Search NASA⌕ Search

SEARCH · Search NASA

Results for “PROLATE SPHEROID FUNCTION”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

24 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Viscous-fluid reaction to a torsionally oscillating spheroid Linearized steady-state weak-separation solution

For both the linearized prolate and oblate problems, perturbation series for all orders of eccentricity are obtained. The 'weak separation' method of solving partial-differential-equation boundary-value problems assumes that each linearly independent solution is a sum of products of single-variable functions. The method is applied to a hierarchy of partial differential equations. The weak-separation solutions are constructed by generalizing only the Bessel functions of the homogeneous solution.

Tompkins, D. R., Jr.↗
NASA NTRS1978

Bar-driven spiral waves in disk galaxies

The response of rotating disks of gas to barlike perturbations in galactic gravitational fields is investigated. In particular, two-dimensional time-dependent numerical hydrodynamical calculations have been performed in order to determine the steady-state response of disks of gas to rotating barlike perturbations. Two types of barlike perturbations are considered: oval distortions in the axisymmetric gravitational field of the disk, and heterogeneous prolate spheroids. The calculations reveal that in the absence of gaseous self-gravity, a viscous differentially rotating disk of gas responds to a rotating barlike perturbation by forming a central gas bar with two trailing spiral waves. The local phase of the gas response is primarily a function of the number and spacing of the principal resonances in the disk. This result may be understood in terms of particle orbit theory. The gas response to barlike perturbations also depends on the relative strength and the effective axial ratio of the bar. In these calculations strong narrow bars produce offset shocks in the central gas bar. These shocks correspond in position to the long narrow dust lanes observed in many barred spiral galaxies.

Huntley, J. M.↗
NASA NTRS1999

Dust Optical Properties derived from Sun/Sky Measurements and Satellite Data

We derive the optical properties of dust originating from the Sahara and nearby regions using a combination of ground based and satellite measurements. The AErosol ROBotic NETwork (AERONET) sun/sky radiances from Cap Verde and Sede Boker are used together with Landsat TM data over Senegal and the Atlantic Ocean. The data introduce a cascade of increasing complexity of dust optical properties: The sky aureole radiance is sensitive mainly to the dust size distribution; the TM data over the ocean at 150 deg scattering angle are also sensitive to the spectral refractive index from 470 to 2,210 nm. The TM data over the land measure the balance between the dust scattering and absorption of light reflected by the bright surface, thus very sensitive to dust spectral absorption. Sky radiance at scattering angle of 120 deg, add sensitivity to the dust nonsphericity. Preliminary results, indicative of the ambient dust in the entire atmospheric column, show that dust is less absorbing and with smaller nonspherical properties than anticipated from in situ measurements. Dust is dominated by particles with effective radius of 2 to 2.5 micron, refractive index for wavelengths less then 1 micron of 1.53-0.001i and nonsphericity that increases the phase function at 120 deg above that of spheres by 1.8 and 1.7 at 673 nm down to 1.2 and 1.3 for 1020 nm for Cap Verde and Sede Boker respectively. No significant nonsphericity effect is noticed for scattering angle of 150 deg. This agrees with a mixture of 30% and 45% respectively of Mishchenko et al (JGR, 102, 1997: plate 5 on page 16,841) "polydisperse equiprobable shape mixture of prolate and oblate spheroids with aspect ratios ranging from 1.4 to 2.21, with the rest being spherical particles.

Kaufman, Yoram J.↗
NASA NTRS1985

Birds and insects as radar targets - A review

A review of radar cross-section measurements of birds and insects is presented. A brief discussion of some possible theoretical models is also given and comparisons made with the measurements. The comparisons suggest that most targets are, at present, better modeled by a prolate spheroid having a length-to-width ratio between 3 and 10 than by the often used equivalent weight water sphere. In addition, many targets observed with linear horizontal polarization have maximum cross sections much better estimated by a resonant half-wave dipole than by a water sphere. Also considered are birds and insects in the aggregate as a local radar 'clutter' source. Order-of-magnitude estimates are given for many reasonable target number densities. These estimates are then used to predict X-band volume reflectivities. Other topics that are of interest to the radar engineer are discussed, including the doppler bandwidth due to the internal motions of a single bird, the radar cross-section probability densities of single birds and insects, the variability of the functional form of the probability density functions, and the Fourier spectra of single birds and insects.

