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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1982

Astrometric observations of the satellites of the outer planets. V - The oppositions of 1978-1979, 1980, and 1981

Accurate photographic positions obtained during the 1978-1979, 1980 and 1981 oppositions are presented for the positions of the Galilean and the Saturn satellites. Spherical-equatorial coordinates are presented for a total of 1032 pairs, for the equator and equinox of 1950.0 and 1316 intersatellite positions. The data were obtained by the Leander McCormick Observatory's 67-cm refractor telescope, and answers the need for more refined orbital element data on these satellites required by the Galileo Jupiter orbiter vehicle.

Rohde, J. R.↗
NASA NTRS1990

The migration of a compound drop due to thermocapillarity

The quasistatic thermocapillary motion of a compound drop in an unbounded fluid possessing a uniform temperature gradient is analyzed. For completeness, gravitational effects are included in the treatment. The general model is formulated, and the equations for the concentric case are solved using spherical polar coordinates, while the eccentric case is handled using bispherical coordinates. Results are given for the velocity of the drop as well as that of the droplet with respect to the drop, along with useful approximations. Illustrative results are presented graphically for the thermocapillary migration of a compound drop in the special case when the droplet is a gas bubble. In addition to the velocities of the drop and the bubble, representative isotherms and streamlines also are presented which display interesting qualitative features.

Morton, David S.↗
NASA NTRS1991

Hypersonic merged layer blunt body flows with wakes

An attempt is made here to understand the basic physics of the flowfield with wake on a blunt body of revolution under hypersonic rarefied conditions. A merged layer model of flow is envisioned. Full steady-state Navier-Stokes equations in spherical polar coordinate system are computed from the surface with slip and temperature jump conditions to the free stream by the Accelerated Successive Replacement method of numerical integration. Analysis is developed for bodies of arbitrary shape, but actual computations have been carried out for a sphere and sphere-cone body. Particular attention is paid to set the limit of the onset of separation, wake closure, shear-layer impingement, formation and dissipation of the shocks in the flowfield. Validity of the results is established by comparing the present results for sphere with the corresponding results of the SOFIA code in the common region of their validity and with the experimental data.

Jain, Amolak C.↗
NASA NTRS1958

Three-Dimensional Orbits of Earth Satellites, Including Effects of Earth Oblateness and Atmospheric Rotation

The principal purpose of the present paper is to present sets of equations which may be used for calculating complete trajectories of earth satellites from outer space to the ground under the influence of air drag and gravity, including oblateness effects, and to apply these to several examples of entry trajectories starting from a circular orbit. Equations of motion, based on an "instantaneous ellipse" technique, with polar angle as independent variable, were found suitable for automatic computation of orbits in which the trajectory consists of a number of revolutions. This method is suitable as long as the trajectory does not become nearly vertical. In the terminal phase of the trajectories, which are nearly vertical, equations of motion in spherical polar coordinates with time as the independent variable were found to be more suitable. In the first illustrative example the effects of the oblateness component of the earth's gravitational field and of atmospheric rotation were studied for equatorial orbits. The satellites were launched into circular orbits at a height of 120 miles, an altitude sufficiently high that a number of revolutions could be studied. The importance of the oblateness component of the earth's gravitational field is shown by the fact that a satellite launched at circular orbital speed, neglecting oblateness, has a perigee some 67,000 feet lower when oblateness forces are included in the equations of motion than when they are not included. Also, the loss in altitude per revolution is double that of a satellite following an orbit not subject to oblateness. The effect of atmospheric rotation on the loss of altitude per revolution was small. As might be surmised, the regression of the line of nodes as predicted by celestial mechanics is unchanged when drag is included. It is clear that the inclination of the orbital plane to the equator will be relatively unaffected by drag for no atmospheric rotation since the drag lies in the orbital plane in this case. With the inclusion of atmospheric rotation it was found that the inclination of the plane changed about one-millionth of a radian per revolution. Thus the prediction of the position of the orbital plane of an earth satellite is not complicated by the introduction of drag. The line of apsides, which without drag but with oblateness moves slowly in space, tends to move with the satellite when drag is included in the calculations. As a results, the usual linearized solutions based on oblateness alone must be basically altered when drag is included to take into account the rapid movement of the line of apsides. In the second illustrative example the final revolution was calculated to impact for a number of trajectories in an orbital plane inclined at 650 to the equator. Of particular interest is the large effect the oblateness gravitational field and atmospheric rotation can have on the impact point. For a value of CDA/m of unity, and for an initial downward angle at 80 miles altitude of 0.01 radian, such as might be utilized for manned re-entry, oblateness had an influence of about 300 miles in the impact point, and atmospheric rotation had about a 150-mile influence.

