On the rotation of a moonlet embedded in planetary rings

We examine the rotation of a small moonlet embedded in planetary rings caused by impacts of ring particles, using analytic calculation and numerical orbital integration for the three-body problem. Taking into account the Rayleigh distribution of particles' orbital eccentricities and inclinations, we evaluate both systematic and random components of rotation, where the former arises from an average of a large number of small impacts and the latter is contribution from large impacts. Calculations for parameter values corresponding to inner parts of Saturn's rings show that a moonlet would spin slowly in the prograde direction if most impactors are small particles whose velocity dispersion is comparable to or smaller than the moonlet's escape velocity. However, we also find that the effect of the random component can be significant, if the velocity dispersion of particles is larger and/or impacts of large particles comparable to the moonlet's size are common: in this case, both prograde and retrograde rotations can be expected. In the case of a small moonlet embedded in planetary rings of equal-sized particles, we find that the systematic component dominates the moonlet rotation when m/M?0.1 (m and M are the mass of a particle and a moonlet, respectively), while the random component is dominant when m/M?0.3. We derive the condition for the random component to dominate moonlet rotation on the basis of our results of three-body orbital integration, and confirm agreement with N-body simulation.     

On a suspected ring external to the visible rings of Saturn

Reexamination of a photograph of Saturn taken on 15 November 1966, when the earth was nearly in the ring plane, indicates that ring material may exist outside the visible rings, extending to more than 6 Saturnian radii. Although the suspected feature on the photograph appears to be real, the possibility of its being a developed pressure mark or a chance alignment of grains cannot be ruled out. The observed brightness in blue light was estimated to be m_B = 19.5 ± 0.5 per linear arcsecond, implying a normal optical thickness, $\text{τ ? 10}{}^{\mathrm{?7}}$, for ice-covered particles. For spacecraft passing through this region, the hazards are found to be minimal.     

Observations of the Saturn E ring and a new satellite

The faint E ring of Saturn appears as a narrow ring 246,000 ± 4,000 km from the center of Saturn on photographs taken when the ring-plane inclination was 5°.4. The apparent brightness of the ring was uniform at all observed orbital longitudes and permits an estimate of the normal optical thickness. A faint satellite (1981S1) was observed near the L₄ triangular libration point of Tethys and is probably the same object as 1980S13.     

Fates of satellite ejecta in the Saturn system

We use conventional numerical integrations to assess the fates of impact ejecta in the Saturn system. For specificity we consider impact ejecta launched from four giant craters on three satellites: Herschel on Mimas, Odysseus and Penelope on Tethys, and Tirawa on Rhea. Speeds, trajectories, and size of the ejecta are consistent with impact on a competent surface (“spalls”) and into unconsolidated regolith. We do not include near-field effects, jetting, or effects peculiar to highly oblique impact. Ejecta are launched at velocities comparable to or exceeding the satellite's escape speed. Most ejecta are swept up by the source moon on time-scales of a few to several decades, and produce craters no larger than 19 km in diameter, with typical craters in the range of a few km. As much as 17% of ejecta reach satellites other than the source moon. Our models generate cratering patterns consistent with a planetocentric origin of most small impact craters on the saturnian icy moons, but the predicted craters tend to be smaller than putative Population II craters. We conclude that ejecta from the known giant craters in the saturnian system do not fully account for Population II craters.     

Features around embedded moonlets in Saturn's rings: The role of self-gravity and particle size distributions

This paper presents the results of N-body simulations of moonlets embedded in broad rings, focusing specifically on the saturnian A ring. This work adds to previous efforts by including particle self-gravity and particle size distributions. The discussion here focuses primarily on the features that form in the background particles as a result of the moonlet. Particle self-gravity tends to damp out features produced by embedded moonlets and this damping is enhanced if the moonlet is simply the largest member of a continuous size distribution. Observable features around an embedded moonlet appear to require that the largest ring particles be no more massive than 1/30 the mass of the moonlet. These results, compared with current and future Cassini observations, will provide insight into the nature of the particle population in the saturnian rings. Some time is also spent analyzing the way in which the background particles cluster around the moonlet. The accretion of small particles onto the moonlet can be limited by disruptive collisions with the largest ring particles in the particle size distribution.     

