Search NASA⌕ Search

SEARCH · Search NASA

Results for “Quadrupole moment”

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.

At least 37 records · Page 2

The magnetic field of Uranus

Aspherical harmonic model of the planetary magnetic field of Uranus is obtained from the Voyager 2 encounter observations using generalized inverse techniques which allow partial solutions to complex (underdetermined) problems. The Goddard Space Flight Center 'Q3' model is characterized by a large dipole tilt (58.6 deg) relative to the rotation axis, a dipole moment of 0.228 G R(Uranus radii cubed) and an unusually large quadrupole moment. Characteristics of this complex model magnetic field are illustrated using contour maps of the field on the planet's surface and discussed in the context of possible dynamo generation in the relatively poorly conducting 'ice' mantle.

Connerney, J. E. P.↗

Precise measurement of charged defects in III-V compounds (supplement 2)

Experimental methods and related theory which will permit the measurement of low concentrations of vacancies and other defects in III-V compound semiconductors are discussed. Once the nature of these defects has been determined, this information can be incorporated into a transport theory for devices constructed from these materials, and experiments conducted to test the theory. The vacancies and other defects in the III-V compounds are detected by measurement of the nuclear magnetic resonance (NMR) line width. Most of the III-V compounds have at least one isotope with a nuclear quadrupole moment. In a crystal with a cubic crystal field (characteristic of most III-V compounds) there is no quadrupole splitting of the Zeeman resonance line. However, a defect removes the cubic symmetry locally and causes splitting which result in a change of the NMR width. This change can be used to detect the presence of vacancies.

Soest, J. F.↗

A test of the galactic origin of gamma-ray bursts

Models in which gamma-ray bursters are young neutron stars may be difficult to reconcile with the apparently isotropic distribution of observed bursts. To justify this statement, the distribution of old neutron stars in the Galaxy was calculated by integrating numerically some 90,000 orbits in the Galactic gravitational potential for up to 10 to the 10th yr. Other calculations included the dipole moment in the angular distribution of neutron stars as a convenient measure of their concentration toward the Galactic center, the quadrupole moment in their angular distribution as a convenient measure of their concentration toward the Galactic plane, and the average value of V/Vmax as a convenient measure of the radial distribution of neutron stars. Models that require accretion from a cold circumstellar disk or from a close companion are only marginally consistent with the isotropic distribution of the observed bursts. Models that require accretion of interstellar matter are ruled out due to a very strong dipole anisotropy. Models that suggest the Galactic halo origin of gamma-ray bursts are briefly discussed. The GRANAT and GRO missions should provide evidence for or against the association of gamma-ray bursts with the Galactic disk neutron stars.

Paczynski, Bohdan↗

The magnetic field and magnetospheric configuration of Uranus

A significant and unique planetary magnetic field discovered by Voyager 2 is presented. A large tilt of 58.6 deg of the magnetic-dipole axis from the rotation axis was found. Combined with a large offset of 0.3 RU of the magnetic dipole from the center of the planet, the moment of 0.23 gauss-RU3 leads to field magnitudes at the surface which vary widely between 0.1 and 1.0 gauss. A simple diagram illustrating the offset tilted dipole of Uranus and some field lines is shown. A more exact and accurate spherical-harmonic model of the planetary field, which includes both dipole and quadrupole moments, is derived. There exists a well-developed bipolar magnetic tail on the night side of the planet which rotates daily about the extended planet-sunline with Uranus because of the large obliquity of the Uranian rotation axis.

Ness, Norman F.↗

Gyroscope test of gravitation: An analysis of the important perturbations

Two perturbations, the earth's quadrupole moment and the earth's revolution around the sun, are discussed. Schiff's proposed gyroscope test of gravitation is analyzed, along with the capability of deciphering each separate contribution to the angular velocity of spin precession.

Oconnell, R. F.↗

Mercury's perihelion advance - Determination by radar.

Measurement of echo delays of radar signals transmitted from earth to Mercury, yielding an accurate value for the advance of the latter's perihelion position. Given that the sun's gravitational quadrupole moment is negligible, the result in terms of the Eddington-Robertson parameters is (2 + 2 gamma-beta)/3 approximately equal to 1.005 plus or minus 0.007, where gamma = beta = 1 in general relativity, and where 0.007 represents the statistical standard error. Inclusion of the probable contribution of systematic errors raises the uncertainty to about 0.02.

Shapiro, I. I.↗

Second virial coefficients for the polar species in steam.

The potential function parameters to fit the data obtained by Kell et al. (1968) are determined. The data of Kell et al. cover the temperature range from 150 to 450 C. Data for the temperature range from 500 to 1000 C are from Sugaware et al. (1964). These calculations have been extended to include OH-OH and OH-H2O pairwise interactions. For the latter interaction the formalism was extended to the case of unequal dipole quadrupole moments in the potential function for the interacting species.