Nielsen, Jack N.↗
NASA NTRS1980

A three-dimensional body-fitted coordinate system for flow field calculations on asymmetric nosetips

A three dimensional body-fitted coordinate system developed for use in the calculation of inviscid flows over ablated, asymmetric reentry vehicle nosetips is described. Because of the potential geometric asymmetries, no standard coordinate system (e.g., spherical, axisymmetric reference surface-normal) is capable of being closely aligned with the nosetip surface. To generate a 3-D, body-fitted coordinate system an analytic mapping procedure is applied that is conformal within each meridional plane of the nosetip; these transformations are then coupled circumferentially to yield a three dimensional coordinate system. The mappings used are defined in terms of hinge points, which are points selected to approximate the body contours in each meridional plane. The selection of appropriate hinge points was automated to facilitate the use of the resulting nosetip flow field code.

Hall, D. W.↗
NASA NTRS1983

An interactive system for compositing digital radar and satellite data

This paper describes an approach for compositing digital radar data and GOES satellite data for meteorological analysis. The processing is performed on a user-oriented image processing system, and is designed to be used in the research mode. It has a capability to construct PPIs and three-dimensional CAPPIs using conventional as well as Doppler data, and to composite other types of data. In the remapping of radar data to satellite coordinates, two steps are necessary. First, PPI or CAPPI images are remapped onto a latitude-longitude projection. Then, the radar data are projected into satellite coordinates. The exact spherical trigonometric equations, and the approximations derived for simplifying the computations are given. The use of these approximations appears justified for most meteorological applications. The largest errors in the remapping procedure result from the satellite viewing angle parallax, which varies according to the cloud top height. The horizontal positional error due to this is of the order of the error in the assumed cloud height in mid-latitudes. Examples of PPI and CAPPI data composited with satellite data are given for Hurricane Frederic on 13 September 1979 and for a squall line on 2 May 1979 in Oklahoma.

Heymsfield, G. M.↗
NASA NTRS1992

Tests of a simple data merging algorithm for the GONG project

The GONG (Global Oscillation Network Group) project proposes to reduce the impact of diurnal variations on helioseismic measurements by making long-term observations of solar images from six sites placed around the globe. The sun will be observed nearly constantly for three years, resulting in the acquisition of l+ terabyte of image data. To use the solar network to maximum advantage, the images from the sites must be combined into a single time series to determine mode frequencies, amplitudes, and line widths. Initial versions of combined, i.e., merged, time series were made using a simple weighted average of data from different sites taken simultaneously. In order to accurately assess the impact of the data merge on the helioseismic measurements, a set of artificial solar disk images was made using a standard solar model and containing a well known set of oscillation modes and frequencies. This undegraded data set and data products computed from it were used to judge the relative merits of various data merging schemes. The artificial solar disk images were subjected to various instrumental and atmospheric degradations, dependent on site and time, in order to create a set of images simulating those likely to be taken at the site. The degraded artificial solar disk images for the six observing sites were combined in various ways to form merged time series of images and mode coefficients. Various forms of a weighted average were used, including an equally-weighted average, an average with weights dependent upon air mass and averages with weights dependent on various quality assurance parameters. Both the undegraded solar disk image time series and several time series made up of various combinations of the degraded solar disk images from the six sites were subjected to standard helioseismic measurement processing. This processing consisted of coordinate remapping, detrending, spherical harmonic transformation, computation of power series for the oscillation mode coefficients, and mode frequency identification. Visual and statistical evaluation of the merged data sets themselves and differences between the merged and undegraded data set shows good agreement between the two data sets. Some slight differences in image scale and registration appear between the undegraded data set and the various merged data sets. In the set of power series made from the mode coefficients of the merged data sets, some power leakage is observed into the background and into slightly lower l-value modes, especially at higher l-value mode frequencies. The results of the comparison of time series and mode oscillation frequencies of the undegraded data with those of the data merged using weighted averages indicate that, at least for p-mode solar oscillations, a weighted average of either the detrended remapped images or the mode coefficients gives good determination of the mode frequencies and adequate-to-good determination of the amplitudes and widths of the mode frequency lines. This conclusion is most advantageous to the analysis of the massive amounts of data to be received by the GONG network.

