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NASA NTRS1973

Minor planets and related objects. XIII - Long-term orbital evolution of /1685/ Toro.

The orbital evolution of (1685) Toro has been investigated over 5000 yr. The asteroid exhibits a locked resonance through an 8:5 commensurability with the earth for the first 3400 yr of integration and a locked resonance with Venus through a 13:5 commensurability for the last 1000 yr. Control of these resonances passes from the earth to Venus as the distance from the earth's orbit gets greater and the distance to Venus' orbit gets closer as a consequence of the precession of the argument of perihelion. The double resonance may give Toro the ability to avoid collisions with the earth and Venus at the present time but this is still uncertain. Mars perturbations could remove Toro from the deepest part of the resonance in about 3,000,000 yrs.

Williams, J. G.↗

NASA NTRS1973

Classification and distribution of WR stars and an interpretation of the WN sequence.

New observational data for Wolf-Rayet stars are interpreted in areas of atmospheric abundances, absolute magnitudes, Galactic distribution, distribution in M33, and bolometric luminosities. The observational data are used in support of arguments (1) that WN stars are helium stars of eight to fourteen solar masses with atmospheres which contain only a very low proportion of hydrogen, (2) that the properties of the stars are very sensitive to this very small amount of hydrogen, and (3) that consequently this structure explains many of the general properties of the subclasses.

Smith, L. F.↗

NASA NTRS1973

Further aspects of weak shock theory applied to the solar chromosphere.

The low chromosphere now seems definitely to require mechanical heating, and dissipation of initially acoustic waves by shocking is one of the most promising possibilities. Results of recent calculations indicate that the weak shock theory may be applicable in this case, but discrepancies exist among various applications of this theory, and the explanations offered to date are not completely satisfactory. It is shown that the different approximations used by different authors to evaluate the mechanical flux integral play an important role in producing these discrepancies, in addition to the already well-known effects of the density scale heights and the wave periods. Arguments are presented favoring Ulmschneider's (1970, 1971) method for evaluation of this flux integral.

Jordan, S. D.↗

NASA NTRS1973

On local inflexional instability in boundary-layer flows.

Development of a linearized theory of the two- and three-dimensional incompressible viscous flows ensuing from locally unstable velocity profiles. Indications of the theory with respect to the instability of the two-dimensional separation bubble and the mechanisms underlying formation of the turbulence wedge behind a fixed roughness element are pointed out. In connection with the aforementioned mechanisms, a theoretically based argument is advanced that, as a result of local inflectional instability of the velocity profile in a succession of skewed planes, a corresponding succession of stationary vortices is induced, the induction process terminating at the boundaries of the turbulence wedge when the velocity profiles along the boundaries themselves become unstable. It is suggested that a rational method of predicting the occurrence of roughness-induced turbulence wedges might be possible if a theory were available for the steady laminar flow caused by the roughness at a stage just prior to transition.

Tobak, M.↗

NASA NTRS1972

The present thermal state of the terrestrial planets

The thermal state of bodies is discussed as an aspect of their internal dynamics for bodies of roughly meteoritic composition in the range of sizes of planetary objects. The rheological behaviour of planetary material is assumed to be represented by a Newtonian viscosity varying exponentially with temperature, and only the consistency of this assumption with the elastic view of the planets is considered. It is shown that for the whole range of physically plausible values of the material parameters, the temperature distribution associated with a solution to the problem of internal dynamics for bodies with external radii larger than about 800 km departs significantly from that predicted on conduction theory arguments. For bodies in the range of sizes of the terrestrial planets, the viscosity-temperature relationship plays a dominant role in setting the absolute temperature of the central regions.

Tozer, D. C.↗

NASA NTRS1972

Viscous stratification of the earth and convection

The shallow model of the earth's mantle is discussed along with a variety of geophysical arguments for its correctness and against the existence of deep convection. The main agrument is summarized in the proposal that the astheno sphere is less viscous (by a factor of 10 to 100) than has generally been assumed. In this shallow model, the return flow is essentially through the asthenosphere. The dynamical agent is the steep temperature gradient in the upper mantle. Speculations as to the historical variation of this gradient are advanced. The effects on the model of a nonuniform earth aggregation are considered and shown to favor shallow convection as well as a top convective layer (lithosphere plus asthenosphere) whose depth increases slowly over the earth's life, leading to a tectonic activity that increases gradually with time.

