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Spaceborne Gravity Gradiometers. Part 2: Role of gravity gradiometers in NASA's programs

Sources of information for present knowledge of Earth's gravitational field are discussed as well as the Goddard Earth models. Improvements to these models can be achieved by using additional data and reprocessing some earlier data. Plans for using satellite-to-satellite tracking and gravity gradiometers for the geopotential research mission are considered as well as the relative merits of each method. Present knowledge of solar system bodies and strategies for their exploration are also described. A core program for planetary exploration through the year 2000 is summarized as well as ten candidate subsequent missions. Of these, the lunar geoscience orbiter has the best justification for a gravity gradiometer since far side gravity data can be acquired without the requirement for a separate communications relay satellite. For rendezvous missions, the gradiometer can permit on-board automation of orbit computation and control thus reducing the time devoted to communication with an orbiter.

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Research relative to the development of a cryogenic microwave cavity gradiometer for orbital use

The noncryogenic, single axis, gravity gradiometer which is characterized by a sensitivity of the order of 10 to the minus 2 power Eovos Units in a few sec integration time was investigated. The prototype of testing gradiometer on the earth surface by the free fall in vacuo method was expanded. An existing free fall tower facility and the possibility of adding inside the falling elevator cabin an air tight, sealed, cylindrical container with inside pressure or = -0.001 Torr were examined to test the gradiometer in free fall conditions inside this evacuated container. Earth's gravity anomalies are simulated with masses of suitable shape, weight, and location. The attitude of the falling gradiometer is monitored by a three axis gyro package mounted on the instrument package. It is concluded that the free fall testing of the gradiometer is both feasible and practical.

Grossi, M. D.

A Transportable Gravity Gradiometer Based on Atom Interferometry

A transportable atom interferometer-based gravity gradiometer has been developed at JPL to carry out measurements of Earth's gravity field at ever finer spatial resolutions, and to facilitate high-resolution monitoring of temporal variations in the gravity field from ground- and flight-based platforms. Existing satellite-based gravity missions such as CHAMP and GRACE measure the gravity field via precise monitoring of the motion of the satellites; i.e. the satellites themselves function as test masses. JPL's quantum gravity gradiometer employs a quantum phase measurement technique, similar to that employed in atomic clocks, made possible by recent advances in laser cooling and manipulation of atoms. This measurement technique is based on atomwave interferometry, and individual laser-cooled atoms are used as drag-free test masses. The quantum gravity gradiometer employs two identical atom interferometers as precision accelerometers to measure the difference in gravitational acceleration between two points (Figure 1). By using the same lasers for the manipulation of atoms in both interferometers, the accelerometers have a common reference frame and non-inertial accelerations are effectively rejected as common mode noise in the differential measurement of the gravity gradient. As a result, the dual atom interferometer-based gravity gradiometer allows gravity measurements on a moving platform, while achieving the same long-term stability of the best atomic clocks. In the laboratory-based prototype (Figure 2), the cesium atoms used in each atom interferometer are initially collected and cooled in two separate magneto-optic traps (MOTs). Each MOT, consisting of three orthogonal pairs of counter-propagating laser beams centered on a quadrupole magnetic field, collects up to 10(exp 9) atoms. These atoms are then launched vertically as in an atom fountain by switching off the magnetic field and introducing a slight frequency shift between pairs of lasers to create a moving rest frame for the trapped atoms. While still in this moving-frame molasses, the laser frequencies are further detuned from the atomic resonance (while maintaining this relative frequency shift) to cool the atom cloud's temperature to 2 K or below, corresponding to an rms velocity of less than 2 cm/s. After launch, the cold atoms undergo further state and velocity selection to prepare for atom interferometry. The atom interferometers are then realized using laser-induced stimulated Raman transitions to perform the necessary manipulations of each atom, and the resulting interferometer phase is measured using laser-induced fluorescence for state-normalized detection. More than 20 laser beams with independent controls of frequency, phase, and intensity are required for this measurement sequence. This instrument can facilitate the study of Earth's gravitational field from surface and air vehicles, as well as from space by allowing gravity mapping from a low-cost, single spacecraft mission. In addition, the operation of atom interferometer-based instruments in space offers greater sensitivity than is possible in terrestrial instruments due to the much longer interrogation times available in the microgravity environment. A space-based quantum gravity gradiometer has the potential to achieve sensitivities similar to the GRACE mission at long spatial wavelengths, and will also have resolution similar to GOCE for measurement at shorter length scales.

