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F Ring Core Stability: Corotation Resonance Plus Antiresonance

The decades-or-longer stability of the narrow F Ring core in a sea of orbital chaos appears to be due to an unusual combination of traditional corotation resonance and a novel kind of "antiresonance". At a series of specific locations in the F Ring region, apse precession between synodic encounters with Prometheus allows semimajor axis perturbations to promptly cancel before significant orbital period changes can occur. This cancellation fails for particles that encounter Prometheus when it is near its apoapse, especially during periods of antialignment of its apse with that of the F Ring. At these times, the strength of the semimajor axis perturbation is large (tens of km) and highly nonsinusoidal in encounter longitude, making it impossible to cancel promptly on a subsequent encounter and leading to chaotic orbital diffusion. Only particles that consistently encounter Prometheus away from its apoapse can use antiresonance to maintain stable orbits, implying that the true mean motion nF of the stable core must be defined by a corotational resonance of the form nF = nP(-kappa)P/m, where (nP, kappaP) are Prometheus' mean motion and epicycle frequency. To test this hypothesis we used the fact that Cassini RSS occultations only sporadically detect a "massive" F Ring core, composed of several-cm-and-larger particles. We regressed the inertial longitudes of 24 Cassini RSS (and VGR) detections and 43 nondetections to a common epoch, using a comb of candidate nP, and then folded them modulo the anticipated m-number of the corotational resonance (Prometheus m = 110 outer CER), to see if clustering appears. We find the "true F Ring core" is actually arranged in a series of short longitudinal arcs separated by nearly empty longitudes, orbiting at a well determined semimajor axis of 140222.4 km (from 2005-2012 at least). Small particles seen by imaging and stellar occultations spread quickly in azimuth and obscure this clumpy structure. Small chaotic variations in the mean motion and/or apse longitude of Prometheus quickly become manifest in the F Ring core, and we suggest that the core must adapt to these changes for the F Ring to maintain stability over timescales of decades and longer

Cassini RSS occultations↗

Dynamics and Structure of Planetary Rings

We developed a novel technique to determine the macroscopic particle size distribution of Saturn's rings by exploiting diffraction effects during stellar occultations. This was a major undertaking, and resulted in two publications now in press. In the latter paper, we derived power-law particle size distributions for each of Saturn's main ring regions, using observations of the 3 July 1989 stellar occultation of 28 Sgr from Palomar, McDonald, and Lick Observatories. We used the Voyager PPS delta Sco optical depth profile to estimate and then remove the directly transmitted signal from the 28 Sgr observations, leaving high SNR scattered light profiles at wavelengths of 3.9, 2.1, and 0.9 micrometers. The angular distribution of this diffracted signal depends on the ring particle size distribution: the sharpness of the forward lobe is set by the largest particles, while the overall breadth and amplitude of the scattered signal reflects the abundance of smaller, cm-sized particles. We developed both a simple one-dimensional scattering model and a more realistic 2-D model. We assumed for simplicity a single power law particle size distribution for each major ring region, and determined the index q and lower and upper size cutoffs a(sub min) and a(sub max) that provide the best match to all three data sets in each region. Our results in the A and C Rings are fairly consistent with values of q and a(sub max) derived from Voyager radio occultation (RSS) measurements. We extended their results by determining lower limits to the particle size distributions and by probing the B Ring. This technique is applicable to imaging observations of the rings during the Cassini mission.

French, Richard G.↗