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Christensen, E. J.

Publications and source records attributed to Christensen, E. J..

36 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Dependence of sea-surface microwave emissivity on friction velocity as derived from SMMR/SASS

The sea-surface microwave emissivity is derived using SMMR brightness temperatures and SASS inferred friction velocities for three North Pacific Seasat passes. The results show the emissivity increasing linearly with friction velocity with no obvious break between the foam-free and foam regimes up to a friction velocity of about 70 cm/sec (15 m/sec wind speed). For horizontal polarization the sensitivity of emissivity to friction velocity greatly increases with frequency, while for vertical polarization the sensitivity is much less and is independent of frequency. This behavior is consistent with two-scale scattering theory. A limited amount of high friction velocity data above 70 cm/sec suggests an additional increase in emissivity due to whitecapping.

Wentz, F. J.↗
NASA NTRS1980

The Seasat scanning multichannel microwave radiometer /SMMR/: Antenna pattern corrections - Development and implementation

The antenna temperatures measured by the Seasat scanning multichannel microwave radiometer (SMMR) differ from the true brightness temperatures of the observed scene due to antenna pattern effects, principally from antenna sidelobe contributions and cross-polarization coupling. To provide accurate brightness temperatures convenient for geophysical parameter retrievals the antenna temperatures are processed through a series of stages, collectively known as the antenna pattern correction (APC) algorithm. A description of the development and implementation of the APC algorithm is given, along with an error analysis of the resulting brightness temperatures.

Njoku, E. G.↗
NASA NTRS1979

Development and analysis of a twelfth degree and order gravity model for Mars

Satellite geodesy techniques previously applied to artificial earth satellites have been extended to obtain a high-resolution gravity field for Mars. Two-way Doppler data collected by 10 Deep Space Network (DSN) stations during Mariner 9 and Viking 1 and 2 missions have been processed to obtain a twelfth degree and order spherical harmonic model for the martian gravitational potential. The quality of this model was evaluated by examining the rms residuals within the fit and the ability of the model to predict the spacecraft state beyond the fit. Both indicators show that more data and higher degree and order harmonics will be required to further refine our knowledge of the martian gravity field. The model presented shows much promise, since it resolves local gravity features which correlate highly with the martian topography. An isostatic analysis based on this model, as well as an error analysis, shows rather complete compensation on a global (long wavelength) scale. Though further model refinements are necessary to be certain, local (short wavelength) features such as the shield volcanos in Tharsis appear to be uncompensated. These are interpreted to place some bounds on the internal structure of Mars.

Christensen, E. J.↗
NASA NTRS1979

Mars gravity field model from Mariner 9, Viking 1 and 2 data

Earth artificial satellite methods are extended by means of two way Doppler data, to the computation of very accurate orbiter trajectories around another planet, and to the determination of its gravity field. It is reported that in the case of Mars, all observations collected by 10 Deep Space Network stations located at three different sites during the Mariner 9 and Viking 1 and 2 missions have been processed and used to compute a full twelfth degree and order spherical harmonic model of the gravitational potential. It is concluded that the aeroid derived from the model shows very large correlations with the Martian topography, raising questions as to the deep structure of the planet which cannot be interpreted on the basis of topographic and isostatic considerations alone.

Balmino, G.↗
NASA NTRS1978

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.↗
NASA NTRS1978

Viking first encounter of Phobos - Preliminary results

Viking Orbiter-1 (VO-1) made a series of close flybys of the Martian satellite Phobos in February and May 1977. A description is presented of the results obtained during the flybys in February. The flyby geometries for the encounter period in February are shown in a graph. The trajectory design gave flybys on the illuminated side of Phobos within 80 to 300 km during the entire encounter period. The primary encounter observations of Phobos included visual and infrared imaging as well as radio tracking of VO-1 while it was under the gravitational influence of Phobos. Visual imaging was obtained from two narrow-angle television cameras. Infrared observations were obtained from an infrared thermal mapper. Radio data included S- and X-band Doppler and ranging data to VO-1 with a 10-second Doppler count. Assuming for Phobos a volume of 500 + or - 900 cu km, a mean density of 1.9 + or - 0.6 g/cu cm is obtained for it on the basis of the processed data.

