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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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NASA NTRS1993

Spectral analysis of the gravity and topography of Mars

New spherical harmonic models of the gravity and topography of Mars place important constraints on the structure and dynamics of the interior. The gravity and topography models are significantly phase coherent for harmonic degrees n less than 30 (wavelengths greater than 700 km). Loss of coherence below that wavelength is presumably due to inadequacies of the models, rather than a change in behavior of the planet. The gravity/topography admittance reveals two very different spectral domains: for n greater than 4, a simple Airy compensation model, with mean depth of 100 km, faithfully represents the observed pattern; for degrees 2 and 3, the effective compensation depths are 1400 and 550 km, respectively, strongly arguing for dynamic compensation at those wavelengths. The gravity model has been derived from a reanalysis of the tracking data for Mariner 9 and the Viking Orbiters, The topography model was derived by harmonic analysis of the USGS digital elevation model of Mars. Before comparing gravity and topography for internal structure inferences, we must ensure that both are consistently referenced to a hydrostatic datum. For the gravity, this involves removal of hydrostatic components of the even degree zonal coefficients. For the topography, it involves adding the degree 4 equipotential reference surface, to get spherically referenced values, and then subtracting the full degree 50 equipotential. Variance spectra and phase coherence of orthometric heights and gravity anomalies are addressed.

Bills, Bruce G.↗
NASA NTRS1985

The non-hydrostatic figures of the terrestrial planets

Solid state creep being exponentially dependent on temperature must dominate the mechanical behavior of the mantles of terrestrial planets beneath their lithospheres. General arguments suggest that the lithospheres of the Moon and Mars are about 200 km thick; the Earth, Venus and Mercury much less. Short wavelength gravity anomalies are explained by the finite strength of the lithosphere: the lunar mascons being an example. The good correlation of the Venus and Mars gravity anomalies with topography up to spherical harmonics of degrees 10-15 is in striking contrast to the lack of correlation between the long wavelength components of the geoid and the continent-ocean distribution or even the plates. Attempts have been made to explain the former correlations by isostatic models but the depths of compensation seem implausible. Low degree harmonics of the gravity fields of the terrestrial planets as is certainly the case in the Earth must arise from the density variations driving solid state convection. In the case of Venus the less dense differentiated materials of the highlands seems to be positioned over the singular points of the convection pattern. Thus the correlated gravity field does not arise from the highlands but from the density difference in the convecting interior. In the Earth lack of correlation seems to arise from the fact that the plates have moved relative to the convection pattern the last 100 M yr.

Runcorn, S. K.↗
NASA NTRS1989

Downward continuation of the free-air gravity anomalies to the ellipsoid using the gradient solution and terrain correction: An attempt of global numerical computations

The formulas for the determination of the coefficients of the spherical harmonic expansion of the disturbing potential of the earth are defined for data given on a sphere. In order to determine the spherical harmonic coefficients, the gravity anomalies have to be analytically downward continued from the earth's surface to a sphere-at least to the ellipsoid. The goal is to continue the gravity anomalies from the earth's surface downward to the ellipsoid using recent elevation models. The basic method for the downward continuation is the gradient solution (the g sub 1 term). The terrain correction was also computed because of the role it can play as a correction term when calculating harmonic coefficients from surface gravity data. The fast Fourier transformation was applied to the computations.

Wang, Y. M.↗
NASA NTRS1972

Error analysis of earth physics satellite systems

Error analysis of distant-satellite-to-close-satellite range-rate, satellite-to-sea altimetry, and ground station to satellite range are made by simulations in which observational variances are assumed, observation equations are formed, and normal equations incremented. The final normal equation matrix is inverted to obtain standard deviations and correlation coefficients. The natural parameters solved for are the broad variations of the gravity field, represented by harmonic coefficients; local variations of gravity, represented by point masses; and the departure of the sea level from the geoid, represented by area means. A standard case of a low (263 km) polar close satellite, three equatorial geosynchronous satellites, and eight ground tracking stations is set up.

