Error analyses of resonant orbits for geodesy
Error analysis of resonant orbits for geodesy, discussing high order geopotential coefficient recovery by resonance and gravity model errors
Douglas, B. C.↗
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Documentation of photogrammetric mission simulator program. Volume 5: Gravity recovery module
Electronic modules used to simulate lunar gravity potential recovery based on spherical harmonics gravity model
Source record↗
Preliminary study of the application of the Timation 3 satellite to earth physics
The Timation 3 is a timing and navigation satellite originally planned for launch in December 1972 into a circular orbit at 98 deg inclination 14,000 km altitude with gravity gradient stabilization. An error analysis indicates a satellite position uncertainty of about one meter, 80 percent of which is attributable to the assumed gravity model errors. The remaining uncertainties have a period equal to that of the satellites and can be filtered out yielding an effective uncertainty of about 10 cm in the study of phenomena having different periodicities. The accomplishment of these results depends on a careful consideration of solar radiation pressure taking account of the spacecraft reflecting properties and variations in the presentation area. Consideration is also given to the displacement of the laser reflectors from the center of mass of the spacecraft and to the dynamic coupling of any libration in attitude with the orbital motion. The results indicate that a good set of well distribution laser observations of Timation 3 could yield determinations of polar motion, sea floor spreading, solid earth tides, and earth rotation at the 10 cm level.
Carpenter, L.↗
A global station coordinate solution based upon camera and laser data - GSFC 1973
Results for the geocentric coordinates of 72 globally distributed satellite tracking stations consisting of 58 cameras and 14 lasers are presented. The observational data for this solution consists of over 65,000 optical observations and more than 350 laser passes recorded during the National Geodetic Satellite Program, the 1968 Centre National d'Etudes Spatiales/Smithsonian Astrophysical Observatory (SAO) Program, and International Satellite Geodesy Experiment Program. Dynamic methods were used. The data were analyzed with the GSFC GEM and SAO 1969 Standard Earth Gravity Models. The recent value of GM = 398600.8 cu km/sec square derived at the Jet Propulsion Laboratory (JPL) gave the best results for this combination laser/optical solution. Solutions are made with the deep space solution of JPL (LS-25 solution) including results obtained at GSFC from Mariner-9 Unified B-Band tracking. Datum transformation parameters relating North America, Europe, South America, and Australia are given, enabling the positions of some 200 other tracking stations to be placed in the geocentric system.
Marsh, J. G.↗
The Mariner 9 celestial mechanics experiment
There are two main objectives in the Mars gravity field analysis. The first is to generate a picture of the gravity field which can be used in conjunction with other types of data to elucidate the interior, surface structure, and history of Mars. The second is to aid the orbit determination aspect of the relativity experiment. In an effort to extract from the data a Mars gravity model of reasonable fidelity, various spherical harmonic models have been made. A parallel effort using a surface mass representation involves the differentiation of Doppler residuals for acceleration contours.
Lorell, J.↗
LAGEOS mission analyses
Two error sources are found to be compatible and significant for the parameters affecting the LAGEOS mission. The first error source is the uncertainty in the gravity model, and the second error source is the radiation pressure which includes direct radiation, albedo radiation, and earth shine. Retrograde orbits increase the number of passes per day over the tracking stations at the expense of also increasing the number of time gaps when no station is observing. It is shown that relativistic effects are significant and must be included in orbit computation and determination systems for this mission. If station locations are known only to one meter, the error in the satellite orbits is comparable with solar pressure induced errors.
Squires, R. K.↗
Studies of liquid floating zones on SL-IV, the third Skylab mission
The behavior of liquid floating zones in a zero-gravity environment was studied by Dr. E. Gibson on SL-4. These experiments were designed from the results of previous work on floating zones in a simulated zero-gravity model. Molten floating zones are used on earth for the crystal growth and zone refining of reactive materials. The Skylab studies give some insight into the problems associated with the development of the technique for the future space processing of materials. Preliminary results are presented on the stability of the liquid zone surface under static, rotational and vibrational conditions without gravitational constraints.
Carruthers, J. R.↗
Lunar gravity analysis results from Explorer-49
An analysis of the lunar gravity field utilizing 234 days of Explorer-49 mean Keplerian elements is presented. A third-degree and third-order gravity model developed at the Goddard Space Flight Center (GSFC) for mission operations is compared with published models derived from Lunar Orbiter data. Improved predictions of e and Omega using the GSFC model are observed. The results suggest that use of Explorer-49 orbital data in a multisatellite solution would lead to improved global estimates of low-order spherical harmonic coefficients of the lunar gravitational potential.
Bryant, W. C., Jr.↗
Tests and comparisons of satellite derived geoids with Skylab altimeter data
The SKYLAB-193 radar altimeter was operated nearly continuously around the world on January 31, 1974. This direct measurement of the sea surface topography provided an independent basis for the evaluation of global geoids computed from satellite derived gravity models. The differences between the altimeter geoid and the satellite geoids were as large as 25 meters with rms values ranging from 8 to 10 meters. These differences also indicated a systematic long wavelength variation (approximately 100 deg) not related to error in the SKYLAB orbits. Truncation of the models to degree and order eight did not eliminate the long wavelength variation, but in every case the rms agreement between satellite and altimeter geoids was improved. Orbits computed with the truncated models were in contrast found to be inferior to those computed using the complete models.