Tolson, R. H.↗
NASA NTRS1977

The mass of Phobos from Viking flybys

The mass of the Martian satellite Phobos has been determined by processing radiometric tracking data obtained from the Viking-1 spacecraft during a series of 14 near encounters which occurred in February 1977. Distances of closest approach ranged from 89 to 213 km from the center of mass of the satellite. Our best estimate for the gravitational constant of Phobos is (6.6 plus or minus 0.8) x 10 to the -4th cu km/sq sec. The corresponding density of Phobos based on a volume estimate of 4800 plus or minus 960 cu km from Mariner 9 imaging is 2.0 plus or minus 0.5 gm/cu cm.

Christensen, E. J.↗
NASA NTRS1977

Viking satellite orbit determination

During the summer of 1976, the two Viking spacecraft, each consisting of an orbiter-lander combination, were inserted into orbit about Mars. The paper describes the experiences of the Viking Satellite Orbit Determination Team in determining Mars centered ephemerides of the orbiters and positions of the landers from the two-way Doppler and range data, and synthesizes the different phases of the navigation plan which involves pre-flight modeling and error analysis for all Viking navigation functions from launch through landing. The problem of initial orbit convergence is solved by using DPODP's (Double Precision Orbit Determination Program) square-root batch data filter, and gravity models for both Viking I and Viking II were produced from the combination of short arc estimates. The importance of synchronous Viking orbits (with the rotational period of Mars) is stressed and future extended missions of the spacecraft are outlined.

Hildebrand, C. E.↗
NASA NTRS1975

Martian topography derived from occultation, radar, spectral, and optical measurements

A new global topographic map of the planet Mars, derived primarily from Mariner 9 data, is presented. Spacecraft radio signal occultation times, remote sensing of infrared and ultraviolet spectra, and earth-based radar measurements are included in the data base. Large-scale topographic relief is seen with definite fluid flow patterns established over much of the surface consistent with earlier analyses. An optical flattening of 0.0059 is obtained with a center-of-mass to center-of-figure offset of approximately 2 km to the south and 1 km toward the Tharsis ridge. Mathematical models approximating the topographic figure and 6.1-mb isobaric surface for Mars are included in this presentation.

Christensen, E. J.↗
NASA NTRS1974

Special perturbations employing osculating reference states

The concept of employing osculating reference position and velocity vectors in the numerical integration of the equations of motion of a satellite is examined. The choice of the reference point is shown to have a significant effect upon numerical efficiency and the class of trajectories described by the differential equations of motion. For example, when the position and velocity vectors on the osculating orbit at a fixed reference time are chosen, a universal formulation is yielded. For elliptical orbits, however, this formulation is unattractive for numerical integration purposes due to Poisson terms (mixed secular) appearing in the equations of motion. Other choices for the reference point eliminate this problem but usually at the expense of universality. A number of these formulations, including a universal one, are considered here. Comparisons of the numerical characteristics of these techniques with those of the Encke method are presented.

Born, G. H.↗
NASA NTRS1973

Satellite orbit determination

A historic account of the activities of the Satellite OD Group during the MM'71 mission is given along with an assessment of the accuracy of the determined orbit of the Mariner 9 spacecraft. Preflight study results are reviewed, and the major error sources described. Tracking and data fitting strategy actually used in the real time operations is itemized, and Deep Space Network data available for orbit fitting during the mission and the auxiliary information used by the navigation team are described. A detailed orbit fitting history of the first four revolutions of the satellite orbit of Mariner 9 is presented, with emphasis on the convergence problems and the delivered solution for the first orbit trim maneuver. Also included are a solution accuracy summary, the history of the spacecraft orbit osculating elements, the results of verifying the radio solutions with TV imaging data, and a summary of the normal points generated for the relativity experiment.

