Saturn's E ring: I. CCD observations of March 1980

The tenuous E ring of Saturn is found to commence abruptly at 3 Saturn radii, to peak sharply in the vicinity of the orbit of the satellite Enceladus (about 4 radii), and to spread out thinly to more than 8 radii. This distribution strongly suggests it to be associated with Enceladus and perhaps to be material ejected from Enceladus. The spread of E-ring material above and below the ring plane is greater in its tenuous outskirts than in its denser inner region, suggesting that the E ring may be at an early stage in its evolution. Thus far, our analysis reveals only a marginal variation of the ring with time or Enceladus azimuth. In this paper we describe the special instrumentation used for photometric observations of the E ring, and we present some of the data obtained in March 1980. In Paper II we shall derive the three-dimensional distribution of material in the E ring and discuss its cosmogonic implications.     

Analysing the New Saturnian Rings, R/2004 S1 and R/2004 S2

The Cassini-Huygens arrival into the Saturnian system brought a large amount of data about the satellites and rings. Two diffuse rings were found in the region between the A ring and Prometheus. R/2004 S1 is coorbital to Atlas and R/2004 S2 is close to Prometheus. In this work we analysed the closest approach between Prometheus and both rings. As a result we found that the satellite removes particles from R/2004 S2 ring. Long-term numerical simulations showed that some particles can cross the F ring region . The well known region of the F ring, where small satellites are present and particles are being taking from the ring, gains a new insight with the presence of particles from R/2004 S2 ring. The computation of the Lyapunov Characteristic Exponent reveled that the R/2004 S2 ring lies in a chaotic region while R/2004 S1 ring and Atlas are in a stable region. Atlas is responsible for the formation of three regimes in the R/2004 S1 ring, as expected for a satellite embedded in a ring.     

A predator–prey model for moon-triggered clumping in Saturn’s rings

UVIS occultation data show clumping in Saturn’s F ring and at the B ring outer edge, indicating aggregation and disaggregation at these locations that are perturbed by Prometheus and by Mimas. The inferred timescales range from hours to months. Occultation profiles of the edge show wide variability, indicating perturbations by local mass aggregations. Structure near the B ring edge is seen in power spectral analysis at scales 200–2000 m. Similar structure is also seen at the strongest density waves, with significance increasing with resonance strength. For the B ring outer edge, the strongest structure is seen at longitudes 90° and 270° relative to Mimas. This indicates a direct relation between the moon and the ring clumping. We propose that the collective behavior of the ring particles resembles a predator–prey system: the mean aggregate size is the prey, which feeds the velocity dispersion; conversely, increasing dispersion breaks up the aggregates. Moons may trigger clumping by streamline crowding, which reduces the relative velocity, leading to more aggregation and more clumping. Disaggregation may follow from disruptive collisions or tidal shedding as the clumps stir the relative velocity. For realistic values of the parameters this yields a limit cycle behavior, as for the ecology of foxes and hares or the “boom-bust” economic cycle. Solving for the long-term behavior of this forced system gives a periodic response at the perturbing frequency, with a phase lag roughly consistent with the UVIS occultation measurements. We conclude that the agitation by the moons in the F ring and at the B ring outer edge drives aggregation and disaggregation in the forcing frame. This agitation of the ring material may also allow fortuitous formation of solid objects from the temporary clumps, via stochastic processes like compaction, adhesion, sintering or reorganization that drives the denser parts of the aggregate to the center or ejects the lighter elements. Any of these more persistent objects would then orbit at the Kepler rate. We would also expect the formation of clumps and some more permanent objects at the other perturbed regions in the rings… including satellite resonances, shepherded ring edges, and near embedded objects like Pan and Daphnis (where the aggregation/disaggregation cycles are forced similar to Prometheus forcing of the F ring).     

Expectations for Cassini observations of ring material with nearby moons

This paper describes N-body simulations of two regions of the saturnian ring system and examines what we might expect the Cassini orbiter to see in those areas. The first region is the edge of the Encke gap in the A ring that is perturbed by the satellite, Pan. Our previous simulations of this region neglected particle self-gravity [Lewis and Stewart, 2000a, Bull. Am. Astron. Soc. 34, 883]. Here we examine the interactions of the wakes caused by Pan with the wakes that form from local gravitational instabilities. We find that the two phenomena do not normally coexist and predict that measurements of particle sizes between the moon wakes should reflect the true particle size distribution of the region and not what is caused by gravitational aggregation. The region between the Encke gap edge and the first wake peak is an exception to this rule because our simulations exhibit the formation of exceptionally large gravity-induced wakes in this region. We also describe simulations of the F ring and explain the nature of braid-like structures that form naturally when the ring is perturbed by a single moon on an eccentric orbit. Finally, we discuss the very dynamic nature of the F ring system and how this should be taken into account when interpreting observations and even when planning future observations of this system.     