Marsh, J. G.↗
Detailed gravimetric geoid for the GEOS-C altimeter calibration area
The GEOS-C spacecraft scheduled for launch in late 1974 will carry a radar altimeter for the purpose of measuring sea surface topography. In order to calibrate and evaluate the performance of the altimeter system, ground truth data are required. In this respect a detailed gravimetric geoid has been computed for the GEOS-C altimeter calibration area in the Atlantic Ocean off the East Coast of the U.S. This geoid is based upon a combination of mean free air surface gravity anomalies and the Goddard Space Flight Center GEM-6 satellite-derived spherical harmonic coefficients. Surface gravity anomalies have been used to provide information on the short wave length undulations of the geoid while the satellite-derived coefficients have provided information on the long wave length components. As part of these analyses, GSFC, SAO and OSU satellite-derived gravity models were used in the computations. Although geoid heights based upon the various satellite models differed by as much as 30 meters in the Southern Hemisphere, the differences in this Atlantic Ocean area were less than 4 meters.
Marsh, J. G.↗
Mariner 9 - An instrument of dynamical science
We review and evaluate the contributions of Mariner 9 in improving our knowledge of the dynamical characteristics of Mars and its two satellites, Phobos and Deimos. Primary results include the discovery of the large gravitational and topographical bulge in the Tharsis region, the development of a detailed gravity model representable as coefficients in a spherical harmonic expansion, the development of a topographic model exhibiting a three kilometer displacement of the center of figure from the center of mass, and the determination of the size, shape and motion of Phobos and Deimos.
Jordan, J. F.↗
High zonal harmonics of rapidly rotating planets
A new perturbation expansion is derived for the structure of rotating bodies in hydrostatic equilibrium. The method uses an expansion of the density on Legendre polynomial functions of angle, and can be developed analytically in a manner analogous to the standard level-surface perturbation theory. The new theory proceeds from a prescribed pressure-density relation rather than from a prescribed density distribution, and is both simpler and more physically transparent than the level-surface approach. High zonal harmonics are shown to arise via a transfer function involving derivatives of the interior sound velocity, and via mixing of multipole density components in the outer shell of the planet. Sample calculations for polytropic sequences are presented, as well as standard gravity models for Jupiter and Saturn. Mathematical subleties of the theory are discussed in an appendix.
Hubbard, W. B.↗
The applications of laser tracking to the measurement of intersite distance
Range data from ruby laser systems tracking Geos-3 and Beacon Explorer C from Greenbelt, Md., Bermuda, and San Diego and Quincy, Calif. were analyzed to establish baselines for these sites. A least-squares adjustment was applied to the data. Results with an estimated precision of 20 cm, obtained using the GEM 8 gravity model (Wagner et al., in press), are: San Diego-Greenbelt, 3606 km; Greenbelt-Bermuda, 1323 km; San Diego-Quincy, 908 km.
Smith, D. E.↗
An intense extreme-ultraviolet source in Cetus
The detection of a second EUV (100-1000 A) probable white dwarf star with the EUV telescope aboard the Apollo Soyuz mission is reported. The positional error box includes Feige 24, a binary system consisting of a very blue white dwarf and a dMe star. A grid of LTE pure-hydrogen, high-surface-gravity model atmospheres, is used, in combination with the EUV data and optical spectrophotometry, to derive the stellar parameters, yielding an effective temperature of 60,000 K, a radius of 17,000 km at 100 pc, and a luminosity of 7(d/100 pc) squared solar luminosities. The Feige 24 models appear to rule out white dwarfs with pure hydrogen atmospheres if the interstellar helium abundance and ionization are not anomalous.
Margon, B.↗
The moment of inertia and isostasy of Mars
The systematic and large deviation of the gravitational equipotential surface (EPS) of Mars from a spheroid of revolution suggests a description of Mars in terms of a spheroid nearly in isostatic equilibrium with an extra mass in the Tharsis region. The displacement from Mars and the shape of the spheroid are calculated by using this description and a Mars gravity model. The EPS is represented as a contour map of its height above the spheroid. This representation provides the first clear demonstration that the Hellas depression coincides with a depression in the EPS. The disequilibrium contribution of Tharsis to the coefficient J2 of the second-degree harmonics of gravitational potential of Mars is estimated to be (126 + or - 5) times 10 to the minus 6th. The optical flattening and dynamic flattening calculated on this basis are in substantially better agreement than are those calculated in the usual way.
Reasenberg, R. D.↗
Gravitational harmonics from shallow resonant orbits
Gravitational constraint (lumped coefficient) equations are derived from GEOS-2 data and a detailed analysis of the shallow resonance problem. The equations follow from elementary perturbation theory and show that all such lumped coefficients are harmonic in the argument of perigee. The best along-track constraints derived from them account for all but about 2% of the 13th-order resonant information in the tracking data. The equations are also in good agreement with recent comprehensive gravity models which use substantial amounts of GEOS-2 data.
Wagner, C. A.↗
Mars gravity field derived from Viking-1 and Viking-2 - The navigation result
Viking-1 and Viking-2 Doppler tracking data taken during orbit phases characterized by 1500 km subperiapse altitudes have provided a basis for a determination of the Martian gravity field. Navigation results show that the linear combination of short-arc gravity estimates is an acceptable technique for obtaining gravity models over multiple data arcs. An ensemble field composed of Viking data and Mariner-9 a priori retains the inherent local accuracy of its constituent fields. At the same time, the model can be made to be valid globally by careful weighting of a priori Mariner-9 data. The sixth degree and order model presented reduces the error concerning the change in period by more than an order of magnitude during the high altitude (1500 km) phases of the Viking mission. The resulting areoid deviates by no more than 150 m from the areoid produced by the a priori Mariner-9 field.
Christensen, E. J.↗
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.↗