Vaughn, C. R.↗
NASA NTRS2002

A Chandra X-Ray Study of Cygnus A: The Cluster of Galaxies - 3

We present an analysis of the Chandra Advanced CCD Imaging Spectrometer (ACIS) observation of the intracluster gas associated with the cluster of galaxies surrounding Cygnus A. The dominant gaseous structure is a roughly elliptical (presumably prolate spheroidal in three dimensions) feature with semimajor axis approximately equal to 1.(prime)1 (approximately equal to 100 kpc). This structure apparently represents intracluster gas that has been swept up and compressed by a cavity inflated in this gas by relativistic material that has passed through the ends of the radio jets. The X-ray-emitting gas shows this prolate spheroidal morphology to approximately equal to 1.(prime)2 (110 kpc) from the radio galaxy but is spherical on larger scales. The X-ray emission from the intracluster gas extends to at least 8 prime (approximately equal to 720 kpc) from the radio galaxy, and a second, extended source of X-ray emission (probably associated with a second cluster of galaxies) is seen some 12 prime (approximately equal to 1 Mpc) to the northwest of Cygnus A. The X-ray spectrum of the integrated intracluster gas imaged on the S3 chip (dimensions 8 prime x 8 prime = 720 x 720 kpc), excluding the contribution from the radio galaxy and other compact sources of X-ray emission, has a gas temperature, metallicity, and unabsorbed 2-10 keV rest-frame luminosity of 7.7 keV, 0.34 times solar, and 3.5 x 10(exp 44) ergs per second, respectively. We have projected the X-ray spectra taken from 12 elliptical and circular annuli in order to derive a run of temperature, metallicity, density, and pressure as a function of radius. The temperature of the X-ray-emitting gas drops from approximately equal to 8 keV more than 100 kpc from the center to approximately equal to 5 keV some 80 kpc from the center, with the coolest gas immediately adjacent to the radio galaxy. "Belts" of slightly cooler (approximately equal to 4 keV) X-ray-emitting gas run around the minor dimension of the cavity created by the radio source, while the limb-brightened edges of the cavity are slightly hotter (approximately equal to 6 keV), perhaps as a result of heating by a bow shock driven by the probably expanding cavity into the intracluster gas. There is a metallicity gradient in the X-ray-emitting gas, with the highest metallicities (approximately solar) found close to the center, decreasing to approximately 0.3 times solar in the outer parts. We have used the assumption of hydrostatic equilibrium to derive a total cluster mass within 500 kpc of 2.0 x 10(exp 14) solar mass and 2.8 x 10(exp 14) solar mass for constant and centrally decreasing temperature profiles, respectively. The total mass of X-ray-emitting gas within the same radius is 1.1 x 10(exp 13) solar mass. Thus, the gas fraction of the cluster within 500 kpc is 0.055 and 0.039 for the constant and centrally decreasing temperature profiles, respectively.

Smith, David A.↗
NASA NTRS1988

Novae as distance indicators

Nova shells are characteristically prolate with equatorial bands and polar caps. Failure to account for the geometry can lead to large errors in expansion parallaxes for individual novae. When simple prescriptions are used for deriving expansion parallaxes from an ensemble of randomly oriented prolate spheroids, the average distance will be too small by factors of 10 to 15 percent. The absolute magnitudes of the novae will be underestimated and the resulting distance scale will be too small by the same factors. If observations of partially resolved nova shells select for large inclinations, the systematic error in the resulting distance scale could easily be 20 to 30 percent. Extinction by dust in the bulge of M31 may broaden and shift the intrinsic distribution of maximum nova magnitudes versus decay rates. We investigated this possibility by projecting Arp's and Rosino's novae onto a composite B - 6200A color map of M31's bulge. Thirty two of the 86 novae projected onto a smooth background with no underlying structure due to the presence of a dust cloud along the line of sight. The distribution of maximum magnitudes versus fade rates for these unreddened novae is indistinguishable from the distribution for the entire set of novae. It is concluded that novae suffer very little extinction from the filamentary and patchy distribution of dust seen in the bulge of M31. Time average B and H alpha nova luminosity functions are potentially powerful new ways to use novae as standard candles. Modern CCD observations and the photographic light curves of M31 novae found during the last 60 years were analyzed to show that these functions are power laws. Consequently, unless the eruption times for novae are known, the data cannot be used to obtain distances.

Ford, Holland C.↗