Kaula, W. M.↗
NASA NTRS2012

High Degree and Order Gravity Fields of the Moon Derived from GRAIL Data

The Gravity Recovery and Interior Laboratory (GRAIL) spacecraft conducted the mapping of the gravity field of the Moon from March 1, 2012 to May 29, 2012. The twin spacecraft acquired highly precise K Band range-rate (KBRR) intersatellite ranging data and Deep Space Network (DSN) data during this prime mission phase from altitudes of 15 to 75 km above the lunar surface over three lunar months. We have processed these data using the NASA GSFC GEODYN orbit determination and geodetic parameter estimation program, and we have determined gravity fields up to degree and order 420 in spherical harmonics. The new gravity solutions show improved correlations with LOLA-derived topography to high degree and order and resolve many lunar features in the geopotential with a resolution of less than 30 km, including for example the central peak of the crater Tycho. We discuss the methodology used for the processing of the GRAIL data, the quality of the orbit determination on the GRAIL satellites and the derivation of the solutions, and their evaluation with independent data, including Lunar Prospector. We show that with these new GRAIL gravity solutions, we can now fit the low altitude, extended mission Lunar Prospector tracking data better than with any previous gravity model that included the LP data.

Lemoine, F. G.↗
NASA NTRS1973

Mars - Crustal structure inferred from Bouguer gravity anomalies.

Bouguer gravity has been computed for the equatorial region of Mars by differencing free air gravity and the gravity predicted from topographic variations. The free air gravity was generated from an eighth-order set of spherical harmonic coefficients. The gravity from topographic variations was generated by integrating a two-dimensional Green's function over each contour level. The Bouguer gravity indicates crustal inhomogeneities on Mars that are postulated to be variations in crustal thickness. The Tharsis ridge is a region of thick continental type crust. The gravity data, structural patterns, topography, and surface geology of this region lead to the interpretation of the Tharsis topographic high as a broad crustal upwarp possibly associated with local formation of lower-density crustal material and subsequent rise of a thicker crust. The Amazonis region is one of several basins of relatively thin crust, analogous to terrestrial ocean basins. The Libya and Hellas basins, which are probable impact features, are also underlain by thin crust and are possible regions of mantle upwelling.

Phillips, R. J.↗
NASA NTRS1974

Detailed gravimetric geoid for the GEOS-C altimeter calibration area

The GEOS-C spacecraft scheduled for launch in late 1974 will carry a radar altimeter for the purpose of measuring sea surface topography. In order to calibrate and evaluate the performance of the altimeter system, ground truth data are required. In this respect a detailed gravimetric geoid has been computed for the GEOS-C altimeter calibration area in the Atlantic Ocean off the East Coast of the U.S. This geoid is based upon a combination of mean free air surface gravity anomalies and the Goddard Space Flight Center GEM-6 satellite-derived spherical harmonic coefficients. Surface gravity anomalies have been used to provide information on the short wave length undulations of the geoid while the satellite-derived coefficients have provided information on the long wave length components. As part of these analyses, GSFC, SAO and OSU satellite-derived gravity models were used in the computations. Although geoid heights based upon the various satellite models differed by as much as 30 meters in the Southern Hemisphere, the differences in this Atlantic Ocean area were less than 4 meters.

Marsh, J. G.↗
NASA NTRS1985

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.↗
NASA NTRS1999

Inversion of Gravity Fields From the Spacecraft Orbital Data Using an Adjoint Operator Approach

In perturbation approximation, the forward problem of orbital dynamics (equations with initial conditions) is linear with respect to variations of coordinates and/or velocities of the spacecraft and to corresponding variations of the gravity field in the models used. The linear operator adjoint to the linear operator of such forward problem turns out to be instrumental in inversion of differences between observed and predicted coordinates/velocities in terms of the updates of harmonics in the initial gravity field model. Based on this approach, the solution of resulting adjoint problem of orbital dynamics can be used to directly evaluate the matrix of partial derivatives of observable differences with respect to the gravity field harmonics. General discussion of the adjoint problem of orbital dynamics is given and an example of a mathematical formalism for the practical retrieval algorithm is presented.