Yu, Nan

Satellite borne gravity gradiometer study

Gravity gradiometry is recognized to be a very difficult instrumentation problem because extremely small differential acceleration levels have to be measured, 0.1 EU corresponds to an acceleration of 10 to the minus 11th power g at two points 1 meter apart. A feasibility model of a gravity gradiometer is being developed for airborne applications using four modified versions of the proven Model VII accelerometers mounted on a slowly rotating fixture. Gravity gradients are being measured to 1.07 EU in a vertical rotation axis orientation. Equally significant are the outstanding operational characteristics such as fast reaction time, low temperature coefficients and high degree of bias stability over long periods of time. The rotating accelerometer gravity gradiometer approach and its present status is discussed and it is the foundation for the orbital gravity gradiometer analyzed. The performance levels achieved in a 1 g environment of the earth and under relatively high seismic disturbances, lend the orbital gravity gradiometer a high confidence level of success.

Metzger, E.

Superconducting tensor gravity gradiometer for satellite geodesy and inertial navigation

A sensitive gravity gradiometer can provide much needed gravity data of the earth and improve the accuracy of inertial navigation. Superconductivity and other properties of materials at low temperatures can be used to obtain a sensitive, low-drift gravity gradiometer; by differencing the outputs of accelerometer pairs using superconducting circuits, it is possible to construct a tensor gravity gradiometer which measures all the in-line and cross components of the tensor simultaneously. Additional superconducting circuits can be provided to determine the linear and angular acceleration vectors. A tensor gravity gradiometer with these features is being developed for satellite geodesy. The device constitutes a complete package of inertial navigation instruments with angular and linear acceleration readouts as well as gravity signals.

Paik, H. J.

Spaceborne Gravity Gradiometers. Part 3: Instrument status and prospects

Various technologies incorporated in the development of gravity gradiometers are demonstrated through descriptions of specific instruments. Concepts covered include: rotating, spherical, cryogenic, and superconducting gravity gradiometers with and without accelerometers. The application of superconducting cavity oscillators to mass-spring gradiometers, and cooperation of Italy's Piano Spaziale Nazionale with the Smithsonian Astrophysics Observatory in the design and development of a high sensitivity gradiometer are described. Schematics are provided for each instrument.

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Geodesy and gravity experiment in earth orbit using a superconducting gravity gradiometer

A superconducting gravity gradiometer is under development with NASA support for space application. It is planned that a sensitive three-axis gravity gradiometer will be flown in a low-altitude (about 160 km) polar orbit in the 1990's for the purpose of obtaining a high-resolution gravity map of the earth. The large twice-an-orbit term in the harmonic expansion of gravity coming from the oblateness of the earth can be analyzed to obtain a precision test of the inverse square law at a distance of 100-1000 km. In this paper, the design, operating principle, and performance of the superconducting gravity gradiometer are described. The concept of a gravity-gradiometer mission (GGM), which is in an initial stage of development is discussed. In particular, requirements that such a mission imposes on the design of the cryogenic spacecraft will be addressed.

Paik, H. J.

Error analyses for a gravity gradiometer mission

This paper addresses the usefulness of an orbiting gravity gradiometer as a sensor for mapping the fine structure of the earth gravity field. The exact knowledge of this field is essential for studies of the solid earth and the dynamics of the oceans. Although the earth gravity tensor, measured by a gradiometer assembly, has nine components, only five components are independent. This latter fact is as a consequence of the symmetry and conservative nature of the earth's gravity field. The most dominant component is the radial one. The error analyses considered here are therefore based only upon a single axis gradiometer sensing this radial component. The expected global gravity and geoid errors for a 50 x 50-km (1/2 x 1/2 deg) area utilizing a spaceborne gradiometer with a precision of 0.001 EU in a 160-km circular polar orbit are about 3 mGAL and 5 cm, respectively.

