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NASA NTRS2019

Efficient On-Orbit Singularity-Free Geopotential Estimation

The complexity of the geopotential model can heavily impact the navigation error in satellites and spacecraft. Geopotential models of the accuracy needed for spaceflight are too complicated for flight computers to run at the rate needed by the navigation system. There are methods to make the geopotential model more efficient while maintaining the needed accuracy, which include: using an efficient method for the full model, propagating to avoid singularities, and running the full model at a low rate and propagating to the needed rate. These methods can decrease the computational requirement enough to be run by the flight computer at the rate required of the navigation system.

Amert, Joel↗

NASA NTRS1973

Eleventh order resonance terms in the geopotential from the orbit of Vanguard 3

The orbit of Vanguard 3 (1959-7A) is strongly resonant with 11th order and odd degree terms in the geopotential. It affords an excellent opportunity to determine a significant linear constraint between these terms. Tracking data on this satellite (in the form of mean Kepler elements) are analyzed over a 3 1/2 year period in the early 1960's, which ends with the orbit having just passed through perfect commensurability. The eccentricity and inclination show the deep resonance variations (up to 0.0002 in e and .02 deg in i) with great clarity. Previous and current geopotential solutions fail to explain these perturbations.

Wagner, C. A.↗

NASA NTRS1974

Eleventh-order geopotential resonance on the orbit of Vanguard 3

The orbit of Vanguard 3 (1959-7A) is strongly resonant with eleventh-order and odd degree terms in the geopotential. It affords an excellent opportunity to determine a significant linear constraint between these terms. Tracking data on this satellite (in the form of mean Kepler elements) are analyzed over a 3.5-year period in the early 1960s, which ends with the orbit having just passed through perfect commensurability. The eccentricity e and inclination I show the deep resonance variations (up to .0002 in e and 0.02 deg in I) with great clarity. Previous and current geopotential solutions fail to explain these perturbations. A constraint for the deep resonant terms is determined in fully normalized harmonics.

Wagner, C. A.↗

NASA NTRS1975

Applications of satellite-to-satellite tracking to orbit determination and geopotential recovery

Recent simulations have demonstrated the applicability of satellite-to-satellite tracking data to the related problems of orbit determination and geopotential recovery. Specifically, satellite-to-satellite tracking between an earth orbiting satellite and a satellite at geosynchronous altitude (36000 km) produces long continuous data arcs which are not available by means of ground-based tracking. This facility, in conjunction with correct estimation techniques, yields exceptional orbit determination accuracy. The data type also has considerable applicability to geopotential determination when the low satellite has a high inclination.

Argentiero, P.↗

NASA NTRS1978

The accuracy of geopotential models

The accuracy of two recent geopotential models, GEM 7 and GEM 8, is evaluated and is found to be about 4.3 m with respect to the global geoid surface for GEM 7 and 3.9 m for GEM 8. The accuracies are root mean square values obtained by the use of 400 coefficients for GEM 7 and 706 coefficients for GEM 8. Independent observations used in the evaluation include 159 lumped coefficients from 35 resonant orbits, two sets of fields derived from optical-only and laser-only data, sets of zonal and resonant coefficients, and geoid undulations. The ratio of estimated commission to formal error in GEM 7 and GEM 8 ranges from 2 to 5. Several other recent geopotential models are examined.

Wagner, C. A.↗

NASA NTRS1980

Determination of the geopotential from satellite-to-satellite tracking data

Ground-based observation of the deviation of artificial satellite trajectories from a reference path is the classical means for determining the parameters of the global geopotential. However, for the short wavelengths (less than 10 deg), tracking coverage from ground stations of sufficient density is impossible to obtain. But one or more satellites can observe another satellite and obtain the needed global data coverage. Results are presented of error analyses of possible satellite-to-satellite tracking missions to determine the geopotential at a resolution of 1 x 1 deg. To achieve an accuracy of a few milligals at this resolution requires a satellite altitude at or near 150 km and measurements of intersatellite speed to 10 to the -6th m/s.

Douglas, B. C.↗

NASA NTRS1981

Geopotential resonance in a Landsat orbit

A Landsat 1 resonance analysis was conducted on the basis of almost continuous range-rate observations provided by the S-Band station at Greenbelt, MD for a twenty-four day period in September 1976. Constraints on the resonance effects of Landsat 1, determined directly from radar tracking data could be summarized in a number of equations for fully normalized geopotential coefficients. The coefficient values for the dominant resonance terms can be directly determined through the estimation scheme, as the resonance constraints are implicit in the spherical harmonic representation chosen for the geopotential. The degree of the constraint equation series may be arbitrarily increased with analytical expressions for the along-track orbital component in terms of Keplerian elements.