Ustinov, E. A.↗
NASA NTRS1972

Theory of an experiment in an orbiting space laboratory to determine the gravitational constant.

An experiment is discussed for determining the gravitational constant with the aid of an isolated system consisting of an artificial satellite moving around an artificial planet. The experiment is to be conducted in a spherical laboratory traveling in an orbit around the earth. Difficulties due to the gravity-gradient term are considered, and the three-tunnel method proposed by Wilk (1969) is examined. The rotation of the sphere is discussed together with aspects of the reference systems used, the equations of motion of the spacecraft and of the test objects, the field from the earth's gravity gradient at the test object, higher harmonic terms in the gravity gradient force, gravitational effects of the spacecraft itself, and a computer simulation.

Vinti, J. P.↗
NASA NTRS1994

Gravity over coronae and chasmata on Venus

The global spherical harmonic model of Venus' gravity field MGNP60FSAAP, with horizontal resolution of about 600 km, shows that most coronae have little or no signature in the gravity field. Nevertheless, some coronae and some segments of chasmata are associated with distinct positive gravity anomalies. No corona has been found to have a negative gravity anomaly. The spatial coincidence of the gravity highs over four closely spaced 300- to 400-km-diameter coronae in Eastern Eistla Regio with the structures themselves is remarkable and argues for a near-surface or lithospheric origin of the gravity signals over such relatively small features. Apparent depths of compensation (ADCs) of the prominent gravity anomalies at Artemis, Latona, and Heng-o Coronae are about 150 to 200 km. The geoid/topography ratios (GTRs) at Artemis, Latona, and Heng-o Coronae lie in the range 32 to 35 m/km. The large ADCs and GTRs of Artemis, Latona, and Heng-o Coronae are consistent with topographically related gravity and a thick Venus lithosphere or shallowly compensated topography and deep positive mass anomalies due to subduction of underthrusting at these coronae. At arcuate segments of Hecate and Parga Chasmata ADCs are about 125 to 150 km, while those at Fauta Corona, four coronae in Eastern Eistla Regio, and an arcuate segment of Wester Parga Chasmata are about 75 km. The GTRs at Fauta Corona, the four coronae in eastern Eistla Regio, and the accurate segments of Hecate, Parga, and Western Parga Chasmata are about 12 to 21 m/km. By analogy with gravity anomalies of similar horizontal scale (600 km-several thousand kilometers) on the concave sides of terrestrial subduction zone arcs, which are due in large part to subducted lithosphere, it is inferred that the gravity anomalies on Venus are consistent with retrograde subduction at Artemis Chasma, along the northern and southern margins of Latona Coronam, and elsewhere along Parga and Hecate Chasmata.

Schubert, Gerald↗
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 NTRS1992

Properties of the gravity fields of terrestrial planets

The properties of the gravity fields of the earth, Mars, and Venus, as expressed by spherical harmonic coefficients, are examined, using the harmonic expansions of the respective planetary topographies reported by Balmino et al. (1973), Bills and Ferrari (1978), and Bills and Kobrick (1985). The items examined include the spectral magnitudes and slopes of the gravity coefficients; the correlations between gravity and topography; and the correlations among different gravity harmonics, expressed by axiality and angularity. It was found that Venus differs from the other two planets in its great apparent depths of compensation, indicating a tectonics dominated by a stiff upper mantle. In addition, Venus has less activity deep in the mantle than do earth or Mars. Mars is marked by large gravity irregularities, as well as by their axial symmetry on a global scale. Although earth is probably the most peculiar planet, spherical harmonics do not bring out its varied characteristics. It is clearly a more active planet than Venus, with activity deep in the mantle. The lower magnitude of its higher harmonics is considered to be due to water recycled to the upper mantle.

