Solar Phase Angle Research Articles

Submillimeter photometry and lightcurves of Ceres and other large asteroids

Photometry and thermal lightcurves of six large asteroids (1-Ceres, 2-Pallas, 3-Juno, 12-Victoria, 85-Io and 511-Davida) have been observed at 870 μm (345 GHz) using the MPIfR 19-Channel Bolometer of the Heinrich–Hertz Submillimeter Telescope. Only Ceres displayed a lightcurve with an amplitude (∼50%, peak to peak) that was significantly greater than the uncertainty in the observations. When thermal fluxes and brightness temperatures are corrected for heliocentric distance and albedo, there is a significant relation with the sub-solar latitude of the asteroid, or the local season of the asteroid. No such trend can be found between observations with solar phase angle. These results are evidence that most of the submillimeter thermal radiation is emitted from below the diurnal thermal wave. Comparing the observed trend with model output suggests that the submillimeter radiation from all the asteroids we observed is best modeled by surface material with low thermal inertia (<15 J m −2 s −0.5 K −1, consistent with mid-infrared observations of large main-belt asteroids) and a refractive index closer to unity relative to densities inferred from radar experiments, implying a veneer of material over the asteroid surface with a density less than 1000 kg m −3. More data with better signal-to-noise and aspect coverage could improve these models and constrain physical properties of asteroid surface materials. This would also allow asteroids to be used as calibration sources with accurately known and stable, broadband fluxes at long wavelengths.

Photometry of 2006 RH120: an asteroid temporary captured into a geocentric orbit

Aims. From July 2006 to July 2007 a very small asteroid orbited the Earth within its Hill sphere. We used this opportunity to study its rotation and estimate its diameter and shape.Methods. Due to its faintness, 2006 RH120 was observed photometrically with the new 10-m SALT telescope at the SAAO (South Africa). We obtained data on four nights: 11, 15, 16, and 17 March 2007 when the solar phase angle remained almost constant at 74°. The observations lasted about an hour each night and the object was exposed for 7-10 s through the “clear” filter.Results. From the lightcurves obtained on three nights we derived two solutions for a synodical period of rotation: P 1 = 1.375 ± 0.001 min and P 2 = 2.750 ± 0.002 min. The available data are not sufficient to choose between them. The absolute magnitude of the object was found to be H = 29.9 ± 0.3 mag (with the assumed slope parameter ) and its effective diameter D = 2-7 m, depending on the geometric albedo p V (with the most typical near-Earth asteroids albedo p V = 0.18 its diameter would be D = 3.3 ± 0.4 m). The body has an elongated shape with the ratio greater than 1.4. It probably originates in low-eccentricity Amor or Apollo orbits. There is still a possibility, which needs further investigation, that it is a typical near-Earth asteroid that survived the aerobraking in the Earth's atmosphere and returned to a heliocentric orbit similar to that of the Earth.

Photometric and spectroscopic investigation of 2867 Steins, target of the Rosetta mission

Context. Rosetta is the cornerstone mission of ESA devoted to the study of minor bodies of the Solar System. During its journey to the comet 67P Churyumov-Gerasimenko, the main target, Rosetta also investigates two main belt asteroids, 2867 Steins (fly-by in September 2008) and 21 Lutetia (fly-by in July 2010). Aims. In Spring 2008, we performed a broad observational campaign in order to complete the ground-based photometric and spectroscopic investigation of Steins. Before the Rosetta fly-by, this was the last opportunity to perform ground-based observations useful for calibrating properly the imaging and spectroscopic data obtained by the instruments on board the Rosetta spacecraft. Methods. Visible photometry was carried out at a wide range of phase angles, and visible spectra were acquired at different rotational phases to retrieve information about the absolute magnitude and surface properties. Results. The lightcurve was completely sampled in V and R bands. A rotational period of $6.057\pm0.003$ h and color index $V-R=0.51\pm0.03$ mag were computed. We investigate Steins' phase relation over the range between 3.3 and 42 degrees in solar phase angle. The opposition effect is not evident down to the phase angle of 3 degrees, as is typical of other E-type asteroids. Assuming for Steins an opposition surge similar to that of other E-type asteroids, we calculated an absolute magnitude $H_R=12.81\pm0.03$, and slope parameter $G_R=0.42\pm0.02$. Eight visible spectra, obtained at different rotational phases, exhibit similar behavior, confirming a homogeneous composition of the asteroid surface and the E[II] classification. All spectra display a spectral feature centered on about 0.49 μ m that is typical of E-type asteroids and usually attributed to the presence of sulfides (e.g. oldhamite). A tentative model of the surface composition is presented.

