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Register a new userA simple model for the location of Saturns F ring
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In this paper, we introduce a simplified model to understand the location of Saturns F ring. The model is a planar restricted five-body problem defined by the gravitational field of Saturn, including its second zonal harmonic $J_2$, the shepherd moons Prometheus and Pandora, and Titan. We compute accurate long-time numerical integrations of (about 2.5 million) non-interacting test-particles initially located in the region between the orbits of Prometheus and Pandora, and address whether they escape or remain trapped in this region. We obtain a wide region of initial conditions of the test particles that remain confined. We consider a dynamical stability indicator for the test particles motion defined by computing the ratio of the standard deviation over the average value of relevant dynamical quantities, in particular, for the mean-motion and the semi-major axis. This indicator separates clearly a subset of trapped initial conditions that appear as very localized stripes in the initial semi-major axis and eccentricity space for the most stable orbits. Retaining only these test particles, we obtain a narrow eccentric ring which displays sharp edges and collective alignment. The semi-major axis of the accumulation stripes of the stable ring-particles can be associated with resonances, mostly involving Prometheus outer Lindblad and co-rotation resonances, but not exclusively. Pandoras inner Lindblad and co-rotation resonances as well as low-order three-body resonances typically coincide with gaps, i.e., regions of instabilities. Comparison of our results with the nominal data for the F ring shows some correspondence.
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The $mu$ and $ u$ rings of Uranus form a secondary ring-moon system with the satellites Puck, Mab,Portia, and Rosalind. These rings are tenuous and dominated by micrometric particles, which can be strongly disturbed by the solar radiation pressure. We performed a numerical analysis of the orbital evolution of a sample of particles under the influence of the solar radiation force and the planetary oblateness, combined with the gravitational interaction with the close satellites. The most likely result is a collisions and the deposition of particles onto the surface of these satellites. Since this mechanism tends to cause a depletion of material of the rings, we investigate additional sources for these dust particles. Adopting a rough estimative of the flux of interplanetary meteoroids, we found that the ejections from Mab could generate a ring with optical depth comparable with the observations. A similar analysis was carried out for the F-ring dust band. The damping due to the Saturns oblateness prevents the overstated changes of the eccentricity and increases in the lifetime of the particles. Therewithal photometric study of the F-ring using Cassini images revealed that substantial secular increase in the brightness of Saturns F ring has occurred in the last 25 years. The shapes of the phase curves from Cassini and Voyager are similar, suggesting that although the number of dust particles has increased, the overall distribution of sizes is unchanged. The dust bands that permeate the rings of Uranus were observed late in 2007 during the equinox, when the Sun crossed the ring plane. Images taken with the VLT were processed and then combined to result in long-exposure frames. For each frame, the north and south radial profiles were extracted. They will be used to develop a photometric model.
Saturns ionosphere is produced when the otherwise neutral atmosphere is exposed to a flow of energetic charged particles or solar radiation. At low latitudes the latter should result in a weak planet-wide glow in infrared (IR), corresponding to the planets uniform illumination by the Sun. The observed low-latitude ionospheric electron density is lower and the temperature higher than predicted by models. A planet-ring magnetic connection has been previously suggested in which an influx of water from the rings could explain the lower than expected electron densities in Saturns atmosphere. Here we report the detection of a pattern of features, extending across a broad latitude band from ~25 to 60 degrees, that is superposed on the lower latitude background glow, with peaks in emission that map along the planets magnetic field lines to gaps in Saturns rings. This pattern implies the transfer of charged water products from the ring-plane to the ionosphere, revealing the influx on a global scale, flooding between 30 to 43% of the planets upper-atmospheric surface. This ring `rain plays a fundamental role in modulating ionospheric emissions and suppressing electron densities.
We present an analytical model to study the dynamics of the outer edge of Saturns A ring. The latter is influenced by 7:6 mean motion resonances with Janus and Epimetheus. Because of the horseshoe motion of the two co-orbital moons, the ring edge particles are alternately trapped in a corotation eccentricity resonance (CER) or a Lindblad eccentricity resonance (LER). However, the resonance oscillation periods are longer than the 4-year interval between the switches in the orbits of Janus and Epimetheus. Averaged equations of motion are used, and our model is numerically integrated to describe the effects of the periodic sweeping of the 7:6 CERs and LERs over the ring edge region. We show that four radial zones (ranges 136715-136723, 136738-136749, 136756-136768, 136783-136791 km) are chaotic on decadal timescales, within which particle semi-major axes have periodic changes due to partial libration motions around the CER fixed points. After a few decades, the maximum variation of semi-major axis is about 11 km (respectively 3 km) in the case of the CER with Janus (respectively Epimetheus). Similarly, particle eccentricities have partial oscillations forced by the LERs every 4 yr. For initially circular orbits, the maximum eccentricity reached is ~0.001. We apply our work to Peggy, an object recently discovered at the ring edge, confirming that it is strongly perturbed by the Janus 7:6 LER. The CER has currently no effect on that body, nevertheless the fitted semi-major axes are just outside the chaotic zone of radial range 136756-136768 km.
The recently discovered ring around the dwarf planet (136108) Haumea is located near the 1:3 resonance between the orbital motion of the ring particles and the spin of Haumea. In the current work is studied the dynamics of individual particles in the region where is located the ring. Using the Poincare Surface of Section technique, the islands of stability associated with the 1:3 resonance are identified and studied. Along all its existence this resonance showed to be doubled, producing pairs of periodic and quasi-periodic orbits. The fact of being doubled introduces a separatrix, which generates a chaotic layer that significantly reduces the size of the stable regions of the 1:3 resonance. The results also show that there is a minimum equivalent eccentricity ($e_{1:3}$) for the existence of such resonance. This value seems to be too high to keep a particle within the borders of the ring. On the other hand, the Poincare Surface of Sections show the existence of much larger stable regions, but associated with a family of first kind periodic orbits. They exist with equivalent eccentricity values lower than $e_{1:3}$, and covering a large radial distance, which encompasses the region of the Haumeas ring. Therefore, this analysis suggests the Haumeas ring is in a stable region associated with a first kind periodic orbit instead of the 1:3 resonance.
Normal mode oscillations in Saturn excite density and bending waves in the C Ring, providing a valuable window into the planets interior. Saturns fundamental modes (f modes) excite the majority of the observed waves, while gravito-inertial modes (rotationally modified g modes) associated with stable stratification in the deep interior provide a compelling explanation for additional density waves with low azimuthal wavenumbers m. However, multiplets of density waves with nearly degenerate frequencies, including an m=3 triplet, still lack a definitive explanation. We investigate the effects of rapid and differential rotation on Saturns oscillations, calculating normal modes for independently constrained interior models. We use a non-perturbative treatment of rotation that captures the full effects of the Coriolis and centrifugal forces, and consequently the mixing of sectoral f modes with g modes characterized by very different spherical harmonic degrees. Realistic profiles for differential rotation associated with Saturns zonal winds can enhance these mode interactions, producing detectable oscillations with frequencies separated by less than 1%. Our calculations demonstrate that a three-mode interaction involving an f mode and two g modes can feasibly explain the finely split m=3 triplet, although the fine-tuning required to produce such an interaction generally worsens agreement with seismological constraints provided by m=2 density waves. Our calculations additionally demonstrate that sectoral f mode frequencies are measurably sensitive to differential rotation in Saturns convective envelope. Finally, we find that including realistic equatorial antisymmetry in Saturns differential rotation profile couples modes with even and odd equatorial parity, producing oscillations that could in principle excite both density and bending waves simultaneously.
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