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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.

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NASA NTRS1975

The V - /2.2 micron/ colors of elliptical galaxies

Infrared photometric measurements of 19 normal and giant elliptical galaxies are reported which were made with apertures having diameters 0.1 to 1.3 times the visual galactic diameters. The derived V (2.2 micron) colors, ranging from 3.15 to 3.60 magnitudes, are compared with the results of Grasdalen (1975) for 28 spiral and elliptical galaxies. All but one of the present magnitudes are found to be systematically brighter than Grasdalen's by 0.07 to 0.46 magnitude, and no significant radial color gradient is observed.

Frogel, J. A.↗
NASA NTRS1976

Isothermal elastohydrodynamic lubrication of point contacts. 2: Ellipticity parameter results

A numerical solution of the isothermal elastohydrodynamic problem for point contacts is presented which reproduces all the essential features of experimental observations based upon optical interferometry. In particular, the two side lobes, in which minimum film thickness regions occur, emerge in the theoretical solutions. The influence of the ellipticity parameter on solutions to the point contact problem is explored. The ellipticity parameter k was varied from 1 (a ball on a plate) to 8 (a configuration approaching line contact). It is shown that the minimum film thickness can be related to the well known line contact solutions by a remarkably simple expression involving either k or the effective radius of curvature ratio R sub y/R sub x.

Hamrock, B. J.↗
NASA NTRS1975

A uniformly valid solution for motion about the interior libration point of the perturbed elliptic-restricted problem

Bounded motion about Lagrange collinear libration points is considered for a perturbed elliptic-restricted problem. A practical application is the motion of a satellite near a libration point collinear with the sun and the earth-moon barycenter. Such a system is treated here as an earth-sun-satellite elliptic restricted problem with lunar perturbations. The method of dual time scales is utilized to develop a uniformly valid three-dimensional analytical solution to the satellite's equations of motion. The analytical development applies somewhat generally to that class of four-body problems where the second primary mass is much greater than the first, and the third primary mass is much greater than the second.

Richardson, D. L.↗
NASA NTRS1975

Isothermal elastohydrodynamic lubrication of point contacts. II - Ellipticity parameter results

A numerical solution of the isothermal elastohydrodynamic problem for point contacts has been presented which reproduces all the essential features of the previously reported experimental observations based upon optical interferometry. In particular, the two 'side lobes' in which minimum film thickness regions occur are shown to emerge in the theoretical solutions. The influence of the ellipticity parameter upon solutions to the point contact problem has been explored in the present paper. The ellipticity parameter (k) was varied from one (a ball on a plate) to eight (a configuration approaching line contact), and it has been shown that both the central and minimum film thicknesses can be related to the well known line contact solutions by remarkably simple expressions involving either (k) or the effective radius of curvature ratio (Ry/Rx).

Hamrock, B. J.↗
NASA NTRS1976

Elliptic integral solutions to a class of space flight optimization problems

This paper is initially concerned with the minimum-time, exoatmospheric flight of a rocket with constant thrust acceleration magnitude, as in the cases of nuclear and solar electric propulsion. Gravitational acceleration is assumed to be a constant scalar multiple of the radius vector, plus a correction term which is a given function of time. The solution to the state equations is obtained in terms of elliptic integrals. A method is presented for the solution of the two-point boundary-condition problem associated with orbital transfer. At most, the latter method requires iteration upon final time, angle of injection, and two other parameters which are bounded. An example problem is provided which involves a rocket with very low thrust and a spiraling trajectory of many revolutions, but an altitude change of only several hundred miles above the earth. Finally, the original elliptic integral solution is extended to a larger class of low and intermediate thrust problems with constant thrust magnitude, mass decreasing with time, and an inverse square gravitational force.

Andrus, J. F.↗
NASA NTRS1977

Elastohydrodynamic lubrication of elliptical contacts for materials of low elastic modulus. I - Fully flooded conjunction

A complete numerical solution is presented to the problem of isothermal elastohydrodynamic lubrication of elliptical contacts for low-elastic-modulus materials operating under fully loaded conditions. No assumption is made for the pressure or film thickness within the contact, and compressibility and viscous effects are taken into account. Because of the dimensionless representation of the coordinates, the actual Hertzian contact ellipse becomes a circle regardless of the value of the ellipticity parameter. A minimum-film-thickness relation and a central-film-thickness relation are derived from examining 17 different cases. Contour plots for detailed illustration of the pressure distribution and film thickness in the conjunction are provided.