Kahn, W. D.

Development of a sensitive superconducting gravity gradiometer for geological and navigational applications

A sensitive and stable gravity gradiometer would provide high resolution gravity measurements from space. The instrument could also provide precision tests of fundamental laws of physics and be applied to inertial guidance systems of the future. This report describes research on the superconducting gravity gradiometer program at the University of Maryland from July 1980 to July 1985. The report describes the theoretical and experimental work on a prototype superconducting gravity gradiometer. The design of an advanced three-axis superconducting gravity gradiometer is also discussed.

Paik, H. J.

Superconducting gravity gradiometer for space and terrestrial applications

A three-axis superconducting gravity gradiometer with a potential sensitivity better than Eotvos per sq root Hz is currently under development for applications in space. Although such a high sensitivity may be needed for only a limited number of terrestrial applications, superconductivity offers many extraordinary effects which can be used to obtain a gravity gradiometer with other characteristics necessary for operation in a hostile moving-base environment. Utilizing a number of recently devised techniques which rely on certain properties of superconductors, a design for a sensitive yet rugged gravity gradiometer with a high degree of stability and a common-mode rejection ratio greater than 10 to the 9th is produced. With a base line of 0.11 m, a sensitivity of 0.1 Eotvos per sq root Hz is expected in an environment monitored to a level of 0.01 m/sq sec sq root Hz for linear vibration and 7 x 10 to the -6th rad/s sq root Hz for angular vibration. A conventional stabilized platform can be used at this level. The intrinsic noise level, which is two orders of magnitude lower, could be achieved by monitoring the attitude with a superconducting angular accelerometer which is under development. In addition, the new gradiometer design has the versatility of adapting the instrument to different gravity biases by adjusting stored dc currents.

Moody, M. V.

Geopotential Error Analysis from Satellite Gradiometer and Global Positioning System Observables on Parallel Architecture

The recovery of a high resolution geopotential from satellite gradiometer observations motivates the examination of high performance computational techniques. The primary subject matter addresses specifically the use of satellite gradiometer and GPS observations to form and invert the normal matrix associated with a large degree and order geopotential solution. Memory resident and out-of-core parallel linear algebra techniques along with data parallel batch algorithms form the foundation of the least squares application structure. A secondary topic includes the adoption of object oriented programming techniques to enhance modularity and reusability of code. Applications implementing the parallel and object oriented methods successfully calculate the degree variance for a degree and order 110 geopotential solution on 32 processors of the Cray T3E. The memory resident gradiometer application exhibits an overall application performance of 5.4 Gflops, and the out-of-core linear solver exhibits an overall performance of 2.4 Gflops. The combination solution derived from a sun synchronous gradiometer orbit produce average geoid height variances of 17 millimeters.

Schutz, Bob E.

Progress towards a space-borne quantum gravity gradiometer

Quantum interferometer gravity gradiometer for 3D mapping is a project for developing the technology of atom interferometer-based gravity sensor in space. The atom interferometer utilizes atomic particles as free fall test masses to measure inertial forces with unprecedented sensitivity and precision. It also allows measurements of the gravity gradient tensor components for 3D mapping of subsurface mass distribution. The overall approach is based on recent advances of laser cooling and manipulation of atoms in atomic and optical physics. Atom interferometers have been demonstrated in research laboratories for gravity and gravity gradient measurements. In this approach, atoms are first laser cooled to micro-kelvin temperatures. Then they are allowed to freefall in vacuum as true drag-free test masses. During the free fall, a sequence of laser pulses is used to split and recombine the atom waves to realize the interferometric measurements. We have demonstrated atom interferometer operation in the Phase I period, and we are implementing the second generation for a complete gradiometer demonstration unit in the laboratory. Along with this development, we are developing technologies at component levels that will be more suited for realization of a space instrument. We will present an update of these developments and discuss the future directions of the quantum gravity gradiometer project.

laser cooling

A proposed lunar orbiting gravity gradiometer experiment.