Williams, W. E.↗
NASA NTRS1996

An MHD Study of the Interaction Between the Solar Wind and the Interstellar Medium

The overall objective of this research program is to obtain a better understanding of the interaction between the solar wind and the interstellar medium through the use of numerical solutions of the time-dependent magnetohydrodynamic (MHD) equations. The simulated results have been compared with observations where possible and with the results from previous analytic and numerical studies. The primary accomplishment of this project has been the development of codes for 2-D models in both spherical and cylindrical coordinates and the application of the codes to the solar wind/interstellar medium interaction. Computations have been carried out for both a relatively simple gas-dynamic interaction and a flow-aligned interstellar magnetic field. The results have been shown to compare favorably with models that use more approximations and to modify and extend the previous results as would be expected. The simulations have also been used along with a data analysis study to provide a quantitative estimate of the distance to the termination and bow shocks. Some of the specific topics that have been studied are: (1) gas dynamic models of the solar wind/interstellar medium interaction, (2) termination shock response to large-scale solar wind fluctuations, and (3) distances to the termination shock and heliopause. The main results from each of these studies are summarized. The results were published in three papers which are included as attachments.

Steinolfson, R. S.↗
NASA NTRS1998

An Alternative Lunar Ephemeris Model for On-Board Flight Software Use

In calculating the position vector of the Moon in on-board flight software, one often begins by using a series expansion to calculate the ecliptic latitude and longitude of the Moon, referred to the mean ecliptic and equinox of date. One then performs a reduction for precession, followed by a rotation of the position vector from the ecliptic plane to the equator, and a transformation from spherical to Cartesian coordinates before finally arriving at the desired result: equatorial J2000 Cartesian components of the lunar position vector. An alternative method is developed here in which the equatorial J2000 Cartesian components of the lunar position vector are calculated directly by a series expansion, saving valuable on-board computer resources.

Simpson, David G.↗
NASA NTRS1999

An Alternative Lunar Ephemeris Model for On-Board Flight Software Use

In calculating the position vector of the Moon in on-board flight software, one often begins by using a series expansion to calculate the ecliptic latitude and longitude of the Moon, referred to the mean ecliptic and equinox of date. One then performs a reduction for precession, followed by a rotation of the position vector from the ecliptic plane to the equator, and a transformation from spherical to Cartesian coordinates before finally arriving at the desired result: equatorial J2000 Cartesian components of the lunar position vector. An alternative method is developed here in which the equatorial J2000 Cartesian components of the lunar position vector are calculated directly by a series expansion, saving valuable onboard computer resources.

Simpson, David G.↗
NASA NTRS1980

Orthogonality of spherical harmonic coefficients

Orthogonality relations are obtained for the spherical harmonic coefficients of functions defined on the surface of a sphere. Following a brief discussion of the orthogonality of Fourier series coefficients, consideration is given to the values averaged over all orientations of the coordinate system of the spherical harmonic coefficients of a function defined on the surface of a sphere that can be expressed in terms of Legendre polynomials for the special case where the function is the sum of two delta functions located at two different points on the sphere, and for the case of an essentially arbitrary function. It is noted that the orthogonality relations derived have found applications in statistical studies of the geomagnetic field.

Mcleod, M. G.↗
NASA NTRS1976

A tensor formulation of the equation of transfer for spherically symmetric flows

A tensor formulation of the equation of radiative transfer is derived in a seven-dimensional Riemannian space such that the resulting equation constitutes a divergence in any coordinate system. After being transformed to a spherically symmetric comoving coordinate system, the transfer equation contains partial derivatives in angle and frequency, as well as optical depth due to the effects of aberration and the Doppler shift. However, by virtue of the divergence form of this equation, the divergence theorem may be applied to yield a numerical differencing scheme which is expected to be stable and to conserve luminosity. It is shown that the equation of transfer derived by this method in a Lagrangian coordinate system may be reduced to that given by Castor (1972), although it is, of course, desirable to leave the equation in divergence form.

Haisch, B. M.↗
NASA NTRS1981

Spherical-earth Gravity and Magnetic Anomaly Modeling by Gauss-legendre Quadrature Integration

The usefulness of long-wavelength potential field anomalies in lithospheric interpretation is greatly increased with spherical Earth modeling techniques. Gauss-Legendre quadrature integration is used to calculate the anomalous potential of gravity and magnetic fields and their spatial derivatives on a spherical Earth for an arbitrary body represented by an equivalent point source distribution of gravity poles or magnetic dipoles. The distribution of equivalent point sources is determined directly from the coordinate limits of the source volume. Variable integration limits for an arbitrarily shaped body are derived from interpolation of points which approximate the body's surface envelope. The versatility of the method is enhanced by the ability to treat physical property variations within the source volume and to consider variable magnetic fields over the source and observation surface. A number of examples verify and illustrate the capabilities of the technique, including preliminary modeling of potential field signatures for Mississippi embayment crustal structure at satellite elevations.

Spherical coordinate gravity modeling↗