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NASA NTRS1977

Intensity of primary cosmic-ray electrons of energy exceeding 8 GeV

Results are reported for measurement of the intensity and energy spectrum of primary cosmic-ray electrons with a spark-chamber-counter-emulsion detector flown at a mean altitude of 3 g/sq cm residual atmosphere. A least-squares fit to the flight data yields an electron spectrum from 8 to 80 GeV of approximately 93E to the -2.91 power electrons/sq m/sec per sr/GeV. The results are compared with those of previous experiments as well as with the spectrum obtained for galactic nonthermal radiation. It is concluded that a 'clumpy' magnetic field proportional to the square root of matter density is consistent with measurements of high-energy electrons and synchrotron radiation toward the center of the Galaxy, that a gradual steepening of the electron spectrum relative to the proton spectrum is consistent with an electron lifetime of 1 million years, and that the density of cosmic-ray nucleons and electrons should be essentially uniform throughout the Galaxy if the nucleons have the same lifetime as the electrons and if they traversed 4 to 5 g/sq cm in that lifetime.

Freier, P.↗

NASA NTRS1977

Relative crater production rates on planets

The relative numbers of impacts on different planets, estimated from the dynamical histories of planetesimals in specified orbits (Wetherill, 1975), are converted by a described procedure to crater production rates. Conversions are dependent on impact velocity and surface gravity. Crater retention ages can then be derived from the ratio of the crater density to the crater production rate. The data indicate that the terrestrial planets have crater production rates within a factor ten of each other. As an example, for the case of Mars, least-squares fits to crater-count data suggest an average age of 0.3 to 3 billion years for two types of channels. The age of Olympus Mons is discussed, and the effect of Tharsis volcanism on channel formation is considered.

Hartmann, W. K.↗

NASA NTRS1977

Comet Halley - The orbital motion

The orbital motion of Comet Halley is investigated over the interval from A.D. 837 to 2061. Using the observations from 1607 through 1911, least-squares differential orbit corrections were successfully computed using the existing model for the nongravitational forces. The nongravitational-force model was found to be consistent with the outgassing-rocket effect of a water-ice cometary nucleus and, prior to the 1910 return, these forces are time-independent for nearly a millennium. For the 1986 return, viewing conditions are outlined for the comet and the related Orionid and Eta Aquarid meteor showers.

Yeomans, D. K.↗

NASA NTRS1977

Redundant integrated flight control/navigation inertial sensor complex

A redundant strapdown inertial navigation system for integrated flight control/navigation use is described. Design of the system, which consists of four tuned-gimbal gyros, eight accelerometers, and four processors, is discussed, with emphasis on its compact configuration (13 by 13 by 14 in.), based on symmetry properties of an octahedron. A matrix operator for least-squares combination of data from an arbitrary number of two-degree-of-freedom gyros is derived, and general parity equations for error analysis are given. Self-contained detection and isolation of a two-axis gyro failure is considered; system failure probability, which depends on component failure rates and self-correction capacities, is analyzed. Test data, including typical parity equation responses during motion and simulated gyro and accelerometer failures, are also presented.

Ebner, R. E.↗

NASA NTRS1977

Reduction of polarizing radiometer data

High-precision polarizing radiometers have been constructed for the measurement of the angular dependence of the intensity and polarization for atmospheric and ground-reflected radiation. When the data are fit with a form containing constant, first harmonic, second harmonic, and slope terms, excellent agreement with data taken with a polarizing radiometer may be obtained. A technique has been derived for rapid data reduction by using a single matrix which, when multiplied by the data values, produces the reduced values in the sense of a least-squares fit.

Walraven, R. L.↗

NASA NTRS1977

Mossbauer spectroscopy of iron in the Luna 20 regolith

Results of the Mossbauer effect measurements on Fe-57 in the average sample of the Luna 20 regolith, and their comparison with similar measurements of the Luna 16 samples are presented. Room temperature measurements of the nonmagnetic as well as magnetic components of the spectra were performed. By careful least-squares analysis, six quadrupole doublets in the inner parts of spectra were resolved. According to their splittings, they were interpreted as four types of iron in silicates (olivine, two inequivalent pyroxene sites, and a glassy fraction) and two types of nonmagnetic iron-titanium oxides (ilmenite and a spinel). Velocity-window measurements, were used to determine the average nickel content of (2.01 plus or minus 0.84) wt. %. These results are discussed in terms of distribution of iron among different phases. In comparison with the Luna 16 sample, the Luna 20 sample contains more olivine and less ilmenite as well as metal with a slightly higher nickel content.

