The earths gravity field to 16th degree and station coordinates from satellite and terrestrial data
Geodetic parameters of earth gravity field and satellite tracking station positions in geocentric reference frame
Gaposchkin, E. M.↗
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Geodetic long baseline interferometry research in Canada
The objectives and results of several studies using the Canadian long baseline interferometry system (LBI) are presented. The precision of measurements from radio telescopes at the Algonquin Radio Observatory (ARO), Lake Traverse, Ontario; the Owens Valley Radio Observatory (OVRO), Big Pine, California; and the Chilbolton Observatory (CHIL), Chilbolton, England, is discussed. Also, since LBI is insensitive to the uncertainty in the geocentric gravitational constant, it is a very useful technique for determining the scales of the coordinate systems used by other precise techniques. Beginning in May 1977, a number of LBI observing sessions were accompanied by simultaneous satellite Doppler observations. The baseline components obtained from the satellite Doppler observations were compared to the LBI values. The weighted mean scale bias of the NSWC 9Z-2 satellite Doppler coordinate system relative to the LBI system was found to be 0.42 + or - 0.05 PPM. The weighted mean difference in the origin of longitude was found to be 0.87 sec + or - 0.01 while the difference in declination origin was found to be 0.06 sec + or - 0.01.
Langley, R. B.↗
The relation of the European Datum to a geocentric reference system
Over 31,000 precision reduced optical observations of GEOS-1 and 2 in 70 two-day orbital arcs were used at Goddard Space Flight Center (GSFC) in a dynamical solution to determine center-of-mass coordinates for 15 tracking stations on the European Datum. Comparisons with the results obtained at Centre National d'Etudes Spatiales (CNES) give agreement of about 1.5 ppm for chord lengths. After considering a scale correction to the European Datum (ED) of 1950 to account for the absence of geoid heights at the time of its reduction, agreement to a few ppm between the CNES/GSFC and the ED chords is obtained. However, a small systematic difference between survey and satellite results remains for stations in southeastern France and Switzerland.
Marsh, J. G.↗
GPS inferred geocentric reference frame for satellite positioning and navigation
Accurate geocentric three-dimensional positioning is of great importance for various geodetic and oceanographic applications. While relative positioning accuracy of a few centimeters has become a reality using Very Long Baseline Interferometry (VLBI), the uncertainty in the offset of the adopted coordinate system origin from the geocenter is still believed to be of the order of one meter. Satellite Laser Ranging (SLR) is capable of determining this offset to better than 10 cm, though, because of the limited number of satellites, this requires a long arc of data. The Global Positioning System (GPS) measurements provide a powerful alternative for an accurate determination of this origin offset in relatively short period of time. Two strategies are discussed, the first utilizes the precise relative positions predetermined by VLBI, whereas the second establishes a reference frame by holding only one of the tracking sites longitude fixed. Covariance analysis studies indicate that geocentric positioning to an accuracy of a few centimeters can be achieved with just one day of precise GPS pseudorange and carrier phase data.
Malla, Rajendra P.↗
Utilization of satellite-satellite tracking data for determination of the geocentric gravitational constant (GM)
Range rate tracking of GEOS 3 through the ATS 6 satellite was used, along with ground tracking of GEOS 3, to estimate the geocentric gravitational constant (GM). Using multiple half day arcs, a GM of 398600.52 + or - 0.12 cu km/sq sec was estimated using the GEM 10 gravity model, based on speed of light of 299792.458 km/sec. Tracking station coordinates were simultaneously adjusted, leaving geopotential model error as the dominant error source. Baselines between the adjusted NASA laser sites show better than 15 cm agreement with multiple short arc GEOS 3 solutions.
Martin, C. F.↗
Atmospheric occultation of a solar flare in hard x rays
The objective of this study is two-fold: to investigate the absorption of hard x rays along a tangential path through the terrestrial atmosphere, and to locate, other than the use of imaging devices, the flare source of x ray emission in the sun. Observational data were taken with the Hard X Ray Burst Spectrometer (HXRBS) on board the Solar Maximum Mission satellite (SMM). The occultation event chosen for investigation is the flare on 14 October 1981. Night fell on SMM during the decaying phase of the flare. In about fifteen seconds, the x ray flux decreased to zero. The model for computing synthetic light curve, which is directly comparable to the observed curve, consists of two computing programs. One is a modified version of an existing code, which compute the coordinates of the tangent points of the SMM-sun lines. The other program computed the atmospheric densities along the angles (N to S and E to W) measured from the center of the sun. The various model also depends on the destination of the terrestrial atmosphere at geocentric positions of SMM and the sun, the mean atmospheric densities at different heights and latitudes, and the x ray absorption cross of nitrogen, oxygen, and argon. The optical length, at a given time and for a x ray energy, is computed with the two angular parameters. The fit of a particular synthetic light, curve, i.e., the exponentials of the optical lengths, to the observed eclipse curve, yields the desired angular parameters.
