On the formation of the rings of saturn

It is shown in this paper that a satellite which revolves round a primary in a circular orbit in tied revolution and which spirals within Roche's limit must form by its disintegration a ring of ellipse-like cross-section which is more than 11 times larger than the original spherical diameter of the disintegrating body. The individual particles have elliptic orbits with small eccentricities and revolve in different planes at small inclinations to each other. By inelastic collisions of particles in differently inclined orbits the original considerable thickness of the ring is very greatly reduced.

Applied to the system of Saturn it is assumed that the Rings A and B are formed by disintegration of two different satellites. It can be shown that the satellite A had an original diameter of 1721 km and a density of 0.95 g/cm³, the satellite B a diameter of 2463 km and a density of 1.95.

Thus the hypothesis of G. P. Kuiper, that the rings of Saturn are composed of H²O-snow contaminated by silicate dust (as Jupiter III), seems to fit very well.     

Rings and moons the rings of saturn and jupiter controlled by spacecraft informations and their origin

The two great divisions of the Saturn rings, one of them discovered by the spacecraft observations of 1979, can be explained as narrow zones of meteorites. The new informations by soacecraft encounters raise the probability of a real value of the series 2ⁿ(3–4–5), pointed out by the author in 1928 as approached by the sequence of Saturn's rings and moons. The Titius-Bode-series of planets and a similar series of Jupiter's moons also profit from this support. The author's attempt to explain these correspondences dynamically (first published in Havemann 1978) starts with the assumption of a thin central disk in the preplanetary nebulas. The chance of the Titius-Bode series concerning the sequence of planets is much raised by the result of spacecraft informations that Saturn contains an iron core comparable with that of the Earth. This supports the author's conjecture that iron cores of planets have first formed without envelopes.     

Gas interaction effects on lunar bonded particles and their implications

Some of the bonded particles of lunar soil samples separated upon exposure to reactive gases such as oxygen, water vapor, their mixtures, acids and bases. The bondings between particles susceptible to gas-disruption seemed to be generally weak and appeared to have taken place via highly radiation-damaged layers at the particle surfaces. These amorphous layers with an average thickness of about 0.05µm were produced by the solar wind exposure of about 2000 years. Therefore, the solar wind was responsible for the formation of these weak bondings and also probably responsible for disruption of these bondings. Apollo 11 and 12 landed in the equatorial region and about 1500 km apart. Thus, the solar wind effects on materials at these sites should have been about the same and the proportion of bonded particles separated by reactive gas exposure should also have been about the same; but the number of separations observed was about 2.7 (average) times greater in the Apollo 11 soil sample than in the Apollo 12 soil sample. This finding suggests that the number of weakly bonded particles and probably the solar-wind damaged amorphous layer particles at these sites was about in the same proportion. It is, therefore, considered that materials from certain depth (practically not exposed to the solar wind) of another site were transported and mixed during recent years (considerably less than 2000 years) with the original materials of the Apollo 12 site. This is consistent with the conclusions made by other investigators.     

Abundance enhancements of silicon to iron in solar energetic particles and their implications

Differential energy spectra of low abundant elements between silicon and iron of energetic solar particles (SEP) in the August 4, 1972 event were measured in the energy region of 10 to 40 MeV amu^–1 using rocket-borne Lexan detectors. The relative abundances of elements were determined and abundance enhancements, i.e., SEP/photospheric ratios, and their energy dependence were derived in 10–40 MeV amu^–1 interval. It is found that there are four types of abundance enhancements as a function of energy as follows: (a) silicon, iron, and calcium show fairly strong energy dependence which decreases with increasing energy and at 20–40 MeV amu^–1 reaches photospheric values; (b) in case of sulphur enhancement factors are independent of energy and the values are close to unity; (c) argon shows energy independent enhancements of about 3 to 4 in 10–40 MeV amu^–1; (d) titanium and chromium show weakly energy-dependent, but very high abundance enhancement factor of about 10 to 40. These features are to be understood in terms of the atomic properties of these elements and on the physical conditions in the accelerating region. These are important not only for solar phenomena but also to gain insight into the abundance enhancements of cosmic-ray heavy nuclei.on leave from Tata Institute of Fundamental Research, Bombay, India.     

