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Goldreich, P.

Publications and source records attributed to Goldreich, P..

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
NASA NTRS1983

The dynamics of elliptical rings

The paper investigates the evolution of eccentric rings under the influence of (1) differential precession due to the planetary quadrupole moment; (2) self-gravity; (3) viscous forces due to interparticle collisions; and (4) eccentricity excitation by shepherd satellites. The principal conclusions are that: (1) uniform precession can be enforced by self-gravity; the resulting configuration is both dynamically and secularly stable. (2) due to viscous forces the line of apsides at the inner ring edge is not exactly aligned with the line of apsides at the outer edge; the apse shift may be detectable in the alpha and beta rings of Uranus; (3) the mean eccentricity is determined by a balance between viscous damping and excitation by shepherds; (4) and the dimensionless eccentricity gradient is expected to be positive and of order unity in most eccentric rings, as observed.

Borderies, N.↗
NASA NTRS1983

Perturbed particle disks

The velocity ellipsoid in a particle disk near an isolated satellite resonance is determined by solving the Boltzmann moment equations, and solutions are obtained that are stationary functions of the azimuthal angle in a coordinate frame which rotates with the pattern speed of the perturbation potential. The magnitude of the deformation rate tensor in a perturbed particle disk is bounded from above by an expression which includes the orbital angular velocity, the optical depth, and a dimensionless constant of order unity. It is also found that, in sufficiently perturbed regions, there are ranges of azimuthal angle over which the radial component of the angular momentum flux is negative. It is also possible for the angular momentum luminosity to be negative. These results are pertinent to the understanding of sharp edges and density wave decay in planetary rings.

Borderies, N.↗
NASA NTRS1983

Precession of inclined rings

It is proposed that node alignment across an inclined ring is maintained by the self-gravity of the ring, which cancels the tendency for differential node precession due to the planet's multiple moments. The analysis is confined to circular rings, which is a self-consistent approximation because the interactions among circular and inclined ringlets do not generate secular perturbations of eccentricity.

Borderies, N.↗
NASA NTRS1983

The variations in eccentricity and apse precession rate of a narrow ring perturbed by a close satellite

The first-order perturbations of orbital eccentricity and apse precession rate for the case of a narrow ring, due to a close satellite whose orbit is also eccentric, are described by means of a Hamiltonian. The present treatment covers cases in which the satellite crosses the ring, and the level curves of the Hamiltonian are displayed for several parameter values. The results obtained are applied to the interaction of Saturn's F ring with its inner shepherd satellite.

Borderies, N.↗
NASA NTRS1982

Sharp edges of planetary rings

The ring systems of Saturn and Uranus exhibit several sharp edges, across which the optical depth drops from order unity to essentially zero. At least two and perhaps all of these features are associated with the location of orbital resonances between a satellite and the ring particles. It is remarkable that the optical depth varies on a distance scale which is much finer than that over which angular momentum can be transferred between a satellite and the ring material. The important features of this phenomenon are: (1) a perturbed band of width Delta a/a of about (satellite mass/planetary mass) to the 1/2 power adjacent to the edge within which the angular momentum transfer occurs, (2) streamlines perturbed such that the angular momentum luminosity decreases smoothly across the band to zero at the edge even though the optical depth remains constant, and (3) dynamical equilibrium requires a relation between the random velocity, the rate of deformation and the optical depth.

Borderies, N.↗
NASA NTRS1982

Radial widths, optical depths, and eccentricities of the Uranian rings

Observations of the stellar occultation by the Uranian rings of 15/16 August 1980 are used to estimate radial widths and normal optical depths for segments of rings 6, 5, 4, alpha, beta, eta, gamma, and delta. Synthetic occultation profiles are generated to match the observed light curves. A review of published data confirms the existence of width-radius relations for rings alpha and beta, and indicates that the optical depths of these two rings vary inversely with their radial widths. Masses are obtained for rings alpha and beta, on the assumption that differential precession is prevented by their self-gravity. A quantitative comparison of seven epsilon-ring occultation profiles obtained over a period of 3.4 yr reveals a consistent structure, which may reflect the presence of unresolved gaps and subrings.

