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NASA NTRS1989

Synopsis of early field test results from the gravity gradiometer survey system

Although the amount of data yielded by the initial airborne and surface tests was modest, it was sufficient to demonstrate that the full gravity gradient tensor was successfully measured from moving platforms both in the air and on the surface. The measurements were effectively continuous with spatial along-track resolution limited only by choice of integration lengths taken to reduce noise. The airborne data were less noisy (800 E squared/Hz typical) than were the Gravity Gradiometer Survey System (GGSS) measurements taken at the surface (5000 E squared/Hz typical). Single tracks of surface gravity disturbances recovered from airborne data were accurate to 3 to 4 mgal in each component of gravity when compared to 5 x 5 mean gravity anomalies over a 90 km track. Multitrack processing yielded 2 to 3 mgal when compared to 5 x 5 mean anomalies. Deflection of the vertical recovery over a distance of 150 km was about one arcsecond.

Brzezowski, S.↗
NASA NTRS1989

Satellite-to-satellite tracking experiment for global gravity field mapping

The satellite-to-satellite (STS) tracking concept for estimating gravitational parameters offers an attractive means to improve on regional and global gravity models in areas where data availability is limited. The extent to which the STS tracking measurements can be effectively utilized in global field models depends primarily on the satellite's altitude, number of satellites, and their orbit constellation. The estimation accuracy of the gravity field recovery also depends on the measurement accuracy of the sensors employed in the STS tracking concept. A comparison of the obtainable accuracies in the gravity field recovery using various STS tracking concepts was presented by Jekeli. The results of a feasibility study for a specific realization of the STS high-low tracking concept are summarized. In this realization, the high altitude satellites are the GPS satellites, and the low orbit satellite is the space shuttle. The GPS satellite constellation consists of 18 satellites in 6 orbital planes inclined at 55 deg. The shuttle orbit is at approximately 300 km, with an inclination of 30 deg. This specific configuration of high-low satellites for measuring perturbation in the gravity field is named the Air Foce STAGE (Shuttle GPS Tracking for Anomalous Gravitation Estimation) mission. The STAGE mission objective is to estimate the perturbations in gravity vector at the shuttle altitude to an accuracy of 1 mgal or better. Recent simulation studies have confirmed that the 1 mgal accuracy objective is near optimum for the STAGE mission.

Upadhyay, Triveni N.↗
NASA NTRS1994

Gravity survey of the Mount Toondina impact structure, South Australia

Gravity and seismic reflection data, together with geologic mapping, indicate that the Mount Toondina feature in South Australia is best interpreted as an eroded 4-km-diameter impact structure consisting of a ring structural depression surrounding a pronounced central uplift. Beds at the center of the structure within the central uplift have been raised as much as 200 m from depth and deformed by convergent flow. Seismic reflection data indicate that deformation extends to depths of only approximately = 800 m; at greater depths the reflectors are nearly flat lying, indicating little or no deformation. Gravity data show residual anomalies of +1.0 mGal coincident with the central uplift and a -0.5 Mgal low associated with the ring structural depression. Modeling of the gravity data indicates that relatively high-density material occurs within the central uplift, whereas the ring depression is filled with low-density material. The deformation at Mount Toondina is typical of a complex impact crater; the 4-km diameter is consistent with the expected threshold size for complex craters formed in weak to moderate strength sedimentary rocks.

Plescia, J. B.↗
NASA NTRS2002

The Crustal Thickness of Mars: Accuracy and Resolution

Since the arrival of the Mars Global Surveyor (MGS) spacecraft at Mars and its entry into its mapping orbit in February 1999, the radio tracking and altimetry data from the mission have been part of the systematic mapping of the planet and used to develop very precise models of the gravity field and topography of Mars. Until the altimetry function of Mars Orbiter Laser Altimeter (MOLA) failed on June 30, 2001, the instrument had acquired close to 700 million measurements of the planet's radius, the majority of which have been used to develop a model of the topography with horizontal resolution of about 500 m and radial accuracy of better than 1 m. Concurrently, Doppler and range tracking of MGS by the Deep Space Network at X-band frequencies, with accuracies of about 50 microns/s and about 5 m respectively, have provided orbital knowledge of MGS to the few meter level and enabled the gravity perturbations of the spacecraft to be used to develop a improved gravity models of Mars. The recent models have horizontal resolutions of about 200 km, or degree 65, when expressed in spherical harmonics, and have accuracies of the order of a few mGals at the poles and about 10 mGals at the equator at the highest resolution.

