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To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2008.08.014 Byline: Nicole J. Rappaport (a), Pierre-Yves Longaretti (b)(c), Richard G. French (d), Essam A. Marouf (e), Colleen A. McGhee (d) Keywords: Saturn; rings Abstract: Cassini radio science experiments have provided multiple occultation optical depth profiles of Saturn's rings that can be used in combination to analyze density waves. This paper establishes an accurate procedure of inversion of the wave profiles to reconstruct the wave kinematic parameters as a function of semi-major axis, in the nonlinear regime. This procedure is established using simulated data in the presence of realistic noise perturbations, to control the reconstruction error. It is then applied to the Mimas 5:3 density wave. There are two important concepts at the basis of this procedure. The first one is that it uses the nonlinear representation of density waves, and the second one is that it relies on a combination of optical depth profiles instead of just one profile. A related method to analyze density waves was devised by Longaretti and Borderies [Longaretti, P.-Y., Borderies, N., 1986. Icarus 67, 211-223] to study the nonlinear density wave associated with the Mimas 5:3 resonance, but the single photopolarimetric profile provided limited constraints. Other studies of density waves analyzing Cassini data [; Tiscareno, M.S., Burns, J.A., Nicholson, P.D., Hedman, M.M., Porco, C.C., 2007. Icarus 189, 14-34] are based on the linear theory and find inconsistent results from profile to profile. Multiple cuts of the rings are helpful in a fundamental way to ensure the accuracy of the procedure by forcing consistency among the various optical depth profiles. By way of illustration we have applied our procedure to the Mimas 5:3 density wave. We were able to recover precisely the kinematic parameters from the radio experiment occultation data in most of the propagation region; a preliminary analysis of the pressure-corrected dispersion allowed us to determine new but still uncertain values for the opacity (Ka0.02 cm.sup.2/g) and velocity dispersion of (c.sub.0a0.6cm/s) in the wave region. Our procedure constitutes the first step in our planned analysis of the density waves of Saturn's rings. It is very accurate and efficient in the far-wave region. However, improvements are required within the first wavelength. The ways in which this method can be used to establish diagnostics of ring physics are outlined. Author Affiliation: (a) Jet Propulsion Laboratory, California Institute of Technology, m.s. 301-150, 4800 Oak Grove Drive, Pasadena, CA 91109, USA (b) Universite Joseph Fourier, Laboratoire d'Astrophysique de Grenoble, BP 53, 38041 Grenoble Cedex 9, France (c) Centre National de la Recherche Scientifique (CNRS)/INSU, France (d) Astronomy Department, Wellesley College, Wellesley, MA 02181, USA (e) San Jose State University, One Washington Square, San Jose, CA 95192, USA Article History: Received 26 November 2007; Revised 11 July 2008; Accepted 19 August 2008

To link to full-text access for this article, visit this link: http://dx.doi.org/10.1016/j.icarus.2007.02.019 Byline: Richard G. French (a), Heikki Salo (b), Colleen A. McGhee (a), Luke Dones (c) Keywords: Planetary rings; Saturn; Radiative transfer Abstract: From 378 Hubble Space Telescope WFPC2 images obtained between 1996-2004, we have measured the detailed nature of azimuthal brightness variations in Saturn's rings. The extensive geometric coverage, high spatial resolution ([approximately equal to]300kmpx.sup.-1), and photometric precision of the UBVRI images have enabled us to determine the dependence of the asymmetry amplitude and longitude of minimum brightness on orbital radius, ring elevation, wavelength, solar phase angle, and solar longitude. We explore a suite of dynamical models of self-gravity wakes for two particle size distributions: a single size and a power law distribution spanning a decade in particle radius. From these N-body simulations, we calculate the resultant wake-driven brightness asymmetry for any given illumination and viewing geometry. The models reproduce many of the observed properties of the asymmetry, including the shape and location of the brightness minimum and the trends with ring elevation and solar longitude. They also account for the 'tilt effect' in the A and B rings: the change in mean ring brightness with effective ring opening angle, |B.sub.eff|. The predicted asymmetry depends sensitively on dynamical ring particle properties such as the coefficient of restitution and internal mass density, and relatively weakly on photometric parameters such as albedo and scattering phase function. The asymmetry is strongest in the A ring, reaching a maximum amplitude A[approximately equal to]25% near a=128,000km. Here, the observations are well-matched by an internal particle density near 450 kgam.sup.-3 and a narrow particle size distribution. The B ring shows significant asymmetry ([approximately equal to]5%) in regions of relatively low optical depth (I[approximately equal to]0.7). In the middle and outer B ring, where Ia'1, the asymmetry is much weaker ([approximately equal to]1%), and in the C ring, A Author Affiliation: (a) Astronomy Department, Wellesley College, Wellesley, MA 02481, USA (b) Department of Physical Sciences, University of Oulu, PO Box 3000, Finland (c) Southwest Research Institute, Boulder, CO 80302, USA Article History: Received 7 September 2006; Revised 5 February 2007