The action of the satellite 1981 S13, and the optical depth profile of the Encke-gap ringlet in the Saturn A ring

The radial optical depth profile of the Encke ringlet obtained by the occultation experiment of the Voyager photopolarimeter (PPS data) is explained to be caused by the gravitational action of the recently discovered stallite 1981 S13 and a second smaller moonlet orbiting near one of its either libration points — L₄ or L₅. To this aim the results of previous and new numerical particle simulations as well as an extension of the scattering theory concerning a single moonlet to a pair of satellites have been used leading to a triple-peaked ringlet near the orbits of the moonlets. The width and the shape of that ringlet and its separate peaks depend on the mass ratio of both moonlets and on their orbital eccentricites. The best resemblance between the PPS data and the theoretical profile is obtained if the mass ratio of the either moonlets takes M₂/M_1981S13 ≈ (0.8 … 3.0) × 10⁻² and the eccentricities hold: e_1981S13 < h_1981S13; e₂ ≈ h₂ (the values h are the Hill scales of either moonlets defined by h_1981S13/2 ≈ (M_1981S13/2/3M_h)^1/3, M_h = Saturn mass). Furthermore, our results yield a size of 1981 S13 of < 15 km in diameter.     

On the damping of the bending waves in Saturn’s ring

We study numerically the motion of a single particle in the bending wave of finite thickness in Saturn’s ring. We include the forcing due to the planet, a moon, the coriolis force and the self gravity of the ring. In particular, we compute the variation of the velocity arising due to the variation of the amplitude and the phase of the epicyclic motion across the local vertical height of the ring. We suggest that the dissipation of energy due to the collision of ring particles in this shear layer damps out the bending wave of Saturn’s ring at the 5:3 vertical resonance of Mimas within a distance of 150 km from the site of its launching as is observed in Voyager data.     

The motion of a satellite in a ring potential

This investigation presents the orbital elements of a satellite moving in a circular ring potential. The ring is considered to be of infinitesimal thickness and of unit radius. The components of the perturbing accelerations due to the ring potential have been substituded into the Gauss form of Lagrange's planetary equations to yield the first-order approximations. The elements of the orbit have been expressed by means of Hansen coefficients. The results include the effects produced by the 2nd, 4th, 6th, and 8th spherical harmonics. Due to their importance we present separately the secular terms from the periodic ones. The general expressions for the orbital elements can be easily extended to include the effects produced by any other higher harmonic.List of Symbols semi-major axis - C _jK ⁿ (u, ) cosine functions ofu and - e eccentricity of the orbit - f sin² - inclination of the orbit - M mean anomaly - n mean motion - p semi-latus rectum of the orbit - R, S, andW components of the perturbing acceleration - r magnitude of position vector - S _jK ⁿ (u, ) sine functions ofu and - T time of periapse passage - u argument of latitude - U gravitational potential - V perturbing potential - G(M _r +m) (gravitational constant times the sum of the masses of ring and satellite) - _{n, k} coefficients ofR component of disturbing acceleration (functions off) - _{n, k} coefficients ofS andW components of disturbing acceleration (functions off) - mean anomaly at timet=0 - X ₀ ^{n, m} zero-order Hansen coefficients - argument of periapse - longitude of the ascending node     

Using wavelet approximation to study the influence of Jupiter on the orbital evolution of a distant satellite of Saturn

We suggest a nonstandard methodology for studying the influence of Jupiter on the secular orbital evolution of a distant satellite of Saturn. This influence is tangible only in short time spans near the times of the smallest separation between Jupiter and Saturn, i.e., when the heliocentric longitudes of the two planets coincide. These times are spaced about 20 years apart. To describe the jumplike behavior of perturbations, we suggest approximating the principal part of the perturbing function averaged over the satellite’s motion by a two-parameter exponential wavelet-type (burst) function. The subsequent averaging (smoothing) of the perturbing function allows us to eliminate the 20-year-period terms and obtain an approximate analytical solution in a special case of the problem. The results are illustrated by plots of the variations in the averaged perturbing function and the orbital eccentricity of Saturn’s outer satellite S/2000 S1, which is most strongly perturbed by Jupiter.     