Size distribution of particles in planetary rings

Harris (Icarus24, 190–192) has suggested that the maximum size of particles in a planetary ring is controlled by collisional fragmentation rather than by tidal stress. While this conclusion is probably true, estimated radius limits must be revised upward from Harris' values of a few kilometers by at least an order of magnitude. Accretion of particles within Roche's limit is also possible. These considerations affect theories concerning the evolution of Saturn's rings, of the Moon, and of possible former satellites of Mercury and Venus. In the case of Saturn's rings, comparison of various theoretical scenarios with available observational evidence suggests that the rings formed from the breakup of larger particles rather than from original condensation as small particles. This process implies a distribution of particle sizes in Saturn's rings possibly ranging up to ～100 km but with most cross-section in cm-scale particles.     

Gravitational accretion of particles in Saturn's rings

Gravitational accretion in the rings of Saturn is studied with local N-body simulations, taking into account the dissipative impacts and gravitational forces between particles. Common estimates of accretion assume that gravitational sticking takes place beyond a certain distance (Roche distance) where the self-gravity between a pair of ring particles exceeds the disrupting tidal force of the central object, the exact value of this distance depending on the ring particles' internal density. However, the actual physical situation in the rings is more complicated, the growth and stability of the particle groups being affected also by the elasticity and friction in particle impacts, both directly via sticking probabilities and indirectly via velocity dispersion, as well as by the shape, rotational state and the internal packing density of the forming particle groups. These factors are most conveniently taken into account via N-body simulations. In our standard simulation case of identical 1 m particles with internal density of solid ice, ρ=900 kg m⁻³, following the Bridges et al., 1984 elasticity law, we find accretion beyond a=137,000-146,000 km, the smaller value referring to a distance where transient aggregates are first obtained, and the larger value to the distance where stable aggregates eventually form in every experiment lasting 50 orbital periods. Practically the same result is obtained for a constant coefficient of restitution εn=0.5. In terms of rp parameter, the sum of particle radii normalized by their mutual Hill radius, the above limit for perfect accretion corresponds to rp<0.84. Increased dissipation (εn=0.1), or inclusion of friction (tangential force 10% of normal force) shifts the accretion region inward by about 5000 km. Accretion is also more efficient in the case of size distribution: with a q=3 power law extending over a mass range of 1000, accretion shifts inward by almost 10,000 km. The aggregates forming in simulations via gradual accumulation of particles are synchronously rotating.     

Adhesion and collisional release of particles in dense planetary rings

We propose a simple theoretical model for aggregative and fragmentative collisions in Saturn’s dense rings. In this model the ring matter consists of a bimodal size distribution: large (meter sized) boulders and a population of smaller particles (tens of centimeters down to dust). The small particles can adhesively stick to the boulders and can be released as debris in binary collisions of their carriers. To quantify the adhesion force we use the JKR theory (Johnson, K., Kendall, K., Roberts, A. [1971]. Proc. R. Soc. Lond. A 324, 301–313). The rates of release and adsorption of particles are calculated, depending on material parameters, sizes, and plausible velocity dispersions of carriers and debris particles. In steady state we obtain an expression for the amount of free debris relative to the fraction still attached to the carriers. In terms of this conceptually simple model a paucity of subcentimeter particles in Saturn’s rings (French, R.G., Nicholson, P.D. [2000]. Icarus 145, 502–523; Marouf, E. et al. [2008]. Abstracts for “Saturn after Cassini–Huygens” Symposium, Imperial College London, UK, July 28 to August 1, p. 113) can be understood as a consequence of the increasing strength of adhesion (relative to inertial forces) for decreasing particle size. In this case particles smaller than a certain critical radius remain tightly attached to the surfaces of larger boulders, even when the boulders collide at their typical speed. Furthermore, we find that already a mildly increased velocity dispersion of the carrier-particles may significantly enhance the fraction of free debris particles, in this way increasing the optical depth of the system.     