Spitzer Space Telescope observations of the nucleus of comet 67P/Churyumov-Gerasimenko

Context. Comet 67P/Churyumov-Gerasimenko is the target of the Rosetta mission, and an early characterization of its nucleus is required to assist in preparing the orbital strategy of the spacecraft, the delivery of the Philae surface module and the science operations. We detected the nucleus using the Hubble Space Telescope in March 2003, but had to assume an albedo to derive its size from its observed magnitudes. Aims. It is important to derive an additional constraint for independently determining both the comet size and albedo. Methods. We implemented the well-known “radiometric method”, which combines visible and infrared photometry. Sixteen thermal images of 67P/C-G were obtained by the Multiband Imaging Photometer (MIPS) 24 μ m channel of the Spitzer Space Telescope (SST) on 25 February 2004: the observations spanned a time interval of ~12.5 h, which sampled the rotational light curve of its nucleus. The comet was then outbound at a heliocentric distance of 4.48 AU, at a distance of 4.04 AU from SST, and at a solar phase angle of 12.1°. The nucleus conspicuously appeared as a bright point source superimposed on a dust trail; it was necessary to apply the point-spread function fitting technique using an adequate model of the trail to correctly determine the thermal flux from the nucleus. The data were analyzed using a standard thermal model that incorporated the thermal inertia. Results. Our preferred solution with a low thermal inertia has overall dimensions measured along the principal axis of 4.40–5.20 km, 4.16–4.30 km, and 3.40–3.50 km, corresponding to an effective radius of a sphere with the same volume in the range of 1.93–2.03 km. Larger values of thermal inertia produce larger sizes but the effective radius cannot exceed ~2.3 km. The albedo is in the range 0.039–0.043, remarkably consistent with the canonical value of 0.04 for cometary nuclei. The success of the landing of the Philae surface module remains critically dependent upon the bulk density of the nucleus: it would be safe if close to 0.35 g cm-3 , but a larger value, for instance 0.5 g cm-3 , would present some risks.

Investigation of the Mars Express HRSC color channel calibration

The High Resolution Stereo Camera (HRSC) onboard the Mars Express spacecraft in orbit about Mars has four detector channels dedicated to produce images in four spectral channels. Utilizing these spectrophotometric data requires understanding the instrument radiometric calibration and other photometric properties of the data. We present here some results of our investigation into the HRSC color data characteristics. This covers comparison of HRSC measurements with those of telescopes and the Observatoire pour la Minéralogie, l’Eau, les Glaces et l’Activité (OMEGA) instrument, also on Mars Express. We also investigate the dependence of HRSC Color measurements on solar phase angle and altitude of the Mars surface. These results confirm and extend our earlier findings [McCord, T.B., Adams, J.B., Bellucci, G., Combe, J.-Ph., Hansen, G., Hoffman, H., Jaumann, R., Lumme, K., Neukum, G., Pinet, P., Poulet, F., the HRSC Co-I Team, The Mars Express high Resolution Stereo Camera spectrophotometric data: characteristics and science analysis. J. Geophys. Res. 112, E6, 2007.]. A basic finding from our study is that there are nearly constant offsets between the I/ F value derived from the HRSC data and those determined from OMEGA and groundbased telescope measurements, especially in the HRSC red bandpass. These offsets are nearly independent of solar phase angle and Mars surface altitude but are considerably larger for the one comparison at Phobos we were able to make. Several hypotheses could explain these effects: atmospheric scattering, surface photometric effects, shift of the spatial registration or calibration. All these possibilities were investigated.

