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NASA NTRS1981

Superconducting tensor gravity gradiometer

The employment of superconductivity and other material properties at cryogenic temperatures to fabricate sensitive, low-drift, gravity gradiometer is described. The device yields a reduction of noise of four orders of magnitude over room temperature gradiometers, and direct summation and subtraction of signals from accelerometers in varying orientations are possible with superconducting circuitry. Additional circuits permit determination of the linear and angular acceleration vectors independent of the measurement of the gravity gradient tensor. A dewar flask capable of maintaining helium in a liquid state for a year's duration is under development by NASA, and a superconducting tensor gravity gradiometer for the NASA Geodynamics Program is intended for a LEO polar trajectory to measure the harmonic expansion coefficients of the earth's gravity field up to order 300.

Paik, H. J.↗

NASA NTRS1981

A spaceborne superconducting gravity gradiometer for mapping the earth's gravity field

The principles of a satellite gravity gradiometer system which measures all five independent components of the gravity gradient tensor with a sensitivity of 0.001 E/Hz to the 1/2 power or better, are analyzed, and the status of development of the system is reviewed. The superconducting gravity gradiometer uses sensitive superconducting accelerometers, each of which are composed of a weakly suspended superconducting proof mass, a superconducting magnetic transducer, and a low-noise superconducting magnetometer. The magnetic field produced by the transducer coils is modulated by the motion of the proof mass and detected by the magnetometer. A combination of two or four of such accelerometers with proper relative orientation of sensitive axes results in an in-line or a cross component gravity gradiometer.

Paik, H. J.↗

NASA NTRS1987

Monocrystalline silicon gradiometer for gravity experiments in space

A very important research effort has been made in the last decade in the field of high precision measurement with laser instrumentation. The development of a space borne gradiometer operating at a high sensitivity level using laser measurement of the distance between proof mass over a short base line of order one meter is discussed. Two aspects of laser technology make it a promising tool for gradiometry measurements: quantum limited accuracy and absolute distance measurements. The quantum limit associated with laser instrumentation was formulated. The relevant quantum and classical sources of errors in laser measurements were reviewed and corresponding laser performance requirements for gradient measurements were evaluated. Some mechanical quality factor measurements were made on simple resonant monocrystalline silicon suspensions. It was discovered that the use of zero derivative restoring forces to position the gradiometer test masses will dramatically reduce the gradiometer temperature control requirements. A laser beam side injection scheme was discovered which permits rejection of common mode accelerations. These concepts are briefly discussed.

Richard, Jean-Paul↗

NASA NTRS1989

Superconducting gravity gradiometer and a test of inverse square law

The equivalence principle prohibits the distinction of gravity from acceleration by a local measurement. However, by making a differential measurement of acceleration over a baseline, platform accelerations can be cancelled and gravity gradients detected. In an in-line superconducting gravity gradiometer, this differencing is accomplished with two spring-mass accelerometers in which the proof masses are confined to motion in a single degree of freedom and are coupled together by superconducting circuits. Platform motions appear as common mode accelerations and are cancelled by adjusting the ratio of two persistent currents in the sensing circuit. The sensing circuit is connected to a commercial SQUID amplifier to sense changes in the persistent currents generated by differential accelerations, i.e., gravity gradients. A three-axis gravity gradiometer is formed by mounting six accelerometers on the faces of a precision cube, with the accelerometers on opposite faces of the cube forming one of three in-line gradiometers. A dedicated satellite mission for mapping the earth's gravity field is an important one. Additional scientific goals are a test of the inverse square law to a part in 10(exp 10) at 100 km, and a test of the Lense-Thirring effect by detecting the relativistic gravity magnetic terms in the gravity gradient tensor for the earth.

Moody, M. V.↗

NASA NTRS1990

Gravity field error analysis: Applications of GPS receivers and gradiometers on low orbiting platforms

The concept of a Global Positioning System (GPS) receiver as a tracking facility and a gradiometer as a separate instrument on a low orbiting platform offers a unique tool to map the Earth's gravitational field with unprecedented accuracies. The former technique allows determination of the spacecraft's ephemeris at any epoch to within 3 to 10 cm, the latter permits the measurement of the tensor of second order derivatives of the gravity field to within 0.01 to 0.0001 Eotvos units depending on the type of gradiometer. First, a variety of error sources in gradiometry where emphasis is placed on the rotational problem pursuing as well a static as a dynamic approach is described. Next, an analytical technique is described and applied for an error analysis of gravity field parameters from gradiometer and GPS observation types. Results are discussed for various configurations proposed on Topex/Poseidon, Gravity Probe-B, and Aristoteles, indicating that GPS only solutions may be computed up to degree and order 35, 55, and 85 respectively, whereas a combined GPS/gradiometer experiment on Aristoteles may result in an acceptable solution up to degree and order 240.

