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At least 1,225 records · Page 68

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NASA NTRS1978

Graphical evaluation of relativistic matrix elements

A graphical representation of angular momentum was used to evaluate relativistic matrix elements between antisymmetrized states of many particle configurations having any number of open shells. The antisymmetrized matrix element was expanded as a sum of semisymmetrized matrix elements. The diagram representing a semisymmetrized matrix element was composed of four diagram blocks; the bra block, the ket block, the spectator block, and the interaction block. The first three blocks indicate the couplings of the two interacting configurations while the last depends on the interaction and is the replaceable component. Interaction blocks for relativistic operators and commonly used potentials were summarized in ready to use forms. A simple step by step procedure was prescribed generally for calculating antisymmetrized matrix elements of one and two particle operators.

Huang, K. N.↗

NASA NTRS1978

A close-up of the sun

NASA's long-range plan for the study of solar-terrestrial relations includes a Solar Probe Mission in which a spacecraft is put into an eccentric orbit with perihelion near 4 solar radii (0.02 AU). The scientific experiments which might be done with such a mission are discussed. Topics include the distribution of mass within the Sun, solar angular momentum, the fine structure of the solar surface and corona, the acceleration of the solar wind and energetic particles, and the evolution of interplanetary dust. The mission could also contribute to high-accuracy tests of general relativity and the search for cosmic gravitational radiation.

Neugebauer, M.↗

NASA NTRS1977

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

Choi, B. H.↗

NASA NTRS1978

Water sprays in space retrieval operations

The water spray technique (WST) for nullifying the angular momentum of a disabled spacecraft is examined. Such a despinning operation is necessary before a disabled spacecraft can be retrieved by the Space Shuttle. The WST involving the use of liquid sprays appears to be less complex and costly than other techniques proposed to despin a disabled vehicle. A series of experiments have been conducted to determine physical properties of water sprays exhausting into a vacuum. A computer model is built which together with the experimental results yields satellite despin performance parameters. The selection and retrieval of an actual disabled spacecraft is considered to demonstrate an application of the WST.

Freesland, D. C.↗

NASA NTRS1978

Extensions of guiding center motion to higher order

In a static magnetic field, some well-known guiding-center equations maintain their form when extended to next order in gyroradius. In these cases, it is only necessary to include the next order term in the magnetic moment series. The differential equation for guiding-center motion which describes both the parallel and perpendicular velocities correctly through first order in gyroradius is given. The question of how to define the guiding center position through second order arises and is discussed, and second order drifts are derived for one usual definition. The toroidal canonical angular momentum, P-phi, of the guiding center in an axisymmetric field is shown to be conserved using the guiding center velocity correct through first order. When second-order motion is included, P-phi is no longer a constant. The above extensions of guiding-center theory help to resolve the different tokamak orbits obtained either by using the guiding-center equations of motion or by using conservation of P-phi.

Northrop, T. G.↗

NASA NTRS1977

Magnetic damping of rotation

Based on Wilson's (1977) article on the magnetic effects on space vehicles and other celestial bodies, the magnetic damping of rotation is considered. The inadequacy of the interstellar magnetic field in overcoming solar wind shielding and thus influencing the rotation of bodies is described. The ionospheric shielding of the interstellar field is discussed along with the permeability and magnetic damping by the solar or stellar wind. Star formation and angular momentum is discussed and attention is given to the magnetic damping of unshielded small bodies. Calculations of the rate for damping through random particle impact are made. Theories concerning the rotation of asteroids and the origin of meteorites are reviewed. The shielding process of ionospheric plasmas is outlined and the damping effect of the geomagnetic field on the rotation of artificial satellites is evaluated.

Opik, E. J.↗

NASA NTRS1977

An element formulation for perturbed motion about the center of mass

The perturbed motion of a rigid body about its center of mass, is formulated in terms of the six elements: l, the magnitude of the angular momentum vector; h, the total energy; delta and epsilon, two linear functions of the independent variable; and psi(1) and theta (1), two Euler angles that orientate the inertial frame with respect to the unperturbed solution. Solutions from the element formulation and the original Euler equations are numerically compared using shuttle-type data. For applied torques smaller than a given magnitude, the element formulation produced the following results: (1) larger step sizes in the numerical integration of the differential equations, resulting in an overall computational time-saving, and (2) more significant figures of accuracy in the computation of the variables describing the state of the rigid body.