Voyager 2 photopolarimeter experiment: Evidence for tenuous outer ring material at Saturn

A statistical analysis of the stellar occultation data from the Voyager 2 photopolarimeter indicates significant amounts of tenuous material in two regions exterior to Saturn's F ring. The first region has a radial width of approximately 200 km starting at a Saturn-centered radial distance of 141,650 km (1500 km outside of the F ring) and its normal optical depth is 0.012 ± 0.004. The second is a very broad region of enhanced opacity, at least 1000 km in radial width, beginning at approximately 144,090 km, with a normal optical depth of approximately 0.009 ± 0.004 (more than 100 times greater than the Saturn E ring).     

Ringlets of the major planets which may consist of coagulated particles

A ringlet of Saturn, Uranus, Neptune or Jupiter may be composed of particles held in contact by their mutual gravitation, without relative motion. Lacking tensile strength, each part of the ringlet orbits as if it were a separate particle, but all parts are constrained to the same orbit by their contacts. Slight shear strength prevents flow. This configuration is stable inside Roche's limit, and outside an inner limit within which it would scatter. These limits depend on the density of the ringlet. Conversely, for an observed radius in a ring, a range of possible density is calculated. For Saturn's ring system, the density of a ringlet at the inner edge of the C ring must be at least 2.0 g cm^-3 and in the outer F ring not more than 0.73. For Uranus, the inner ring must be at least 2.3, and the outer between 1.0 and 2.3. Jupiter's ring must be in the range 1.4 to 3.9, and Neptune's, in the range 0.6 to 1.5. In extended crowded regions of a ring system, the gaps between ringlets must be at least 38% as wide as the ringlets, in the outer portions of the system, and wider than that at smaller radii. Certain observations can be explained by this model, including the sharp edges of the rings, a long life of the system, the possible existence of a partial ring, asymmetry of brightness of Saturn ring A, and forward scattering of radio waves.     

A close look at Saturn's rings with Cassini VIMS

Soon after the Cassini-Huygens spacecraft entered orbit about Saturn on 1 July 2004, its Visual and Infrared Mapping Spectrometer obtained two continuous spectral scans across the rings, covering the wavelength range 0.35-5.1 μm, at a spatial resolution of 15-25 km. The first scan covers the outer C and inner B rings, while the second covers the Cassini Division and the entire A ring. Comparisons of the VIMS radial reflectance profile at 1.08 μm with similar profiles at a wavelength of 0.45 μm assembled from Voyager images show very little change in ring structure over the intervening 24 years, with the exception of a few features already known to be noncircular. A model for single-scattering by a classical, many-particle-thick slab of material with normal optical depths derived from the Voyager photopolarimeter stellar occultation is found to provide an excellent fit to the observed VIMS reflectance profiles for the C ring and Cassini Division, and an acceptable fit for the inner B ring. The A ring deviates significantly from such a model, consistent with previous suggestions that this region may be closer to a monolayer. An additional complication here is the azimuthally-variable average optical depth associated with “self-gravity wakes” in this region and the fact that much of the A ring may be a mixture of almost opaque wakes and relatively transparent interwake zones. Consistently with previous studies, we find that the near-infrared spectra of all main ring regions are dominated by water ice, with a typical regolith grain radius of 5-20 μm, while the steep decrease in visual reflectance shortward of 0.6 μm is suggestive of an organic contaminant, perhaps tholin-like. Although no materials other than H₂O ice have been identified with any certainty in the VIMS spectra of the rings, significant radial variations are seen in the strength of the water-ice absorption bands. Across the boundary between the C and B rings, over a radial range of ∼7000 km, the near-IR band depths strengthen considerably. A very similar pattern is seen across the outer half of the Cassini Division and into the inner A ring, accompanied by a steepening of the red slope in the visible spectrum shortward of 0.55 μm. We attribute these trends—as well as smaller-scale variations associated with strong density waves in the A ring—to differing grain sizes in the tholin-contaminated icy regolith that covers the surfaces of the decimeter-to-meter sized ring particles. On the largest scale, the spectral variations seen by VIMS suggest that the rings may be divided into two larger ‘ring complexes,’ with similar internal variations in structure, optical depth, particle size, regolith texture and composition. The inner complex comprises the C and B rings, while the outer comprises the Cassini Division and A ring.     