We present delay-Doppler images of Saturn's rings based on radar observations made at Arecibo Observatory between 1999 and 2003, at a ] wavelength of 12.6 cm and at ring opening angles of 20.1[degrees] [less than or equal to] |B| [less than or equal to] 26.7[degrees]. The average radar cross-section of the A ring is ~77% relative to that of the B ring, while a stringent upper limit of 3% is placed on the cross-section of the C ring and 9% on that of the Cassini Division. These results are consistent with those obtained by Ostro et al. [1982, Icarus 49, 367-381] from radar observations at |B| = 21.4[degrees], but provide higher resolution maps of the rings' reflectivity profile. The average cross-section of the A and B rings, normalized by their projected unblocked area, is found to have decreased from 1.25 [+ or -] 0.31 to 0.74 [+ or -] 0.19 as the rings have opened up, while the circular polarization ratio has increased from 0.64 [+ or -] 0.06 to 0.77 [+ or -] 0.06. The steep decrease in cross-section is at variance with previous radar measurements [Ostro et al., 1980, Icarus 41, 381-388], and neither this nor the polarization variations are easily understood within the framework of either classical, many-particle-thick or monolayer ring models. One possible explanation involves vertical size segregation in the rings, whereby observations at larger elevation angles which see deeper into the rings preferentially see the larger particles concentrated near the rings' mid-plane. These larger particles may be less reflective and/or rougher and thus more depolarizing than the smaller ones. Images from all four years show a strong m = 2 azimuthal asymmetry in the reflectivity of the A ring, with an amplitude of [+ or -] 20% and minima at longitudes of 67 [+ or -] 4[degrees] and 247 [+ or -] 4[degrees] from the sub-Earth point. We attribute the asymmetry to the presence of gravitational wakes in the A ring as invoked by Colombo et al. [1976, Nature 264, 344-345] to explain the similar asymmetry long seen at optical wavelengths. A simple radiative transfer model suggests that the enhancement of the azimuthal asymmetry in the radar images compared with that seen at optical wavelengths is due to the forward-scattering behavior of icy ring particles at decimeter wavelengths. A much weaker azimuthal asymmetry with a similar orientation may be present in the B ring.