Smith, David E.↗
NASA NTRS2000

Feeling Gravity's Pull: Gravity Modeling. The Gravity Field of Mars

Most people take the constant presence of gravitys pull for granted. However, the Earth's gravitational strength actually varies from location to location. This variation occurs because mass, which influences an object's gravitational pull, is not evenly distributed within the planet. Changes in topography, such as glacial movement, an earthquake, or a rise in the ocean level, can subtly affect the gravity field. An accurate measurement of the Earth's gravity field helps us understand the distribution of mass beneath the surface. This insight can assist us in locating petroleum, mineral deposits, ground water, and other valuable substances. Gravity mapping can also help notice or verify changes in sea surface height and other ocean characteristics. Such changes may indicate climate change from polar ice melting and other phenomena. In addition, gravity mapping can indicate how land moves under the surface after earthquakes and other plate tectonic processes. Finally, changes in the Earth's gravity field might indicate a shift in water distribution that could affect agriculture, water supplies for population centers, and long-term weather prediction. Scientists can map out the Earth's gravity field by watching satellite orbits. When a satellite shifts in vertical position, it might be passing over an area where gravity changes in strength. Gravity is only one factor that may shape a satellite's orbital path. To derive a gravity measurement from satellite movement, scientists must remove other factors that might affect a satellite's position: 1. Drag from atmospheric friction. 2. Pressure from solar radiation as it heads toward Earth and. as it is reflected off the surface of the Earth 3. Gravitational pull from the Sun, the Moon, and other planets in the Solar System. 4. The effect of tides. 5. Relativistic effects. Scientists must also correct for the satellite tracking process. For example, the tracking signal must be corrected for refraction through the atmosphere of the Earth. Supercomputers can calculate the effect of gravity for specific locations in space following a mathematical process known as spherical harmonics, which quantifies the gravity field of a planetary body. The process is based on Laplace's fundamental differential equation of gravity. The accuracy of a spherical harmonic solution is rated by its degree and order. Minute variations in gravity are measured against the geoid, a surface of constant gravity acceleration at mean sea level. The geoid reference gravity model strength includes the central body gravitational attraction (9.8 m/sq s) and a geopotential variation in latitude partially caused by the rotation of the Earth. The rotational effect modifies the shape of the geoid to be more like an ellipsoid, rather than a perfect, circle. Variations of gravity strength from the ellipsoidal reference model are measured in units called milli-Galileos (mGals). One mGal equals 10(exp -5) m/sq s. Research projects have also measured the gravity fields of other planetary bodies, as noted in the user profile that follows. From this information, we may make inferences about our own planet's internal structure and evolution. Moreover, mapping the gravity fields of other planets can help scientists plot the most fuel-efficient course for spacecraft expeditions to those planets.

Lemoine, Frank↗
NASA NTRS2003

Gravity Models from CHAMP and other Satellite Data

CHAMP spacecraft is the first of a series of new spacecraft missions that are revolutionizing our ability to model the Earth's geopotential. We report on the analysis of over 100 days of CHAMP data in 2001 and 2002, merged with tracking data of other satellites such as Jason, Topex, GFO, Starlette, Stella, Spot-2, as well as satellite altimetry. We find that the CHAMP-only component of these solutions is a significant improvement over pre-CHAMP satellite only models with respect to the high degree information expressed by the geopotential model coefficients. For example, the variance of the differences with altimeter-derived anomalies through degree 70 is 2.80 mGal(sup 2) for the CHAMP-only solution based on 87 days of data vs. 10.19 mGal(sup 2) for EGM96S. Nonetheless, in order to model properly the various resonances to which different satellites are sensitive, we must include other satellite data. We evaluate the performance of these new CHAMP derived solutions with EGM96 and the EIGEN series of solutions. We review carefully the performance of these models for altimetric satellites.

Lemoime, Frank G.↗
NASA NTRS1994

Gravity Survey of the Mt. Toondina Impact Structure South Australia

Gravity and seismic reflection data, together with geologic mapping, indicate that the Mt. Toondina feature in South Australia is best interpreted as an eroded 4-km-diameter impact structure consisting of a ring structural depression surrounding a pronounced central uplift. Beds at the center of the structure within the central uplift have been raised as much as 200 m from depth and deformed by convergent flow. Seismic reflection data indicate that deformation extends to depths of only about 800 m; at greater depths the reflectors are nearly flat lying indicating little or no deformation. Gravity data show residual anomalies of +1.0 mGal coincident with the central uplift and a -0.5 mGal low associated with the ring structural depression. Modeling of the gravity data indicates that relatively high-density material occurs within the central uplift, whereas the ring depression is filled with low-density material. The deformation at Mt. Toondina is typical of a complex impact crater; the 4-km diameter is consistent with the expected threshold size for complex craters formed in weak to moderate strength sedimentary rocks.