Hamrock, B. J.↗
NASA NTRS1978

Marching methods for elliptic problems. II, III

Higher-order operators for marching methods for elliptic equations are considered. Higher-order is understood in the sense of higher-order accuracy solutions to second-order Poisson equations, and in the sense of higher-order elliptic equations such as the biharmonic equation. The use of deferred corrections for overcoming stability problems is illustrated. Direct and iterative methods of extending the mesh size are considered. Multiple marching, patching, and influence extending techniques are described.

Roache, P. J.↗
NASA NTRS1978

NGC 2110 - An X-ray/radio galaxy with elliptical morphology

The detection of X-ray emission from NGC 2110, a narrow-emission-line galaxy of apparently elliptical morphology, is reported. A relatively hard 2-11-keV energy spectrum with an index of 0.1 + or - 0.3 is obtained, and the X-ray luminosity in this energy band is shown to be 1.2 x 10 to the 43rd erg/s for the redshift distance of 43 Mpc. Optical and radio observations are discussed which indicate a galactocentric redshift of approximately 0.0071, a resolved nonstellar optical nucleus about 4 arcsec in extent, Seyfert type 2 emission lines from the nucleus, and a nonthermal radio source located 3.0 arcsec from the position of the optical nucleus. No evidence is found for X-ray source variability in NGC 2110. It is suggested that the four to seven known X-ray-emitting high-excitation narrow-emission-line galaxies appear to be nearby examples of the Seyfert type 2 phenomenon and that the elliptical morphology of NGC 2110, if confirmed, may be unique among known Seyfert galaxies.

Bradt, H. V.↗
NASA NTRS1979

Stress-intensity factors for a wide range of semi-elliptical surface cracks in finite-thickness plates

Surface cracks are among the more common flaws in aircraft and pressure vessel components. Several calculations of stress-intensity factors for semi-elliptical surface cracks subjected to tension have appeared in the literature. However, some of these solutions are in disagreement by 50-100%. In this paper, stress-intensity factors for shallow and deep semi-elliptical surface cracks in plates subjected to tension are presented. To verify the accuracy of the three-dimensional finite-element models employed, convergence was studied by varying the number of degrees of freedom in the models from 1500 to 6900. The 6900 degrees of freedom used here were more than twice the number used in previously reported solutions. Also, the stress-intensity variations in the boundary-layer region at the intersection of the crack with the free surface were investigated.

Raju, I. S.↗
NASA NTRS1980

The elliptic anomaly

An independent variable different from the time for elliptic orbit integration is used. Such a time transformation provides an analytical step-size regulation along the orbit. An intermediate anomaly (an anomaly intermediate between the eccentric and the true anomaly) is suggested for optimum performances. A particular case of an intermediate anomaly (the elliptic anomaly) is defined, and its relation with the other anomalies is developed.

Janin, G.↗
NASA NTRS1980

Boundary conditions for the numerical solution of elliptic equations in exterior regions

Elliptic equations in exterior regions frequently require a boundary condition at infinity to ensure the well-posedness of the problem. Examples of practical applications include the Helmholtz equation and Laplace's equation. Computational procedures based on a direct discretization of the elliptic problem require the replacement of the condition on a finite artificial surface. Direct imposition of the condition at infinity along the finite boundary results in large errors. A sequence of boundary conditions is developed which provides increasingly accurate approximations to the problem in the infinite domain. Estimates of the error due to the finite boundary are obtained for several cases. Computations are presented which demonstrate the increased accuracy that can be obtained by the use of the higher order boundary conditions. The examples are based on a finite element formulation but finite difference methods can also be used.

Bayliss, A.↗
NASA NTRS1980

The radius and ellipticity of Uranus from its occultation of SAO 158687

From occultation timings obtained from the Kuiper Airborne Observatory and from Cape Town for Mar. 10, 1977 occultation of SAO 158687 by Uranus, the equatorial radius, Re, of the planet has been determined to be 26,228 + or - 30 km and its ellipticity epsilon = 1 - Rp/Re = 0.033 + or - 0.007. These values refer to the 1.0 x 10 to the 14th/cu cm number-density level, under the assumption that the upper atmosphere is composed of H2 and He with a mean molecular weight mu = 2.20. The dominant source of uncertainty is the position of the center of the ring system, which was used to define the center of Uranus in our analysis. A rotation rate of 12.8 + or - 1.7 hours for the planet is implied by our value for the ellipticity, under the assumption that Uranus is in hydrostatic equilibrium below the 1.0 x 10 to the 14th/cu cm number density level.

Elliot, J. L.↗
NASA NTRS1980

The retention of hot gas in elliptical galaxies

The X-ray emission is interpreted from the fast-moving elliptical galaxy M86 (Forman et al. 1979) as evidence for the accumulation of an extensive gaseous envelope. The gas within this envelope is relatively hot, yet has until now been confined to the galaxy by the thermal pressure of the outer atmosphere of the Virgo cluster. The ram pressure of the intracluster gas in the cluster core is now stripping this envelope away. It is suggested that significant quantities of hot gas may be found in many elliptical galaxies.

