Methods of regularization for computing orbits in celestial mechanics
Numerical and analytical methods for orbit computation in celestial mechanics during and beyond collision by introduction of regularized coordinates
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Numerical and analytical methods for orbit computation in celestial mechanics during and beyond collision by introduction of regularized coordinates
In rotating machinery dynamics an orbit (Lissajous curve) represents the dynamic path of the shaft centerline motion during shaft rotation and resulting precession. The orbit can be observed with an oscilloscope connected to XY promixity probes. The orbits can also be simulated by a computer. The software for HP computer simulates orbits for two cases: (1) Symmetric orbit with four frequency components with different radial amplitudes and relative phase angles; and (2) Nonsymmetric orbit with two frequency components with two different vertical/horizontal amplitudes and two different relative phase angles. Each orbit carries a Keyphasor mark (one-per-turn reference). The frequencies, amplitudes, and phase angles, as well as number of time steps for orbit computation, have to be chosen and introduced to the computer by the user. The orbit graphs can be observed on the computer screen.
Orbit computation and tracking system for Iris satellite using differential correction program
Lunar gravity models for improved Apollo orbit computation
Generalized, cyclic, and modified multistep numerical integration methods are developed and evaluated for application to problems of satellite orbit computation. Generalized methods are compared with the presently utilized Cowell methods; new cyclic methods are developed for special second-order differential equations; and several modified methods are developed and applied to orbit computation problems. Special computer programs were written to generate coefficients for these methods, and subroutines were written which allow use of these methods with NASA's GEOSTAR computer program.
Methods of regularization for computing orbits in celestial mechanics
Earth satellite orbit computations - Diliberto general perturbation method application in improved coordinate system
QUIKVIS computer program calculates times during orbit around Earth when geometric requirements satisfied for observing celestial objects. Observed objects fixed (e.g. stars) or moving (Sun, Moon, planets). Useful for preflight analysis by those needing information on availability of celestial objects to be observed. Performs two types of analyses: One used when specific objects known, other when targets unknown and potentially useful regions of sky must be identified. Results useful in selecting candidate targets, examining effects of observation requirements, and doing gross assessments of effects of right ascension of ascending node (RAAN) of orbit. Written in FORTRAN 77.
Recent efforts to recompute orbits for the Geosat Exact Repeat Mission have resulted in a substantial reduction in the satellite's orbit error. The improved orbits are based on Doppler tracking and on the new earth gravity models being developed at the Goddard Space Flight Center in support of requirements for the TOPEX/Poseidon mission. The first set of orbit solutions based on the Goddard Earth Model (GEM T1) gravity model and tracking data from the U.S. Navy's Operational Network system are accurate to about 85 cm root mean square (rms) in height. Preliminary tests of orbits computed with the GEM-T2 model, along with tracking data from an augmented network consisting of the Navy's Operational Network and selected Tracking Network sites, indicate that radial accuracies of 35 cm rms can be achieved.
Satellite orbit computation program for izsak second-order solution of vinti dynamical problem
The Flight Design System (FDS) and the Unified System for Orbit Computation (USOC) are compared and described in relation to mission planning for the shuttle transportation system (STS). The FDS is designed to meet the requirements of a standardized production tool and the USOC is designed for rapid generation of particular application programs. The main emphasis in USOC is put on adaptability to new types of missions. It is concluded that a software system having a USOC-like structure, adapted to the specific needs of MPAD, would be appropriate to support planning tasks in the area unique to STS missions.
Taking advantage of the improvements to the Earth's gravitation field and tracking station coordinates, an orbital computational consistency of the order of 5 meters was achieved for total position differences between orbital solutions for the Seasat and GEOS-3. The main source of error in these solutions was in the mathematical models that are required to generate these results, i.e., gravitation, atmospheric drag, etc. Different Earth gravitation fields and tracking coordinates were analyzed and evaluated in obtaining these computational results. Comparisons and evaluations of the Seasat results were obtained in terms of different solution types such as the Doppler only, Laser only, Doppler and Laser, etc. Other investigation using the Seasat data were made in order to determine their effect on the computational results at this particular level of consistency.
Atmospheric density effect on computation of earth satellite orbits
The Starlette satellite, launched in February 1975 was designed to minimize the effects of nongravitational forces and to obtain the highest possible accuracy for laser range measurements. Analyses of the first four months of laser tracking data from nine stations have confirmed the stability of the orbit and the precision to which the satellite's position can be established. Initial orbit computations using the GSFC GEM - 7 gravity model produced rms fits of about 8 to 10 meters for arc lengths of 5 days. After tailoring a gravity model specifically to Starlette, the rms fits for the 5 day arcs were reduced significantly to the 1 to 2 meter level. An rms fit of 4.3 meters was obtained for a 90 day arc. Five day arcs overlapped by 2.5 days showed rms satellite position differences generally less than 2 meters. Prediction errors at the end of two months were less than 30 milliseconds.
As part of a continuing effort to provide improved orbits for use with existing altimeter data, we have recomputed ephemerides for both the Seasat and Geosat Exact Repeat altimeter missions. The orbits were computed in a consistent fashion, using the Goddard Earth Model T2 (GEM-T2) gravity field along with available ground-based tracking data. Such an approach allows direct comparisons of sea level between the two altimeter systems. Evaluation of the resulting ephemerides indicates that root-mean-square accuracies of 30-50 cm have been achieved for the radial component of the orbits for both satellites. An exception occurs for the last year of the Geosat Exact Repeat Mission, when the rms radial orbit accuracy degrades to the 1-m level at times owing to the inability to adequately model the drag force arising from the increased solar activity.
The research project described below is part of a long-term program at Delft University of Technology aiming at the application of European Remote Sensing satellite (ERS-1) and TOPEX/POSEIDON altimeter measurements for geophysical purposes. This program started in 1980 with the processing of Seasat laser range and altimeter height measurements and concentrates today on the analysis of Geosat altimeter data. The objectives of the TOPEX/POSEIDON research project are the tracking of the satellite by the Dutch mobile laser tracking system MTLRS-2, the computation of precise TOPEX/POSEIDON orbits, the analysis of the spatial and temporal distribution of the orbit errors, the improvement of ERS-1 orbits through the information obtained from the altimeter crossover difference residuals for crossing ERS-1 and TOPEX/POSEIDON tracks, the combination of ERS-1 and TOPEX/POSEIDON altimeter data into a single high-precision data set, and the application of this data set to model the sea surface. The latter application will focus on the determination of detailed regional mean sea surfaces, sea surface variability, ocean topography, and ocean currents in the North Atlantic, the North Sea, the seas around Indonesia, the West Pacific, and the oceans around South Africa.
Cowell numerical integration and satellite orbit calculation
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.