Superconducting Gravity Gradiometer Research Articles

Predicted performance of the superconducting gravity gradiometer on the Space Shuttle

A high-resolution global gravity map would provide tremendous benefits to the Earth sciences. Mapping the lateral fluctuations of a planet's gravity field is one of the few means of probing its interior. For the Earth, a high-resolution gravity map would also reveal dynamic ocean current information presently hidden in existing sea surface height data. The use of gradiometers for gravity mapping has inherent advantages over other techniques and has the potential of providing the highest spatial resolution for global surveys from orbit. Extremely sensitive superconducting gravity gradiometers (SGGs) have been developed for space applications under NASA support. The present laboratory model has demonstrated a sensitivity almost two orders of magnitude better than any other gradiometer (< 20 mE Hz −1 2 , where 1 mE ≡ 10 −12 m s −2 m −1 ≈ 10 −13 g E m −1). In preparation for a dedicated gravity mapping mission, we have proposed a flight test of a spaceworthy version of the instrument in the SHOOT (Superfluid Helium On Orbit Transfer) dewars, which flew on the Shuttle in 1993. We have examined potential error sources for the instrument operating in the Shuttle environment. Of the largest error sources, most are motion-related. We obtained the motion of the Orbiter in six degrees of freedom (d.o.f.) by examining the SAMS (shuttle acceleration measurement system) and the CAS (calibrated ancillary system) data sets. Using this information and the measured error coupling coefficients of the laboratory SGG, we can predict the resolution with which the Earth's gravity gradient signal can be recovered on this Shuttle test flight. Although the Orbiter provides a much worse environment for the SGG than a dedicated satellite, our analysis shows that during quiet periods on the Orbiter, the ability to recover gravity data will approach the limit imposed by the instrument thermal noise.

Superconducting accelerometry: its principles and applications

After giving a brief historical review of their technological development, we discuss the principle of a superconducting accelerometer. We then expand into the design and optimization of various specialized accelerometers: superconducting gravity gradiometers and a superconducting six-axis accelerometer. We report the performance of these devices. Finally, we discuss how the superconducting accelerometer techniques are applied to various differential accelerometers in proposed space missions.

Null test of the inverse-square law of gravity

A differential equivalent of the inverse-square force law is Gauss's law for the field, , where . Thus, by summing the outputs of an in-line gravity gradiometer rotated in three orthogonal directions, one can perform a near-null test of the inverse-square law. The primary advantage of this type of experiment is its reduced sensitivity to the density and metrology errors of the source. We have developed a three-axis superconducting gravity gradiometer and carried out such a test using a lead (Pb) pendulum to produce a time-varying field. This experiment places a new () limit of at , where and are parameters of the generalized potential . This result represents an improvement of an order of magnitude over the best existing limit at . To achieve further improvement in the resolution of with the present instrument, a near-null source is needed. We plan to carry out an improved test of the inverse-square law using a long cylindrical shell as the source. Looking farther into the future, we hope to be able to conduct a geological-scale null experiment by moving the gradiometer up and down a tower above a plain.

Performance of a superconducting gravity gradiometer

We report the laboratory operation of an rf SQUID-based superconducting gravity gradiometer designed to measure from an aircraft, off-diagonal components of the earth's gravity gradient tensor. A detailed numerical model of the multi-mode electromechanical system shows excellent agreement with the experimental observations. We have demonstrated a common mode rejection ratio to linear accelerations of 180dB, as well as 60dB of active thermal compensation below 0.01Hz. Short term measurements show the instrument to be SQUID noise limited at 0.5Eo¨/√Hz in a frequency band from 50mHz to 1Hz. After correcting for the remaining effects of thermal fluctuations and flux creep the noise below 50mHz has a 1/f characteristic which is also dominated by the SQUID.

Gauss's law test of gravity at short range.

A null test of the gravitational inverse-square law can be performed by testing Gauss's law for the field. We have constructed a three-axis superconducting gravity gradiometer and carried out such a test. A lead pendulum weighing 1500 kg was used to produce a time-varying field. This experiment places a new (2-sigma) limit of alpha = (0.9 + or - 4.6) x 10 exp -4 at lambda of 1.5 m, where alpha and lambda are parameters for the generalized potential phi = -(GM/r)(l + alpha e exp -r/lambda).

Gravity gradiometer with coupled superconducting suspensions

The analysis of superconducting suspensions and SQUID- and cavity resonator-based superconducting gravity gradiometers on their basis have been carried out. In the gravity gradiometers designed to operate on a movable base it was found advantageous to use the suspensions with in-series connected superconducting coils. The simple sensitivity equations for SCGG have been deduced. The theoretical and experimental studies have shown that application of coupled suspensions allows to increase the SCGG sensitivity and dynamic range and to decrease the disturbance signal introduced by nonidentity of suspensions.

