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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Methods for local gravity field approximation

The most widely known modern method for estimating gravity field values from observed data is least-squares collocation. Its advantages are that it can make estimates at arbitrary locations based on irregularly spaced observations, and that it makes use of statistical information about errors in the input data while providing corresponding information about the quality of the output estimates. Disadvantages of collocation include the necessity of inverting square matrices of dimension equal to the number of data values and the need to assume covariance models for the gravity field and the data errors. Fourier methods are an important alternative to collocation; having the advantage of greater computational efficiency, but requiring data estimates to be on a regular grid and not using or providing statistical accuracy information. The GEOFAST algorithm is an implementation of collocation that achieves high computational efficiency by transforming the estimation equations into the frequency domain where an accurate approximation may be made to reduce the workload. The forward and inverse Fast Fourier Transforms (FFTs) are utilized. The accuracy and computational efficiency of the GEOFAST algorithm is demonstrated using two sets of synthetic gravity data: marine gravity for an ocean trench region including wavelengths longer than 200 km; and local land gravity containing wavelengths as short as 5 km. These results are discussed along with issues such as the advantages of first removing reference field models before carrying out the estimation algorithm.

Sailor, R. V.↗
NASA NTRS2016

Seasonal and static Gravity Field of Mars from MGS, Mars Odyssey and MRO Radio Science

We present a spherical harmonic solution of the static gravity field of Mars to degree and order 120, GMM-3, that has been calculated using the Deep Space Network tracking data of the NASA Mars missions, Mars Global Surveyor (MGS), Mars Odyssey (ODY), and the Mars Reconnaissance Orbiter (MRO). We have also jointly determined spherical harmonic solutions for the static and time-variable gravity field of Mars, and the Mars k(sub 2) Love numbers, exclusive of the gravity contribution of the atmosphere. Consequently, the retrieved time-varying gravity coefficients and the Love number k(sub 2) solely yield seasonal variations in the mass of the polar caps and the solid tides of Mars, respectively. We obtain a Mars Love number k(sub 2) of 0.1697 +/- 0.0027 (3- sigma). The inclusion of MRO tracking data results in improved seasonal gravity field coefficients C(sub 30) and, for the first time, C 50. Refinements of the atmospheric model in our orbit determination program have allowed us to monitor the odd zonal harmonic C(sub 30) for approximately 1.5 solar cycles (16 years). This gravity model shows improved correlations with MOLA topography up to 15% larger at higher harmonics ( l = 60-80) than previous solutions.

Genova, Antonio↗
NASA NTRS1992

Estimation of local planetary gravity fields using line of sight gravity data and an integral operator

A novel method is presented for mapping line-of-sight gravity data (LOSGD) joining planetary probes and observers during Doppler tracking operations, with a view to geodetic and geophysical applications. LOSGD are in this case mapped as gravity anomalies along a radial direction, at constant altitude, using an inversion procedure in conjunction with a Tikhonov-Arsenine regularization method. The application of different regularization-parameter choices to a synthetic case is followed by application to the real case of Pioneer-Venus orbiter data for Venus' Gula Mons.

Barriot, J. P.↗
NASA NTRS2016

Gravity Field of the Orientale Basin from the Gravity Recovery and Interior Laboratory Mission

The Orientale basin is the youngest and best-preserved major impact structure on the Moon. We used the Gravity Recovery and Interior Laboratory (GRAIL) spacecraft to investigate the gravitational field of Orientale at 3- to 5-kilometer (km) horizontal resolution. A volume of at least (3.4 +/- 0.2) × 10(exp 6) cu km of crustal material was removed and redistributed during basin formation. There is no preserved evidence of the transient crater that would reveal the basin's maximum volume, but its diameter may now be inferred to be between 320 and 460 km. The gravity field resolves distinctive structures of Orientale's three rings and suggests the presence of faults associated with the outer two that penetrate to the mantle. The crustal structure of Orientale provides constraints on the formation of multiring basins.

Zuber, Maria T.↗
NASA NTRS1998

The Study of Effects of Time Variations in the Earth's Gravity Field on Geodetic Satellites

The temporal variations in the Earth's gravity field are the consequences of complex interactions between atmosphere, ocean, solid Earth, hydrosphere and cryosphere. The signal ranges from several hours to 18.6 years to geological time scale. The direct and indirect consequences of these variations are manifested in such phenomena as changes in the global sea level and in the global climate pattern. These signals produce observable geodetic satellites. The primary objectives of the proposed effects on near-Earth orbiting investigation include (1) the improved determination of the time-varying gravity field parameters (scale from a few hour to 18.6 year and secular) using long-term satellite laser rs ranging (SLR) observations to multiple geodetic satellites, and (2) the enhanced understanding of these variations with their associated meteorological and geophysical consequences.