Astrometry and dynamics of Anthe (S/2007 S 4), a new satellite of Saturn

We describe the astrometry and dynamics of Anthe (S/2007 S 4), a new satellite of Saturn discovered in images obtained using the Imaging Science Subsystem (ISS) of the Cassini spacecraft. Included are details of 63 observations, of which 28 were obtained with Cassini's narrow-angle camera (NAC) and 35 using its wide-angle camera (WAC), covering an observation time-span of approximately 3 years. We estimate the diameter of Anthe to be ∼1.8 km. Orbit modeling based on a numerical integration of the full equations of motion fitted to the observations show that Anthe is in a first-order 11:10 mean motion resonance with Mimas. Two resonant arguments are librating: ?₁=11λ^′−10λ−? and ?₂=11λ^′−10λ−?^′−Ω^′+Ω, where λ, ? and Ω refer to the mean longitude, longitude of pericenter and longitude of ascending node of Mimas and Anthe, with the primed quantities corresponding to Anthe. These resonances cause periodic variations in the orbital elements. The semi-major axis varies by ±26 km over a 913-day period. Anthe is also close to a second-order eccentricity-type mean motion resonant relationship of the form 77:75 with Methone. Since Methone is also in a first-order resonance with Mimas [Spitale, J.N., Jacobson, R.A., Porco, C.C., Owen, W.M., 2006. Astron. J. 132, 692-710], an additional indirect perturbation exists between Methone and Anthe via Mimas. Neither effect is detectable in the orbit fitting and the short-term dynamical evolution of Anthe is dominated by the Mimas-Anthe resonances alone. The expected modulation effect from the Mimas-Tethys 4:2 inclination resonance is also insignificant over this time period. By including Cassini ISS observations of Mimas in the numerical integration fit, we estimate the GM of Mimas to be , consistent with Jacobson et al. [Jacobson, R.A., Spitale, J., Porco, C.C., Owen, W.M., 2006. Astron. J. 132, 711-713].     

Constraints on the C ring parameters of Saturn at the Titan −1:0 resonance

A one-armed spiral bending wave in Saturn's rings excited by Titan's −1:0 inner vertical resonance is one of the most prominent oscillatory features observed by Voyager 1 . We study detailed dynamics of the particles inside the ring, and show that one of the main causes of the complete dissipation of the bending wave within a distance of ∼85 km from the resonance site could be as a result of the presence of a strong shear caused by radial velocity variation along the vertical direction. Assuming this to be the only source, Voyager data would suggest that if the surface density of matter is around 0.45 g cm⁻² and the amplitude of the bending wave is around 1200 m, then the upper limit of total vertical thickness of the C ring near this resonance is around 40 m.     

General relativity and satellite orbits: The motion of a test particle in the Schwarzschild metric

The motion of a satellite with negligible mass in the Schwarzschild metric is treated as a problem in Newtonian physics. The relativistic equations of motion are formally identical with those of the Newtonian case of a particle moving in the ordinary inverse-square law field acted upon by a disturbing function which varies asr ^?3. Accordingly, the relativistic motion is treated with the methods of celestial mechanics. The disturbing function is expressed in terms of the Keplerian elements of the orbit and substituted into Lagrange's planetary equations. Integration of the equations shows that a typical Earth satellite with small orbital eccentricity is displaced by about 17 cm from its unperturbed position after a single orbit, while the periodic displacement over the orbit reaches a maximum of about 3 cm. Application of the equations to the planet Mercury gives the advance of the perihelion and a total displacement of about 85 km after one orbit, with a maximum periodic displacement of about 13 km.     