Laboratory tests of a mobile superconducting gravity gradiometer

We describe a gravity gradiometer designed to measure off-diagonal components of the earth's gravity gradient tensor, and intended for airborne geophysical exploration. The instrument consists of an orthogonal pair of mass quadrupoles pivoted about a common vertical axis. Each quadrupole is a rectangular bar of niobium having square cross section and with integrally machined flexural micro-pivots. Superconducting niobium pancake coils form the basis of the SQUID based transducers and provide supplementary magnetic springs to enable matching of mechanical parameters.

Laboratory tests of a mobile superconducting gravity gradiometer

Laboratory tests of a mobile superconducting gravity gradiometer

Detection of the gravitomagnetic field using an orbiting superconducting gravity gradiometer. Theoretical principles.

The angular momentum of the Earth produces gravitomagnetic components of the Riemann curvature tensor, which are of the order of ${10}^{\mathrm{\ensuremath{-}}10}$ of the Newtonian tidal terms arising from the mass of the Earth. These components could be detected in principle by sensitive superconducting gravity gradiometers currently under development. We lay out the theoretical principles of such an experiment by using the parametrized post-Newtonian formalism to derive the locally measured Riemann tensor in an orbiting proper reference frame, in a class of metric theories of gravity that includes general relativity. A gradiometer assembly consisting of three gradiometers with axes at mutually right angles measures three diagonal components of a 3\ifmmode\times\else\texttimes\fi{}3 ``tidal tensor,'' related to the Riemann tensor. We find that, by choosing a particular assembly orientation relative to the orbit and taking a sum and difference of two of the three gradiometer outputs, one can isolate the gravitomagnetic relativistic effect from the large Newtonian background.

Tests of general relativity in earth orbit using a superconducting gravity gradiometer

According to general relativity, the gravitational field is fully described by the Riemann curvature tensor. The Riemann tensor near the Earth has two components, one arising from the mass of the Earth (Schwarzschild term) and the other from the angular momentum of the Earth (Lense-Thirring term). A sensitive three-axis superconducting gravity gradiometer in a polar orbit could detect both of these terms. Two interesting space experiments are discussed in this paper. First, the tracelessness of the Riemann tensor, which represents a relativistic generalization of the inverse square law, could be tested by summing the three outputs of the gradiometer. This experiment would also constitute a very sensitive search for a new feeble force. Second, the Lense-Thirring term, which is caused by the gravitational analog of the magnetic field, could be separated from the large Newtonian background by its frequency characteristic and its unique symmetry property. We discuss the principles of these experiments, and derive the instrument, spacecraft, and orbit requirements imposed by such experiments.

Global gravity survey by an orbiting gravity gradiometer

Three dedicated space missions proposed for the 1990s promise to provide data for recovering the Earth's gravity anomaly with unprecedented accuracy and resolution: the Geopotential Research Mission (GRM), the Aristoteles Mission, and the Superconducting Gravity Gradiometer Mission (SGGM). SGGM, the most ambitious of the three, aims at recovering the global gravity field to a precision of 2–3 mGal with a resolution of 50 km. Such accuracy and resolution are required to answer many key questions in geophysics. The SGGM instrument package is a three‐axis superconducting gravity gradiometer which is integrated with a six‐axis superconducting accelerometer and a six‐axis shaker for active platform control. The intrinsic sensitivity of the gradiometer is 10−4 E Hz−½ (where E represents the unit of gravity gradient (1 E = 1 Eötvös = 10−9 s−2)) and that of the accelerometer is 10−13 gE Hz −½ in linear acceleration and 10−11 rad s−2 Hz−½ in angular acceleration. While precise attitude control of the Experiment Module is essential to mission success and is also technically the most challenging, pointing accuracy and disturbance isolation requirements of SGGM are less stringent compared to that of other missions such as the Hubble Space Telescope (HST) and Gravity Probe‐B (GP‐B). Thus they are within the reach of technologies of the 1990s. In the recently completed Phase A study, the SGGM Study Team addressed the problem of scientific requirements and mission feasibility. Marshall Space Flight Center is continuing with mission and spacecraft design, while mission simulation is being done at Goddard Space Flight Center, Greenbelt, Md. At the University of Maryland, prototypes of the three‐axis gradiometer and the six‐axis accelerometer are being fabricated, improved, and tested. A Shuttle flight test of the Experiment Module with the actual instrument package is suggested for 1994–1995. The full science mission hopefully will take place before the year 2000.

Superconducting gravity gradiometer for sensitive gravity measurements. II. Experiment.