Hubble Space Telescope (HST) images of Prometheus and Pandora show longitude discrepancies of about 20[degrees] with respect to the Voyager ephemerides, with an abrupt change in mean motion at the end of 2000 (French et al., 2003, Icarus 162, 143-170; French and McGhee, 2003, Bull. Am. Astron. Soc. 34, 06.07). These discrepancies are anti-correlated and arise from chaotic interactions between the two moons, occurring at interval of 6.2 yr, when their apses are anti-aligned (Goldreich and Rappaport, 2003a, Icarus 162, 391-399). This behavior is attributed to the overlap of four 121:118 apse-type mean motion resonances (Goldreich and Rappaport, 2003b, Icarus 166, 320-327). We study the Prometheus-Pandora system using a Radau-type integrator taking into account Saturn's oblateness up to and including terms in [J.sub.6], plus the effects of the major satellites. We first confirm the chaotic behavior of Prometheus and Pandora. By fitting the numerical integrations to the HST data (French et al., 2003, Icarus 162, 143-170; French and McGhee, 2003, Bull. Am. Astron. Soc. 34, 06.07), we derive the satellite masses. The resulting GM values (with their standard 3-[sigma] errors) for Prometheus and Pandora are respectively [GM.sub.PR] = ([1.41.sup.+0.10.sub.-0.25]) x [10.sup.2] and [GM.sub.PA] = ([1.03.sup.+0.10.sub.-0.19]) x [10.sup.-2] [km.sup.3] [s.sup.-2]. Using the nominal shape of the two moons (Thomas, 1989, Icarus 77, 248-274), we derive Prometheus and Pandora's densities, [0.40.sup.+0.03.sub.-0.07] and [0.49.sup.+0.05.sub.-0.09] g [cm.sup.-3], respectively. Our numerical fits also enable us to constrain the time of the latest apse anti-alignment in 2000. Finally, using our fit, we predict the orbital positions of the two satellites during the Cassini tour, and provide a lower limit of the uncertainties due to chaos. These uncertainties amount to about 0.2[degrees] in mean longitude at the arrival of the Cassini spacecraft in July 2004, and to about 3[degrees] in 2008, at the end of the nominal tour. Keywords: Satellites of Saturn; Celestial mechanics; Orbits; Chaos; Resonances

As part of a long-term study of Saturn's rings, we have used the Hubble Space Telescope's (HST) Wide Field and Planetary Camera (WFPC2) to obtain several hundred high resolution images from 1996 to 2004, spanning the full range of ring tilt and solar phase angles accessible from the Earth. Using these multiwavelength observations and HST archival data, we have measured the photometric properties of spokes in the B ring, visible in a substantial number of images. We determined the spoke particle size distribution by fitting the wavelength-dependent extinction efficiency of a prominent, isolated spoke, using a Mie scattering model. Following Doyle and Grun (1990, Icarus 85, 168-190), we assumed that the spoke particles were sub-micron size spheres of pure water ice, with a Hansen-Hovenier size distribution (Hansen and Hovenier, 1974, J. Atmos. Sci. 31, 1137-1160). The WFPC2 wavelength coverage is broader than that of the Voyager data, resulting in tighter constraints on the nature of spoke particles. The effective particle size was [r.sub.eff] = 0.57 [+ or -] 0.05 [micro]m, and the size distribution was quite narrow with a variance of b = 0.09 [+ or -] 0.03, very similar to the results of Doyle and Grun (1990, Icarus 85, 168-190), and consistent with predictions of plasma cloud models for spoke production from meteoritic impacts (Goertz and Morrill, 1983, Icarus 53, 219-229; Goertz, 1984, Adv. Space Res. 4, 137-141). In all, we identified 36 spokes or spoke complexes, predominantly on the morning (east) ansa. The photometric contrast of the spokes is strongly dependent on effective ring opening angle, [B.sub.eff]. Spokes were clearly visible on the north face of the rings in 1994, just prior to the most recent ring plane crossing (RPX) epoch, and on the south face shortly after RPX. However, spokes were both less abundant and fainter as the rings opened up, and no spokes were detected after 18 October 1998 ([B.sub.eff] = -15.43[degrees]), when a single faint spoke was seen on the morning ansa. The high resolution and photometric quality of the WFPC2 images enabled us to set a detection limit of [less than or equal to] 1% in fractional brightness contrast for spokes for the post-1998 observations. We compare the observed trend of spoke contrast with [B.sub.eff] to radiative transfer calculations based on three models of the distribution of spoke material. In the first, the spoke 'haze' is uniformly mixed with macroscopic B ring particles. No variation in spoke contrast is predicted for single-scattering, in this case, and only a modest decrease in contrast with [B.sub.eff] is predicted when multiple scattering is taken into account. In the second model, the spoke dust occupies an extended layer that is thicker than the B ring, which gives virtually identical results to a third case, when the haze layer lies exclusively above the ring. Multiple-scattering Monte Carlo calculations for these two extended haze models match the trend of spoke contrast exceptionally well. We compute the predicted spoke contrast for a wide variety of viewing geometries, including forward- and backscattering. Based on these results, spokes should be easily detectable during the Cassini mission when the rings are viewed at relatively small ([[absolute value] of B] [less than or equal to] 10[degrees]) ring opening angles. Keywords: Planetary rings, Saturn; Radiative transfer