Fabian, A. C.↗
NASA NTRS1981

Construction of composite three dimensional grids from subregion grids generated by elliptic systems

A technique is presented for constructing a boundary-conforming grid throughout a general three-dimensional flow region as a composite of subregion grids. Each subregion grid is generated numerically by solving a nonlinear system of elliptic equations. The boundary values represent nodal points in a quasi-two-dimensional grid that covers the curved surface bounding the subregion, and are generated numerically by a modified elliptic system. A primary feature of the technique is that the composite three-dimensional grid remains both continuous and smooth across the surface of juncture between any two adjoining subregions. Sample results are given for a wing-body combination.

Thomas, P. D.↗
NASA NTRS1981

The structure of giant elliptical galaxies in poor clusters of galaxies

Detailed photographic surface photometry is presented of the nine first brightest galaxies in poor clusters suspected of being cD galaxies. The surface photometry is put on an absolute scale, using multiaperture photoelectric photometry. Oemler (1976) and de Vaucouleurs (1948) laws are fitted to the profiles to derive structural parameters, and the structural properties of the galaxies are compared with those of the cD galaxies in rich clusters studied by Oemler (1976) and those of normal ellipticals studied by Kormendy (1977). It is found that (1) the profiles of first brightest galaxies are well fitted by an r to the 1/4 power law over a range of more than nine magnitudes and down to the faintest light levels observed and (2) structural parameters characterizing only the central part of first brightest galaxies in poor and rich clusters, and excluding the envelope component in the case of rich clusters, smoothly extend properties exhibited by normal ellipticals. These observations are consistent with the idea that the central part of first brightest galaxies in both poor and rich clusters is made up by the mergers of smaller galaxies.

Thuan, T. X.↗
NASA NTRS1950

Penetration of Air Jets Issuing from Circular, Square, and Elliptical Orifices Directed Perpendicularly to an Air Stream

An experimental investigation was conducted to determine the penetration of air jets d.irected perpendicularlY to an air stream. Jets Issuing from circular, square, and. elliptical orifices were investigated. and. the jet penetration at a position downstream of the orifice was determined- as a function of jet density, jet velocity, air-stream d.enaity, air-stream velocity, effective jet diameter, and. orifice flow coeffIcient. The jet penetrations were determined for nearly constant values of air-stream density at three tunnel-air velocities arid for a large range of Jet velocities and. densities. The results were correlated in terms of dimensionless parameters and the penetrations of the various shapes were compared. Greater penetration was obtained. with the square orifices and the elliptical orifices having an axis ratio of 4:1 at low tunnel-air velocities and low jet pressures than for the other orifices investigated. The square orifices gave the best penetrations at the higher values of tunnel-air velocity and jet total pressure.

Ruggeri, Robert S.↗
NASA NTRS1982

Neutral hydrogen in elliptical galaxies with nuclear radio sources and optical emission lines

An H I detection survey of eleven elliptical galaxies with powerful nuclear radio sources was conducted, using the 305 m antenna of Arecibo Observatory, to test the hypothesis that large H I mass is conductive to the formation of nuclear radio sources in elliptical galaxies. The H I was detected in emission in UGC 09114 and was possibly detected in absorption in UGC 06671. Observations of the remaining galaxies were not sensitive enough to support or refute the hypothesis. Data was combined from other H I surveys and spectroscopic surveys to search for correlations of H I mass with other galactic properties and environmental conditions. Strong correlations of (O II) lambda 3727 emission with H I content and with nuclear radio power were found. The latter two properties may simply indicate, respectively, whether a significant amount of gas is available to be ionized and whether energy is provided by nuclear activity for ionization. No dependence of H I content on optical luminosity or on degree of isolation from other galaxies was found.

Dressel, L. L.↗
NASA NTRS1982

IUE observations of NGC 4649, an elliptical galaxy with a strong ultraviolet flux

As in the previously studied elliptical galaxies, the flux f(lambda) in NGC 4649 has a minimum at 2500 A followed by a rapid increase towards shorter wavelengths. In NGC 4649, the flux level of this rising branch is the highest so far observed and seems not to be correlated with the luminosity or activity in the galaxy. The excess shortward of 4000 A, observed in M87, another high level rising branch galaxy, is not present in NGC 4649. The UV spectrum of NGC 4649 down to 2500 A matches closely those of NGC 3379 and NGC 4472. The implications of the UV properties of elliptical galaxies on the stellar content as well as on magnitudes and colors of distant galaxies are discussed

Bertola, F.↗