Mars Gravity Field Modeling with MGS
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Mars gravity Mars Global Surveyor (MGS) Mars gravi↗
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Thermo-hydro-dynamic characteristics of a zero-gravity, spherical model of the troposphere
A model that exploits the radial inertia forces of a rotating fluid contained in a spherical annulus is described. The model would be flown in a satellite and experiments would be performed in very low or zero gravity. In such a model it would not be necessary to artificially simulate a radial gravity field. Thus small amounts of electrical energy would be sufficient to perform experiments. Since the only forces involved are thermo-hydro-dynamic ones, electromagnetic equations need not be considered.
Srivatsangam, S.↗
Orbit Determination of the SELENE Satellites Using Multi-Satellite Data Types and Evaluation of SELENE Gravity Field Models
The SELENE mission, consisting of three separate satellites that use different terrestrial-based tracking systems, presents a unique opportunity to evaluate the contribution of these tracking systems to orbit determination precision. The tracking data consist of four-way Doppler between the main orbiter and one of the two sub-satellites while the former is over the far side, and of same-beam differential VLBI tracking between the two sub-satellites. Laser altimeter data are also used for orbit determination. The contribution to orbit precision of these different data types is investigated through orbit overlap analysis. It is shown that using four-way and VLBI data improves orbit consistency for all satellites involved by reducing peak values in orbit overlap differences that exist when only standard two-way Doppler and range data are used. Including laser altimeter data improves the orbit precision of the SELENE main satellite further, resulting in very smooth total orbit errors at an average level of 18m. The multi-satellite data have also resulted in improved lunar gravity field models, which are assessed through orbit overlap analysis using Lunar Prospector tracking data. Improvements over a pre-SELENE model are shown to be mostly in the along-track and cross-track directions. Orbit overlap differences are at a level between 13 and 21 m with the SELENE models, depending on whether l-day data overlaps or I-day predictions are used.
Goossens, S.↗
Global and Local Gravity Field Models of the Moon Using GRAIL Primary and Extended Mission Data
The Gravity Recovery and Interior Laboratory (GRAIL) mission was designed to map the structure of the lunar interior from crust to core and to advance the understanding of the Moon's thermal evolution by producing a high-quality, high-resolution map of the gravitational field of the Moon. The mission consisted of two spacecraft, which were launched in September 2011 on a Discovery-class NASA mission. Ka-band tracking between the two satellites was the single science instrument, augmented by tracking from Earth using the Deep Space Network (DSN).
Moon↗
Simulation and analysis of a geopotential research mission
Methods for the determination of the initial conditions for the two satellites that will satisfy Geopotential Research Mission (GRM) requirements are investigated. For certain gravitational recovery techniques, the satellites must remain close to a specified separation distance and their groundtracks must repeat after a specified interval of time. Since the objective of the GRM mission is to improve the gravity model, any pre-mission orbit predicted using existing gravity models will be in error. A technique has been developed to eliminate the drift between the two satellites caused by gravitational modeling errors and return them to repeating groundtracks. The concept of frozen orbits, which minimize altitude variations over given latitudes, was investigated. Finally, the effects of temporal perturbations on the relative range-rate signal were studied. At the proposed altitude of 160 km, the range-rate signal produced by perturbations other than the static geopotential field are dominated by the luni-solar effect. This study demonstrates that the combined effects of all the temporal perturbations does not prevent the orbit from being frozen or the satellites from obtaining a repeating groundtrack to within a specified closure distance.
White, Lisa K.↗
A nonreflecting upper boundary condition for anelastic nonhydrostatic mesoscale gravity-wave models
A sponge layer is formulated to prevent spurious reflection of vertically propagating quasi-stationary gravity waves at the upper boundary of a two-dimensional numerical anelastic nonhydrostatic model. The sponge layer includes damping of both Newtonian-cooling type and Rayleigh-friction type, whose coefficients are determined in such a way that the reflectivity of wave energy at the bottom of the layer is zero. Unlike the formulations in earlier studies, our formulation includes the effects of vertical discretization, vertical mean density variation, and nonhydrostaticity. This sponge formulation is found effective in suppressing false downward reflection of waves for various types of quasi-stationary forcing.