Elsasser, W. M.↗

NASA NTRS1972

Transport properties of liquid metal hydrogen under high pressures

A theory is developed for the compressibility and transport properties of liquid metallic hydrogen, near to its melting point and under high pressure. The interionic force law is assumed to be of the screened Coulomb type, because hydrogen has no core electrons. The random phase approximation is used to obtain the structure factor S(k) of the system in terms of the Fourier transform of this force law. The long wavelenth limit of the structure factor S(o) is related to the compressibility, which is much lower than that of alkali metals at their melting points. The diffusion constant at the melting point is obtained in terms of the Debye frequency, using a frequency spectrum analogous with the phonon spectrum of a solid. A similar argument is used to obtain the combined shear and bulk viscosities, but these depend also on S(o). The transport coefficients are found to be about the same size as those of alkali metals at their melting points.

Brown, R. C.↗

NASA NTRS1973

Reflection and interference of electromagnetic waves in inhomogeneous media

Solutions were obtained of the wave equation for a plane horizontally polarized electro-magnetic wave incident on a semi infinite two dimensional inhomogeneous medium. Two problems were considered: An inhomogeneous half space, and an inhomogeneous layer of arbitrary thickness. Solutions of the wave equation were obtained in terms of Hankel functions with complex arguments. Numerical calculations were made of the reflection coefficient R at the interface of the homogeneous medium. The startling results show that the reflection coefficient for a complex dielectric constant with gradient, can be less than that of the same medium with zero gradient.

Geiger, F. E.↗

NASA NTRS1973

Apollo 17 site selection

The scientific arguments and recommendations concerning the selection of the Apollo 17 landing site are presented. The final selection was influenced by the accomplishments and circumstances of previous Apollo flights and by the proposed experiments for Apollo 17. The decisive factors in selecting the Taurus-Littrow landing area were: (1) certainty of acquiring highlands lunar samples, (2) superior orbital coverage, and (3) better use of the lunar roving vehicle capabilities.

Hinners, N. W.↗

NASA NTRS1973

The Environmental Heat Flux Routine, Version 4 (EHFR-4) and Multiple Reflections Routine (MRR). Volume 2: Programmers reference manual

The EHFR program reference information which is presented consists of the following subprogram detailed data: purpose-description of the routine, a list of the calling programs, an argument list description, nomenclature definition, flow charts, and a compilation listing of each subprogram. Each of the EHFR subprograms were developed specifically for this routine and do not have an applicability of a general nature. Single precision accuracy available on the Univac 1108 is used exclusively in all but two of the 31 EHFR subprograms. The double precision variables required are identified in the nomenclature definition of the two subprograms that require them. A concise definition of the purpose, function, and capabilities is made in the subprogram description. The description references the appropriate Volume 1 sections of the report which contain the applicable detailed definitions, governing equations, and assumptions used. The compilation listing of each subprogram defines the program/data storage requirements, identifies the labeled block common data required, and identifies other subprograms called during execution. For Vol. 1, see N73-31842.

Dietz, J. B.↗

NASA NTRS1974

A forward speed effects study on jet noise from several suppressor nozzles in the NASA/Ames 40- by 80-foot wind tunnel

A test program was conducted in a 40 by 80 foot wind tunnel to evaluate the effect of relative velocity on the jet noise signature of a conical ejector, auxiliary inlet ejector, 32 spokes and 104 tube nozzle with and without an acoustically treated shroud. The freestream velocities in the wind tunnel were varied from 0 to 103.6 m/sec (300 ft/sec) for exhaust jet velocities of 259.1 m/sec (850 ft/sec) to 609.6 m/sec (2000 ft/sec). Reverberation corrections for the wind tunnel were developed and the procedure is explained. In conjunction with wind tunnel testing the nozzles were also evaluated on an outdoor test stand. The wind tunnel microphone arrays were duplicated during the outdoor testing. The data were then extrapolated for comparisons with data measured using a microphone array placed on a 30.5 meter (100 ft) arc. Using these data as a basis, farfield to nearfield arguments are presented with regards to the data measured in the wind tunnel. Finally, comparisons are presented between predictions made using existing methods and the measured data.

Beulke, M. R.↗

NASA NTRS1974

A comparison of computational methods and algorithms for the complex gamma function

A survey and comparison of some computational methods and algorithms for gamma and log-gamma functions of complex arguments are presented. Methods and algorithms reported include Chebyshev approximations, Pade expansion and Stirling's asymptotic series. The comparison leads to the conclusion that Algorithm 421 published in the Communications of ACM by H. Kuki is the best program either for individual application or for the inclusion in subroutine libraries.

Ng, E. W.↗

NASA NTRS1974

Commutative semigroups of real and complex matrices

The computation of divergence is studied. Covariance matrices to be analyzed admit a common diagonalization, or even triangulation. Sufficient conditions are given for such phenomena to take place, the arguments cover both real and complex matrices, and are not restricted to Hermotian or other special forms. Specifically, it is shown to be sufficient that the matrices in question commute in order to admit a common triangulation. Several results hold in the case that the matrices in question form a closed and bounded set, rather than only in the finite case.

