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The optimal solution time that minimizes the sum of the two applied impulses necessary to rendezvous is obtained analytically for the Clohessy-Wiltshire equations with a linear gravity model assumption. A plume impingement inequality constraint on the solution is examined, and an optimal policy is developed. Numerical tests are conducted to verify the analysis and to illustrate the optimal solution algorithm.
Laser data from the Greenbelt, Bermuda, and Grand Turk Island tec tracking stations, and from observation at Patrick Air Force Base were used in an experiment to determine precise inter-station baselines and relative heights in short orbital arcs of no more than 12 minutes duration. The relative locations obtained are sensitive to reasonable variations in the gravity field to less than 15 cm in inter-station baseline and less than 35 cm in relative height. The formal standard deviations for range measurements at the observed 7 cm noise level are less than 10 cm for either baseline or relative height determinations from the twenty-arc combination solution. The method of data analysis is described, the baseline and relative height results are presented, and gravity model dependence is considered.
One of the main goals of the LAGEOS satellite mission is the detection of regional geotectonic movements. A parametric study with the intention to obtain the optimal baseline precision from dynamic solutions of laser ranging to LAGEOS is presented. The varied parameters are: length of reduced arc, number of tracking stations, data noise and rate, biases, refraction errors, system efficiency, gravity model errors in the value of GM. The baseline precisions are 1-10 cm depending upon the set of parameters adopted. General principles obtained are also presented.
African magmatism is largely related to the tensional stress regimes of the crust which are induced by the hotter upwelling mantle rocks. These mantle rocks may provide emanating forces and thermal energy for the upward movements of primary ore bodies with fluid inclusions in the tensional stress regimes of the crust. In this paper, the Goddard Earth Gravity Model is used to calculate a detailed subcrustal stress system exerted by mantle convection under Africa. The resulting system is found to be correlated with the African metallogenic provinces. Recognition of the full spectrum of ore deposits in Africa that may be associated with the hotter upwelling mantle rocks has provided an independent evidence to support the hypothesis of mantle-derived heat source for ore deposits.
A mean sea surface map has been determined for the global ocean areas between +62 deg and -62 deg latitude using GEOS 3 altimeter data. A grid of laser reference orbits computed using the GEM 10B gravity model has been used to orient the altimeter data in a center of mass coordinate system. The density of the altimeter tracks has enabled the computation of the sea surface heights above the reference ellipsoid on 1 deg x 1 deg grid in most of the oceanic areas. In the northwest Atlantic the dense coverage has enabled computations on a 0.25 deg x 0.25 deg grid. Comparisons of the global surface with an independently computed mean sea surface based upon SEASAT altimeter data indicate an rms agreement of a little over a meter. Comparisons of the regional solution in the northwest Atlantic with SEASAT profiles indicate a precision of a few decimeters in this surface. An analysis of the global crossover differences has indicated the possibility of a timing error in the altimeter data. Timing bias values of within 0.5 msec of 9.2 msec for 1975 and within 0.6 msec of 18.7 msec for 1976 have been recovered from an analysis of the altimeter data.
In this paper the tectonic features of the Elysium region are identified and characterized. Identification of features was made using USGS controlled photomosaics (Elysium quadrangle, and portions of Amenthes and Cebrenia quadrangles); Viking Orbiter photographic data were used in individual cases to assist in identification. The positions and orientations of tectonic features can then be used, in conjunction with estimates of the mass of the volcanic load obtained from gravity modelling, to constrain the thickness of the elastic lithosphere in the region.
Precise ephemerides for the High Energy Astronomy Observatory-2 (HEAO-2) were computed to assist in the Charles Stark Draper Laboratory development of an onboard orbit determination technique. Weighted least-squares, batch orbit solutions were calculated using a high-precision earth gravity model and an approximate model for intermittent spacecraft thrusting. With these improvements, orbit solution consistencies at the 50- to 100-meter level were attained using the Goddard Trajectory Determination System and NASA S-band tracking data.
The acceleration (gravity) anomaly estimates by spacecraft tracking, determined from Doppler residuals, are components of the gravity field directed along the spacecraft Earth line of sight (LOS). These data constitute a set of vector components of a planet's gravity field, the specific component depending upon where the Earth happened to be at the time of each measurement, and they are at varying altitudes above the planet surface. From this data set the gravity field vector components were derived using the method of harmonic splines which imposes a smoothness criterion to select a gravity model compatible with the LOS data. Given the piecewise model it is now possible to upward and downward continue the field quantities desired with a few parameters unlike some other methods which must return to the full dataset for each desired calculation.