Schrama, E.↗

NASA NTRS1991

Gravity field error analysis - Applications of Global Positioning System receivers and gradiometers on low orbiting platforms

The concept of a Global Positioning System (GPS) receiver as a tracking facility and a gradiometer as a separate instrument on a low-orbiting platform offers a unique tool to map the earth's gravitational field with unprecedented accuracies. The former technique allows determination of the spacecraft's ephemeris at any epoch to within 3-10 cm, the latter permits the measurement of the tensor of second order derivatives of the gravity field to within 0.01 to 0.0001 Eotvos units depending on the type of gradiometer. First, a variety of error sources in gradiometry where emphasis is placed on the rotational problem pursuing as well a static as a dynamic approach is described. Next, an analytical technique is described and applied for an error analysis of gravity field parameters from gradiometer and GPS observation types. Results are discussed for various configurations proposed on Topex/Poseidon, Gravity Probe-B, and Aristoteles, indicating that GPS only solutions may be computed up to degree and order 35, 55, and 85, respectively, whereas a combined GPS/gradiometer experiment on Aristoteles may result in an acceptable solution up to degree and order 240.

Schrama, Ernst J. O.↗

NASA NTRS2016

Design of Superconducting Gravity Gradiometer Cryogenic System for Mars Mission

Measurement of a planet's gravity field provides fundamental information about the planet's mass properties. The static gravity field reveals information about the internal structure of the planet, including crustal density variations that provide information on the planet's geological history and evolution. The time variations of gravity result from the movement of mass inside the planet, on the surface, and in the atmosphere. NASA is interested in a Superconducting Gravity Gradiometer (SGG) with which to measure the gravity field of a planet from orbit. An SGG instrument is under development with the NASA PICASSO program, which will be able to resolve the Mars static gravity field to degree 200 in spherical harmonics, and the time-varying field on a monthly basis to degree 20 from a 255 x 320 km orbit. The SGG has a precision two orders of magnitude better than the electrostatic gravity gradiometer that was used on the ESA's GOCE mission. The SGG operates at the superconducting temperature lower than 6 K. This study developed a cryogenic thermal system to maintain the SGG at the design temperature in Mars orbit. The system includes fixed radiation shields, a low thermal conductivity support structure and a two-stage cryocooler. The fixed radiation shields use double aluminized polyimide to emit heat from the warm spacecraft into the deep space. The support structure uses carbon fiber reinforced plastic, which has low thermal conductivity at cryogenic temperature and very high stress. The low vibration cryocooler has two stages, of which the high temperature stage operates at 65 K and the low temperature stage works at 6 K, and the heat rejection radiator works at 300 K. The study also designed a second option with a 4-K adiabatic demagnetization refrigerator (ADR) and two-stage 10-K turbo-Brayton cooler.

Gradiometer↗

NASA NTRS1973

Development of a rotating gravity gradiometer for earth orbit applications (AAFE)

Some preliminary mission studies are described along with the design, fabrication, and test of a breadboard model of an earth orbital, rotating gravity gradiometer with a design goal of 10 to the minus 11th power/sec sq (0.01 EU) in a 35-sec integration time. The proposed mission uses a Scout vehicle to launch one (or two orthogonally oriented) spin-stabilized satellites into a 330-km circular polar orbit some 20 days before an equinox. During the short orbital lifetime, the experiment would obtain two complete maps of the gravity gradient field with a resolution approaching 270 km (degree 75). The breadboard model of the gradiometer demonstrated a combined thermal and electronic noise threshold of 0.015 EU per data channel. The design changes needed to reduce the noise to less than 0.01 EU were identified. Variations of the sensor output signal with temperature were experimentally determined and a suitable method of temperature compensation was developed and tested. Other possible error sources, such as sensor interaction with satellite dynamics and magnetic fields, were studied analytically and shown to be small.

Forward, R. L.↗

NASA NTRS1976

Rotating Gravity Gradiometer Study

The application of a Rotating Gravity Gradiometer (RGG) system on board a Lunar Polar Orbiter (LPO) for the measurement of the Lunar gravity field was investigated. A data collection simulation study shows that a gradiometer will give significantly better gravity data than a doppler tracking system for the altitudes under consideration for the LOP, that the present demonstrated sensitivity of the RGG is adequate for measurement of the Lunar gravity gradient field, and that a single RGG instrument will provide almost as much data for geophysical interpretation as an orthogonal three axis RGG system. An engineering study of the RGG sensor/LPO spacecraft interface characteristics shows that the RGG systems under consideration are compatible with the present models of the LPO spacecraft.

Forward, R. L.↗

NASA NTRS1984

Spaceborne Gravity Gradiometers. Part 5: Development plan

The critical steps needed to develop a gravity gradiometer instrument and a conceptual design for a Gravity Gradiometer Mission (GGM) are defined and organized into a logical sequence. Funding requirements for an advanced development program beginning in FY-1985 are estimated.