Mt. Toondina Australia↗
NASA NTRS2013

High-degree Gravity Models from GRAIL Primary Mission Data

We have analyzed Ka‒band range rate (KBRR) and Deep Space Network (DSN) data from the Gravity Recovery and Interior Laboratory (GRAIL) primary mission (1 March to 29 May 2012) to derive gravity models of the Moon to degree 420, 540, and 660 in spherical harmonics. For these models, GRGM420A, GRGM540A, and GRGM660PRIM, a Kaula constraint was applied only beyond degree 330. Variance‒component estimation (VCE) was used to adjust the a priori weights and obtain a calibrated error covariance. The global root‒mean‒square error in the gravity anomalies computed from the error covariance to 320×320 is 0.77 mGal, compared to 29.0 mGal with the pre‒GRAIL model derived with the SELENE mission data, SGM150J, only to 140×140. The global correlations with the Lunar Orbiter Laser Altimeter‒derived topography are larger than 0.985 between l = 120 and 330. The free‒air gravity anomalies, especially over the lunar farside, display a dramatic increase in detail compared to the pre‒GRAIL models (SGM150J and LP150Q) and, through degree 320, are free of the orbit‒track‒related artifacts present in the earlier models. For GRAIL, we obtain an a posteriori fit to the S‒band DSN data of 0.13 mm/s. The a posteriori fits to the KBRR data range from 0.08 to 1.5 micrometers/s for GRGM420A and from 0.03 to 0.06 micrometers/s for GRGM660PRIM. Using the GRAIL data, we obtain solutions for the degree 2 Love numbers, k20=0.024615+/-0.0000914, k21=0.023915+/-0.0000132, and k22=0.024852+/-0.0000167, and a preliminary solution for the k30 Love number of k30=0.00734+/-0.0015, where the Love number error sigmas are those obtained with VCE.

Primary 1↗
NASA NTRS2022

World’s Largest Liquid Hydrogen Tank Nearing Completion

Construction of the world’s largest liquid hydrogen (LH 2 ) storage tank is almost complete at launch pad 39B at NASA Kennedy Space Center (KSC) in Florida. With a usable capacity of 4732 m 3 (1.25 Mgal), this new vessel is roughly 50% larger than its sister tank, which is located 170 m (550 ft) to the southeast. Once the new sphere is fully commissioned these two tanks will provide a combined LH 2 storage capacity of 7950 m 3 (2.1 Mgal) to fuel the new Space Launch System rocket in support of future Artemis exploration missions to the Moon and Mars.

Adam Swanger↗
NASA NTRS1973

Traverse gravimeter experiment

The primary goal of the traverse gravimeter experiment (TGE) was to make relative gravity measurements at a number of sites in the Apollo 17 landing area and to use these measurements to obtain information about the geological substructure. A secondary goal was to obtain the value of the gravity at the landing site relative to an accurately known value on earth. Both these goals were successfully achieved by the experiment. A gravity tie has been obtained between the Taurus-Littrow landing site and the earth with an estimated accuracy of approximately 5 mgal. Relative gravity measurements that can be used to infer the substructure of the area have been obtained at stations visited during each period of extravehicular activity (EVA).

Talwani, M.↗
NASA NTRS1974

Strategies for estimating the marine geoid from altimeter data

In processing altimeter data from a spacecraft borne altimeter to estimate the fine structure of the marine geoid, a problem is encountered. In order to describe the geoid fine structure, a large number of parameters must be employed and it is not possible to simultaneously estimate all of them. Unless the parameterization exhibits good orthogonality in the data, serious aliasing results. From simulation studies it has been found that amongst several competing parameterizations, the mean free air gravity anomaly model (i.e., Stokes' formula) exhibited promising geoid recovery characteristics. Using covariance analysis techniques, this report provides quantitative measures of the orthogonality properties associated with the above mentioned parameterization. It has been determined that a 5 deg x 5 deg area mean free air gravity anomaly can be estimated with an uncertainty of 1 mgal (40 cm undulation) provided that all free air gravity anomalies within a spherical radius of 10 arc degrees are simultaneously estimated.

Argentiero, P.↗
NASA NTRS1976

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.↗
NASA NTRS1976

Contributions to the National Geodetic Satellite Program by Goddard Space Flight Center

The major scientific contributions of Goddard Space Flight Center to the National Geodetic Satellite Program between 1965 and 1973 are presented and discussed. The primary results described are the determination of the earth's gravitational field from satellite tracking and surface gravimeter data to an accuracy of about 4 mGal for wavelengths of about 1000 km and larger; the construction of a detailed geoid suitable for geodetic, tectonic, and altimetry data analysis accurate to about 2 m over continents and to 2-5 m over the northeast Pacific and Atlantic oceans; and the positioning of globally distributed tracking stations to an accuracy of 5-10 m for the interconnecting of local geodetic datums. In addition, work on the observation of the earth and ocean tidal perturbations of satellites is discussed and reviewed.