First High Solar Phase Angle Observations of Rhea UsingCassiniVIMS: Upper Limits on Water Vapor and Geologic Activity

Using radiances acquired with Cassini's Visual and Infrared Mapping Spectrometer (VIMS), we construct high solar phase angle curves for Saturn's second largest moon, Rhea. Ground-based studies of Rhea and Saturnian icy satellites are focussing on low phase angles; to our knowledge, these are the first solar phase curve data for Rhea on phase angles >70°. We compare these data to similar phase curves for Enceladus at near-infrared wavelengths to estimate the amount of water vapor that could possibly be generated and thus set an upper limit on the amount of geologic activity that may be occurring on Rhea. We find that Enceladus's plume manifests itself in the VIMS solar phase curve at a phase angle near 160° and peaks most strongly for -->λ = 2.017810 μm. No such peak can be found in the Rhea VIMS phase curve. Absence of a forward scattering peak supports the recent determination that particles in Rhea's surrounding ring are not small. We calculate that the maximum water vapor column density that could be supplied from Rhea ranges from -->1.52 × 1014 to -->1.91 × 1015 cm−2, 2 orders of magnitude less than what is calculated by Cassini UVIS for Enceladus. This implies that for Rhea, the level of active internal (endogenic) processes is exceedingly small, if any.

Constraining spiral structure parameters through Galactic pencil-beam and large-scale radial velocity surveys

We investigate the effect of spiral structure on the Galactic disc as viewed by pencil beams centred on the Sun, relevant to upcoming surveys such as ARGOS, SEGUE and GAIA. Using a steady-state spiral structure model, we create synthetic Galactic maps which we call pencil-beam maps (PBMs) of the following observables: line-of-sight velocities, the corresponding velocity dispersion and the stellar number density that are functions of distance from the observer. We show that PBMs are a powerful tool for analysing spiral patterns but the uncertainty of the Milky Way structure prevents their simple interpretation. For the case of steady-state spiral structure, we show that such maps can be used to infer spiral structure parameters, such as pattern speed, solar phase angle and number of arms. The mean line-of-sight velocity and velocity dispersion are affected by up to ∼35 km s -1 , which is well within the detectable limit for forthcoming radial velocity surveys. One can measure the pattern speed by searching for imprints of resonances. In the case of a two-armed spiral structure it can be inferred from the radius of a high velocity dispersion ring situated at the 2:1 inner Lindblad resonance (ILR). This information, however, must be combined with information related to the velocities and stellar number density in order to distinguish from a four-armed structure. If the pattern speed is such that the 2:1 ILR is hidden inside the Galactic bulge, the 2:1 outer Lindblad resonance will be present in the outer Galaxy and thus can equivalently be used to estimate the pattern speed. Once the pattern speed is known, the solar angle can be estimated from the line-of-sight velocities and the number density PBMs. The models presented here are preliminary as transient spiral structure models should also be considered. Forthcoming radial velocity surveys are likely to provide powerful constraints of the structure of the Milky Way disc.

Spinning particles in Saturn's C ring from mid-infrared observations: Pre-Cassini mission results