Source record↗

NASA NTRS1985

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

Technical approaches to increase the sensitivity of a non-cryogenic gradiometer toward the goal of 0.001 EU/square root of Hz, with solutions that have the potential of achieving an even more ambitious threshold, such as 0.0001 EU/square root of Hz are discussed. This goal can be achieved with a gradiometer design in which the proof masses are each suspended from two small arms, the torsion of which is directly related to the displacement of the sensing element. A negative-spring action, aimed at reducing the resonance frequency, is provided in this design by means of an external electrostatic field. This configuration of the instrument is also suitable for use in a tensorial arrangement.

Grossi, M. D.↗

NASA NTRS1987

Three-Axis Superconducting Gravity Gradiometer

Gravity gradients measured even on accelerating platforms. Three-axis superconducting gravity gradiometer based on flux quantization and Meissner effect in superconductors and employs superconducting quantum interference device as amplifier. Incorporates several magnetically levitated proof masses. Gradiometer design integrates accelerometers for operation in differential mode. Principal use in commercial instruments for measurement of Earth-gravity gradients in geo-physical surveying and exploration for oil.

Paik, Ho Jung↗

NASA NTRS1987

Gravity field fine structure estimation techniques for a spaceborne gravity gradiometer

Use of standard estimation techniques to recover geopotential fine structure from gradiometer data requires the adjustment of small subsets of parameters while constraining others to their a priori values in order to minimize the computational load. Here, gravitational anomalies are selected as a parametrization of the gravity field which permits such an approach. Techniques coupled with numerical results for a spaceborne gravity gradiometer mission simulation are described which demonstrate that if a satellite is in a polar/circular orbit at an altitude of 160 km, 1 deg mean free air gravity anomalies can be recovered to an accuracy of 0.4 mgal, where 1 mgal = 0.001 cm/sq s.

Kahn, W. D.↗

NASA NTRS1988

Global gravity survey by an orbiting gravity gradiometer

The scientific aims, design, and mission profile of the Superconducting Gravity Gradiometer Mission (SGGM), a NASA spacecraft mission proposed for the late 1990s, are discussed and illustrated with drawings and diagrams. SGGM would complement the two other planned gravimetry missions, GRM and Aristoteles, and would provide gravitational-field measurements with accuracy 2-3 mGal in 55 x 55-km blocks. The principal instruments are a (1) three-axis superconducting gravity gradiometer with intrinsic sensitivity 100 microeotvos/sq rt Hz, (2) a six-axis superconducting accelerometer with sensitivity 100 fg(E)/sq rt Hz linear and 10 prad/sec squared sq rt Hz angular, and (3) a six-axis shaker for active control of the platform. Consideration is given to the error budget and platform requirements, the orbit selection criteria, and the spacecraft design.

Paik, Ho Jung↗

NASA NTRS1989

Signals and accuracies to be expected from a satellite gradiometer mission

The actual signals that a satellite gradiometer would measure over several geographic regions are discussed. Calculations are performed using high-degree expansions of the earth's gravitational potential. Some recent studies that estimate the accuracy of certain gravimetric quantities as determined from several gradiometer mission scenarios are discussed.

Rapp, Richard H.↗

NASA NTRS1989

Studies of an orbital gradiometer mission

The goal of using an orbital gradiometer mission to provide an accurate (1 to 2 mgal), high resolution (1 by 1 deg), global map of the earth's geopotential is currently being investigated. This investigation involves the simulation of the satellite ephemeris and the corresponding gradiometer measurements which can be used in the study of various techniques and methodologies that were proposed to recover the parameters used in modeling the geopotential. Also, the effects on the mission of various time varying forces acting on the spacecraft were included in the studies.

Schutz, B. E.↗

NASA NTRS1994

Measuring attitude with a gradiometer

This paper explores using a gravity gradiometer to measure the attitude of a satellite, given that the gravity field is accurately known. Since gradiometers actually measure a combination of the gradient and attitude rate and acceleration terms, the answer is far from obvious. The paper demonstrates that it can be done and at microradian accuracy. The technique employed is dynamic estimation, based on the momentum biased Euler equations. The satellite is assumed nominally planet pointed, and subject to control, gravity gradient, and partly radom drag torques. The attitude estimator is unusual. While the standard method of feeding back measurement residuals is used, the feedback gain matrix isn't derived from Kalman theory. instead, it's chosen to minimize a measure of the terminal covariance of the error in the estimate. This depends on the gain matrix and the power spectra of all the process and measurement noises. An integration is required over multiple solutions of Lyapunov equations.

Sonnabend, David↗

NASA NTRS2004

Exploring the Moon and Mars Using an Orbiting Superconducting Gravity Gradiometer

Gravity measurement is fundamental to understanding the interior structure, dynamics, and evolution of planets. High-resolution gravity maps will also help locating natural resources, including subsurface water, and underground cavities for astronaut habitation on the Moon and Mars. Detecting the second spatial derivative of the potential, a gravity gradiometer mission tends to give the highest spatial resolution and has the advantage of requiring only a single satellite. We discuss gravity missions to the Moon and Mars using an orbiting Superconducting Gravity Gradiometer and discuss the instrument and spacecraft control requirements.

Paik, Ho Jung↗