the gravity-gradient tensor by the conditions of integrability needed for reconstruction of the gravitational potential. These constraints are derived from the basic equation for the gravitational potential and from mathematical identities that apply to the gravitational potential and its partial derivatives with respect to spatial coordinates. Consider the gravitational potential in a Cartesian coordinate system {x1,x2,x3}. If one measures all the components of the gravity-gradient tensor at all points of interest within a region of space in which one seeks to characterize the gravitational field, one obtains redundant information. One could utilize the constraints to select a minimum (that is, nonredundant) set of measurements from which the gravitational potential could be reconstructed. Alternatively, one could exploit the redundancy to reduce errors from noisy measurements. A convenient example is that of the selection of a minimum set of measurements to characterize the gravitational field at n3 points (where n is an integer) in a cube. Without the benefit of such a selection, it would be necessary to make 9n3 measurements because the gravitygradient tensor has 9 components at each point. The problem of utilizing the redundancy to reduce errors in noisy measurements is an optimization problem: Given a set of noisy values of the components of the gravity-gradient tensor at the measurement points, one seeks a set of corrected values - a set that is optimum in that it minimizes some measure of error (e.g., the sum of squares of the differences between the corrected and noisy measurement values) while taking account of the fact that the constraints must apply to the exact values. The problem as thus posed leads to a vector equation that can be solved to obtain the corrected values.
Numerical analysis of sensor for mass detection by measuring gravity gradients
We construct long-term time series of Greenland and Antarctic ice sheet mass change from satellite gravity measurements. A statistical reconstruction approach is developed based on a principal component analysis (PCA) to combine high-resolution spatial modes from the Gravity Recovery and Climate Experiment (GRACE) mission with the gravity information from conventional satellite tracking data. Uncertainties of this reconstruction are rigorously assessed; they include temporal limitations for short GRACE measurements, spatial limitations for the low-resolution conventional tracking data measurements, and limitations of the estimated statistical relationships between low- and high-degree potential coefficients reflected in the PCA modes. Trends of mass variations in Greenland and Antarctica are assessed against a number of previous studies. The resulting time series for Greenland show a higher rate of mass loss than other methods before 2000, while the Antarctic ice sheet appears heavily influenced by interannual variations.
This is the Engineering Test Report, AMSU-A2 S/N 108 Weight and Center of Gravity Measurements, for the Integrated Advanced Microwave Sounding Unit-A (AMSU-A).
This is the Engineering Test Report, METSAT AMSU-AL S/N 108 Weight and Center of Gravity Measurements, for the Integrated Advanced Microwave Sounding Unit-A (AMSU- A).
This is the Engineering Test Report, Meteorological Satellites (METSAT) AMSU-A1 S/N 109 Weight and Center of Gravity Measurements, for the Integrated Advanced Microwave Sounding Unit-A (AMSU-A).
Gravity anomaly and lunar radius measurement at Apollo 12 landing site, using data telemetered to earth from surface module
The paper describes the superconducting gravity gradiometers (SGGs) and superconducting accelerometers being developed at the University of Maryland, which take advantage of many exotic properties of superconductivity to obtain the required low noise, high stability, and large dynamic range. Results of laboratory demonstrations of some of these instruments are presented together with the design and operating principles. Particular attention is given to the three-axis Model II SGG and a six-axis superconducting accelerometer model (Model I SSA). Model II SGG, after a residual common-mode balance, exhibited a noise level of 0.05/sq rt Hz above 0.1 Hz and a 1/f-squared noise below 0.1 Hz. All six channels of Model I SSA operated simultaneously with linear and angular acceleration noise levels of 3 x 10 exp -10 g(E)/sq rt Hz and 5 x 10 exp -8 rad/sec per sec per sq rt Hz, respectively.
Position determination on planetary surface from gravity and star line-of-sight direction measurements, presenting numerical results for Apollo lunar landing missions
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Gravity data, believed to be relevant to unknown questions of earthquake premonitory crustal processes, are discussed and presented.
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A laser ranging instrument is being developed to measure the spatial variations in the Earth's gravity field. It will range in space to a cube corner on a passive co-orbiting sub-satellite with a velocity accuracy of 20 to 50 microns/sec by using AlGaAs lasers intensity modulated at 2 GHz.
Future missions to the moon should include a detailed high-resolution global gravity survey from a low (15-30 km) polar orbiting spacecraft. The use of gravity gradiometer instruments on board the spacecraft will give higher-resolution data at lower total mission cost than the present Doppler tracking technique. Simulations show that although a three axis gradiometer system is preferred, and can even be used to estimate spacecraft attitude and altitude variation, a properly oriented single rotating gravity gradiometer can be used to resolve closely spaced mascons in both the along-track and cross-track directions.