Kaula, William M.↗
NASA NTRS1973

Mars gravity derived from long-period motion of Mariner 9

The spherical harmonic coefficients in the gravity field of Mars are determined using a two stage filtering process. In the first stage, a weighted least squares orbit determination processor is applied to Mariner 9 Doppler tracking data to estimate Kepler elements and rates. In the second stage, the Kepler element rates are used as input to another weighted least squares processor that estimates gravity coefficients using the Lagrange perturbation equations. The novelty in this method is the fitting of element rates rather than the elements themselves. This procedure decouples the results from the effects of internal spacecraft dynamics.

Ferrari, A. J.↗
NASA NTRS2011

Simulations of Recovery of Time-Varying Gravity from DECIGO Pathfinder

We simulated time-varying Earth's gravity field recovered from DPF to evaluate an impact of DPF and future satellite gradiometry mission on earth science. From hydrological water movement data and orbit information, gravity gradients to be measured at altitude about ~500km were generated. Errors caused by atmospheric and oceanic variations and instrumental noise were added. Monthly gravity fields were estimated solving normal equations between spherical harmonic coefficients and simulated gravity gradient data. Simulation results show that DPF likely provides monthly hydrological water storage change with spatial scale between 400 and 1000km. Sensitivities to large scale estimates depends on long-term stability of gravity gradient measurement, and errors in short scale estimates are caused by instrumental noise and imperfections in atmospheric and ocean model. With acceleration noise level is lower than ~5 x 10(exp -14) [m/s2/sqrtHz] at frequency higher than 3mHz, water storage changes at limited small basins will be provided by DPF. To monitor continental scale hydrological water movement, noise level must be lower than ~5 x 10(exp -14) [m/s2/sqrtHz] at frequency higher than 1mHz.

Hasegawa, Takashi↗
NASA NTRS1992

Simulations of lunar gravity field determination for Lunar Observer

The current plan for the Lunar Observer (LO) mission is to launch in the late 1990s and insert LO into a 100 km polar circular mapping orbit. However, prior to the mapping orbit, LO will be placed in a gravity calibration orbit (GCO) at a higher altitude to determine the gravity field of the moon. This paper examines the abilities of two GCO orbits (at 200 and 500 km altitudes) to recover a high degree and order gravity truth model that includes spherical harmonics and mascons by estimating different degree and order gravity fields with spherical harmonics only. This is achieved by comparing radial accelerations from the true and estimated models at the mapping altitude and by comparing trajectory propagations. For the gravity fields estimated (up to 30th degree and order), the 500 km GCO was just as successful as the 200 km GCO in determining the gravity field.

Konopliv, Alex↗
NASA NTRS1999

Preliminary Correlations of Gravity and Topography from Mars Global Surveyor

The Mars Global Surveyor (MGS) spacecraft is currently in a 400-km altitude polar mapping orbit and scheduled to begin global mapping of Mars in March of 1999. Doppler tracking data collected in this Gravity Calibration Orbit prior to the nominal mapping mission combined with observations from the MGS Science Phasing Orbit in Spring - Summer 1999 and the Viking and mariner 9 orbiters has led to preliminary high resolution gravity fields. Spherical harmonic expansions have been performed to degree and order 70 and are characterized by the first high spatial resolution coverage of high latitudes. Topographic mapping by the Mars Orbiter Laser Altimeter on MGS is providing measurements of the height of the martian surface with sub-meter vertical resolution and 5-30 m absolute accuracy. Data obtained during the circular mapping phase are expected to provide the first high resolution measurements of surface heights in the southern hemisphere. The combination of gravity and topography measurements provides information on the structure of the planetary interior, i.e. the rigidity and distribution of internal density. The observations can also be used to address the mechanisms of support of surface topography. Preliminary results of correlations of gravity and topography at long planetary wavelengths will be presented and the implications for internal structure will be addressed.

Zuber, M. T.↗