Jordan, J. F.↗
NASA NTRS1973

Mars gravity derived from long-period motion of Mariner 9

The spherical harmonic coefficients in the gravity field of Mars are determined using a two stage filtering process. In the first stage, a weighted least squares orbit determination processor is applied to Mariner 9 Doppler tracking data to estimate Kepler elements and rates. In the second stage, the Kepler element rates are used as input to another weighted least squares processor that estimates gravity coefficients using the Lagrange perturbation equations. The novelty in this method is the fitting of element rates rather than the elements themselves. This procedure decouples the results from the effects of internal spacecraft dynamics.

Ferrari, A. J.↗
NASA NTRS1973

Mars gravity derived from the long-period motion of Mariner 9

The spherical harmonic coefficients in the Mars gravity field are determined using a two-stage filtering process. In the first stage, a weighted least-squares orbit determination processor is applied to Mariner 9 radio data to estimate the mean Kepler elements of each orbit. A finite difference method is then used to generate orbital element rates. In the second stage, the gravity coefficients are determined using another weighted least-squares processor which fits the long period Lagrange perturbation equations to the estimated rates. The resulting gravity potential and associated equipotential surface is presented and error sources discussed. Gravity field results are applied to various physical properties of Mars, such as moments of inertia.-

Ferrari, A. J.↗
NASA NTRS1973

Gravity field of Mars from Mariner 9 tracking data.

Further reduction of Doppler tracking data from Mariner 9 confirms our earlier conclusion that the gravity field of Mars is considerably rougher than the fields of either the earth or the moon. The largest positive gravity anomaly uncovered is in the Tharsis region which is also topographically high and geologically unusual. The value obtained for the inverse mass of Mars is in good agreement with prior determinations from Mariner fly by trajectories. The direction found for the rotational pole of Mars is in excellent agreement with Sinclair's recent value, determined from earth-based observations of Mars' satellites. Other important physical constants that have either been refined or confirmed by the Mariner 9 data include: (1) the dynamical flattening, (2) the maximum principal moment of inertia, and (3) the period of precession of Mars' pole.

Lorell, J.↗
NASA NTRS1972

The determination of the satellite orbit of Mariner 9.

This paper presents a comprehensive analysis of the Mars orbital phase of the Mariner 9 trajectory as determined from Earth based radio data. Both the method and accuracy of the orbit determination process are reviewed. Analysis is presented to show the effects of Mars gravity model and node in the plane of the sky errors on the accuracy of orbit determination. In addition the long term evolution of the orbit from insertion to date is presented, and is decomposed into effects from the Mars gravity field, n-body perturbations, and solar radiation pressure. Since the orbit period is nearly commensurable with the Mars rotational period, the orbit experiences significant resonance perturbations. The primary perturbation is in-track with a maximum amplitude of 1000 km and a wavelength of 39 revolutions.

Born, G. H.↗
NASA NTRS1972

Mariner 9 celestial mechanics experiment - Gravity field and pole direction of Mars.

Analysis of the Mariner 9 radio-tracking data shows that the Martian gravity field is rougher than that of earth or the moon, and that the accepted direction of the Mars rotation axis is in error by about 0.5 deg. Contours of equivalent surface heights deduced from a sixth-degree solution for the Martian gravity field are presented. These contours represent the deviations from sphericity of a uniformly dense body with an external potential which is given by the first sixth-degree solution. In addition to Doppler observations, ranging or group-delay measurements have been made regularly since orbit insertion.

Lorell, J.↗
NASA NTRS1972

Preliminary results of the satellite orbit determination of Mariner Mars 1971.

The preflight planning and real-time experience relating to the navigation of the first artificial satellite placed about a distant planet is presented. Results of determining the orbit of Mariner 9 are presented and contrasted against the preflight simulation test results. It is concluded that the position of Mariner 9 was located to 40 km before coefficients of the gravity field of Mars were estimated. The planet Mars has been found to be 3 to 4 times gravitationally rougher than expected, with the dominant features, the 2nd order tesserals C22 and S22, causing the orbital period of Mariner 9 to oscillate with an amplitude of 40 seconds and a wavelength of 19.5 days. The direction of the Mars spin axis has been relocated from the Camichel-Burton value by 1/2 degree.

Jordan, j. F.↗