Kim, Young-Joon↗
The role of topography in geodetic gravity field modelling
Masses associated with the topography, bathymetry, and its isostatic compensation are a dominant source of gravity field variations, especially at shorter wavelengths. On global scales the topographic/isostatic effects are also significant, except for the lowest harmonics. In practice, though, global effects need not be taken into account as such effects are included in the coefficients of the geopotential reference fields. On local scales, the short-wavelength gravity variations due to the topography may, in rugged terrain, be an order of magnitude larger than other effects. In such cases, explicit or implicit terrain reduction procedures are mandatory in order to obtain good prediction results. Such effects may be computed by space-domain integration or by fast Fourier transformation (FFT) methods. Numerical examples are given for areas of the Canadian Rockies. In principle, good knowledge of the topographic densities is required to produce the smoothest residual field. Densities may be determined from sample measurements or by gravimetric means, but both are somewhat troublesome methods in practice. The use of a standard density, e.g., 2.67 g/cu cm, may often yield satisfactory results and may be put within a consistent theoretical framework. The independence of density assumptions is the key point of the classical Molodensky approach to the geodetic boundary value problem. The Molodensky solutions take into account that land gravity field observations are done on a non-level surface. Molodensky's problem may be solved by integral expansions or more effective FFT methods, but the solution should not be intermixed with the use of terrain reductions. The methods are actually complimentary and may both be required in order to obtain the smoothest possible signal, least prone to aliasing and other effects coming from sparse data coverage, typical of rugged topography.
Forsberg, R.↗
A 40th deg and order gravitational field model for Mars
Understanding the origin and evolution of major photographic features on Mars, such as the hemispheric dichotomy and Tharsis rise, will require improved resolution of that planet's gravitational and topographic fields. The highest resolution gravity model for Mars published to date was derived from Doppler tracking data from the Mariner 9 and Viking 1 and 2 spacecraft, and is of 18th degree and order. That field has a maximum spatial resolution of approx. 600 km, which is comparable to that of the best topographic model. The resolution of previous gravity models was limited not by data density, but rather by the computational resources available at the time. Because this restriction is no longer a limitation, the Viking and Mariner data sets were reanalyzed and a gravitational field was derived complete to the 40th degree and order with a corresponding maximum spatial resolution of 300 km where the data permit.
Zuber, M. T.↗
Tests and comparisons of satellite-derived geoids with Skylab altimeter data
During the Skylab 4 mission, the S-193 radar altimeter was operated nearly continuously for a revolution around the world on Jan. 31, 1974. This direct measurement to the sea surface has provided an independent basis for the evaluation of the precision of global geoids computed from satellite-derived earth gravity models. This paper presents comparisons between the Skylab data and several recent gravity models published by Goddard Space Flight Center, the Smithsonian Astrophysical Observatory, and the National Oceanic and Atmospheric Administration. The differences between the altimeter geoid and the satellite geoids were as large as 20 m, rms values ranging from 8 to 10 m. These differences also indicated a systematic long-wavelength variation (about 100 deg) not related to error in the Skylab orbits. Truncation of the models to degree and order 8 did not eliminate the long-wavelength variation, but in every case the rms agreement between the satellite geoids and the altimeter geoid was slightly improved. Orbits computed with the truncated models were found to be inferior to those computed with the complete models.
Marsh, J. G.↗
On determining the large-scale ocean circulation from satellite altimetry
It is contended that a spherical harmonic expansion of the difference between the altimeter-derived mean sea surface and the geoid estimate should reveal the large-scale circulation of the ocean surface layer when the low-degree terms are examined. Methods based on this principle are proposed and partially demonstrated over the Pacific Ocean with the aid of the mean sea surface derived from the Seasat altimeter and the Goddard Earth Model 9 earth gravity model. The preliminary results reveal a well-defined clockwise gyre in the North Pacific and a much less well defined counterclockwise gyre in the South Pacific. When the dynamic topography thus obtained is compared with Wyrtki's (1975) dynamic topography derived from hydrographic data, the agreement is found to be within the limit of geoid uncertainties and satellite orbital errors.