Kubin, R. F.↗

The generation of gravitational waves. 1. Weak-field sources: A plug-in-and-grind formalism

A plug-in-and-grind formalism is derived for calculating the gravitational waves emitted by any system with weak internal gravitational fields. If the internal fields have negligible influence on the system's motions, then the formalism reduces to standard linearized theory. Whether or not gravity affects the motions, if the motions are slow and internal stresses are weak, then the new formalism reduces to the standard quadrupole-moment formalism. In the general case the new formalism expresses the radiation in terms of a retarded Green's function for slightly curved spacetime, and then breaks the Green's-function integral into five easily understood pieces: direct radiation, produced directly by the motions of the sources; whump radiation, produced by the the gravitational stresses of the source; transition radiation, produced by a time-changing time delay (Shapiro effect) in the propagation of the nonradiative, 1/r field of the source; focussing radiation produced when one portion of the source focusses, in a time-dependent way, the nonradiative field of another portion of the source, and tail radiation, produced by backscatter of the nonradiative field in regions of focussing.

Thorne, K. S.↗

Analysis of the Capability and Limitations of Relativistic Gravity Measurements Using Radio Astronomy Methods

The uses of radar observations of planets and very-long-baseline radio interferometric observations of extragalactic objects to test theories of gravitation are described in detail with special emphasis on sources of error. The accuracy achievable in these tests with data already obtained, can be summarized in terms of: retardation of signal propagation (radar), deflection of radio waves (interferometry), advance of planetary perihelia (radar), gravitational quadrupole moment of sun (radar), and time variation of gravitational constant (radar). The analyses completed to date have yielded no significant disagreement with the predictions of general relativity.

Shapiro, I. I.↗

The generation of gravitational waves. I - Weak-field sources

This paper derives and summarizes a 'plug-in-and-grind' formalism for calculating the gravitational waves emitted by any system with weak internal gravitational fields. If the internal fields have negligible influence on the system's motions, the formalism reduces to standard 'linearized theory'. Independent of the effects of gravity on the motions, the formalism reduces to the standard 'quadrupole-moment formalism' if the motions are slow and internal stresses are weak. In the general case, the formalism expresses the radiation in terms of a retarded Green's function for slightly curved spacetime and breaks the Green's function integral into five easily understood pieces: direct radiation, produced directly by the motions of the source; whump radiation, produced by the 'gravitational stresses' of the source; transition radiation, produced by a time-changing time delay ('Shapiro effect') in the propagation of the nonradiative 1/r field of the source; focusing radiation, produced when one portion of the source focuses, in a time-dependent way, the nonradiative field of another portion of the source; and tail radiation, produced by 'back-scatter' of the nonradiative field in regions of focusing.

Thorne, K. S.↗

Tests of general relativity using astrometric and radiometric observations of the planets

Current least squares fits to solar system data, including transit circle observations of the terrestrial and giant planets, radar observations of the terrestrial planets, Mariner 9 range fixes to Mars, and Pioneer 10/11 range fixes to Jupiter, have yielded some new results of interest to experimental relativity. Solutions have been obtained for the parameterized post-Newtonian (PPN) parameters beta and gamma, the solar gravitational quadrupole moment J2, a time variation in the gravitational constant G, and four Nordtvedt parameters.

Anderson, J. D.↗

Gravitational experiments on solar probe

A covariance analysis was performed for a solar probe trajectory which encounters the sun at four solar radii. The unknown parameters in the analysis are the six initial cartesian coordinates for the probe, six initial cartesian coordinates for the earth, the astronomical unit, the solar gravitational quadrupole coefficient and two post Newtonian meters (beta, gamma). Errors in the unknown parameters were computed as a function of standard errors on the radio tracking data and on the nongravitational forces which act on the probe. Results were obtained for several tracking geometries and for several orbital inclinations to the ecliptic. The analysis shows that the principal scientific result from the radio tracking of a solar probe would be the determination of the quadrupole moment, which would place a constraint on models of the solar interior.

Anderson, J. D.↗

Possible measurements of J sub 2 and the sun's angular momentum with the solar probe

The metric tensor is given for describing the dynamical effects of the sun on a solar probe and the gravitational redshift of a probe-based clock in a covariance analysis for the detectability of the solar quadrupole moment and the solar angular momentum. Unknown parameters were determined by least squares fit to the probe tracking data. A polar orbit was assumed with perihelion at 5 solar radii and with an earth-sun-probe angle of 135 deg at perihelion. Tracking was assumed to be Doppler only, with a basic uncertainity of .1 mm/sec in the radial velocity. A drag-free system which could reduce nongravitational forces below the level of 2 times 10 to the minus 12th power was found necessary to preserve this same level of accuracy. Both one way and two way Doppler were supposed in order to determine the gravitational redshift as well as the pure spacecraft dynamics.

Nordtvedt, K.↗

The generation of gravitational waves. IV - Bremsstrahlung

Previously derived waveforms for gravitational bremsstrahlung are discussed along with their spectra and their limiting structure at high and low relative velocities. Waveforms and spectra are presented for a low-velocity bremsstrahlung encounter, and waveforms are given for encounters of arbitrary relative velocity. Limiting forms for the gravitational-wave amplitudes in the 'forward', 'intermediate', and 'backward' regions are derived in the high-velocity limit. The energy spectra seen by observers in the three regions are computed for arbitrary and high velocities. Simpler methods for analyzing special cases of the bremsstrahlung problem are examined, and the results of those methods are compared with the present results. Those methods include the quadrupole-moment and post-Newtonian formalisms, linear perturbations of the Schwarzschild metric, the method of colliding plane waves, the method of virtual quanta, and the zero-frequency limit. Classical gravitational bremsstrahlung is then compared with classical electromagnetic bremsstrahlung.

Kovacs, S. J., Jr.↗