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All sourcesNASA NTRSDOE OSTI
NASA NTRS1994

Lifetimes of lunar satellite orbits

The Space Exploration Initiative has generated a renewed interest in lunar mission planning. The lunar missions currently under study, unlike the Apollo missions, involve long stay times. Several lunar gravity models have been formulated, but mission planners do not have enough confidence in the proposed models to conduct detailed studies of missions with long stay times. In this report, a particular lunar gravitational model, the Ferrari 5 x 5 model, was chosen to determine the lifetimes for 100-km and 300-km perilune altitude, near-circular parking orbits. The need to analyze orbital lifetimes for a large number of initial orbital parameters was the motivation for the formulation of a simplified gravitational model from the original model. Using this model, orbital lifetimes were found to be heavily dependent on the initial conditions of the nearly circular orbits, particularly the initial inclination and argument of perilune. This selected model yielded lifetime predictions of less than 40 days for some orbits, and other orbits had lifetimes exceeding a year. Although inconsistencies and limitations are inherent in all existing lunar gravity models, primarily because of a lack of information about the far side of the moon, the methods presented in this analysis are suitable for incorporating the moon's nonspherical gravitational effects on the preliminary design level for future lunar mission planning.

Meyer, Kurt W.↗
NASA NTRS1988

On estimating the basin-scale ocean circulation from satellite altimetry. Part 1: Straightforward spherical harmonic expansion

Direct estimation of the absolute dynamic topography from satellite altimetry has been confined to the largest scales (basically the basin-scale) owing to the fact that the signal-to-noise ratio is more unfavorable everywhere else. But even for the largest scales, the results are contaminated by the orbit error and geoid uncertainties. Recently a more accurate Earth gravity model (GEM-T1) became available, providing the opportunity to examine the whole question of direct estimation under a more critical limelight. It is found that our knowledge of the Earth's gravity field has indeed improved a great deal. However, it is not yet possible to claim definitively that our knowledge of the ocean circulation has improved through direct estimation. Yet, the improvement in the gravity model has come to the point that it is no longer possible to attribute the discrepancy at the basin scales between altimetric and hydrographic results as mostly due to geoid uncertainties. A substantial part of the difference must be due to other factors; i.e., the orbit error, or the uncertainty of the hydrographically derived dynamic topography.

Tai, Chang-Kou↗
NASA NTRS1974

Evaluation and comparisons of recent geopotential solutions

A statistical evaluation of some of the recent satellite determined gravity models, including some with distinct data base, indicates that the geopotential coefficients of these models are individually meaningful for frequencies with wave numbers n = 2 through 7 certainly and wave numbers n = 8 through 10 probably. Geopotential coefficients in higher frequency ranges while apparently important for computing accurate satellite orbits seem to have little geophysical significance in an individual sense. Differences between various gravity models and those satellite purely between determined geopotential models and their associated combination models show no consistent relationship to surface gravimetric coverage. Additional classical tracking data are important in improving the existing description of the earth's gravity field but their contribution in extending its frequency range beyond what is now available is uncertain.

Khan, M. A.↗
NASA NTRS1994

GPS tracking of TOPEX/POSEIDON: Results and implications

A reduced dynamic filtering strategy that exploits the unique geometric strength of the Global Positioning System (GPS) to minimize the effects of force model errors has yielded orbit solutions for TOPEX/POSEIDON which appear accurate to better than 3 cm (1 sigma) in the radial component. Reduction of model error also reduces the geographic correlation of the orbit error. With a traditional dynamic approach, GPS yields radial orbit accuracies of 4-5 cm, comparable to the accuracy delivered by satellite laser ranging and the Doppler orbitography and radio positioning integrated by satellite (DORIS) tracking system. A portion of the dynamic orbit error is in the Joint Gravity Model-2 (JGM-2); GPS data from TOPEX/POSEIDON can readily reveal that error and have been used to improve the gravity model.

Bertiger, W. I.↗
NASA NTRS1987

Kinematics and dynamics of the Uranian rings

The self-gravity model of apse alignment was tested by comparing its predictions about structure within the epsilon ring with an extensive set of observed occultation profiles covering a wide range of ring longitudes. The self-gravity model as presently constructed is inconsistent with the observations. The Lindblad resonance survey and Shepherd satellite ring perturbation are discussed. The kinematic model of the Uranian ring orbit was enhanced to accommodate Voyager observations as well as ground-based occultation observations.

French, Richard G.↗
NASA NTRS1992

Incorporation of a priori gravity field information in satellite orbit determination using bin parameters

A method to determine satellite orbits using tracking data and a priori gravitational field is described. The a priori constraint on the orbit dynamics is determined by the covariance matrix of the spherical harmonic coefficients for the gravity model, so that the optimal combination of the measurements and gravitational field is achieved. A set of bin parameters is introduced to represent the perturbation of the gravitational field on the position of the satellite orbit. The covariance matrix of a conventional gravity model is transformed into that for the bin parameters by the variational partial derivatives. The covariance matrices of the bin parameters and the epoch state are combined to form the covariance matrix of the satellite positions at the measurement times. The combined matrix is used as the a priori information to estimate the satellite positions with measurements.