Hubble Space Telescope (HST) Wide-Field Planetary Camera (WFPC2) observations at phase angles in the range [alpha] = 0.26[degrees]-6.4[degress] obtained at every opposition and near quadrature between October 1996 and December 2002 reveal the opposition effect of Enceladus. We present a photometric analysis of nearly 200 images obtained through the five broadband UVBRI filters (F336W, F439W, F555W, F675W, and F814W) and the F785LP and F1042M filters from which we generate mutually consistent solar and rotational phase curves. Our solar phase curves reveal a dramatic, sharp increase in the albedo (from 0.11 mag in the F675W filter to 0.17 mag in the F785LP filter) as phase angles decrease from 2[degrees] to 0.26[degrees]. A slight opposition effect is evident in data from the F1042M filter ([lambda] eff = 1022 nm); however, the smallest phase angle currently available for observations from this filter is a = 0.58[degrees]. With the addition of data from the F255W filter we demonstrate the wavelength dependence of the albedo of the trailing hemisphere from 275 to 1022 nm. Our rotation curves show that the trailing hemisphere is ~0.06 mag brighter than the leading when observed at wavelengths between 338 and 868 nm and 0.11 mag brighter than the leading at 1022 nm. We have supplemented the phase curve from the F439W filter ([lambda] eff = 434 nm) with Voyager clear filter ([lambda] eff = 480 nm) observations made at larger phase angles ([alpha] = 13[degrees] - 43[degees]) to produce a phase curve with the most extensive phase angle coverage possible to date. This newly expanded range of phase angles enhances the ability of the Hapke photometric model (Hapke B., 2002, Icarus 157, 523-534) to relate physical characteristics of the surface of Enceladus to the manner in which incident light is reflected from it. We present Hapke 2002 model fits to solar phase curves from each UVBRI filter as well as from the F785LP and F1042M filters. Geometric albedos derived from these model fits range from p = 0.92 4[plus or minus] 0.01 at 1022 nm to p = 1.41 4- 0.03 at 549 nm, necessitating an increase of about 20% from previously derived values. Our Hapke fits demonstrate that the opposition surge of Enceladus is best described by a model which combines both moderate shadow-hiding and narrow coherent backscattering components. Keywords: Enceladus; Spectrophotometry; Satellites of Saturn; Satellite surfaces; Photometry

We have obtained numerically integrated orbits for Saturn's coorbital satellites, Janus and Epimetheus, together with Saturn's F-ring shepherding satellites, Prometheus and Pandora. The orbits are fit to astrometric observations acquired with the Hubble Space Telescope and from Earth-based observatories and to imaging data acquired from the Voyager spacecraft. The observations cover the 38 year period from the 1966 Saturn ring plane crossing to the spring of 2004. In the process of determining the orbits we have found masses for all four satellites. The densities derived from the masses for Janus, Epimetheus, Prometheus, and Pandora in units of [gcm.sup.-3] are [0.61.sup.+0.07.sub.-0.06], [0.64.sup.+0.13.sub.-0.09], [0.42.sup.+0.27.sub.-.013], and [0 54.sup.+0.30.sub.-0.15], respectively. Keywords: Satellites, general; Satellites of Saturn; Orbits