Accurate orbits are necessary for altimeter satellites for operational computation of sea surface heights and for the determination of any bias in the altimeter measurement. These satellites require high accuracy throughout the orbit, in general a difficult task due to gravity model, solar radiation pressure, and atmospheric drag effects. Extensive analysis has reduced such errors for Seasat only to the 50 cm level. For calibration purposes the use of such an orbit would require a very large number of tracks to reduce the error to the sub-10 cm level even if all passes had only random errors. Since altimeter calibration orbits require high accuracy only over a limited geographical area, the use of a ranging station, such as a laser tracker in the calibration area can provide the required accuracy. The Bermuda laser provided such orbits for Seasat, with satellite-station height accuracy estimated to be at the sub-3 cm level. Because the station height is accurately known, such orbits can also be used to test global orbit accuracies.
The damping for structural dynamic models of flexible spacecraft is usually ignored and then added after modal frequencies and mode shapes are calculated. It is common practice to assume the same damping ratio for all modes, although it is known that damping due to bending and that due to torsion are sometimes ignored. Two methods of including damping in the modeling process from its onset are examined. First, the partial derivative equations of motion are analyzed for a pinned-pinned beam with damping. The end conditions are altered to handle bodies with mass and inertia for the Spacecraft Control Laboratory Experiment (SCOLE) configuration. Second, a massless beam approximation is used for the modes with low frequencies, and a clamped-clamped system is used to approximate the modes for arbitrarily high frequency. The model is then modified to include gravity effects and is compared with experimental results.
The accuracy and validation of global gravity models based on satellite data are discussed, responding to the statistical analysis of Lambeck and Coleman (1983) (LC). Included are an evaluation of the LC error spectra, a summary of independent-observation calibrations of the error estimates of the Goddard Earth Models (GEM) 9 and L2 (Lerch et al., 1977, 1979, 1982, 1983, and 1985), a comparison of GEM-L2 with GRIM-3B (Reigber et al., 1983), a comparison of recent models with LAGEOS laser ranging, and a summary of resonant-orbit model tests. It is concluded that the accuracy of GEMs 9, 10, and L2 is much higher than claimed by LC, that the GEMs are in good agreement with independent observations and with GRIM-3B, and that the GEM calibrations were adequate. In a reply by LC, a number of specific questions regarding the error estimates are addressed, and it is pointed out that the intermodel discrepancies of the greatest geophysical interest are those in the higher-order coefficients, not discussed in the present comment. It is argued that the differences among the geoid heights of even the most recent models are large enough to call for considerable improvements.
The two principle objectives of the project Thematic Mapper Study of Alaskan Ophiolites were to further develop techniques for producing geologic maps, and to study the tectonics of the ophiolite terrains of the Brooks Range and Ruby Geanticline of northern Alaska. Ophiolites, sections of oceanic lithosphere emplaced along island arcs and continental margins, are important to the understanding of mountain belt evolution. Ophiolites also provide an opportunity to study the structural, lithologic, and geochemical characteristics of ocean lithosphere, yielding a better understanding of the processes forming lithosphere. The first part of the report is a description of the methods and results of the TM mapping and gravity modeling. The second part includes papers being prepared for publication. These papers are the following: (1) an analysis of basalt spectral variations; (2) a study of basalt geochemical variations; (3) an examination of the cooling history of the ophiolites using radiometric data; (4) an analysis of shortening produced by thrusting during the Brooks Range orogeny; and (5) a study of an ophiolite using digital aeromagnetic and topographic data. Additional papers are in preparation.
The use of atmospheric drag for slowing satellite in high energy, high apogee orbits to a lower energy, lower apogee orbit about the Earth is investigated. The high energy orbit is assumed to intercept the Earth's atmosphere. Guidance for the atmospheric phase of the trajectory may be done using the aerodynamic forces generated by the passage through the atmosphere. This research was concerned with the investigation of several methods of guidance during the atmospheric phase to cause a significant reduction in the final velocity as the vehicle leaves the atmosphere. In addition, the velocity direction was controlled to exit to a desired target orbit. Lastly excess aerodynamic lift was used to effect a plane change between the entry orbit plane and the exit orbit plane to achieve a desired orbit plane. The guidance methods were applied to a 3 degree-of-freedom simulation which included an oblate Earth gravity model and a rotating atmosphere. Simulation results were compared on the basis of speed of computation of the guidance parameters and amount of added velocity necessary to achieve the desired orbit.