Tai, C.-K.↗
Geophysical Interpretation of Venus Gravity Data
The subsurface distribution of Venus was investigated through the analysis of the data from Pioneer Venus Orbiter (PVO). In particular, the Doppler tracking data were used to map the gravitational potential. These were compared to the topographic data from the PVO radar (ORAD). In order to obtain an unbiased comparison, the topography data obtained from the PVO-ORAD were filtered to introduce distortions which are the same as those of the gravity models. Both the gravity and filtered topography maps are derived by two stage processes with a common second stage. In the first stage, the topography was used to calculate a corresponding spacecraft acceleration under the assumptions that the topography has a uniform given density and no compensation. In the second stage, the acceleration measures found in the first stage were passed through a linear inverter to yield maps of gravity and topography. Because these maps are the result of the same inversion process, they contain the same distortion; a comparison between them is unbiased to first order.
Reasenberg, R. D.↗
From Mars to Greenland: Charting gravity with space and airborne instruments - Fields, tides, methods, results
This symposium on space and airborne techniques for measuring gravity fields, and related theory, contains papers on gravity modeling of Mars and Venus at NASA/GSFC, an integrated laser Doppler method for measuring planetary gravity fields, observed temporal variations in the earth's gravity field from 16-year Starlette orbit analysis, high-resolution gravity models combining terrestrial and satellite data, the effect of water vapor corrections for satellite altimeter measurements of the geoid, and laboratory demonstrations of superconducting gravity and inertial sensors for space and airborne gravity measurements. Other papers are on airborne gravity measurements over the Kelvin Seamount; the accuracy of GPS-derived acceleration from moving platform tests; airborne gravimetry, altimetry, and GPS navigation errors; controlling common mode stabilization errors in airborne gravity gradiometry, GPS/INS gravity measurements in space and on a balloon, and Walsh-Fourier series expansion of the earth's gravitational potential.
Colombo, Oscar L.↗
Lunar Reconnaissance Orbiter Orbit Determination Accuracy Analysis
LRO definitive and predictive accuracy requirements were easily met in the nominal mission orbit, using the LP150Q lunar gravity model. center dot Accuracy of the LP150Q model is poorer in the extended mission elliptical orbit. center dot Later lunar gravity models, in particular GSFC-GRAIL-270, improve OD accuracy in the extended mission. center dot Implementation of a constrained plane when the orbit is within 45 degrees of the Earth-Moon line improves cross-track accuracy. center dot Prediction accuracy is still challenged during full-Sun periods due to coarse spacecraft area modeling - Implementation of a multi-plate area model with definitive attitude input can eliminate prediction violations. - The FDF is evaluating using analytic and predicted attitude modeling to improve full-Sun prediction accuracy. center dot Comparison of FDF ephemeris file to high-precision ephemeris files provides gross confirmation that overlap compares properly assess orbit accuracy.
Gravitation↗
A numerical model of gravity wave breaking and stress in the mesosphere
The goal of the study is to calculate numerically the deceleration and heating caused by breaking gravity waves. The effect of the radiative dissipation of the wave is included as vertical-wavelength-dependent Newtonian cooling. The parameterization for zonal deceleration is extended by breaking gravity waves (Lindzen, 1981) to include the turbulent diffusion of heat and momentum. After describing the numerical model, the numerical results are presented and compared with the parameterizations in a noninteractive model of the mean zonal wind. Attention is then given to the transport of constituents by gravity waves and the attendant turbulent zone. It is noted that if gravity wave breaking were not an intermittent process, gravity wave stresses would produce an adiabatic mesosphere with a zonal mean velocity close to the phase speed of the breaking wave.