Saturn's C ring thermal emission has been observed in mid-infrared wavelengths, at three different epochs and solar phase angles, using ground based instruments (CFHT in 1999 and VLT/ESO in 2005) and the Infrared Radiometer Instrument Spectrometer (IRIS) onboard the Voyager 1 spacecraft in 1980. Azimuthal variations of temperature in the C ring's inner region, observed at several phase angles, have been analyzed using our new standard thermal model [Ferrari, C., Leyrat, C., 2006. Astron. Astrophys. 447, 745–760]. This model provides predicted ring temperatures for a monolayer ring composed of spinning icy spherical particles. We confirm the very low thermal inertia (on the order of 10 J m −2 K −1 s − 1 / 2 ) found previously by Ferrari et al. [Ferrari, C., Galdemard, P., Lagage, P.O., Pantin E., Quoirin, C., 2005. Astron. Astrophys. 441, 379–389] that reveals the very porous regolith at the surface of ring particles. We are able to explain both azimuthal variations of temperature and the strong asymmetry of the emission function between low and high phase angles. We show that large particles spinning almost synchronously might be present in the C ring to explain differences of temperature observed between low and high phase angle. Their cross section might represent about 45% of the total cross section. However, their numerical fraction is estimated to only ∼0.1% of all particles. Thermal behavior of other particles can be modeled as isothermal behavior. This work provides an indirect estimation of the particle's rotation rate in Saturn's rings from observations.

EVIDENCE OF FRAGMENTING DUST PARTICLES FROM NEAR-SIMULTANEOUS OPTICAL AND NEAR-INFRARED PHOTOMETRY AND POLARIMETRY OF COMET 73P/SCHWASSMANN-WACHMANN 3

We report imaging polarimetry of segments B and C of the Jupiter-family comet 73P/Schwassmann–Wachmann 3i n theI and H bandpasses at solar phase angles of approximately 35 ◦ and 85 ◦ . The level of polarization was typical for active comets, but larger than expected for a Jupiter-family comet. The polarimetric color was slightly red (δP /δλ = +1.2 ± 0.4) at a phase angle of ∼35 ◦ and either neutral or slightly blue at a phase angle of ∼85 ◦ . Observations during the closest approach from 2006 May 11–13 achieved a resolution of 35 km at the nucleus. Both segments clearly depart from a 1/ρ surface brightness for the first 50–200 km from the nucleus. Simulations of radiation-driven dust dynamics can reproduce some of the observed coma morphology, but only with a wide distribution of initial dust velocities (at least a factor of 10) for a given grain radius. Grain aggregate breakup and fragmentation are able to reproduce the observed profile perpendicular to the Sun–comet axis, but fit the observations less well along this axis (into the tail). The required fragmentation is significant, with a reduction in the mean grain aggregate size by about a factor of 10. A combination of the two processes could possibly explain the surface brightness profile of the comet.

The 2004 Las Campanas/Lowell Observatory Itokawa campaign: I. Simultaneous visible and near-infrared photometry of the Hayabusa mission target

Abstract In 2004, Asteroid 25143 Itokawa made its final close approach to the Earth prior to its encounter with the Japanese spacecraft Hayabusa. This apparition was superb with Itokawa reaching magnitude 12 (two magnitudes brighter than the 2001 apparition and the brightest since its discovery in 1998) and covering a large range of observable solar phase angles. An extensive visible and near-infrared observing campaign of Itokawa was undertaken at Las Campanas and Lowell Observatories to obtain full rotational coverage and cover the largest possible range of solar phase angles (4–129°). Unresolved global color mapping over the complete light curve (best fit synodic period of 12.118 hr) shows no sign of rotational color variability with upper limits of a few percent across the full U-thru-K spectrum. These combined multi-wavelength (UBVRIJHK) rotational light curves allow for the concrete deconvolution of shape from albedo variation in the rotational models and as required for Hapke modeling presented in Paper II (Lederer et al., this issue), permits the removal of the rotational light curve effects from the solar phase curve. Furthermore, these derived solar phase curves can be fit with the IAU H,G magnitude system (Bowell et al., 1989) thus allowing the calculation of geometric albedos (p v = 0.23 ± 0.02) as well as an estimate of the asteroid’s elongated shape (a/b = 1.9 ± 0.1) via the amplitudephase relationtionship (Zappalà et al., 1990). Results derived from the extensive ground-based campaigns are compared and contrasted with the much higher spatial resolution in situ measurements made by the Hayabusa spacecraft. The ‘ground-truth’ provided by the Hayabusa mission results shed light on the inferences that can begin to be made for the general asteroid population.