Donaldson, J. D.↗

NASA NTRS1978

Deflection of polarised radiation - Relative phase delay technique

The article discusses the geodesic motion of photons, considering particularly whether oppositely polarized photons fall at the same rate. It is assumed that orthogonally polarized photons would be equally deflected by the gravitational field of a nonrotating mass. Upon the introduction of rotation, the angular momentum of the deflecting source couples to the photon spin through gravitational field action. Thus there arise separate trajectories for orthogonal polarizations. Searching for changes in polarization in a deflected beam is accomplished by a relative phase delay technique. If the beam is split into orthogonal linear polarization, final polarization is elliptical. Experiments have been performed on searching for ellipticity developments in the linearly polarized carrier waves from Helios 1 and 2, and the results are presented.

Dennison, B.↗

NASA NTRS1978

Physics of the primitive solar accretion disk

The theory of viscous accretion disks developed by Lynden-Bell and Pringle (1974) has been applied to the evolution of the primitive solar nebula. The additional physical input needed to determine the structure of the disk is described. A series of calculations was carried out using a steady flow approximation to explore the effects on the disk properties of variations in such parameters as the angular momentum and accretion rate of the infalling material from a collapsing interstellar cloud fragment. The more detailed evolutionary calculations involved five cases with various combinations of parameters. It was concluded that the late stages of evolution of the disks would be dominated by the effects of mass loss from the expansion of a hot disk corona into space, and the effects of this were included in the evolutionary calculations. A new theory of comet formation is formulated upon these results. The most important result is the conclusion that the primitive solar accretion disk was repeatedly unstable against axisymmetric perturbations, in which rings would form and collapse upon themselves, with the subsequent formation of giant gaseous protoplanets.

Cameron, A. G. W.↗

NASA NTRS1977

The magnetic attitude control of the Atmosphere Explorer-E spacecraft

The Atmosphere Explorer-E spacecraft was launched in November 1975, as the last of the Atmosphere Explorer series. It is a dual spin satellite and has on-board magnetic coils to maintain the spin axis of the spacecraft within 2 degrees of orbit normal. There is a constraint on the total angular momentum to keep it at a constant level, at around 1200 in-lb-sec +/-10 percent. On the previous AE satellites, the attitude and momentum were controlled separately, with dipoles mounted parallel to the spin axis for pure attitude control, and with coils in the spin plane to desaturate the momentum wheel. Due to the near-equatorial orbit of the AE-E spacecraft, spin axis coils would be inefficient, because the dipoles would have been closely aligned with the geomagnetic field vector. For this reason it was decided to control both attitude and momentum magnitude with dipoles in the spin plane. However, for spin plane coils the attitude and momentum control are strongly coupled, which required a special control theory to be worked out.

Grell, M. G.↗

NASA NTRS1978

Hydrogen emission-line spectra in quasars and active galactic nuclei

An attempt is made to account for the observational fact that the intensity ratios of the lower Balmer lines seen in emission from QSOs, type 1 Seyfert galaxies, and other related active galaxies are not what would be expected from the conventional picture of lines generated in a recombining hydrogen plasma. Previous observations of emission-line intensities in QSOs and Seyfert galaxies are reviewed. The various processes included in the rate coefficients of the calculations are then described, viz., free-free, bound-free, and bound-bound transitions, radiative transfer, and angular-momentum mixing. The strengths of the various emission lines are calculated by using more accurate values for the transition rates, including excitation and deexcitation simultaneously, and providing for finite rates in optically forbidden transitions. Numerical results are presented for the cases of ground-state collisional excitation, reabsorption of the upper Balmer lines, and collisional deexcitation. The results are applied to construct a model for the emission-line gas in a QSO and to discuss limits on models of Seyfert galaxies.

Krolik, J. H.↗

NASA NTRS1978

Fission origin of the moon - Cause and timing

A new scenario is offered for the origin of the moon. It is assumed that the earth formed initially with about the maximum amount of angular momentum consistent with dynamical stability. This state is approximated by the secularly unstable Maclaurin spheroids (highly flattened hamburger-shaped bodies). It is shown that the earth cannot depart from this state at a reasonable rate as long as its viscosity is in the range of liquid rock. Since core formation supplies about 1600 kJ/kg, the earth will not leave this state until core formation is complete. When cooling produces a rise in viscosity, the earth will necessarily evolve along a path which is approximated by the Riemann ellipsoids (which have rapid internal motion). The evolution is toward a Jacobi ellipsoid, but it is intercepted by the development of a third-harmonic (pear-shaped) instability, which is catastrophic and leads to fission. The process of fission itself may be fundamentally analogous to the breaking of a wave in water. We cannot exclude the possibility that some other planets evolved similarly.