A sensitive superconducting gravity gradiometer has been constructed and tested. Coupling to gravity signals is obtained by having two superconducting proof masses modulate magnetic fields produced by persistent currents. The induced electrical currents are differenced by a passive superconducting circuit coupled to a superconducting quantum interference device. The experimental behavior of this device has been shown to follow the theoretical model closely in both signal transfer and noise characteristics. While its intrinsic noise level is shown to be 0.07 E ${\mathrm{Hz}}^{\ensuremath{-}\mathrm{\textonehalf{}}}$ (1 E\ensuremath{\equiv}${10}^{\ensuremath{-}9}$ ${\mathrm{sec}}^{\ensuremath{-}2}$), the actual performance of the gravity gradiometer on a passive platform has been limited to 0.3-0.7 E ${\mathrm{Hz}}^{\ensuremath{-}\mathrm{\textonehalf{}}}$ due to its coupling to the environmental noise. The detailed structure of this excess noise is understood in terms of an analytical error model of the instrument. The calibration of the gradiometer has been obtained by two independent methods: by applying a linear acceleration and a gravity signal in two different operational modes of the instrument. This device has been successfully operated as a detector in a new null experiment for the gravitational inverse-square law. In this paper we report the design, fabrication, and detailed test results of the superconducting gravity gradiometer. We also present additional theoretical analyses which predict the specific dynamic behavior of the gradiometer and of the test.

Superconducting gravity gradiometer for sensitive gravity measurements. I. Theory.

Because of the equivalence principle, a global measurement is necessary to distinguish gravity from acceleration of the reference frame. A gravity gradiometer is therefore an essential instrument needed for precision tests of gravity laws and for applications in gravity survey and inertial navigation. Superconductivity and SQUID (superconducting quantum interference device) technology can be used to obtain a gravity gradiometer with very high sensitivity and stability. A superconducting gravity gradiometer has been developed for a null test of the gravitational inverse-square law and space-borne geodesy. Here we present a complete theoretical model of this instrument. Starting from dynamical equations for the device, we derive transfer functions, a common mode rejection characteristic, and an error model of the superconducting instrument. Since a gradiometer must detect a very weak differential gravity signal in the midst of large platform accelerations and other environmental disturbances, the scale factor and common mode rejection stability of the instrument are extremely important in addition to its immunity to temperature and electromagnetic fluctuations. We show how flux quantization, the Meissner effect, and properties of liquid helium can be utilized to meet these challenges.

Superconducting gravity gradiometer for space and terrestrial applications

A three-axis superconducting gravity gradiometer with a potential sensitivity better than 10−3 Eötvös Hz−1/2 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, we have produced a design for a sensitive yet rugged gravity gradiometer with a high degree of stability and a common-mode rejection ratio greater than 109. With a base line of 0.11 m, a sensitivity of 0.1 Eötvös Hz−1/2 is expected in an environment monitored to a level of 10−2 m s−2 Hz−1/2 for linear vibration and 7×10−6 rad s−1 Hz−1/2 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.

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 (~ 160-km) polar orbit in the 1990's for the purpose of obtaining a highresolution 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 100 ~ 1000-km distance. In this paper, we describe the design, operating principle, and performance of the superconducting gravity gradiometer. We discuss the concept of a gravity-gradiometer mission (GGM), which is in an initial stage of development. In particular, requirements that such a mission imposes on the design of the cryogenic spacecraft will be addressed.

Preliminary tests of a newly developed superconducting gravity gradiometer

We have recently completed a series of tests on a newly developed superconducting gravity gradiometer consisting of two 400 g niobium proof masses separated by a distance of 15 cm. The resonance frequency of the proof mass suspension systems is 25 Hz. The sensitivity of this gradiometer obtained during these tests was 1 to 2 Eötvös Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/2</sup> (1 Eötvös = 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-9</sup> s <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-2</sup> <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\equiv1</tex> E) below 1Hz, and 0.2 E Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1/2</sup> between 15 and 20 Hz. Using this gradiometer, a prototype experiment has been performed to demonstrate a new source-independent null test of the inverse square law of gravitation. The result, assuming a potential of the form <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\phi(r) = -(GM/r) [1 + \alpha \exp(-\mur)]</tex> , is α = + 0.024 ± 0.036 at μ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-1</sup> = 1m.

Null Test of the Gravitational Inverse Square Law

An experiment has been performed to demonstrate a new source-independent null test of the inverse square law of gravitation. A single-axis superconducting gravity gradiometer was rotated into three orthogonal orientations to measure the Laplacian of the gravitational potential produced by a 1600-kg lead pendulum at an average distance of 2.3 m. The result is that if one assumes a potential of the form $\ensuremath{\phi}(\mathcal{r})=\ensuremath{-}(\frac{\mathrm{GM}}{\mathcal{r}})[1+\ensuremath{\alpha}\mathrm{exp}(\ensuremath{-}\ensuremath{\mu}\mathcal{r})]$, the value of $\ensuremath{\alpha}$ is + 0.024\ifmmode\pm\else\textpm\fi{}0.036 at ${\ensuremath{\mu}}^{\ensuremath{-}1}=1$ m.