The 2004 Las Campanas/Lowell Observatory campaign II. Surface properties of Hayabusa target Asteroid 25143 Itokawa inferred from Hapke modeling

Abstract We present an analysis of Hapke photometric modeling applied to uniform ground-based UBVRIJHK broadband data of asteroid 25143 Itokawa collected over a wide range of solar phase angles (4°–130°) during the 2004 apparition (Thomas-Osip et al., this issue, hereafter Paper I). Our photometric analyses indicate that Itokawa has a blocky surface with properties different from other, albeit larger, S-class asteroids studied using similar Hapke modeling analyses. Images from the Hayabusa spacecraft affirm the Hapke modeling results, demonstrating the ability of Hapke photometric modeling to predict a rocky asteroid surface correctly; this is the first time that a predicted rocky surface has been observed by a spacecraft. The single particle scattering functions are dominantly forward scattering, suggesting the surface material is composed primarily of clear particles whose scattering is dictated by the particle’s surface as opposed to internal scatterers (more typical of S-class asteroids), while the opposition parameters indicate that the regolith may be more compact than most of the limited number of asteroids visited by spacecraft to date. The roughness properties, single particle scattering properties, and opposition surge characteristics are all indicative of a surface where multiple scattering does not play a major role in defining the photometric properties of the regolith.

Rotation rates in the Koronis family, complete to [formula omitted

We report the results of an observational survey of rotation lightcurves for members of the Koronis asteroid family that we conducted using CCD imaging cameras at seven different observatories during the period 1998–2005. A total of 375 individual lightcurves yield new or refined rotation periods for the 24 survey objects (658) Asteria, (761) Brendelia, (811) Nauheima, (975) Perseverantia, (1029) La Plata, (1079) Mimosa, (1100) Arnica, (1245) Calvinia, (1336) Zeelandia, (1350) Rosselia, (1423) Jose, (1482) Sebastiana, (1618) Dawn, (1635) Bohrmann, (1725) CrAO, (1741) Giclas, (1742) Schaifers, (1848) Delvaux, (1955) McMath, (2123) Vltava, (2144) Marietta, (2224) Tucson, (2729) Urumqi, and (2985) Shakespeare. Most of the data have been calibrated to standard magnitudes. Several previously unpublished lightcurves recorded using a photoelectric photometer during the period 1987–1989 are also reported here. We present composite lightcurves and report derived synodic rotation periods. For those objects with sufficient coverage in solar phase angle we also determined Lumme–Bowell solar phase parameters, and for four objects we obtained V – R colors. Our results reduce selection biases among known rotation lightcurve parameters for Koronis family members by completing the sample down to H ≈ 11.2 , and they lay the foundation for future spin vector and shape determinations. The distribution of rotation rates in the available sample of N = 40 Koronis members is non-Maxwellian at a confidence level of 99%. It also seems to be qualitatively consistent with the effects of long-term modification by thermal YORP torques, as proposed by Vokrouhlický et al. [Vokrouhlický, D., Nesvorný, D., Bottke, W.F., 2003. Nature 425, 147–151] to explain the distribution of the ten Koronis member spin vectors that have already been determined [Slivan, S.M., 2002. Nature 419, 49–51; Slivan, S.M., Binzel, R.P., Crespo da Silva, L.D., Kaasalainen, M., Lyndaker, M.M., Krčo, M., 2003. Icarus 162, 285–307].