Zemcik, T.↗

NASA NTRS1977

Correction factors for on-line microprobe analysis of multielement alloy systems

An on-line correction technique was developed for the conversion of electron probe X-ray intensities into concentrations of emitting elements. This technique consisted of off-line calculation and representation of binary interaction data which were read into an on-line minicomputer to calculate variable correction coefficients. These coefficients were used to correct the X-ray data without significantly increasing computer core requirements. The binary interaction data were obtained by running Colby's MAGIC 4 program in the reverse mode. The data for each binary interaction were represented by polynomial coefficients obtained by least-squares fitting a third-order polynomial. Polynomial coefficients were generated for most of the common binary interactions at different accelerating potentials and are included. Results are presented for the analyses of several alloy standards to demonstrate the applicability of this correction procedure.

Unnam, J.↗

NASA NTRS1978

The galactic distribution of carbon monoxide: An out-of-plane survey

Galactic CO line emission at 115 GHz has been surveyed. This survey confirms the finding that CO is concentrated in a ring. It provides a determination of the thickness of this molecular ring as a function of galactic radius and shows that CO is displaced from the conventional galactic plane. These results were arrived at by least-squares fitting the survey data to a circularly symmetric model of the Galaxy. A comparison of the CO and HI distributions shows that there are marked differences in the distributions of these species, both radially and out of the plane. A detailed discussion of the antenna characteristics, including the radiation pattern and pointing characteristics is presented.

Cohen, R. S.↗

NASA NTRS1978

Pioneer 10 observation of the solar wind proton temperature heliocentric gradient

Solar wind isotropic proton temperatures as measured out to 12.2 AU heliocentric distance by the Ames plasma analyzer aboard Pioneer 10 are presented as consecutive averages over three Carrington solar rotations and discussed. The weighted least-squares fit of average temperature to heliocentric radial distance, R, yields the power law R sup -.52. These average proton temperatures are not correlated as well with Pioneer 10's heliocentric radial distance (-.85) as are the corresponding average Zurich sunspot numbers R sub z (-.95). Consequently, it is difficult to isolate the spatial gradient in the Pioneer 10 solar wind proton temperatures using that data alone.

Mihalov, J. D.↗

NASA NTRS1978

Simplified contact analysis

A simple and straightforward method for calculating the elastic deformation at the center of contact between two solids with different radii of curvature is proposed instead of the conventional contact deformation analysis for ball bearings, gears, and cams, which usually involves tedious iterative procedures or the use of design charts. Ellipticity of the contact is approximated from a least-squares power fit. Simplified expressions are derived which allow rapid calculation of deformation from the material properties and geometry of the contacting elements.

Brewe, D. E.↗

NASA NTRS1977

Orbit determination for earth survey satellites

A technique is described for improving the positioning accuracy of earth survey satellites. Tracking data from Landsat-1, taken in contiguous spans equal in length to the repeat period of 18 days, have been reduced in a least-squares orbit-determination scheme to estimate two pairs of lumped resonance coefficients. Seven separate data spans yielded resonance coefficient pairs consistent to better than 10% of their values, based on the GEM-1 gravity model. Constraint equations were developed. The resonance terms were embedded in the GEM-8 gravity field to yield further improvements in orbital fit to the tracking data, and tests suggest a 20 m position capability for Landsat orbits when the resonance model is adopted. The lumped terms may be used to improve the perturbation model for all Landsat orbits, and the approach is applicable to the orbit of any satellite whose repeat period is long enough for geopotential resonance to have a significant effect on its motion.

Dunn, P. J.↗

NASA NTRS1978

On the supposed anticorrelation of solar polar and equatorial rotation rates

The anticorrelation between two of the three parameters used to calculate the angular velocity of the sun's differential rotation is here said to be due to numerical coupling. A computer simulation technique shows that the relationship between the two parameters is caused by the effect of noise on the least-squares analysis used to obtain the three parameters used to determine the angular velocity in terms of the heliographic latitude. The computer simulation technique is described. The supposed anticorrelation had been used to infer that variations of the sun's polar and equatorial rotation rates are anticorrelated.

Duvall, T. L., Jr.↗

NASA NTRS1977

Apparent depth/apparent diameter relation for lunar craters

Photogrammetric measurements from Apollo metric-quality pictures ensure high accuracy of apparent depth (R sub a) and apparent diameter (D sub a) data for fresh lunar craters. R sub a is a direct function of D sub a and the R sub a/D sub a distribution inflects sharply at an apparent diameter of about 15 km. Each of the two resulting subgroups of craters requires two separate least-squares fits. For simple lunar craters (less than 15 km across), the ratio of R sub a to D sub a is about 0.2; the ratio for complex (larger) craters ranges from 0.1 to 0.01. Apparent depth does not exceed 3400 m, regardless of crater size, possibly as a result of isostasy, substrate layering, or curvature of the moon. R sub a/D sub a differences for mare versus terra craters are either absent or are equivocal. The ratio of apparent diameter to rim-crest diameter (D sub a/D sub r) averages 0.83 for smaller craters and 0.86 for larger craters, indicating another simple-to-complex contrast in crater morphology on the moon, and confirms a prediction by R. B. Baldwin for simple craters. Close similarity of D sub a/D sub r for terrestrial experimental craters and simple lunar craters is especially consistent with impact origin for the moon's craters.