Smith, D. E.↗
NASA NTRS1975

Methods for the computation of detailed geoids and their accuracy

Two methods for the computation of geoid undulations using potential coefficients and 1 deg x 1 deg terrestrial anomaly data are examined. It was found that both methods give the same final result but that one method allows a more simplified error analysis. Specific equations were considered for the effect of the mass of the atmosphere and a cap dependent zero-order undulation term was derived. Although a correction to a gravity anomaly for the effect of the atmosphere is only about -0.87 mgal, this correction causes a fairly large undulation correction that was not considered previously. The accuracy of a geoid undulation computed by these techniques was estimated considering anomaly data errors, potential coefficient errors, and truncation (only a finite set of potential coefficients being used) errors. It was found that an optimum cap size of 20 deg should be used. The geoid and its accuracy were computed in the Geos 3 calibration area using the GEM 6 potential coefficients and 1 deg x 1 deg terrestrial anomaly data. The accuracy of the computed geoid is on the order of plus or minus 2 m with respect to an unknown set of best earth parameter constants.

Rapp, R. H.↗
NASA NTRS1977

Ocean gravity and geoid determination

Gravity anomalies have been recovered in the North Atlantic and the Indian Ocean regions. Comparisons of 63 2 deg x 2 deg mean free air gravity anomalies recovered in the North Atlantic area and 24 5 deg x 5 deg mean free air gravity anomalies in the Indian Ocean area with surface gravimetric measurements have shown agreement to + or - 8 mgals for both solutions. Geoids derived from the altimeter solutions are consistent with altimetric sea surface height data to within the precision of the data, about + or - 2 meters.

Kahn, W. D.↗
NASA NTRS1978

On the unification of geodetic leveling datums using satellite altimetry

Techniques are described for determining the height of Mean Sea Level (MSL) at coastal sites from satellite altimetry. Such information is of value in the adjustment of continental leveling networks. Numerical results are obtained from the 1977 GEOS-3 altimetry data bank at Goddard Space Flight Center using the Bermuda calibration of the altimeter. Estimates are made of the heights of MSL at the leveling datums for Australia and a hypothetical Galveston datum for central North America. The results obtained are in reasonable agreement with oceanographic estimates obtained by extrapolation. It is concluded that all gravity data in the Australian bank AUSGAD 76 and in the Rapp data file for central North America refer to the GEOS-3 altimeter geoid for 1976.0 with uncertainties which do not exceed + or - 0.1 mGal.

Mather, R. S.↗
NASA NTRS1978

Mean gravity anomalies and sea surface heights derived from GEOS-3 altimeter data

Approximately 2000 GEOS-3 altimeter arcs were analyzed to improve knowledge of the geoid and gravity field. An adjustment procedure was used to fit the sea surface heights (geoid undulations) in an adjustment process that incorporated cross-over constraints. The error model used for the fit was a one or two parameter model which was designed to remove altimeter bias and orbit error. The undulations on the adjusted arcs were used to produce geoid maps in 20 regions. The adjusted data was used to derive 301 5 degree equal area anomalies and 9995 1 x 1 degree anomalies in areas where the altimeter data was most dense, using least squares collocation techniques. Also emphasized was the ability of the altimeter data to imply rapid anomaly changes of up to 240 mgals in adjacent 1 x 1 degree blocks.

Rapp, R. H.↗
NASA NTRS1978

High-precision gravimetric survey in support of lunar laser ranging at Haleakala, Maui, 1976 - 1978

The planning, observations and adjustment of high-precision gravity survey networks established on the islands of Maui and Oahu as part of the geodetic-geophysical program in support of lunar laser ranging at Haleakala, Maui, Hawaii are described. The gravity survey networks include 43 independently measured gravity differences along the gravity calibration line from Kahului Airport to the summit of Mt. Haleakala, together with some key points close to tidal gauges on Maui, and 40 gravity differences within metropolitan Honolulu. The results of the 1976-1978 survey are compared with surveys made in 1961 and in 1964-1965. All final gravity values are given in the system of the international gravity standardization net 1971 (IGSN 71); values are obtained by subtracting 14.57 mgal from the Potsdam value at the gravity base station at the Hickam Air Force Base, Honolulu.

Schenck, B. E.↗