Engineering topics
Publications and source records attributed to Borderies, N..
Acquisition of a new high quality gravity data set has begun. The data set presently covers one third of the Venusian longitude. Better spatial resolution is obtained from a 60th degree and order spherical harmonic solution. Plans for aerobraking in May 1993 into a near circular orbit will provide excellent data for higher latitude regions.
A model describing the physical libration in longitude and latitude for Phobos is derived. The major effect is the well-known longitude variation with the anomalistic orbital period and amplitude. Several additional meter-sized periodic librations in longitude exist. The latitude variation is dominated by the forced precession of Phobos' figure axis with the precession of Phobos' orbital plane. The contribution of Phobos' topography to its gravity field is estimated using the control network model of Duxbury and Callahan (1989).
The new observations of planetary rings, including those acquired during the encounters of Voyager with Jupiter, Saturn, and Uranus, and the discovery of incomplete rings around Neptune, reveal the great importance of resonances in determining the dynamics and the shape of planetary rings. Several types of resonances play a part in planetary rings. Current questions of interest are related to the nonlinear theory of density waves, the confinement of the Uranian rings, and the arcs of rings around Neptune.
It is proposed that the incomplete rings of Neptune consist of a number of short arcs centered on the corotation resonances of a single satellite. The satellite must have a radius of the order of 100 km or more and move on an inclined orbit. Corotation resonances are located at potential maxima. Thus, mechanical energy dissipated by interparticle collisions must be continually replenished to prevent the arcs from spreading. It is shown that each corotation resonance is associated with a nearby Lindblad resonance, which excites the ring particles' orbital eccentricity, thus supplying the energy required to maintain the arc. The ultimate energy reservoir is the satellite's orbital energy. Therefore, interaction with the arcs damps the satellite's orbital inclination. The self-gravity of the arcs limits their contraction and enforces a relation between arc length and mass. The estimated arc masses are so small, of the order of 10 to the 16th g, that the satellite's orbital inclination suffers negligible decay over the age of the solar system. The inferred surface mass densities are comparable to those found in the major rings of Saturn and Uranus.
In the present study of the viscosity of a differentially rotating particle disk, in the limiting case where the particles are densely packed and their collective behavior resembles that of a liquid, the pressure tensor is derived from both the equations of hydrodynamics and a simple kinetic model of collisions due to Haff (1983). Density waves and narrow circular rings are unstable if the liquid approximation applies, and the consequent nonlinear perturbations may generate 'splashing' of the ring material in the vertical direction. These results are pertinent to the origin of the ellipticities of ringlets, the nonaxisymmetric features near the outer edge of the Saturn B ring, and unexplained residuals in kinematic models of the Saturn and Uranus rings.
The shapes and kinematics of the Titan and Maxwell ringlets of Saturn's C ring are studied. The ringlets are narrow and eccentric, with mean widths of about 25 km for Titan and abut 64 km for Maxwell, and with eccentricities of order 10 to the -4th. They have sharp edges on a scale of about 1 km, normal optical depths of roughly 0.5-2.0, normal optical depth of the surrounding region, and positive linear width-radius relations. The Titan ringlet is the only feature whose dynamics appears to be completely determined by an external satellite; the kinematics of the Maxwell ringlet are determined solely by Saturn's nonspherical gravity field. The comparatively large measured optical depths and large inferred mass extinction coefficients for the ringlets suggest an environment and particle size distribution different from the remainder of the C ring and presumably caused by the mechanism responsible for ring confinement.
Resonant gravitational interactions between a ring and a satellite produce secular variations of their orbital inclinations. Interactions at vertical resonances, analogous to Lindblad resonances but involving inclinations instead of eccentricities, excite inclinations. There is no inclination analog of the corotation resonance. An equatorial ring changes the inclination of a nearby satellite in qualitatively the same way that a satellite in an equatorial orbit changes the inclination of a nearby ring. Viscous dissipation in a ring leads to an equilibrium value of its inclination. These results provide a basis for discussing the origins of the inclinations of planetary rings.
Henrad's (1982) method, which is based on an extension of the theory of adiabatic invariants, is presently applied to a simplified analytic derivation of the capture probabilities for the j + 1 : j and j + 2 : j orbital resonances. The results originally obtained by Yoder (1979) are thereby recovered.
Voyager photographic data are used for microscopic and macroscopic analyses of the dynamics of the Saturn rings. Attention is given to particle collisions, local velocity dispersion, the particle size distribution, mechanisms governing the ring structure and interactive effects with Saturn satellite orbits. The mechanical properties and collision dynamics of the particles are discussed, along with models for perturbed and unperturbed disks. The forces involved and true scale of particle erosion are considered, as are instabilities in the rings, satellite torques, resonances, and the time scale for the evolution of the satellite orbits. Finally, the possibility that angular momentum exchanges are occurring between individual rings and satellite orbits is examined.
The results of Voyager experiments to characterize the eccentric ringlet at 1.45 Saturn radius are discussed. The Voyager I carried out microwave occultation trials with a dual-frequency transmitter, while Voyager 2 observed the occultation of delta Scorpii using an UV spectrometer and a photopolarimeter. The ringlet was associated with a basically empty region next to an edge of the C ring which decreased to a few hundred meters thickness. The width of the ringlet in the gap was estimated to vary from 38-88 km, and it maintains an elliptical shape. It precesses within the 265 km gap it occupies, and has a double-peaked core 15 km wide. The bulk of the ringlet is particles of less than 1 cm radius.
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.
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.
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.
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.
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.
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.