Chen, Kwan-Yu↗
Effect of parallactic refraction correction on station height determination
The effect of omitting the parallactic refraction correction for satellite optical observations in the determination of station coordinates is analyzed for a large satellite data distribution. A significant error effect is seen in station heights. A geodetic satellite data distribution of 23 close earth satellites, containing 30,000 optical observations obtained by 13 principal Baker-Nunn camera sites, is employed. This distribution was used in a preliminary Goddard Earth Model (GEM 1) for the determination of the gravity field of the earth and geocentric tracking station locations. The parallactic refraction correction is modeled as an error on the above satellite data and a least squares adjustment for station locations is obtained for each of the 13 Baker-Nunn sites. Results show an average station height shift of +8 meters with a dispersion of plus or minus 0.7 meters for individual sites. Station latitude and longitude shifts amounted to less than a meter. Similar results are obtained from a theoretical method employing a probability distribution for the satellite optical observations.
Lerch, F. J.↗
Deep-space navigation with differenced data types. Part 3: An expanded information content and sensitivity analysis
An approximate six-parameter analytic model for Earth-based differential range measurements is presented and is used to derive a representative analytic approximation for differenced Doppler measurements. The analytical models are tasked to investigate the ability of these data types to estimate spacecraft geocentric angular motion, Deep Space Network station oscillator (clock/frequency) offsets, and signal-path calibration errors over a period of a few days, in the presence of systematic station location and transmission media calibration errors. Quantitative results indicate that a few differenced Doppler plus ranging passes yield angular position estimates with a precision on the order of 0.1 to 0.4 micro-rad, and angular rate precision on the order of 10 to 25 x 10(exp -12) rad/sec, assuming no a priori information on the coordinate parameters. Sensitivity analyses suggest that troposphere zenith delay calibration error is the dominant systematic error source in most of the tracking scenarios investigated; as expected, the differenced Doppler data were found to be much more sensitive to troposphere calibration errors than differenced range. By comparison, results computed using wideband and narrowband (delta) VLBI under similar circumstances yielded angular precisions of 0.07 to 0.4 micro-rad, and angular rate precisions of 0.5 to 1.0 x 10(exp -12) rad/sec.
Estefan, J. A.↗
The influence of the direction of the geomagnetic dipole on the position of the neutral sheet
An analysis of neutral sheet crossings detected by the NASA-Goddard Space Flight Center magnetometer on the Explorer 34 satellite has shown that the diurnal wobble of the geomagnetic dipole measurably influences the position of the neutral sheet at 30 earth radii. Viewed in the solar-ecliptic coordinate system, the dipole wobble originates from the 11 deg angle between the earth's spin axis and the dipole axis, has a period of 24 hours, and can be resolved into components of motion perpendicular and parallel to the earth-sun line. The perpendicular component exerts a torque on the magnetotail and causes the neutral sheet to pivot about an axis approximately parallel to the solar wind direction. The parallel component encourages the neutral sheet to move above and below the solar-magnetospheric equatorial plane with an amplitude of 1 earth radius. This latter motion is consistent with the neutral sheet's being hinged at a geocentric distance of 5.25 earth radii.
Bowling, S. B.↗
Efficient Trajectory Propagation for Orbit Determination Problems
Regularized formulations of orbital motion apply a series of techniques to improve the numerical integration of the orbit. Despite their advantages and potential applications little attention has been paid to the propagation of the partial derivatives of the corresponding set of elements or coordinates, required in many orbit-determination scenarios and optimization problems. This paper fills this gap by presenting the general procedure for integrating the state-transition matrix of the system together with the nominal trajectory using regularized formulations and different sets of elements. The main difficulty comes from introducing an independent variable different from time, because the solution needs to be synchronized. The correction of the time delay is treated from a generic perspective not focused on any particular formulation. The synchronization using time-elements is also discussed. Numerical examples include strongly-perturbed orbits in the Pluto system, motivated by the recent flyby of the New Horizons spacecraft, together with a geocentric flyby of the NEAR spacecraft.
numerical methods↗
Comparison of earth-based radio metric data strategies for deep space navigation
Spacecraft angular coordinates can be determined with a variety of radio tracking measurements, such as Doppler, range, and Very Long Baseline Interferometry (VLBI)-derived data types. A relatively new interferometric tracking technique under development is Connected Element Interferometry (CEI), which uses a single frequency standard, distributed to two antennas spaced 10 to 100 km apart, to make highly accurate measurements of the phase-delay of incoming radio signals. The angular navigation accuracies attainable with Doppler, range, CEI, and VLBI data strategies are compared, using simple analytic models for these data types. The measurement accuracies assumed for Doppler, range, and VLBI data represent the performance expected from these systems in the Magellan and Galileo missions, while the assumed CEI data accuracy represents the anticipated performance of an experimental connected element system being constructed at the Deep Space Network's Goldstone, California complex. The results indicate that the Galileo VLBI system can deliver 20- to 25-nrad accuracy throughout the ecliptic plane. A hypothetical CEI dual-baseline sysem at Goldstone yielded accuracies in the 35- to 50-nrad range, while another hypothetical Goldstone-based system, consisting of a single CEI baseline and an X-band (8.4 GHz) Doppler system, produced accuracies of 25 to 100 nrad. Angular accuracies obtained from Doppler and range were found to be highly dependent upon the sensitivity of earth-spacecraft differential acceleration to small changes in geocentric spacecraft position.
Thurman, Sam W.↗