Saturn's narrow F ring is flanked by two nearby small satellites, Prometheus and Pandora, discovered in Voyager images taken in 1980 and 1981 (Synnott et al., 1983, Icarus 53, 156-158). Observations with the Hubble Space Telescope (HST) during the ring plane crossings (RPX) of 1995 led to the unexpected finding that Prometheus was ~ 19[degrees] behind its predicted orbital longitude, based on the Synnott et al. (1983) Voyager ephemeris (Bosh and Rivkin, 1996 Science 272, 518-521; Nicholson et al., 1996, Science 272, 509-515). Whereas Pandora was at its predicted location in August 1995, McGhee (2000, Ph.D. thesis, Cornell University) found from the May and November 1995 RPX data that Pandora also deviates from the Synnott et al. (1983) Voyager ephemeris. Using archival HST data from 1994, previously unexamined RPX images, and a large series of targeted WFPC2 observations between 1996 and 2002, we have determined highly accurate sky-plane positions for Prometheus, Pandora, and nine other satellites found in our images. We compare the Prometheus and Pandora measurements to the predictions of substantially revised and improved ephemerides for the two satellites based on an extensive analysis of a large set of Voyager images (Murray et al., 2000, Bull. Am. Astron. Soc. 32, 1090; Evans, 2001 Ph.D. thesis, Queen Mary College). From December 1994 to December 2000, Prometheus' orbital longitude lag was changing by -0.71[degrees] [year.sup.-1] relative to the new Voyager ephemeris. In contrast, Pandora is ahead of the revised Voyager prediction. From 1994 to 2000, its longitude offset changed by +0.44[degrees] [year.sup.-1], showing in addition an ~585 day oscillatory component with amplitude [DELTA][[lambda].sub.C[R.sub.0] = 0.65 [+ or -] 0.07[degrees] whose phase matches the expected perturbation due to the nearby 3:2 corotation resonance with Mimas, modulated by the 71-year libration in the longitude of Mimas due to its 4:2 resonance with Tethys. We determine orbital elements for freely precessing equatorial orbits from fits to the 1994-2000 HST observations, from which we conclude that Prometheus' semimajor axis was 0.31 km larger, and Pandora's was 0.20 km smaller, than during the Voyager epoch. Subsequent observations in 2001-2002 reveal a new twist in the meanderings of these satellites: Prometheus' mean motion changed suddenly by an additional -0.77[degrees] [year.sup.-1] , equivalent to a further increase in semimajor axis of 0.33 km, at the same time that Pandora's mean motion changed by +0.92[degrees] [year.sup.-1], corresponding to a change of -0.42 km in its semimajor axis. There is an apparent anticorrelation of the motions of these two moons seen in the 2001-2002 observations, as well as over the 20-year interval since the Voyager epoch. This suggests a common origin for their wanderings, perhaps through direct exchange of energy between the satellites as the result of resonances, possibly involving the F ring. Keywords: Satellites of Saturn; Celestial mechanics; Resonances; Orbits

The main rings of Saturn were observed with the Planetary Camera of the WFPC2 instrument on the Hubble Space Telescope (HST) from September 1996 to December 2000 as the ring opening angle to Earth and Sun increased from 4[degrees] to 24[degrees], with a spread of phase angles between 0.3[degrees] and 6[degrees] at each opening angle. The rings were routinely observed in the five HST wideband UBVRI filters (F336W, F439W, F555W, F675W, and F814W) and occasionally in the F255W, F785LP, and F1042M filters. The emphasis in this series of papers will be on radial color (implying compositional) variations. In this first paper we describe the analysis technique and calibration procedure, note revisions in a previously published Voyager ring color data analysis, and present new results based on over 100 HST images. In the 300-600 nm spectral range where the rings are red, the 555/336-nm ratio increases by about 14% as the phase angle increases from 0.3[degrees] to 6[degrees]. This effect, never reported previously for the rings, is significantly larger than the phase reddening which characterizes other icy objects, primarily because of the redness of the rings. However, there is no discernible tendency for color to vary with ring opening angle at a given phase angle, and there is no phase variation of color where the spectrum is flat. We infer from this combination of facts that multiple intraparticle scattering, either in a regolith or between facts of an unusually rough surface, is important in these geometries, but that multiple interparticle scattering in a vertically extended layer is not. Voyager color ratios at a phase angle of 14[degrees] are compatible with this trend, but calibration uncertainties prevent their use in quantitative modeling. Overall ring average spectra are compatible with those of earlier work within calibration uncertainties, but ring spectra vary noticeably with region. We refine and subdivide the regions previously defined by others. The variation seen between radial profiles of ratios between different wavelengths suggests the presence of multiple compositional components with different radial distributions. We present new radial profiles of far-UV color ratio (F336W/F255W) showing substantial global variations having a different radial structure than seen between 555 and 336 nm. We constrain radial variation in the strength of a putative 850-nm spectral feature to be at the percent level or less. There seem to be real variations in the shape of regional ring spectra between 800 and 1000 nm.