Nicholson, P. D.↗
NASA NTRS1982

The dynamics of planetary rings

The physical processes that occur in planetary rings are discussed. The theoretical arguments leading to the conclusion that Saturn's rings are solid particles in nonuniform rotation are summarized, and the optical depth, thickness, and particle size of the rings are discussed. The influence of nearby satellites on the rings is analyzed, and asymmetries in the rings are briefly discussed. What is known of the rings of Uranus and of Jupiter's ring is summarized. Some of the dynamical processes and influences that are expected to be incorporated in more advanced theories of planetary rings are reviewed in detail, including radiation drag, plasma drag, interparticle collisions and viscosity, resonances with external satellites, shepherd satellites and moonlets. Finally, the orbital evolution of the shepherd satellites caused by the rings is estimated.

Goldreich, P.↗
NASA NTRS1982

The eccentric ringlet at 1.29 R sub S

Voyager 1 images, UV stellar occultation, and radio data on the eccentric ringlet in Saturn's C ring near the Titan 1:0 apsidal resonance are discussed. Kinematic analysis shows a ringlet precession rate equal to the mean motion of Titan and a width-radius relation expected for a ring maintaining itself against differential precession by self-gravity. The specific opacity estimated for this ringlet, 0.056 sqcm/gm, is comparable to that found for the eccentric ringlet at 1.45 Rs. Assuming that the eccentricity is completely forced by Titan, a more precise value can be determined for the location of the resonance than can be computed using the current values of Saturn's gravity coefficients.

Porco, C.↗
NASA NTRS1981

The origin of the eccentricities of the rings of Uranus

The effect of gravitational perturbations from a nearby satellite on the eccentricity e of a narrow particulate ring is considered. The perturbations near a resonance in an eccentric ring may be divided into corotation and Lindblad terms. For small e, the corotation terms damp e, whereas the Lindblad terms excite e. In the absence of saturation the corotation terms win by a small margin, and e damps. However, if the perturbations open gaps at the strongest resonances, then the Lindblad terms win, and e grows. This result offers an explanation for the existence of both circular and eccentric rings around Uranus. It is also shown that eccentricity changes induced by circular rings on eccentric satellite orbits are similar to those induced by satellites with circular orbits on eccentric rings.

Goldreich, P.↗
NASA NTRS1980

Theoretical studies of solar oscillations

Possible sources for the excitation of the solar 5 minute oscillations were investigated and a linear non-adiabatic stability code was applied to a preliminary study of the solar g-modes with periods near 160 minutes. Although no definitive conclusions concerning the excitation of these modes were reached, the excitation of the 5 minute oscillations by turbulent stresses in the convection zone remains a viable possibility. Theoretical calculations do not offer much support for the identification of the 160 minute global solar oscillation (reported by several independent observers) as a solar g-mode. A significant advance was made in attempting to reconcile mixing-length theory with the results of the calculations of linearly unstable normal modes. Calculations show that in a convective envelope prepared according to mixing length theory, the only linearly unstable modes are those which correspond to the turbulent eddies which are the basic element of the heuristic mixing length theory.

Goldreich, P.↗
NASA NTRS1980

Disk-satellite interactions

The rate at which angular momentum and energy are transferred between a disk and a satellite which orbit a central mass is calculated. It is shown that the angular momentum and energy transfer at Lindblad resonances tends to increase the satellite's orbit to lowest order in eccentricity, whereas the transfer at corotation resonances tends to decrease it. The results are applied to the interaction between Jupiter and the protoplanetary disk. The angular momentum transfer is shown to be so rapid that substantial changes in both the structure of the disk and the orbit of Jupiter must have taken place on a time scale of a few thousand years.