Analysis of the gravity gradiometer developed by Forward and Bell (1970) suggest that an accuracy, in the range 0.1 to 0.5 EU can be expected in a lunar orbiter application. This accuracy will allow gradient anomalies associated with mascons to be mapped with 1% accuracy and should reveal a great deal of new information about the lunar gravity field. The proposed experiment calls for putting such a gradiometer into a closely circular polar orbit at an average height of about 30 km above the lunar surface. This orbit allows the entire lunar surface to be covered in fourteen days, the gradiometer to be checked twice per revolution and results in successive passes above the lunar surface being spaced at about the resolution limit of about 30 km set both by the satellite altitude and instrumental integration time.

Debra, D. B.

Simulation of a lunar gradiometer mission

A lunar gradiometer mission involves the mounting of a gradiometer on a satellite which is in a low, polar, and circular lunar orbit. The results of a numerical simulation of the mission is presented. It is shown that if the satellite is in a 50 km orbit, 1 deg and 2 deg gravity anomalies may be estimated with accuracies of 12 mgal and 1 mgal respectively. At a 100 km altitude, 2 deg gravity anomalies can be estimated with an accuracy of 12 mgal. These results assume a rotating type gradiometer with a .1E accuracy. The results can be readily scaled to reflect another level.

Argentiero, P. D.

A spacecraft-borne gradiometer mission analysis

Numerical simulations were performed to obtain the orbit- and attitude-determination requirements of a spacecraft-borne gradiometer mission. Results demonstrated that position determination of 300 meters in the along-track and cross-track directions and 50 meters in the radial direction are mission requirements. The optimal orientation of the gradiometer sensing plane is achieved when the spin vector elevation is 0 degrees. The attitude-determination requirements are 5 degrees resolution for spin-vector azimuth and 0.2 degree resolution for spin-vector elevation. When these requirements are met, 3-degree gravity anomalies can be recovered globally with an accuracy of 0.025/mm/sq s (2.5 mgals). The Appendix documents the mathematical procedures for estimating detailed gravity fields from gradiometer data.

Argentiero, P.

On estimating gravity anomalies from gradiometer data

The Gravsat-gradiometer mission involves flying a gradiometer on a gravity satellite (Gravsat) which is in a low, polar, and circular orbit. Results are presented of a numerical simulation of the mission which demonstrates that, if the satellite is in a 250-km orbit, 3- and 5-degree gravity anomalies may be estimated with accuracies of 0.03 and 0.01 mm/square second (3 and 1 mgal), respectively. At an altitude of 350 km, the results are 0.07 and 0.025 mm.square second (7 and 2.5 mgal), respectively. These results assume a rotating type gradiometer with a 0.1 -etvos unit accuracy. The results can readily be scaled to reflect another accuracy level.

Argentiero, P.

Study to develop gradiometer techniques

The primary goal of the current gravity gradiometer research at Stanford has been to establish the feasibility of using a gravity gradiometer with 1 E accuracy, as the primary sensor in various applications. The two applications considered here in detail are geodesy missions and inertial navigation systems. Preliminary sections on gravity models and gravity gradiometer bias estimation are also included.

Schaechter, D.

Measurement of solar gravitational oblateness with gravity gradiometers

A very high sensitivity rotating gravity gradiometer onboard the spacecraft is described for measuring the gravitational oblateness of the Sun during a solar probe mission. The proposed instrument would be a self-contained structure in a thermal-vacuum-magnetic shield in the shape of a cross, with a mass of 20 kg and arm length of 1.0 m and thickness of 0.1 m. The sensor inside would have a resonant frequency of 1/30 Hz, a mechanical Q of one million and would use gravitational radiation antenna technology to achieve a sensitivity of 6 x 10 to the minus 8th power Eotvos, which would provide a measurement of the solar oblateness to an accuracy of 1.5 to 6 x 10 to the minus 8th power. The gravity gradiometer will require a spinning spacecraft, so that it will not sense the spacecraft gravity fields, but the gradiometer does not need to be at the spacecraft center of mass, or even on the spacecraft spin axis. Major problem areas to be addressed are demonstration of the instrument sensitivity prior to flight and the measurement and compensation for any residual spacecraft angular rates.

Forward, R. L.