Radio Occultation Investigation of the Rings of Saturn and Uranus

The proposed work addresses two main objectives: (1) to pursue the development of the random diffraction screen model for analytical/computational characterization of the extinction and near-forward scattering by ring models that include particle crowding, uniform clustering, and clustering along preferred orientations (anisotropy). The characterization is crucial for proper interpretation of past (Voyager) and future (Cassini) ring, occultation observations in terms of physical ring properties, and is needed to address outstanding puzzles in the interpretation of the Voyager radio occultation data sets; (2) to continue the development of spectral analysis techniques to identify and characterize the power scattered by all features of Saturn's rings that can be resolved in the Voyager radio occultation observations, and to use the results to constrain the maximum particle size and its abundance. Characterization of the variability of surface mass density among the main ring, features and within individual features is important for constraining the ring mass and is relevant to investigations of ring dynamics and origin. We completed the developed of the stochastic geometry (random screen) model for the interaction of electromagnetic waves with of planetary ring models; used the model to relate the oblique optical depth and the angular spectrum of the near forward scattered signal to statistical averages of the stochastic geometry of the randomly blocked area. WE developed analytical results based on the assumption of Poisson statistics for particle positions, and investigated the dependence of the oblique optical depth and angular spectrum on the fractional area blocked, vertical ring profile, and incidence angle when the volume fraction is small. Demonstrated agreement with the classical radiative transfer predictions for oblique incidence. Also developed simulation procedures to generate statistical realizations of random screens corresponding to uniformly packed ring models, and used the results to characterize dependence of the extinction and near-forward scattering on ring thickness, packing fraction, and the ring opening angle

Computing Spacecraft-Pointing Vectors for Limb Tracking

LMBTRK is a computer program that is used together with two software libraries known as ERHAND and HYBRRD to generate spacecraft-pointing vectors for limb-tracking maneuvers needed for experiments on propa gation of radio signals through planetary atmospheres. LMBTRK determi nes, as a function of time, the direction in which one must point a ray (representing a radio beam) emitted by a spacecraft in order to make the ray pass through a planetary atmosphere on its way to a receiving station at a known location

Subcentimeter-size particle distribution functions in planetary rings from Voyager radio and photopolarimeter occultation data

Analysis of measurements of the scattered and direct components of Voyager 1 radio occultation signals at 3.5 and 13 cm wavelengths yield estimates of the distribution functions of supracentimeter-size particles and thickness of relatively broad regions in Saturn's rings. If mearurements of signal amplitude at a shorter wavelength are combined with the previously analyzed data, the shape of the distribution functions characterizing the smaller particles can be constrained. If size distributions of arbitrary form were considered, many solutions are found that are consistent with the three available observations of signal amplitude. The best-fit power law was calculated to the three observations at three wavelengths for several of the embedded Saturn ringlets. Mie scattering theory predicts that the measured phase of the radio occultation signal is highly sensitive to particles ranging from 0.1 to 1.0 wavelengths in size, thus additional constraints on the subcentimeter-size distribution functions for both the Saturn and Uranus rings can in principle be derived from radio phase measurements

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 longe

The Structure of Titan's Atmosphere from Cassini Radio Occultations

We present results from the two radio occultations of the Cassini spacecraft by Titan in 2006, which probed mid-southern latitudes. Three of the ingress and egress soundings occurred within a narrow latitude range, 31.34 deg S near the surface, and the fourth at 52.8 deg S. Temperature - altitude profiles for all four occultation soundings are presented, and compared with the results of the Voyager 1 radio occultation (Lindal et al., 1983), the HASI instrument on the Huygens descent probe (Fulchignoni et al., 2005), and Cassini CIRS results (Flasar et al., 2005; Achterberg et al., 2008b). Sources of error in the retrieved temperature - altitude profiles are also discussed, and a major contribution is from spacecraft velocity errors in the reconstructed ephemeris. These can be reduced by using CIRS data at 300 km to make along-track adjustments of the spacecraft timing. The occultation soundings indicate that the temperatures just above the surface at 31-34 deg S are about 93 K, while that at 53 deg S is about 1 K colder. At the tropopause, the temperatures at the lower latitudes are all about 70 K, while the 53 deg S profile is again 1 K colder. The temperature lapse rate in the lowest 2 km for the two ingress (dawn) profiles at 31 and 33 deg S lie along a dry adiabat except within approximately 200m of the surface, where a small stable inversion occurs. This could be explained by turbulent mixing with low viscosity near the surface. The egress profile near 34 deg S shows a more complex structure in the lowest 2 km, while the egress profile at 53 deg S is more stable

First results from the ionospheric radio occultations of Saturn by the Cassini spacecraft

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/94835/1/jgra18257.pd

First results from the Cassini radio occultations of the Titan ionosphere

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/95691/1/jgra19260.pd

On The Linear Damping Relation For Density Waves In Saturn\u27S Rings

We revisit the equation for viscous damping of density waves derived from linearized theory and show that the damping is not only determined by the magnitudes of shear and bulk viscosity. Modifications arise from the dependence of the viscosity on the ring\u27s surface mass density. This was noted more than 30 years ago by Goldreich & Tremaine (1978b). Still, to date the consequences have not been explored. In the literature these terms have been neglected throughout when fitting the rings\u27 viscosity from observations of wave damping. Therefore, one must suspect that these viscosities, as well as the dispersion velocities inferred from them, suffer from systematic bias, which might be small or significant, depending on the local conditions in the ring. We show that the modified damping formula, to linear order, is related to the stability threshold for viscous overstability and argue that the appearance of density waves may be altered by this instability