Okeefe, J. A.↗

NASA NTRS1979

Method and turbine for extracting kinetic energy from a stream of two-phase fluid

An axial flow separator turbine is described which includes a number of nozzles for delivering streams of a two-phase fluid along linear paths. A phase separator which responsively separates the vapor and liquid is characterized by concentrically related annuli supported for rotation within the paths. The separator has endless channels for confining the liquid under the influence of centrifugal forces. A vapor turbine fan extracts kinetic energy from the liquid. Angular momentum of both the liquid phase and the vapor phase of the fluid is converted to torque.

Elliott, D. G.↗

NASA NTRS1979

Ion beam probing of electrostatic fields

The determination of a cylindrically symmetric, time-independent electrostatic potential V in a magnetic field B with the same symmetry by measurements of the deflection of a primary beam of ions is analyzed and substantiated by examples. Special attention is given to the requirements on canonical angular momentum and total energy set by an arbitrary, nonmonotone V, to scaling laws obtained by normalization, and to the analogy with ionospheric sounding. The inversion procedure with the Abel analysis of an equivalent problem with a one-dimensional fictitious potential is used in a numerical experiment with application to the NASA Lewis Modified Penning Discharge. The determination of V from a study of secondary beams of ions with increased charge produced by hot plasma electrons is also analyzed, both from a general point of view and with application to the NASA Lewis SUMMA experiment. Simple formulas and geometrical constructions are given for the minimum energy necessary to reach the axis, the whole plasma, and any point in the magnetic field. The common, simplifying assumption that V is a small perturbation is critically and constructively analyzed; an iteration scheme for successively correcting the orbits and points of ionization for the electrostatic potential is suggested.

Persson, H.↗

NASA NTRS1978

Space construction base control system

Aspects of an attitude control system were studied and developed for a large space base that is structurally flexible and whose mass properties change rather dramatically during its orbital lifetime. Topics of discussion include the following: (1) space base orbital pointing and maneuvering; (2) angular momentum sizing of actuators; (3) momentum desaturation selection and sizing; (4) multilevel control technique applied to configuration one; (5) one-dimensional model simulation; (6) N-body discrete coordinate simulation; (7) structural analysis math model formulation; and (8) discussion of control problems and control methods.

Source record↗

NASA NTRS1978

Computer experiments on the effect of retrograde stars in disk galaxies

Using large-scale N-body calculations for flat disk galaxies, we examine the effect of reversing the angular momentum for various fractions of the stars upon the global bar-forming mode. The initial conditions for these simulations are based on stationary states of two classes of models: the isochrones studied recently by Kalnajs by means of linear theory, and a model resembling the Schmidt model of our own Galaxy. In both cases, as the fraction of retrograde stars is increased, the growth of the bar-forming mode is inhibited (although not eliminated). These N-body results for the isochrones agree with the predictions of linear theory, quantitatively as well as qualitatively.

Zang, T. A.↗

NASA NTRS1979

Dynamics of a stellar bar

The dynamical properties of a prolate bar have been studied by means of a three-dimensional computer model. The bar pattern rotates in the sense of the total angular momentum. The mean particle motion is a rapid streaming in the direction of pattern rotation as seen from a frame that rotates with the bar. Rotation rates that would be inferred from observation are significantly (2-3 times) faster than the pattern rotation speed. Velocity dispersions are anisotropic with the largest component along the bar. Particles oscillate in the bar potential significantly faster than pattern rotation. About 25% of the star orbits are near 2:2:1 resonance with the slow motion along the bar. Particle motion is highly ordered in the bar. Observable properties are described; where comparisons can be made, observable properties are in agreement with observations of brightness contours, velocity fields, and velocity dispersions. The bar has nearly exponential density profiles.

Miller, R. H.↗

NASA NTRS1979

Coupled motion of rigid bodies about their center of mass

Nontrivial analytical solutions for the coupled motion of two rigid bodies about their center of mass are obtained on the assumptions that the rigid bodies are coupled by a massless rigid boom and that no external forces are acting on the system. Both relative rotational and translational motions of the two bodies are considered. General equations of motion are derived by regarding the two bodies as consisting of two distinct systems of particles and by applying the principle of conservation of angular momentum. It is shown that a basic nontrivial solution can be obtained for the translational problem if an assumption is made concerning the relative orientation of one principal axis of inertia of each body and that fundamental nontrivial solutions are readily obtained for the rotational problem if an additional assumption is made with respect to the symmetry of one body. Certain stability criteria are found for some of these motions by defining regions of constraint for the relative translational and rotational elements.

Jezewski, D. J.↗