Infrared (0.83–5.1 μm) photometry of Phoebe from the Cassini Visual Infrared Mapping Spectrometer

Three weeks prior to the commencement of Cassini's 4 year tour of the saturnian system, the spacecraft executed a close flyby of the outer satellite Phoebe. The infrared channel of the Visual Infrared Mapping Spectrometer (VIMS) obtained images of reflected light over the 0.83–5.1 μm spectral range with an average spectral resolution of 16.5 nm, spatial resolution up to 2 km, and over a range of solar phase angles not observed before. These images have been analyzed to derive fundamental photometric parameters including the phase curve and phase integral, spectral geometric albedo, bolometric Bond albedo, and the single scattering albedo. Physical properties of the surface, including macroscopic roughness and the single particle phase function, have also been characterized. Maps of normal reflectance show the existence of two major albedo regimes in the infrared, with gradations between the two regimes and much terrain with substantially higher albedos. The phase integral of Phoebe is 0.29 ± 0.03 , with no significant wavelength dependence. The bolometric Bond albedo is 0.023 ± 007 . We find that the surface of Phoebe is rough, with a mean slope angle of 33°. The satellite's surface has a substantial forward scattering component, suggesting that its surface is dusty, perhaps from a history of outgassing. The spectrum of Phoebe is best matched by a composition including water ice, amorphous carbon, iron-bearing minerals, carbon dioxide, and Triton tholin. The characteristics of Phoebe suggest that it originated outside the saturnian system, perhaps in the Kuiper Belt, and was captured on its journey inward, as suggested by Johnson and Lunine (2005).

Thermal observations of Saturn's main rings by Cassini CIRS: Phase, emission and solar elevation dependence

Two and a half years after Saturn orbit insertion (SOI) the Cassini composite infrared spectrometer (CIRS) has acquired an extensive set of thermal measurements (including physical temperature and filling factor) of Saturn's main rings for a number of different viewing geometries, most of which are not available from Earth. Thermal mapping of both the lit and unlit faces of the rings is being performed within a multidimensional observation space that includes solar phase angle, spacecraft elevation and solar elevation. Comprehensive thermal mapping is a key requirement for detailed modeling of ring thermal properties. To first order, the largest temperature changes on the lit face of the rings are driven by variations in phase angle while differences in temperature with changing spacecraft elevation are a secondary effect. Ring temperatures decrease with increasing phase angle suggesting a population of slowly rotating ring particles [Spilker, L.J., Pilorz, S.H., Wallis, B.D., Pearl, J.C., Cuzzi, J.N., Brooks, S.M., Altobelli, N., Edgington, S.G., Showalter, M., Michael Flasar, F., Ferrari, C., Leyrat, C. 2006. Cassini thermal observations of Saturn's main rings: implications for particle rotation and vertical mixing. Planet. Space Sci. 54, 1167–1176, doi: 10.1016/j.pss.2006.05.033]. Both lit A and B rings show that temperature decreases with decreasing rings solar elevation while temperature changes in the C ring and Cassini Division are more muted. Variations in the geometrical filling factor, β , are primarily driven by changes in spacecraft elevation. For the optically thinnest region of the C ring, β variations are found to be nearly exclusively determined by spacecraft elevation. Both a multilayer and a monolayer model provide an excellent fit to the data in this region. In both cases, a ring infrared emissivity > 0.9 is required, together with a random and homogeneous distribution of the particles. The interparticle shadowing function required for the monolayer model is very well constrained by our data and matches experimental measurements performed by Froidevaux [1981a. Saturn's rings: infrared brightness variation with solar elevation. Icarus 46, 4–17].