A methodology to construct a reduced chemical scheme for 2D-3D photochemical models: Application to Saturn

We present a methodology to build a reduced chemical scheme adapted to the study of hydrocarbons in the atmospheres of giant planets and Titan. As an example, we have built a reduced chemical scheme, containing only 25 compounds and 46 reactions (including photolysis), which is well adapted to compute the abundance of the main hydrocarbons observed so far in the atmosphere of Saturn (CH₃, CH₄, C₂H₂, C₂H₄, C₂H₆, CH₃C₂H, C₃H₈ and C₄H₂). This scheme gives similar results, within the error bars of the model, as a 1D photochemical model using an initial chemical scheme containing 90 compounds and more than 600 reactions. As a consequence, such a methodology can be used to build a reduced scheme well adapted to future 2D (or 3D) photochemical models and GCMs.     

Precession of the orbital nodes of Jupiter and Saturn triggered by the mutual perturbation: A model of two rings

The problem of the precession of the orbital planes of Jupiter and Saturn under the influence of mutual gravitational perturbations was formulated and solved using a simple dynamical model. Using the Gauss method, the planetary orbits are modeled by material circular rings, intersecting along the diameter at a small angle α. The planet masses, semimajor axes and inclination angles of orbits correspond to the rings. What is new is that each ring has an angular momentum equal to the orbital angular momentum of the planet. Contrary to popular belief, it was proved that the orbital resonance 5: 2 does not preclude the use of the ring model. Moreover, the period of averaging of the disturbing force (T ≈ 1332 yr) proves to be appreciably greater than a conventionally used period (≈900 yr). The mutual potential energy of rings and the torque of gravitational forces between the rings were calculated. We compiled and solved the system of differential equations for the spatial motion of rings. It was established that a perturbing torque causes the precession and simultaneous rotation of the orbital planes of Jupiter and Saturn. Moreover, the opposite orbit nodes on the Laplace plane coincide and perform a secular movement in retrograde direction with the same velocity of 25.6″/yr and the period T _J = T _S ≈ 50687 yr. These results are close to those obtained in the general theory (25.93″/yr), which confirms the adequacy of the developed model. It was found that the vectors of the angular velocity of orbital rings move counterclockwise over circular cones and describe circles on the celestial sphere with radii β₁ ≈ 0.8403504° (Saturn) and β₂ ≈ 0.3409296° (Jupiter) around the point which is located at an angular distance of 1.647607° from the ecliptic pole.     

Optical reflectance polarimetry of Saturn's globe and rings: IV. Aerosols in the upper atmosphere of Saturn

From 1958 to 1976 the degree and direction of polarization of the light at Saturn's disk center were measured in orange light over 74 nights and at five wavelenghts over 19 nights. Measurements were also recorded at limb, terminator, and pole. In addition, extensive regional polarization measurements were collected over Saturn's disk and several polarization maps were produced. These data were analyzed on the basis Mie scattering theory and of transfer theory in planetary atmospheres. A model of the Saturn upper atmosphere aerosol structure is derived in which the top part of the the main cloud layer is composed of spherical transparent particles of radius 1.4 μm and refractive index 1.44. Above this layer, a fine haze of submicron-sized grains was detected by its production of a component of polarization which is always directed poleward; this upper haze is interpreted as having nonspherical particles which are systematically oriented. This upper haze layer covers approximately the whole planet uniformly but varies in thickness from year to year. The clear gas above the cloud layer has an optical thickness of around 0.1.     