Noncircular Features In Saturn\u27S Rings I: The Edge Of The B Ring

A comprehensive investigation of all available radio and stellar occultation data for the outer edge of Saturn\u27s B ring, spanning the period 1980-2010, confirms that the m=2 distortion due to the strong Mimas 2:1 inner Lindblad resonance circulates slowly relative to Mimas in a prograde direction, with a frequency ΩL=0.1819°d-1. Our best-fitting model implies that the radial amplitude of this distortion ranges from a minimum of 3km to a maximum of 71km, with short-lived minima recurring every 5.42yrs. In addition to the dominant m=2 pattern, the edge of the B ring also exhibits at least four other perturbations. An m=1 component with a radial amplitude of ~20km rotates at a rate very close to the expected local apsidal precession rate of π{variant}̇B~5.059°d-1, while smaller perturbations are seen with m=3 (amplitude 12.5km), m=4 (5.9km), and m=5 (5.6km), each of which has a pattern speed consistent with that expected for a spontaneously-generated normal mode (French, R.G. et al. [1988]. Icarus 73, 349-378). Our results for m=1, m=2 and m=3 are compatible with those obtained by Spitale and Porco (Spitale, J.N., Porco, C.C. [2010]. Astron. J. 140, 1747-1757), which were based on Cassini imaging data. The pattern speed of each normal mode slightly exceeds that expected at the mean edge radius, supporting their conclusion that they may represent a series of free modes, each of which is trapped in a narrow region between the mode\u27s resonant radius and the ring\u27s edge. However, both our model and that of Spitale and Porco fail to provide complete descriptions of this surprisingly complex feature, with post-fit root-mean-square residuals of ~8km considerably exceeding typical measurement errors of 1km or less. © 2013 Elsevier Inc

Noncircular Features In Saturn\u27S Rings Ii: The C Ring

•We model the shapes of all known non-circular features in Saturn\u27s C ring.•We use data from Cassini radio and stellar occultations between 2005 and 2010.•Updated precessing ellipse models are presented for the Titan and Maxwell ringlets.•Resonant forcing of the Titan, Bond and Dawes ringlets is confirmed.•Many sharp ring edges exhibit one or more \u27normal modes\u27 of oscillation. We present a comprehensive survey of sharp-edged features in Saturn\u27s C ring, using data from radio and stellar occultation experiments carried out by the Cassini spacecraft over a period of more than five years. Over 100 occultations are included in the combined data set, enabling us to identify systematic radial perturbations as small as 200. m on the edges of ringlets and gaps. We systematically examine all of the noncircular features in the C ring, refine the eccentricities, precession rates and width variations of the known eccentric ringlets, identify connections between several noncircular gap and ringlet edges and nearby satellite resonances, and report the discovery of a host of free normal modes on ring and gap edges. We confirm a close association between the Titan (or Colombo) ringlet ( a= 77878.7. km) and the Titan 1:0 apsidal resonance: the apoapse of the ringlet is nearly aligned with Titan\u27s mean longitude, and the pattern speed closely matches Titan\u27s mean motion. Similar forced perturbations associated with the Titan resonance are detectable in more than two dozen other features located throughout the inner C ring as far as 3500. km from the Titan resonance. The inner edge of the Titan ringlet exhibits several strong outer Lindblad resonance (OLR-type) normal modes, and scans of the outer edge reveal inner Lindblad resonance (ILR-type) normal modes. The Maxwell ringlet ( a= 87,510. km), in contrast, appears to be a freely-precessing eccentric ringlet, with post-fit RMS residuals for the inner and outer edges of only 0.23 and 0.16. km, respectively. The best-fitting edge precession rates differ by over 10 times the estimated uncertainty in the rate of the inner edge, consistent with a slow libration about an equilibrium configuration on a decadal timescale. Using self-gravity models for ringlet apse alignment, we estimate the masses and surface densities of the Titan and Maxwell ringlets. The Bond ringlet ( a= 88,710. km), about 17. km wide, shows no free eccentricity but lies near two strong resonances: the Mimas 3:1 inner vertical resonance (IVR) at 88702.2. km and the Prometheus 2:1 ILR at 88713.1. km. We find no measurable perturbation from the Mimas IVR, but a clear m = 2 signature of the appropriate phase and pattern speed for the Prometheus ILR on the outer edge of the ringlet, along with free ILR-type normal modes with wave numbers m = 3,4, 5, 6 and 7. The Dawes gap, located at 90,210. km, and its associated embedded ringlet, also show both free and forced perturbations, and as in the case of the Maxwell gap, the outer edge of the Dawes gap appears to be sympathetically forced by the nearby ringlet. The pattern of newly identified normal modes coexisting on the sharp edges of ringlets and gaps is in excellent agreement with theoretical predictions, with ILR-type modes on outer ringlet (and inner gap) edges and OLR-type modes on inner ringlet (and outer gap) edges, representing standing waves between the resonance locations and the ring edges. Modes with larger |. m| generally have narrower resonant cavities, and of the dozens of detected normal modes, none has been identified with a resonance radius that falls outside the ring material. © 2014 Elsevier Inc