Linking large-parallax Spitzer–CFHT–VLT astrometry of asteroids

We show that the new ephemeris-space multiple-address-comparison (eMAC) method solves asteroid linking problems despite large parallaxes by applying the method to astrometric asteroid observation sets obtained nearly simultaneously with the Spitzer space telescope, the Canada–France–Hawaii Telescope (CFHT), and European Southern Observatory's Very Large Telescope (VLT). For main-belt asteroids, the parallax between Spitzer and the Earth-based telescopes is approximately one degree which is large as compared to a typical parallax for solely Earth-based telescopes in the arcseconds regime. In the eMAC method, we reduce the initially huge amount of possible linkages between observation sets by comparing samples of ephemerides that have been computed separately for all sets at, say, three common dates. If the non-zero ephemeris probability densities overlap at all common dates, we try to find an orbit solution for these so-called trial linkages. If there exists an orbit which reproduces all the astrometric observations assuming predefined observational errors, we call it a linkage. Known asteroids are independently identified among Spitzer, CFHT, and VLT astrometry, and comparing the identified observations to the linkages found shows that the method found all known correct linkages present in the data. In addition, we also found five previously unpublished linkages between Spitzer astrometry and Earth-based astrometry. Based on our simulations, we found virtually all Spitzer-related linkages between two single-night observation sets, and more than 99.4% of linkages between two single-night observation sets obtained by Earth-based observatories. Virtually all correct linkages consisting of at least three single-night sets were also detected. The results show that large-parallax discovery observations made from a spacecraft can be linked to Earth-based follow-up observations to ensure that the objects are not lost. Furthermore, we compute the heliocentric and Spitzer-centric distances as well as the corresponding solar phase angles at the dates of Spitzer observations. Based on comparisons to simulated geocentric observations, we also show that, for typical nearly-simultaneous observations, the parallax reduces the distance uncertainties by several orders of magnitude.

Saturn’s Rings at True Opposition

ABSTRACTOn 2005 January 14, the Saturn system was observed at true opposition with the planetary camera of the Wide Field Planetary Camera 2 (WFPC2) on the Hubble Space Telescope. This was the culmination of nearly a decade of similar UBVRI observations, yielding a uniform set of over 400 high spatial resolution and photometrically accurate radial profiles of the rings that spans the full range of ring inclinations and solar phase angles accessible from the Earth. Using a subset of these images at similar effective ring opening angles Beff∼ -23°, we measured the normalized ring reflectivity I/F over broad regions of the A, B, and C rings as a function of solar phase angle and wavelength. There is a strong surge in brightness near opposition. To measure the width and amplitude of the opposition effect, we fitted two models to the observations: a simple four‐parameter linear‐exponential model and a more complex model (B. Hapke) that incorporates a wavelength‐dependent description of the coherent backscatter opposition effect, as well as the shadow‐hiding opposition effect by a particulate surface. From fits to the linear‐exponential model, the half‐width at half‐maximum for the rings is ∼0.1° at BVRI wavelengths, increasing to ∼0.16° and ∼0.19° for the A and B rings, respectively, in the U filter (338 nm). To assess the contribution of the shadowing of ring particles by each other to the opposition surge, we used Monte Carlo simulations of dynamical models of the rings for a variety of optical depths and particle size distributions, both with and without self‐gravity. Multiple scattering is very weak at low phase angles, and thus these simulations are nearly wavelength independent. The interparticle shadow‐hiding opposition surge increases in strength with ring optical depth and with broadened size distributions. Self‐gravity produces wakes that somewhat complicate the picture, because mutual shadowing by wakes is strongly dependent on illumination and viewing geometry. The observed opposition surge in the rings is much stronger and narrower than that caused by interparticle shadowing. We examined regional variations in the opposition surge across the A, B, and C rings using linear‐exponential model fits. Some of these are most easily explained on the basis of optical depth, volume filling factor, and the relative width of the particle size distribution. The opposition effect for the A, B, and C rings is substantially narrower than for two nearby icy satellites, Mimas and Enceladus, indicating that they have distinctly different surface properties.

Ceres lightcurve analysis—Period determination

The sidereal period of Ceres is refined from 9.075 h to 9.074170 ± 0.000002 , making use of recent and historical lightcurves spanning almost 50 years. An observed increase in the amplitude of the lightcurve with solar phase angle is consistent with bright, discrete albedo features contributing a greater fraction of light as the defect of illumination increases. Observations near the same phase angle over this time span show no evidence of changes that would indicate active surface processes.