Dunn, P.↗

NASA NTRS1982

Signal analysis and error analysis studies for a Geopotential Research Mission (GRM)

The signal characteristics and the geopotential parameter recovery capability of the SST Doppler sensor flown on the geopotential research mission (GRM) are discussed. Simulation studies of the velocity profiles resulting from the perturbation produced by a 1 deg/w/1 deg, 1 mgal anomaly as sensed by two GRM spacecraft orbiting altitudes of 160 km and 200 km respectively are described. It was found that the amplitude of the gravity signal drops off by a factor of 1.5 when going from an altitude of 160 km to 200 km. By extrapolation the signal amplitude is further decreased by a factor of 3 when the orbital altitude is increased to 250 km. Thus the amplitude of the measurement drops off as the altitude is increased to the point where it is insignificant at the 1 mgal level for altitudes above 200 km. Spectral analysis results show that for a GRM mission altitude of 160 km and a system precision of 1 micrometer/sec, gravity field information can be sensed up to 230 cycles per orbital revolution - beyond that frequency the gravity signal is characterized by white noise. It follows that at the GRM mission altitude of 160 km and a satellite to satellite Doppler system precision of 1 micrometer per second, 1/1 deg gravity and geoid anomalies can be determined to an accuracy of 3.4 mgals and 8.6 cm respectively.

Kahn, W. D.↗

NASA NTRS1983

Diagnoses of tropical geopotential during the Southern Hemisphere summer

The effect of strong amplitude and high frequency oscillations of divergent circulations in the Southern Hemisphere on estimates of tropical geopotential during the summer is quantified. FGGE data are analyzed in order to determine the mass-flow balance in the upper troposphere, and outgoing longwave radiation averaged over two periods, January and February 1979, is given. It is found that the divergence terms for balance equations may represent geopotential perturbations on the order of 20 to 30 m, and that the influence of strong latent heat releases and divergent circulations in the Southern Hemisphere can invalidate analysis schemes based on quasi-nondivergent solutions.

Paegle, J. N.↗

NASA NTRS1987

Simulation and analysis of a geopotential research mission

Computer simulations were performed for a Geopotential Research Mission (GRM) to enable the study of the gravitational sensitivity of the range rate measurements between the two satellites and to provide a set of simulated measurements to assist in the evaluation of techniques developed for the determination of the gravity field. The simulations were conducted with two satellites in near circular, frozen orbits at 160 km altitudes separated by 300 km. High precision numerical integration of the polar orbits were used with a gravitational field complete to degree and order 360. The set of simulated data for a mission duration of about 32 days was generated on a Cray X-MP computer. The results presented cover the most recent simulation, S8703, and includes a summary of the numerical integration of the simulated trajectories, a summary of the requirements to compute nominal reference trajectories to meet the initial orbit determination requirements for the recovery of the geopotential, an analysis of the nature of the one way integrated Doppler measurements associated with the simulation, and a discussion of the data set to be made available.

Schutz, B. E.↗

NASA NTRS1987

The error associated with use of various forms of the divergence equation to diagnose geopotential and temperature

This study utilizes a model-generated data set to evaluate the errors associated with the diagnosis of geopotential height using three approximate forms of the divergence equation (DE). The DE was solved on the original sigma-coordinate surfaces of the model to exclude any error produced in the process of interpolating the data from observation points to the coordinate surface of the DE. An inviscid, nonlinear, divergent DE produced rms geopotential height errors as large as 3 m and rms temperature errors of over 26 C in the lower planetary boundary layer (PBL), with minimal errors above 800 mb. Elimination of the isobaric divergence in the velocity field caused additional height errors of 5-6 m and temperature errors of 0.4-1.2 C in the free troposphere. Use of a further-degraded DE without nonlinear terms caused height errors of 10-15 m in the upper troposphere with modestly increased temperature errors. Error fields at all levels had synoptic-scale features, with some mesoalpha structure. No spatial noise was apparent. Use of a temporal spectral filter to eliminate high-frequency modes from the model-generated data did not significantly influence the error associated with use of various forms of the DE.

Modica, George M.↗

NASA NTRS1987

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.↗

NASA NTRS1988

Developments in the simulation of a geopotential research mission

An essential element of any satellite system that will be used to recover information about high degree and order terms in the geopotential model of the earth is one or more low altitude (about 160 km) satellites equipped with a drag compensation mechanism. To study the effects of various error sources and to test the new theoretical and numerical techniques that will be developed for such a mission, two simulated scenarios have been used with a geopotential model complete to degree and order 360 and Encke's method to numerically integrate the equations of motion. The two scenarios include the low-low dual satellite system with integrated, one-way Doppler measurements and the single satellite system with gradiometer measurements. The simulations include a reference orbit which is assumed to be available from conventional tracking systems.