Brown, D. R.↗

NASA NTRS1974

Pioneer 10 observations of the solar wind interation with Jupiter

Pioneer 10 Plasma Analyzer experiment flight data during the Jupiter flyby are presented. The observations show that the interaction of Jupiter's magnetic field with the solar wind is similar in many ways to that at earth, but the scale size is over 100 times larger. Jupiter is found to have a detached standing bow shock wave of high Alfven Mach number. Jupiter has a prominent magnetopause which deflects the magnetosheath plasma and excludes its direct entry into the Jovian magnetosphere. The sunward hemisphere of Jupiter's outer magnetosphere is found to be highly inflated with thermal plasma and a high beta region which is highly responsive to changes in solar wind dynamic pressure. Observational arguments are presented which tend to discount a thin disklike magnetosphere but, rather, favor a Jovian magnetosphere, albeit probabily considerably flattened as compared to the earth's magnetosphere, yet still with reasonable thickness. Results concerning the shock jump conditions, the magnetosheath flow field and inferred internal magnetospheric plasma are presented.

Wolfe, J. H.↗

NASA NTRS1974

The dyadic diffraction coefficient for a curved edge

A compact dyadic diffraction coefficient for electromagnetic waves obliquely incident on a curved edge formed by perfectly conducting curved or plane surfaces is obtained. This diffraction coefficent remains valid in the transition regions adjacent to shadow and reflection boundaries, where the diffraction coefficients of Keller's original theory fail. The method is on Keller's method of the canonical problem, which in this case is the perfectly conducting wedge illuminated by plane, cylindrical, conical, and spherical waves. When the proper ray fixed coordinate system is introduced, the dyadic diffraction coefficient for the wedge is found to be the sum of only two dyads, and it is shown that this is also true for the dyadic diffraction coefficients of higher order edges. One dyad contains the acoustic soft diffraction coefficient; the other dyad contains the acoustic hard diffraction coefficient. The expressions for the acoustic wedge diffraction coefficients contain Fresnel integrals, which ensure that the total field is continuous at shadow and reflection boundaries. The diffraction coefficients have the same form for the different types of edge illumination; only the arguments of the Fresnel integrals are different. Since diffraction is a local phenomenon, and locally the curved edge structure is wedge shaped, this result is readily extended to the curved edge.

Kouyoumjian, R. G.↗

NASA NTRS1974

Mutual impedance of nonplanar-skew sinusoidal dipoles

The mutual impedance of nonplanar-skew sinusoidal dipoles is presented as a summation of several exponential integrals with complex arguments. Mathematical models are developed to show the near-zone field of the sinusoidal dipole. The mutual impedance of coupled dipoles is expressed as the sum of four monopole-mobopole impedances to simplify the analysis procedure. The subroutines for solving the parameters of the dipoles are discussed.

Richmond, J. H.↗

NASA NTRS1973

Noble gas concentrations and cosmic ray exposure ages of eight recently fallen chondrites

Abundances and isotopic compositions of He, Ne, Ar, and Xe have been measured in eight recently fallen chondrites. Ratios of concentrations of cosmic ray-produced He-3, Ne-21, Ne-22, and Ar-38 indicate that all eight samples experienced less than average cosmic ray shielding. He-3 and Ne-21 exposure ages were calculated using shielding corrected chondritic production rates and the measured Ne-22/Ne-21. Exposure ages calculated from Na-22/Ne-22 and Al-26/Ne-21 ratios and constant relative production rates show a bias between the two ages due to variations in Na-22/Al-26. Arguments are presented that this bias is due to irradiation hardness differences, and therefore the use of constant values for both the Na-22/Ne-22 and Al-26/Ne-21 production ratios is not permitted.

Bogard, D. D.↗

NASA NTRS1973

The physical librations of the moon, including higher harmonic effects

The equations of the physical libration of the moon are developed using a representation of the earth-moon orbit as a Kepler ellipse referred to the lunar equator and expanding the lunar potential in terms of these Kepler elements. The Improved Lunar Ephemeris is used to calculate solar perturbations, and a linear integration of all effects arising from lunar gravitational harmonics through the fourth degree is performed. Aside from unobservable constant offsets of the principal axes, the main effects of the higher harmonics on longitude are: 10-sec six-yearly (argument omega), 1.2-sec three-yearly, 0.5-sec annual, and 0.1-sec monthly; on pole direction they are on the order of 0.5-sec six-yearly and 1.0-sec monthly. The higher harmonics must hence be taken into account in analyzing ranging data of 10 cm accuracy.

Kaula, W. M.↗