Plans for a Topex/Poseiden flight experiment to test the accuracy of using GPS data for precision orbit determination of earth satellites are presented. It is expected that the GPS-based precision orbit determination will provide subdecimeter accuracies in the radial component of the Topex orbit when the extant gravity model is tuned for wavelengths longer than about 1000 kms. The concept, design, flight receiver, antenna system, ground processing, and data processing of GPS are examined. Also, an accurate quasi-geometric orbit determination approach called nondynamic or reduced dynamic tracking which relies on the use of the pseudorange and the carrier phase measurements to reduce orbit errors arising from mismodeled dynamics is discussed.
In the 1990s low earth orbit operations are anticipated which will include the Space Station and orbital maneuver vehicle (OMV) serviceable satellites requiring reboost and coordination despite drag decay and oblateness effects. A low thrust targeting algorithm is described applicable to Space Station and the OMV. Tests were made with Space Station reboost requirements and an oblate gravity model. The reboost requirements were determined based on projected station growth, atmospheric models and anticipated flight profiles. The targeting algorithm as well as the algorithm for predicting orbital decay are perturbation formulations of more 'transcendental' systems and are used in interactive personal computer simulations. Performance results and a discussion for the Space Station problems are provided.
The Orbital Maneuvering Vehicle (OMV) will be remotely piloted during rendezvous, docking, or proximity operations with target spacecraft from a ground control console (GCC). The real-time mission simulator and graphics being used to design a console pilot-machine interface are discussed. A real-time orbital dynamics simulator drives the visual displays. The dynamics simulator includes a J2 oblate earth gravity model and a generalized 1962 rotating atmospheric and drag model. The simulator also provides a variable-length communication delay to represent use of the Tracking and Data Relay Satellite System (TDRSS) and NASA Communications (NASCOM). Input parameter files determine the graphics display. This feature allows rapid prototyping since displays can be easily modified from pilot recommendations. A series of pilot reviews are being held to determine an effective pilot-machine interface. Pilots fly missions with nominal to 3-sigma dispersions in translational or rotational axes. Console dimensions, switch type and layout, hand controllers, and graphic interfaces are evaluated by the pilots and the GCC simulator is modified for subsequent runs. Initial results indicate a pilot preference for analog versus digital displays and for two 3-degree-of-freedom hand controllers.
The Global Positioning System (GPS) can be applied in a number of ways to track remote sensing satellites at altitudes below 3000 km with accuracies of better than 10 cm. All techniques use a precise global network of GPS ground receivers operating in concert with a receiver aboard the user satellite, and all estimate the user orbit, GPS orbits, and selected ground locations simultaneously. The GPS orbit solutions are always dynamic, relying on the laws of motion, while the user orbit solution can range from purely dynamic to purely kinematic (geometric). Two variations show considerable promise. The first one features an optimal synthesis of dynamics and kinematics in the user solution, while the second introduces a novel gravity model adjustment technique to exploit data from repeat ground tracks. These techniques, to be demonstrated on the Topex/Poseidon mission in 1992, will offer subdecimeter tracking accuracy for dynamically unpredictable satellites down to the lowest orbital altitudes.
Results are reported from an extensive investigation of orbit-determination strategies for the Geosat Exact Repeat Mission (ERM). The goal is to establish optimum geodetic parameters and procedures for the computation of the most accurate Geosat orbits possible and to apply these procedures for routine computation during the ERM for the following purposes: (1) to enhance the value of the Geosat oceanographic investigations by providing the user community with improved ephemerides, (2) to develop orbit determination techniques for the upcoming altimetric mission Topex/Poseidon, and (3) to assess the radial orbit accuracy obtainable with recently developed gravity models. To this end, ephemerides for the entire first year of the ERM have been computed using the GEODYN II orbit program on the Cyber 205 supercomputer system at the NASA Goddard.