Shum, C. K.↗
NASA NTRS2012

Local Lunar Gravity Field Analysis over the South Pole-aitken Basin from SELENE Farside Tracking Data

We present a method with which we determined the local lunar gravity field model over the South Pole-Aitken (SPA) basin on the farside of the Moon by estimating adjustments to a global lunar gravity field model using SELENE tracking data. Our adjustments are expressed in localized functions concentrated over the SPA region in a spherical cap with a radius of 45deg centered at (191.1 deg E, 53.2 deg S), and the resolution is equivalent to a 150th degree and order spherical harmonics expansion. The new solution over SPA was used in several applications of geophysical analysis. It shows an increased correlation with high-resolution lunar topography in the frequency band l = 40-70, and admittance values are slightly different and more leveled when compared to other, global gravity field models using the same data. The adjustments expressed in free-air anomalies and differences in Bouguer anomalies between the local solution and the a priori global solution correlate with topographic surface features. The Moho structure beneath the SPA basin is slightly modified in our solution, most notably at the southern rim of the Apollo basin and around the Zeeman crater

Lunar Gravity↗
NASA NTRS2005

Adjoint Sensitivity Analysis of Orbital Mechanics: Application to Computations of Observables' Partials with Respect to Harmonics of the Planetary Gravity Fields

An approach is presented to the inversion of gravity fields based on evaluation of partials of observables with respect to gravity harmonics using the solution of adjoint problem of orbital dynamics of the spacecraft. Corresponding adjoint operator is derived directly from the linear operator of the linearized forward problem of orbital dynamics. The resulting adjoint problem is similar to the forward problem and can be solved by the same methods. For given highest degree N of gravity harmonics desired, this method involves integration of N adjoint solutions as compared to integration of N2 partials of the forward solution with respect to gravity harmonics in the conventional approach. Thus, for higher resolution gravity models, this approach becomes increasingly more effective in terms of computer resources as compared to the approach based on the solution of the forward problem of orbital dynamics.

gravity fields↗
NASA NTRS1999

An Analysis of Gravity-Field Estimation Based on Intersatellite Dual-1-Way Biased Ranging

The GRACE (Gravity Recovery And Climate Experiment) mission is designed to make global, highly accurate measurements of the Earth's gravity field with high spatial resolution. Ancillary GPS occultation measurements are also to be carried out for atmospheric monitoring. In the dual-1-way biased ranging of this mission, the range between two satellites separated by 100 to 200 km in nearly polar, coplanar, circular orbits, is measured to very high precision, to within an additive constant, through the exchange of K- and Ka-band sinusoidal signals. Such biased ranging data, along with GPS L-band range and phase data, can be processed and fit over successive multiday intervals to obtain accurate estimates of the Earth's gravity field. This report approximately models and analyzes this process, from the generation of the RF signals at the two satellites through the extraction of the geopotential. The steps include generation of the transmitted signals, processing the received signals to extract high-rate baseband phase, carrying out a dual-1-way combination of baseband phase to extract high-rate biased range for each band, combining K- and Ka-band ranges to correct for the ionosphere effect, and processing the resulting high-rate biased range values to extract three types of reduced-rate observables: biased range, range rate and range acceleration. The version of dual-1-way biased ranging developed by this report improves upon previous versions in a number of ways: highly accurate satellite-timetag corrections derived from concurrent GPS data, better baseband phase extraction using highly digital processing, highly accurate USO-rate calibration derived from concurrent GPS data, an improved method for extracting high-rate biased range from baseband phase, improved filtering for extracting reduced- rate observables from high-rate biased range, and parallel extraction of three observable types.

SINUSOIDAL SIGNALS↗
NASA NTRS1993

A preliminary error analysis of the gravity field recovery from a lunar Satellite-to-Satellite mission

A low cost lunar Satellite-to-Satellite radio tracking mission in a low-low configuration could considerably improve the existing knowledge about the lunar gravity field. The impact of various mission parameters that may contribute to the recovery of the gravity field, such as satellite altitude, satellite separation mission duration, measurement precision and sampling interval were quantified using the Jekeli-Rapp algorithm. Preliminary results indicate that the gravity field resolution up to harmonic degree 40 to 80 is feasible depending on various mission configurations. Radio tracking data from a six-month mission with a precision of 1 mm/s every 10 s and 300 km satellite separation at 150 km altitude will permit the determination of 5 deg x 5 deg mean gravity anomalies with an error of approximately 15 mgals. Consideration of other unaccounted error sources of instrumental, operational, and environmental nature may lower this resolution.

Iz, Huseyin B.↗
NASA NTRS1990

Gravity field determination for Mars Observer

Mars Observer will be the first near circular, low altitude and short-periodic orbiter of Mars. From previous Mars orbiters, such as Mariner 9 and Vikings 1 and 2, a large gravitational oblateness and in general a gravity field ten times stronger than the earth's field have been determined. Because of these, the gravity field will dominate the evolution of the spacecraft's orbital motion and is the principal error source for reconstructing the spacecraft's motion. Thus a gravity calibration (GC) period has been established prior to the mapping phase in order to refine the gravitational field model. This paper describes the plan being made by Navigation to implement the GC strategy. By analyzing simulated Doppler data acquired during the seven day GC period, we give (1) the expected improvement in the gravity field model and (2) the resulting improvement in reconstructed spacecraft orbital motion. In addition, we have developed a strategy for converging the GC gravity model.