Pike, R. J.↗

NASA NTRS1977

Energies of formation for ejecta blankets of giant impacts

Ejection energy-diameter scaling relations for impact craters are studied by assuming the energy is equal to a constant times the diameter raised to a (different) constant power. These scaling relations are derived from least-squares fits to calculated ejection energies over a range of crater diameters and vary according to ejection angle, ejecta blanket distribution, planetary radius, and the depth-diameter ratio. Extremely broad changes in ejection angle and ejecta blanket distribution result in relatively small changes in the total energy. The way in which the exponent in the scaling relation is dependent on the planetary radius of curvature as well as on the exponent of the power-law depth-diameter scaling relation is described. Two ejection energy-diameter scaling relations, one for simple craters with depth-diameter ratios of approximately 0.2 and the other for large complex craters, are presented. The scaling relations explicitly include target density, surface gravity, and planetary radius.

Croft, S. K.↗

NASA NTRS1978

On the determination and investigation of the terrestrial ionospheric refractive indices using GEOS-3/ATS-6 satellite-to-satellite tracking data

An analysis of the shortening and lengthening of the phase of satellite-to-satellite (SST) data that passed within 40-700 km above the earth surface during its ATS-6 to GEOS-3 to ATS-6 path resulted in refractivity vs height profiles. The SST Doppler data were used directly to adjust the GEOS-3 orbit. Perturbations from the moon, sun, and a 15th-order/degree earth gravity field were included in the orbit solution. This orbit was continued through the occulation period and a model ionosphere was estimated by a least-squares adjustment of the Chapman ionosphere parameters from the SST data residuals. The refractivity profile obtained by this model ionosphere was compared to a refractivity profile obtained by a direct integral inversion of the SST data residuals. Systematic differences between the two methods were caused by orbital errors, which propagated into the solution.

Liu, A. S.↗

NASA NTRS1978

The radii of Uranian rings alpha, beta, gamma, delta, epsilon, eta, 4, 5, and 6 from their occultations of SAO 158687

All available timing data for the occultations of SAO 158687 on March 10, 1977, by the cited rings of Uranus are analyzed. Least-squares fits to the data are performed using a model which postulates that rings alpha, beta, gamma, and delta are circular and coplanar. A solution obtained under the assumption that the ring plane coincides with the plane of the satellite orbits is adopted which yields radii of 44,844 km for ring alpha, 45,799 km for ring beta, 47,746 km for ring gamma, and 48,423 km for ring delta. The uncertainties in these values are discussed along with the apparent shapes and inclinations of these main rings. The mean radii estimated for the other rings are: 47,323 km for ring eta, 42,663 km for ring 4, 42,360 km for ring 5, and 41,980 km for ring 6.

Elliot, J. L.↗

NASA NTRS1978

The radial dependences of the interplanetary magnetic field between 1 and 5 AU Pioneer 10

Pioneer 10 vector helium magnetometer data acquired in 1972-1973 during Bartels solar rotations 1896-1918 are used to investigate the radial dependences of the distant interplanetary magnetic field (IMF) between 1 and 5 AU. Least-square fits were determined for the radial dependences of the averages of the magnitudes of IMF components and total field and plane projections, and radial fits were prepared for the standard deviations of these variables over the solar rotation, one day, and three-hour intervals. The variation of the weighted averages of the radial component of the field with respect to the heliocentric distance, the variation of the tangential component of the field, and the characteristics of a subset corresponding to a relatively low average solar wind velocity are reported.

Rosenberg, R. L.↗

NASA NTRS1978

Detailed gravity anomalies from GEOS-3 satellite altimetry data

A technique for deriving mean gravity anomalies from dense altimetry data was developed. A combination of both deterministic and statistical techniques was used. The basic mathematical model was based on the Stokes' equation which describes the analytical relationship between mean gravity anomalies and geoid undulations at a point; this undulation is a linear function of the altimetry data at that point. The overdetermined problem resulting from the excessive altimetry data available was solved using Least-Squares principles. These principles enable the simultaneous estimation of the associated standard deviations reflecting the internal consistency based on the accuracy estimates provided for the altimetry data as well as for the terrestrial anomaly data. Several test computations were made of the anomalies and their accuracy estimates using GOES-3 data.

Gopalapillai, G. S.↗