Detection of submillimeter size particles in the inner coma of a comet through their forward scattering

During the occultation of a star by the inner coma region of a comet, specific forward-scattering effects could be observable if submillimeter size particles contribute significantly to the net extinction of star light. In this paper we investigate the possibility of detecting the signature of such particles by observing the dependence of extinction on the angular size of the acceptance aperture used at the focal plane of the telescope. Calculations based on a simple model assuming spherically-symmetric and homogeneous coma are presented.     

The Voyager 1/Saturn encounter and the cosmogonic shadow effect

If an electrically conducting medium (e.g. a dusty plasma) rotates around a gravitating central body, which possesses an axisymmetric dipole field, the medium is supported to two-thirds by the centrifugal force and to one-third by electromagnetic forces under the condition that the magnetic field is strong enough to controll the motion. If the electromagnetic forces disappear — e.g. by a de-ionisation of the dusty plasma — the medium will fall down to two-thirds of its original central distance. The result of this process will be a cosmogonic shadow effect which is described in some detail.The Voyager 1/Saturn results demonstrate that the macro-structure of the Saturnian ring system can be explained as a result of this effect working at the formation of the system. The agreement between the theoretical results and the observations is better than a few percent.A similar analysis of the asteroidal belt shows that its macro-structure can also be explained by the cosmogonic shadow effect. The agreement between theory and observations is perhaps even better than in the Saturnian ring system.The observational results demonstrate that during their formation both the Saturnian ring and the asteroidal belt passed a plasma state dominated by electromagnetic effects.     

Strong interaction between the ring system and the ionosphere of saturn

An abnormally low electron density in the Saturnian ionosphere observed by the radio occultation experiment of the Pioneer 11 may be explained in terms of the contamination of water in the Saturnian upper atmosphere from its ring system.     

Interplanetary dust particles collected from the stratosphere: physical, chemical, and mineralogical properties and implications for their sources

The suggestion that significant quantities of interplanetary dust are produced by both main-belt asteroids and comets is based on the Infrared Astronomical Satellite detection of dust trails or bands associated with these objects. Gravitational focusing strongly biases all near-Earth collections of interplanetary dust in favor of particles with the lowest geocentric velocities, that is the dust from main-belt asteroids spiraling into the Sun under the influence of Poynting-Robertson radiation drag.

The major dust bands in the main-belt appear to be associated with the catastrophic disruptions which produced the Eos, Themis and Koronis families of asteroids. If dust particles are produced in the catastrophic collision process, then Poynting-Robertson radiation drag is such an efficient transport mechanism from the main-belt to 1 AU that near-Earth collections of interplanetary dust should include, and perhaps be dominated by, this material. The physical, chemical and mineralogical properties of this asteroidal dust can provide constraints on the properties of the asteroidal parent bodies.

Interplanetary dust particles from 5 to 100 μm in diameter have been recovered from the stratosphere of the Earth by NASA sampling aircraft since the mid1970s. The densities of a large fraction of these interplanetary dust particles are significantly lower than the densities of their constituent silicate mineral phases, indicating significant porosities. Direct examination of ultra-microtome thin-sections of interplanetary dust particles also shows significant porosities. The majority of the particles are chemically and mineralogically similar to, but not identical to, the carbonaceous chondrite meteorites.