Wu, Jiun-Tsong↗
NASA NTRS1972

Tracking-station coordinates from Geos 1 and Geos 2 optical flash data.

Center-of-mass coordinates for 28 NASA MOTS and SAO Baker-Nunn camera sites have been obtained from optical flash data from Geos 1 (1965 89A) and Geos 2 (1968 002A). More than 25,000 observations in about 100 two-day arcs were used in dynamical solutions (SAO 1969 AGU gravity model). Comparison of results with local survey solutions and with solutions from deep-space vehicle tracking suggests accuracy of about 2 meters in longitude and height and 5 meters in latitude. The relatively larger error in latitude arose from propagation of gravity-model error largely along the track of these high-inclination satellites. The results have also been compared with the solutions of the SAO 1969 standard earth for station coordinates on the North American datum. The solution obtained in the present work is much closer to the survey results in chord length between stations.

Marsh, J. G.↗
NASA NTRS2016

Trajectory Design Employing Convex Optimization for Landing on Irregularly Shaped Asteroids

Mission proposals that land spacecraft on asteroids are becoming increasingly popular. However, in order to have a successful mission the spacecraft must reliably and softly land at the intended landing site with pinpoint precision. The problem under investigation is how to design a propellant optimal powered descent trajectory that can be quickly computed onboard the spacecraft, without interaction from the ground control. The propellant optimal control problem in this work is to determine the optimal finite thrust vector to land the spacecraft at a specified location, in the presence of a highly nonlinear gravity field, subject to various mission and operational constraints. The proposed solution uses convex optimization, a gravity model with higher fidelity than Newtonian, and an iterative solution process for a fixed final time problem. In addition, a second optimization method is wrapped around the convex optimization problem to determine the optimal flight time that yields the lowest propellant usage over all flight times. Gravity models designed for irregularly shaped asteroids are investigated. Success of the algorithm is demonstrated by designing powered descent trajectories for the elongated binary asteroid Castalia.

Pinson, Robin M.↗
NASA NTRS1987

Analysis and simulations of a troposphere-stratosphere gravity wave model. I

An analytical model is presented that accommodates nonhydrostatic shearing stratified flow over an obstacle, and that can be modified to include a superposed stratosphere with constant wind and higher stability. A simulation code is used in parallel with the analytic calculations to demonstrate a methodology for determining the wavelength and magnitude of gravity wave energy reflected, and that transmitted, by the tropopause.

Wurtele, M. G.↗
NASA NTRS1994

Observations of geographically correlated orbit errors for TOPEX/Poseidon using the global positioning system

We have compared Global Positioning System (GPS)-based dynamic and reduced-dynamic TOPEX/Poseidon orbits over three 10-day repeat cycles of the ground-track. The results suggest that the prelaunch joint gravity model (JGM-1) introduces geographically correlated errors (GCEs) which have a strong meridional dependence. The global distribution and magnitude of these GCEs are consistent with a prelaunch covariance analysis, with estimated and predicted global rms error statistics of 2.3 and 2.4 cm rms, respectively. Repeating the analysis with the post-launch joint gravity model (JGM-2) suggests that a portion of the meridional dependence observed in JGM-1 still remains, with global rms error of 1.2 cm.

Christensen, E. J.↗
NASA NTRS1990

Interpretation of ground-based radiometric observations in terms of a gravity wave model

An analysis is presented of 2-hour and 4-hour segments of data taken at Denver, Colorado, on February 3, 1984, by a ground-based radiometer designed and operated by the Wave Propagation Laboratory of the National Oceanic and Atmospheric Administration (NOAA). The zenith-viewing instrument has two moisture-sensing and four temperature-sensing channels. It is demonstrated that a peak at a period of 10 min, present in the spectra of the measured brightness temperature and of the derived geopotential heights, thicknesses, and vertically integrated water vapor content, is due to an internal gravity wave generated by wind shear in the jet aloft. This analysis shows that the radiometer has the sensitivity to detect such disturbances and that the mathematical inversion technique used to retrieve the geopotential field and other integrated quantities retains the derived information as well. Finally, a linear expression is derived which relates the brightness temperature to the atmospheric temperature, density, humidity, and cloud liquid perturbation fields.

Canavero, F. G.↗
NASA NTRS1999

The 1998 to 1999 GEOS-3 Tracking Campaign: Analysis and Results

The GEOS-3 spacecraft was launched by NASA on April 23, 1975. The payload of the gravity-gradient stabilized spacecraft consisted of a radar altimeter, Doppler beacons, and a Laser retroreflector. The GEOS-3 satellite-to-satellite tracking (SST) Doppler data and the satellite laser ranging (SLR) data have been an integral and valuable part of gravity model solutions developed at the Goddard Space Flight Center from GEM 9 through EGM96. GEOS-3 is Located in an unique orbit at 850 km attitude and 115 degrees inclination. The data included in these solutions were acquired from 1975 through 1980. Since 1980, the SLR system precision has improved from 8 to 10 cm in 1980 to the subcm level for the best stations in the 1990's. The ILRS (International laser ranging service) initiated a new tracking campaign for this spacecraft in October 1998, and through January, 1999, some 850 passes and 10,000 normal points were acquired. The quality of the "new" data obtained during this tracking campaign is assessed, and the impact of these "new" data on Earth gravity model solutions is evaluated.