P/2008 T1 (Boattini): Another comet under transition from Saturn to Jupiter

The newly discovered periodic comet P/2008 T1 (Boattini) is found to have experienced a recent capture into its present orbit, following a close approach to Saturn in 1995 to within 0.17 AU. This orbital change transferred the comet into an orbit tangent to that of Jupiter, which lead to an even closer passage within 0.02 AU with that planet in 2003 decoupling it from the influence of Saturn (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Force function of a slightly elliptical Gaussian ring and its generalization to a nearly coplanar system of rings

An analytical expression of the force function of a slightly elliptical Gaussian ring is proposed. The obtained power expansion of ellipse eccentricity contains the terms up to the third power inclusive. The coefficients of this expansion depend on the coordinates of the sampling point and semi-major axis of the ellipse. In the advanced application to the system of the major moons of Uranus for the investigation into secular mutual perturbations, the generalization of the force function is performed for the case of a nearly coplanar system of rings. The force function obtained in this work is more accurate than the earlier known ones and includes the terms up to the third power inclusive with respect to the eccentricities and equatorial inclinations of the moons’ orbits.     

Orbital evolution of new distant Neptunian satellites and ω-librators in the satellite systems of Saturn and Jupiter

We used data on the recently discovered three outer Neptunian satellites to analyze the long-period evolution of their orbits. We estimated the ranges of eccentricities and inclinations as well as approximate circulation periods of the pericenter arguments and the longitudes of the ascending nodes. The results were mainly obtained by using two different versions of the averaged Hill problem. Plane sections of the phase space of satellite orbital elements are given. We discuss the peculiarity of the evolution of several satellite orbits related to the librational variation of the pericenter argument ω. The ω-librators of Saturn’s system were found to qualitatively differ from the libration orbit in the system of Jupiter.     

Compositional mapping of Saturn's satellite Dione with Cassini VIMS and implications of dark material in the Saturn system

Cassini VIMS has obtained spatially resolved imaging spectroscopy data on numerous satellites of Saturn. A very close fly-by of Dione provided key information for solving the riddle of the origin of the dark material in the Saturn system. The Dione VIMS data show a pattern of bombardment of fine, sub-0.5-μm diameter particles impacting the satellite from the trailing side direction. Multiple lines of evidence point to an external origin for the dark material on Dione, including the global spatial pattern of dark material, local patterns including crater and cliff walls shielding implantation on slopes facing away from the trailing side, exposing clean ice, and slopes facing the trailing direction which show higher abundances of dark material. Multiple spectral features of the dark material match those seen on Phoebe, Iapetus, Hyperion, Epimetheus and the F-ring, implying the material has a common composition throughout the Saturn system. However, the exact composition of the dark material remains a mystery, except that bound water and, tentatively, ammonia are detected, and there is evidence both for and against cyanide compounds. Exact identification of composition requires additional laboratory work. A blue scattering peak with a strong UV-visible absorption is observed in spectra of all satellites which contain dark material, and the cause is Rayleigh scattering, again pointing to a common origin. The Rayleigh scattering effect is confirmed with laboratory experiments using ice and 0.2-μm diameter carbon grains when the carbon abundance is less than about 2% by weight. Rayleigh scattering in solids is also confirmed in naturally occurring terrestrial rocks, and in previously published reflectance studies. The spatial pattern, Rayleigh scattering effect, and spectral properties argue that the dark material is only a thin coating on Dione's surface, and by extension is only a thin coating on Phoebe, Hyperion, and Iapetus, although the dark material abundance appears higher on Iapetus, and may be locally thick. As previously concluded for Phoebe, the dark material appears to be external to the Saturn system and may be cometary in origin. We also report a possible detection of material around Dione which may indicate Dione is active and contributes material to the E-ring, but this observation must be confirmed.     

P/2004 A1 (Loneos) – a comet under transition from Saturn to Jupiter

The newly discovered periodic comet P/2004 A1 (LONEOS) is found to have experienced a recent capture into its present orbit, following a close approach to Saturn in 1992 to within 0.032 AU. This induced orbital change transfered the comet into an orbit tangent to that of Jupiter, which will, after a close passage in 2026, gain control by further decoupling it from the influence of Saturn. A long‐term orbital investigation yields support that the comet is on its first sojourn into the inner solar system. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)