Most stony interplanetary dust particles have carbon contents exceeding those of Allende, a carbonaceous chondrite meteorite having a low albedo. The population of interplanetary dust does not appear to exhibit the full range of compositional diversity inferred from reflection spectroscopy of the main-belt asteroids. In particular, higher albedo particles corresponding to S-type asteroids are underrepresented or absent from the stratospheric collections, and primitive carbonaceous particles seem to be overrepresented in the stratospheric collections compared to the fraction of mainbelt asteroids classified as primitive. This suggests that much of the interplanetary dust may be generated by a stochastic process, probably preferentially sampling a few most recent collisional events.     

Consistency tests of cosmogonic theories from models of Uranus and Neptune

The planetary ratios of ice to rock $\text{(}\text{I}\text{R}\text{)}$ abundances expected in Uranus and Neptune are derived on the basis of several cosmogonic theories. For both Uranus and Neptune the value of $\text{I}\text{R}$ lies between about 1.0 and 3.6. This value is difficult to reconcile with a scenario in which N and C are accreted primarily in the form of N₂ and CO. It is consistent with some versions of both giant protoplanet theories and equilibrium accretion theories.     

Observation and photometry of an outer ring of saturn

A faint outer ring (E ring), which lies outside the classical rings A, B, C, and F, has been detected out to eight Saturn radii. We first observed it on November 1, 1979, and thereby confirmed the 1966 observation by Feibelman. Our plates were taken with a coronographic design and are specially intended for photometry. They are directly scaled in reflectance by reference to the Saturn disk which is properly attenuated. Photometry of the edge-on ring E lineament shows a strong brightness increase at small phase angles, which is compatible with scattering by particles of several microns in radius. The excess reflectivity in blue compared to the B ring implies a significant contribution of small particles in the scattering process. The E ring shows brightness and radial gradient changes, with condensations, which differ between east and west limbs and are not always the same from night to night. The E ring is probably a flat structure with a condensation centered at a distance of 4 R_s, but without a simple axial symmetry. It is probably shaped by segments or lumps and may have streamerlike structures.     

Dynamics of ring-satellite sytems around saturn and uranus

We first recall the observations concerning the opaque rings of Saturn and Uranus. Then we describe a model which represents the kinematics of these rings. Finally we review how we treat collisions, self-gravity and satellite perturbations and what are the basic effects of these forces.     

Analytical theory of motion of phoebe,the ninth satellite of saturn

The literal solution of the restricted three body problem obtained by the authors up to the eleventh order with respect to the minor parameter is applied to the investigation of the motion of Phoebe, the ninth satellite of Saturn. As distinct from the existing analytical theories of the motion of the satellite, in the present paper the planetary perturbations are taken into account. A comparison with the modern numerical theory of the motion of Phoebe has shown that the new analytical theory of the satellite motion represents observations with the same degree of accuracy.     

Radial drift of particles in the solar nebula: implications for planetesimal formation

For standard cosmic abundances of heavy elements, a layer of small particles in the central plane of the solar nebula cannot attain the critical density for gravitational instability. Youdin and Shu (2002, Astrophys. J. 580, 494-505) suggest that the local surface density of solids can be enhanced by radial migration of particles due to gas drag. However, they consider only motions of individual particles. Collective motion due to turbulent stress on the particle layer acts to inhibit such enhancement and may prevent gravitational instability.     

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.     

Moonlet induced wakes in planetary rings: Analytical model including eccentric orbits of moon and ring particles