Schutz, B. E.↗

NASA NTRS1988

The effects of geopotential resonance on orbit determination for Landsat-4

Analysis is presented demonstrating improved performance for Landsat-4 orbit determination using the Goddard Trajectory Determination System with an adjusted Goddard Earth Model-9 (GEM-9) for geopotential coefficients of the 15th degree and order. The orbital state is estimated along with the sine and cosine coefficients of degree and order 15, (C, S) sub 15,15. The estimates are made for two 5-day intervals of range and doppler data, primarily from the Tracking and Data Relay Satellite, during a period of low solar activity in January 1987. The average values of the estimated coefficients (C, S) sub 15,15 are used to modify the GEM-9 model, and orbit determination performance is tested on 17 consecutive 34-hour operational tracking data arcs in January 1987. Significant reductions in the mean values and standard deviations of the along-track position difference and the drag model scaling parameter from solution to solution are observed. The approach is guided by the shallow resonance theory of geopotential orbit perturbations.

Hoge, S. L.↗

NASA NTRS1988

Evaluation of advanced geopotential models for operational orbit determination

To meet future orbit determination accuracy requirements for different NASA projects, analyses are performed using Tracking and Data Relay Satellite System (TDRSS) tracking measurements and orbit determination improvements in areas such as the modeling of the Earth's gravitational field. Current operational requirements are satisfied using the Goddard Earth Model-9 (GEM-9) geopotential model with the harmonic expansion truncated at order and degree 21 (21-by-21). This study evaluates the performance of 36-by-36 geopotential models, such as the GEM-10B and Preliminary Goddard Solution-3117 (PGS-3117) models. The Earth Radiation Budget Satellite (ERBS) and LANDSAT-5 are the spacecraft considered in this study.

Radomski, M. S.↗

NASA NTRS1990

The relationship of extratropical outgoing longwave radiation to monthly geopotential teleconnection patterns

The relationship between low frequency variations in extratropical fields of outgoing longwave radiation (OLR) and geopotential teleconnection patterns as determined by rotated principal components analysis of the NMC 500-mb heights is investigated in the Northern Hemisphere. The monthly broadband OLR is obtained from the Nimbus-6 and Nimbus-7 Wide-Field-Of-View radiometer record. Each of the main 500-mb teleconnection patterns has a characteristic signal in the OLR field for the month in which the 500-mb pattern occurs. The OLR signals mark cloud and diabatic heating events that are associated with the teleconnection patterns. A demonstration is given of correlation between extratropical monthly OLR and geopotential height. Coupled with the expected tropospheric response to radiation on monthly time scale. This demonstration stresses the importance of the radiation simulation in model studies of the low frequency variability of atmospheric circulation. The extratropical OLR does not appear to be a useful predictor for the 500-mb teleconnection patterns on a monthly time scale.

Charlock, Thomas P.↗

NASA NTRS1991

The Ohio State 1991 geopotential and sea surface topography harmonic coefficient models

The computation is described of a geopotential model to deg 360, a sea surface topography model to deg 10/15, and adjusted Geosat orbits for the first year of the exact repeat mission (ERM). This study started from the GEM-T2 potential coefficient model and it's error covariance matrix and Geosat orbits (for 22 ERMs) computed by Haines et al. using the GEM-T2 model. The first step followed the general procedures which use a radial orbit error theory originally developed by English. The Geosat data was processed to find corrections to the a priori geopotential model, corrections to a radial orbit error model for 76 Geosat arcs, and coefficients of a harmonic representation of the sea surface topography. The second stage of the analysis took place by doing a combination of the GEM-T2 coefficients with 30 deg gravity data derived from surface gravity data and anomalies obtained from altimeter data. The analysis has shown how a high degree spherical harmonic model can be determined combining the best aspects of two different analysis techniques. The error analysis was described that has led to the accuracy estimates for all the coefficients to deg 360. Significant work is needed to improve the modeling effort.

Rapp, Richard H.↗

NASA NTRS1993

Present-day secular variations in the zonal harmonics of earth's geopotential

The mathematical formulation required for predicting secular variation in the geopotential is developed for the case of a spherically symmetric, self-gravitating, viscoelastic earth model and an arbitrary surface load which can include a gravitational self-consistent ocean loading component. The theory is specifically applied to predict the present-day secular variation in the zonal harmonics of the geopotenial arising from the surface mass loading associated with the late Pleistocene glacial cycles. A procedure is outlined in which predictions of the present-day geopotential signal due to the late Pleistocene glacial cycles may be used to derive bounds on the net present-day mass flux from the Antarctic and Greenland ice sheets to the local oceans.

Mitrovica, J. X.↗