The 11 July 1992 occultation of Uranus by U103 ([m.sub.K] = 10.1) was observed using the 5-m Hale telescope on Palomar Mountain in California, the 4-m telescope at Cerro Tololo Inter-American Observatory (CTIO) in Chile, and the nearby 2.2-m telescope at European Southern Observatory (ESO). All observations were taken using InSb aperture photometers and K ([Lambda] [similar to] 2.2 [[micro]meter]) filters and provided high-quality profiles of the uranian rings. The ESO and Palomar ring event times have been incorporated into a comprehensive orbit model for the elliptical rings using all available Earth-based and Voyager occultation data. The kinematical model was used to determine the radius scale and geometry of the U103 occultation, as well as to provide absolute timing calibration for the CTIO light curve, which was reconstructed from two-dimensional digital scans of a high-speed strip chart. All nine classical rings were clearly observed during both ingress and egress. In addition, a sharp feature appeared in the CTIO ingress light curve with an orbital radius of 50,026.89 [+ or -] 0.39 km, very close to the mean radius of the [Lambda] ring of 50,026.3 [+ or -] 0.6 km found by M. R. Showalter (Science 267, 490-493, 1995) from an analysis of Voyager 2 images. The CTIO feature is well above the noise: its equivalent width of E = 0.32 [+ or -] 0.14 km corresponds to a 5-[Sigma] detection. It is the only such signature in the entire CTIO lightcurve, other than the previously known rings. The characteristic ring-like shape of the profile, its high SNR, and its radial location all support the identification of this feature as an Earth-based detection of the A ring. At the same time, if the ring were azimuthally homogeneous with E [greater than or equal to] 0.32 km, it would have been clearly visible in the CTIO egress and Palomar light curves, but no such features were found. The [Lambda] ring is thus azimuthally clumpy, resembling to some degree Neptune's arc-like Adams ring. At the nearby ESO station, a suggestive ingress feature appeared with a radius of 50,023.01 [+ or -] 0.28 km, but the data are too noisy to permit a positive identification. The orbital characteristics of the A ring and its azimuthal brightness profile cannot be uniquely extrapolated from the Voyager encounter epoch to the time of the U103 occultation because the mean motion and orbital radius of the ring are too uncertain. However, additional detections in archival Earth-based occultation data or from future observations could allow a much better determination of the dynamics of this dusty and clumpy ring.

Observation of Saturn's central flash during the 28 Sgr occultation by the planet enables the development of a new model to study the stratospheric zonal winds in giant planets during central occultations. Observations performed in July 1989 with instruments at McDonald and Palomar Observatories revealed multiple stellar images near the limb of the planet in the infrared wavelengths. The flash of multiple images was strongly influenced by the midlatitude zonal winds.

Saturn's pole direction and the radius scale for measuring the ring system are determined by combining the observations of the 3 July 1989 Saturn occultation of 28 Sgr with the occultation measurements obtained from Voyager 1 and 2. The McDonald Observatory 2.7 meter telescope and Palomar 5-m telescope were used in the 3 July 1989 observation. The results reveal that the radius scale for measuring the ring system is approximately 1 kilometer less than that determined earlier by P.D. Nicholson, M.L. Cooke and E. Pelton. The rate of motion of Saturn's pole on the sky is 0.86 plus or minus 0.31 times the theoretically predicted rate of 0.339 inches per year.

Occultations of the few stars in Neptune's path during the 1990s may shed light on the uncertainties about the nature of the planet's rings. Conditions for Neptune's close approach to 68 stars between 1992 to 1999 are examined. Out of 40 ring plane occultations, 17 possible ring arc occultations are found. Photometric readings of a select few show that these have greater than 11 K magnitudes.