HST observations of azimuthal asymmetry in Saturn's rings

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 ( ∼ 300 km px −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 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 ∼ 25 % near a = 128 , 000 km . Here, the observations are well-matched by an internal particle density near 450 kg m −3 and a narrow particle size distribution. The B ring shows significant asymmetry (∼5%) in regions of relatively low optical depth ( τ ∼ 0.7 ). In the middle and outer B ring, where τ ≫ 1 , the asymmetry is much weaker ( ∼ 1 % ), and in the C ring, A < 0.5 % . The asymmetry diminishes near opposition and at shorter wavelengths, where the albedo of the ring particles is lower and multiple-scattering effects are diminished. The asymmetry amplitude varies strongly with ring elevation angle, reaching a peak near | B eff | = 10 ° in the A ring and at | B eff | = 15 – 20 ° in the B ring. These trends provide an estimate of the thickness of the self-gravity wakes responsible for the asymmetry. Local radial variations in the amplitude of the asymmetry within both the A and B rings are probably caused by regional differences in the particle size distribution.

Hubble Space Telescope observations of the nucleus of Comet 9P/Tempel 1

The nucleus of Comet 9P/Tempel 1, the target of the Deep Impact mission, was detected during Hubble Space Telescope observations taken with the wide-field planetary camera 2 (WFPC2) on 31 December 1997 when the comet's solar phase angle was 3 . ° 8 , its heliocentric distance was 4.48 AU, and its geocentric distance was 3.53 AU. Sixteen images were taken through the F675W filter, and all of them revealed a point-like source without any detectable coma. From these images, we derived the R magnitude of the nucleus in the Johnson–Kron–Cousins photometric system for the entire 11.5-h time span of the observations. Assuming a prolate spheroid whose spin axis lies close to the plane of the sky, the partial lightcurve indicates semi-axes a − 3.9 km and b − 2.8 km (assuming a geometric albedo of 0.04 for the R band and a phase coefficient of 0.04 mag deg −1) and a rotational period in the range of ∼ 25 − 33 h . The upper limit of the parameter Afρ, which characterizes the dust production rate, is 1 cm. We also derive a fractional active area at 1.78 AU of ∼ 4 % .

Rotational state of the nucleus of Comet 9P/Tempel 1: Results from Hubble Space Telescope observations in 2004

The nucleus of Comet 9P/Tempel 1 was first observed with the Hubble Space Telescope (HST) in December 1997 [Lamy, P., Toth, I., A'Hearn, M.F., Weaver, H., Weissman, P.R., 2001. Icarus 154, 337–344], but the temporal coverage was insufficient to determine its rotational period. Because the success of the Deep Impact mission was critically dependent on understanding the rotational state and approximate shape and size of the nucleus, we extensively re-observed 9P/Tempel 1, this time with the Advanced Camera for Surveys (HST/ACS), from May 7.9 to 9.5, 2004 (UT). At the mid-point of the observing window, the comet was 3.52 AU from the Sun, 4.03 AU from the Earth, and at a solar phase angle of 13.3°. The program was comprised of 18 separate visits, each one corresponding to an HST orbit filled with 3 ACS exposures of either 800 or 857 s duration with the F606W broadband filter. These very deep exposures revealed a star-like object, without any apparent coma. The light curve, defined by 49 data points, is characterized by a mean apparent V magnitude of 21.8 and an amplitude of 0.5 mag, indicating that we were viewing the varying cross-section of a rotating, elongated body. The periodicity was analyzed with seven different techniques yielding a rotational period in the range 39.40 to 43.00 h, and a mean value of 41.27 ± 1.85 h (1 σ). Using an albedo p V = 0.04 and a linear phase law with a coefficient β = 0.0465 mag deg −1 , we determined an effective radius of 3.01 km; a possible prolate spheroid solution has semi-axes a = 3.71 km , b = 2.36 km and a minimum axial ratio a / b ∼ 1.57 . By comparing the light curves obtained in 1997 and in 2004, we were able to constrain the phase function of the nucleus. Finally, an upper limit of A f ρ < 0.04 cm is set based on the non-detection of the coma.