Esposito, Pasquale B.↗
NASA NTRS2002

High-Resolution Gravity and Time-Varying Gravity Field Recovery using GRACE and CHAMP

This progress report summarizes the research work conducted under NASA's Solid Earth and Natural Hazards Program 1998 (SENH98) entitled High Resolution Gravity and Time Varying Gravity Field Recovery Using GRACE (Gravity Recovery and Climate Experiment) and CHAMP (Challenging Mini-satellite Package for Geophysical Research and Applications), which included a no-cost extension time period. The investigation has conducted pilot studies to use the simulated GRACE and CHAMP data and other in situ and space geodetic observable, satellite altimeter data, and ocean mass variation data to study the dynamic processes of the Earth which affect climate change. Results from this investigation include: (1) a new method to use the energy approach for expressing gravity mission data as in situ measurements with the possibility to enhance the spatial resolution of the gravity signal; (2) the method was tested using CHAMP and validated with the development of a mean gravity field model using CHAMP data, (3) elaborate simulation to quantify errors of tides and atmosphere and to recover hydrological and oceanic signals using GRACE, results show that there are significant aliasing effect and errors being amplified in the GRACE resonant geopotential and it is not trivial to remove these errors, and (4) quantification of oceanic and ice sheet mass changes in a geophysical constraint study to assess their contributions to global sea level change, while the results improved significant over the use of previous studies using only the SLR (Satellite Laser Ranging)-determined zonal gravity change data, the constraint could be further improved with additional information on mantle rheology, PGR (Post-Glacial Rebound) and ice loading history. A list of relevant presentations and publications is attached, along with a summary of the SENH investigation generated in 2000.

Shum, C. K.↗
NASA NTRS1989

Gravity field determination and error assessment techniques

Linear estimation theory, along with a new technique to compute relative data weights, was applied to the determination of the Earth's geopotential field and other geophysical model parameters using a combination of satellite ground-based tracking data, satellite altimetry data, and the surface gravimetry data. The relative data weights for the inhomogeneous data sets are estimated simultaneously with the gravity field and other geophysical and orbit parameters in a least squares approach to produce the University of Texas gravity field models. New techniques to perform calibration of the formal covariance matrix for the geopotential solution were developed to obtain a reliable gravity field error estimate. Different techniques, which include orbit residual analysis, surface gravity anomaly residual analysis, subset gravity solution comparisons and consider covariance analysis, were applied to investigate the reliability of the calibration.

Yuan, D. N.↗
NASA NTRS2012

Spacecraft Thermal and Optical Modeling Impacts on Estimation of the GRAIL Lunar Gravity Field

We summarize work performed involving thermo-optical modeling of the two Gravity Recovery And Interior Laboratory (GRAIL) spacecraft. We derived several reconciled spacecraft thermo-optical models having varying detail. We used the simplest in calculating SRP acceleration, and used the most detailed to calculate acceleration due to thermal re-radiation. For the latter, we used both the output of pre-launch finite-element-based thermal simulations and downlinked temperature sensor telemetry. The estimation process to recover the lunar gravity field utilizes both a nominal thermal re-radiation accleration history and an apriori error model derived from that plus an off-nominal history, which bounds parameter uncertainties as informed by sensitivity studies.

thermal modeling↗
NASA NTRS2010

Lunar Gravity Field Determination Using SELENE Same-Beam Differential VLBI Tracking Data

A lunar gravity field model up to degree and order 100 in spherical harmonics, named SGM 100i, has been determined from SELENE and historical tracking data, with an emphasis on using same-beam S-band differential VLBI data obtained in the SELENE mission between January 2008 and February 2009. Orbit consistency throughout the entire mission period of SELENE as determined from orbit overlaps for the two sub-satellites of SELENE involved in the VLBI tracking improved consistently from several hundreds of metres to several tens of metres by including differential VLBI data. Through orbits that are better determined, the gravity field model is also improved by including these data. Orbit determination performance for the new model shows improvements over earlier 100th degree and order models, especially for edge-on orbits over the deep far side. Lunar Prospector orbit determination shows an improvement of orbit consistency from I-day predictions for 2-day arcs of 6 m in a total sense, with most improvement in the along and cross-track directions. Data fit for the types and satellites involved is also improved. Formal errors for the lower degrees are smaller, and the new model also shows increased correlations with topography over the far side. The estimated value for the lunar GM for this model equals 4902.80080 +/- 0.0009 cu km/sq s (10 sigma). The lunar degree 2 potential Love number k2 was also estimated, and has a value of 0.0255 +/- 0.0016 (10 sigma as well).

Goossens, S.↗