Goldreich, P.↗
NASA NTRS1979

The excitation of density waves at the Lindblad and corotation resonances by an external potential

The linear response of a differentially rotating two-dimensional gas disk, both with and without self-gravity, to a rigidly rotating external potential is calculated on the assumptions that the speed of sound is much smaller that the orbital velocity and that the external potential varies on the scale of the disk radius. The results show that: (1) the external potential exerts torques on the disk only at the Lindblad and corotation resonances; (2) the torque is positive at the outer Lindblad resonance and negative at the inner Lindblad resonance; (3) the torque at corotation has the sign of the radial vorticity gradient; and (4) the torques are of the same order of magnitude at both types of resonance and independent of the speed of sound in the disk. It is found that the external potential also excites density waves in the vicinity of the Lindblad and corotation resonances, that the long trailing wave is excited at a Lindblad resonance, and that short trailing waves are excited at the corotation resonance. The behavior of particle disks is briefly discussed, and the external torques on particle disks are proven to be identical to those on gas disks

Goldreich, P.↗
NASA NTRS1979

Precession of the epsilon ring of Uranus

It is noted that the outer and inner boundaries of the epsilon ring of Uranus can be fitted by aligned Keplerian ellipses. Four possible mechanisms for maintaining uniform precession in the epsilon ring are considered: the ring's self-gravity, precession due to a satellite, smooth pressure gradients, and shocklike phenomena. It is proposed that apse alignment is maintained by the self-gravity of the ring. In this case, a ring mass of approximately 5 x 10 to the 18th g and a mean surface density at quadrature of about 25 g/sq cm are estimated.

Goldreich, P.↗
NASA NTRS1979

Towards a theory for the Uranian rings

Interparticle collisions, radiation drag, and differential precession all tend to disrupt the rings of Uranus. The first two effects lead to radial spreading which would disrupt a free ring in less than or approximately 100,000,000 yr. It is proposed that the rings are confined in radius by gravitational torques from a series of small satellites that orbit with the ring system. Differential precession tends to destroy the apse alignment of the elliptical epsilon ring. It is suggested that apse alignment is maintained by the self-gravity of the ring. The resulting mass of the epsilon ring is approximately 5 times 10 to the 18th power g. Its radial confinement requires (for example) a pair of satellites of mass approximately 10 to the 19th power g, in circular orbits roughly 500 km away on either side of the ring

Goldreich, P.↗
NASA NTRS1979

The rings of Saturn and Uranus

Saturn has bright, broad rings separated by narrow gaps, while the rings of Uranus are dark, narrow and widely spaced. Presumably, both sets of rings lie inside the Roche limit, which is why the ring material has not condensed into satellites. This paper briefly reviews what is known about each ring system, with emphasis on properties of significance to dynamical astronomy.

Goldreich, P.↗
NASA NTRS1978

The rings of Uranus - Results of the 10 April 1978 occultation

Observations of the April 10, 1978, stellar occultation by the rings of Uranus are presented. Nine rings were observed, and their radii and widths are calculated. Rings eta, gamma, and delta are found to be most likely circular and coplanar, in agreement with previous analyses; the remaining rings are either noncircular or slightly inclined. The width of the epsilon ring is a linear function of its radius from the center of Uranus, projected onto the satellites' orbital plane; this suggests that it forms one continuous noncircular ring. The optical-depth profile of the epsilon ring has not changed significantly since March 1977. A model of this ring which fits all available observations adequately is that of a uniformly precessing Keplerian ellipse coplanar with the satellites' orbits. This model permits predictions of the radius and width of the epsilon ring for future occultations. The precession rate is used to determine J2 for Uranus, on the assumption that precession is caused solely by the planetary oblateness and not by satellite-ring interactions.

Nicholson, P. D.↗
NASA NTRS1978

The velocity dispersion in Saturn's rings

The collisional dynamics of a differentially rotating disk of particles are considered. The investigation is to some extent an analytic counterpart of the numerical studies of Brahic (1977). Following Brahic, it is assumed that the particles are identical, indestructible, imperfectly elastic, smooth spheres. Gravitational interactions between the particles are neglected. The main result of the reported analysis is the derivation of the relation between the coefficient of restitution and the optical depth for a differentially rotating disk of identical, inelastic, smooth spheres. Questions concerning the applicability of the obtained results to Saturn's rings are studied. It is felt that the calculations should give accurate quantitative results if the rings' filling factor is small. If this assumption is not justified, the calculations should be at least qualitatively correct.

Goldreich, P.↗