Schoeberl, M. R.↗
Global mean sea surface computation based upon a combination of SEASAT and GEOS-3 satellite altimeter data
A mean sea surface map was computed for the global ocean areas between 70 deg N latitude and 62 deg S latitude based upon the 70 day SEASAT and 3.5 year GEOS-3 altimeter data sets. The mean sea surface is presented in the form of a global contour map and a 0.25 deg x 0.25 deg grid. A combination of regional adjustments based upon crossover techniques and the subsequent adjustment of the regional solutions into a global reference system was employed in order to minimize the effects of radial orbit error. A global map of the crossover residuals after the crossover adjustments are made is in good agreement with earlier mesoscale variability contour maps based upon the last month of SEASAT collinear data. This high level of agreement provides good evidence that relative orbit error was removed to the decimeter level on a regional basis. This represents a significant improvement over our previous maps which contained patterns, particularly in the central Pacific, which were due to radial orbit error. Long wavelength, basin scale errors are still present with a submeter amplitude due to errors in the PGS-S4 gravity model. Such errors can only be removed through the improvement of the Earth's gravity model and associated geodetic parameters.
Marsh, J. G.↗
Modelling the gravity and magnetic field anomalies of the Chicxulub crater
The approximately 180-km-diameter Chicxulub crater lies buried by approximately 1 km of sediment on the northwestern corner of the Yucatan Peninsula, Mexico. Geophysical, stratigraphic and petrologic evidence support an impact origin for the structure and biostratigraphy suggests that a K/T age is possible for the impact. The crater's location is in agreement with constraints derived from proximal K/T impact-wave and ejecta deposits and its melt-rock is similar in composition to the K/T tektites. Radiometric dating of the melt rock reveals an age identical to that of the K/T tektites. The impact which produced the Chicxulub crater probably produced the K/T extinctions and understanding the now-buried crater will provide constraints on the impact's lethal effects. The outstanding preservation of the crater, the availability of detailed gravity and magnetic data sets, and the two-component target of carbonate/evaporites overlying silicate basement allow application of geophysical modeling techniques to explore the crater under most favorable circumstances. We have found that the main features of the gravity and magnetic field anomalies may be produced by the crater lithologies.
Aleman, C. Ortiz↗
Implications of Flexural Flanks at the Valles Marineris, Mars
The presence or absence of flexural flanks at the Valles Marineris (VM), Mars, have strong implications for the properties of the lithosphere, information which is critical for models of compensation state and formation of the troughs. Two hypotheses are favored for the formation of the VM, tectonic extension or subsurface withdrawal potentially related to dike emplacement; in either case, the formation of the large troughs at the VM requires a flexural response. After discussing preliminary models of flexure for VM from released Mars Global Surveyor (MGS) Mars Orbiting Laser Altimeter (MOLA) topography, this abstract considers the implications of flexure for gravity modeling and the lithosphere at VM. With future MGS topography and gravity data, and constraints on T(sub e) from this study, significantly better gravity modeling can be done to understand the state of the lithosphere at VM. Additional information is contained in the original extended abstract.
Anderson, F. S.↗
Zonal and tesseral harmonic coefficients for the geopotential function, from zero to 18th order
Zonal and tesseral harmonic coefficients for the geopotential function are usually tabulated in normalized form to provide immediate information as to the relative significance of the coefficients in the gravity model. The normalized form of the geopotential coefficients cannot be used for computational purposes unless the gravity model has been modified to receive them. This modification is usually not done because the absolute or unnormalized form of the coefficients can be obtained from the simple mathematical relationship that relates the two forms. This computation can be quite tedious for hand calculation, especially for the higher order terms, and can be costly in terms of storage and execution time for machine computation. In this report, zonal and tesseral harmonic coefficients for the geopotential function are tabulated in absolute or unnormalized form. The report is designed to be used as a ready reference for both hand and machine calculation to save the user time and effort.
Kirkpatrick, J. C.↗