Saturn’s rings host two known moons, Pan and Daphnis, which are massive enough to clear circumferential gaps in the ring around their orbits. Both moons create wake patterns at the gap edges by gravitational deflection of the ring material (Cuzzi, J.N., Scargle, J.D. [1985]. Astrophys. J. 292, 276-290; Showalter, M.R., Cuzzi, J.N., Marouf, E.A., Esposito, L.W. [1986]. Icarus 66, 297-323). New Cassini observations revealed that these wavy edges deviate from the sinusoidal waveform, which one would expect from a theory that assumes a circular orbit of the perturbing moon and neglects particle interactions. Resonant perturbations of the edges by moons outside the ring system, as well as an eccentric orbit of the embedded moon, may partly explain this behavior (Porco, C.C., and 34 colleagues [2005]. Science 307, 1226-1236; Tiscareno, M.S., Burns, J.A., Hedman, M.M., Spitale, J.N., Porco, C.C., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, C.C., Tiscareno, M.S., Burns, J.A., Dones, L. [2005]. Bull. Am. Astron. Soc. 37, 767; Weiss, J.W., Porco, C.C., Tiscareno, M.S. [2009]. Astron. J. 138, 272-286). Here we present an extended non-collisional streamline model which accounts for both effects. We describe the resulting variations of the density structure and the modification of the nonlinearity parameter q. Furthermore, an estimate is given for the applicability of the model. We use the streamwire model introduced by Stewart (Stewart, G.R. [1991]. Icarus 94, 436-450) to plot the perturbed ring density at the gap edges.We apply our model to the Keeler gap edges undulated by Daphnis and to a faint ringlet in the Encke gap close to the orbit of Pan. The modulations of the latter ringlet, induced by the perturbations of Pan (Burns, J.A., Hedman, M.M., Tiscareno, M.S., Nicholson, P.D., Streetman, B.J., Colwell, J.E., Showalter, M.R., Murray, C.D., Cuzzi, J.N., Porco, C.C., and the Cassini ISS team [2005]. Bull. Am. Astron. Soc. 37, 766), can be well described by our analytical model. Our analysis yields a Hill radius of Pan of 17.5 km, which is 9% smaller than the value presented by Porco (Porco, C.C., and 34 colleagues [2005]. Science 307, 1226-1236), but fits well to the radial semi-axis of Pan of 17.4 km. This supports the idea that Pan has filled its Hill sphere with accreted material (Porco, C.C., Thomas, P.C., Weiss, J.W., Richardson, D.C. [2007]. Science 318, 1602-1607). A numerical solution of a streamline is used to estimate the parameters of the Daphnis-Keeler gap system, since the close proximity of the gap edge to the moon induces strong perturbations, not allowing an application of the analytic streamline model. We obtain a Hill radius of 5.1 km for Daphnis, an inner edge variation of 8 km, and an eccentricity for Daphnis of 1.5 × 10⁻⁵. The latter two quantities deviate by a factor of two from values gained by direct observations (Jacobson, R.A., Spitale, J., Porco, C.C., Beurle, K., Cooper, N.J., Evans, M.W., Murray, C.D. [2008]. Astron. J. 135, 261-263; Tiscareno, M.S., Burns, J.A., Hedman, M.M., Spitale, J.N., Porco, C.C., Murray, C.D., and the Cassini Imaging team [2005]. Bull. Am. Astron. Soc. 37, 767), which might be attributed to the neglect of particle interactions and vertical motion in our model.     

Ice Ages on the Earth and their astronomical implications

It is pointed out that while the long-periodic variations of the elements of the terrestrial orbit around the Sun are probably sufficient to account for the frequency-spectrum of recurrent ice-ages established from the geological record of climatic changes experiences by the Earth in the course of the past half a million years, such kinematic phenomena cannot account naturally for the sudden onset of the Ice Age at the end of the Tertiary Epoch; nor for the fact that previous Ice Ages (in the Permian or pre-Cambrian times) are separated by milder (ice-free) intervals lasting 100 times longer than the periods of intermittent glaciation). Other astronomical phenomena (such as the galactic orbit of the solar system, which may cause our Earth temporarily to pass through different types of galactic climate; or temporary fluctuations in the energy output of the Sun), as well as geophysical phenomena (changes in atmospheric chemistry, and consequent fluctuations of the greenhouse effect), may have to be invoked to account for the geological facts by their combined effects.Lecture delivered on 11 October 1979 before the Serbian Academy of Sciences in Belgrade, Yugoslavia, at an International Conference in honour of Milutin Milankovich.