Lemoine, Frank G.↗
NASA NTRS1987

Development and testing of a unique carousel wind tunnel to experimentally determine the effect of gravity and the interparticle force on the physics of wind-blown particles

In the study of planetary aeolian processes the effect of gravity is not readily modeled. Gravity appears in the equations of particle motion along with the interparticle forces but the two are not separable. A wind tunnel that perimits multiphase flow experiments with wind blown particles at variable gravity was built and experiments were conducted at reduced gravity. The equations of particle motion initiation (saltation threshold) with variable gravity were experimentally verified and the interparticle force was separated. A uniquely design Carousel Wind Tunnel (CWT) allows for the long flow distance in a small sized tunnel since the test section if a continuous loop and develops the required turbulent boundary layer. A prototype model of the tunnel where only the inner drum rotates was built and tested in the KC-135 Weightless Wonder 4 zero-g aircraft. Future work includes further experiments with walnut shell in the KC-135 which sharply graded particles of widely varying median sizes including very small particles to see how interparticle force varies with particle size, and also experiments with other aeolian material.

Leach, R. N.↗
NASA NTRS1972

Models of gravity wave perturbations of the neutral upper atmosphere of the earth

Observational data from an array of CW Doppler sounding stations were analyzed and traveling ionospheric disturbances (TID's) were identified and analyzed using spectral analysis techniques. Seasonal variations in frequency, direction, and speed of propagation of TID's were found, which could be explained as manifestations of internal acoustic gravity waves, where propagation was influenced by the thermodynamic structure of the mesosphere and lower thermosphere.

Rao, G. L.↗
NASA NTRS1977

Analysis of the depletion of a stored aerosol in low gravity

The depletion of an aerosol stored in a container has been studied in l-g and in low gravity. Models were developed for sedimentation, coagulation and diffusional losses to the walls. The overall depletion caused by these three mechanisms is predicted to be of order 5 to 8 percent per hour in terrestrial conditions, which agrees with laboratory experience. Applying the models to a low gravity situation indicates that there only coagulation will be significant. (Gravity influences diffusional losses because of convection currents caused by random temperature gradients). For the types of aerosol studied, the rate of depletion of particles should be somewhat less than 0.001 N percent per hour, where N is the concentration per cu cm.

Squires, P.↗
NASA NTRS1985

A ray tracing model of gravity wave propagation and breakdown in the middle atmosphere

Lindzen (1981, 1984) has considered the effects of monochromatic, steady gravity waves propagating into the upper atmosphere. These waves reach such large amplitudes in the mesosphere that they become convectively unstable. The wave is effectively dissipated by the convection, and the pseudomomentum carried by the wave is transferred to the basic flow. The net effect is to accelerate the background flow to the phase speed of the breaking gravity wave. Schoeberl et al. (1983) have discussed modifications to Lindzen's parameterization. The present paper has the objective to develop a type of parameterization scheme for wave breaking that, in principle, can handle lateral wave propagation. Ray tracing is used to follow the gravity wave packets through varying wind conditions. The theory considered uses both the propagation properties of the wave packet and the concept of the conservation of wave action density to determine the local amplitude and position of the wave packet.

Schoeberl, M. R.↗
NASA NTRS1986

Design and calibration of the carousel wind tunnel

In the study of planetary aeolian processes the effect of gravity is not readily modeled. Gravity appears in the equations of particle motion along with interparticle forces but the two terms are not separable. A wind tunnel that would permit variable gravity would allow separation of the forces and aid greatly in understanding planetary aeolian processes. The design Carousel Wind Tunnel (CWT) allows for a long flow distance in a small sized tunnel since the test section is a continuo us circuit and allows for a variable pseudo gravity. A prototype design was built and calibrated to gain some understanding of the characteristics of the design and the results presented.

Leach, R. N.↗
NASA NTRS1987

Design and calibration of the carousel wind tunnel

In the study of planetary aeolian processes the effect of gravity is not readily modeled. Gravity appears in the equations of particle motion along with interparticle forces but the two terms are not separable. A wind tunnel that would permit variable gravity would allow separation of the forces and aid greatly in understanding planetary aeolian processes. The design of the Carousel Wind Tunnel (CWT) allows for a long flow distance in a small sized tunnel since the test section is a continuous circuit and allows for a variable pseudo-gravity. A prototype design was built and calibrated to gain some understanding of the characteristics of the design and the results presented.

Leach, R. N.↗