Keck observations of the 2002-2003 jovian ring plane crossing

We present new observations of Jupiter's ring system at a wavelength of 2.2 μm obtained with the 10-m W.M. Keck telescopes on three nights during a ring plane crossing: UT 19 December 2002, and 22 and 26 January 2003. We used conventional imaging, plus adaptive optics on the last night. Here we present detailed radial profiles of the main ring, halo and gossamer rings, and interpret the data together with information extracted from radio observations of Jupiter's synchrotron radiation. The main ring is confined to a 800-km-wide annulus between 128,200 and 129,000 km, with a ∼5000 km extension on the inside. The normal optical depth is 8×¹⁰⁻⁶, 15% of which is provided by bodies with radii a?5 cm. These bodies are as red as Metis. Half the optical depth, τ≈4×¹⁰⁻⁶, is attributed to micron-sized dust, and the remaining τ≈3×¹⁰⁻⁶ to grains tens to hundreds of μm in size. The inward extension consists of micron-sized (a?10 μm) dust, which probably migrates inward under Poynting-Robertson drag. The inner limit of this extension falls near the 3:2 Lorentz resonance (at orbital radius r=122,400 km), and coincides with the outer limit of the halo. The gossamer rings appear to be radially confined, rather than broad sheets of material. The Amalthea ring is triangularly shaped, with a steep outer dropoff over ∼5000 km, extending a few 1000 km beyond the orbit of Amalthea, and a more gradual inner dropoff over 15,000-20,000 km. The inner edge is near the location of the synchronous orbit. The optical depth in the Amalthea ring is ∼5×¹⁰⁻⁷, up to 20% of which is comprised of macroscopic material. The optical depth in the Thebe ring is a factor of 3 smaller.     

Observations of Pg pulsations in the Northern Auroral zone and at lower latitude conjugate regions

An analysis is made of giant pulsation (Pg) data recorded at ground stations in the Northern Auroral Zone in Scandanavia (mainly at Tromsø, L = 6.4 and Kiruna, L = 5.5) during the period September 1976 to December 1977. They are shown to have a meridional variation of amplitude and polarization consistent with a field line resonance structure and their vertical component behaviour suggests that they also have a rapid azimuthal phase variation. Limited data from conjugate stations at L = 4.4 are used to show that Pg's are odd mode oscillations of the field line. Pg's are equated to the observation of a unique compressional wave in space at synchronous orbit and it is suggested that they result from the drift wave instability of the compressional Alfven wave at the outer edge of the quiet time ring current.     

Stochastic models of hot planetary and satellite coronas: Atomic oxygen in Europa’s corona

This paper analyzes the formation, kinetics, and transport of hot oxygen atoms in the atmosphere of the Jovian satellite Europa. Atmospheric sources of suprathermal oxygen atoms are assumed to be represented by the processes of dissociation of molecular oxygen, which is the main component of the atmosphere, by solar UV radiation and electron fluxes from the inner magnetosphere of Jupiter, as well as by the reaction of dissociative recombination of the main ionospheric ion O ₂ ⁺ which thermal electrons. It is shown that dissociation in Europa’s near-surface atmosphere is balanced by the processes of the loss of atomic oxygen due to the effective escape of suprathermal oxygen atoms into the inner magnetosphere of Jupiter along the orbit of Europa and due to ionization by magnetospheric electrons and catalytic recombination of oxygen atoms on the icy surface of the satellite. It thus follows that atomic oxygen is only a small admixture to the main atmospheric component—molecular oxygen—in the near-surface part of the atmosphere. However, the outer exospheric layers of Europa’s atmosphere are populated mostly by suprathermal oxygen atoms. The near-surface molecular envelope of Europa is therefore surrounded by a tenuous extended corona of hot atomic oxygen.     

Embedded star clusters and the formation of the Oort cloud: II. The effect of the primordial solar nebula

This paper deals with Oort cloud formation while the Sun was in an embedded cluster and surrounded by its primordial nebula. This work is a continuation of Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82], building on the model presented therein, and adding the aerodynamic drag and gravitational potential of the primordial solar nebula. Results are presented of numerical simulations of comets subject to the gravitational influence of the Sun, Jupiter, Saturn, star cluster and primordial solar nebula; some of the simulations included the gravitational influence of Uranus and Neptune as well. The primordial solar nebula was approximated by the minimum-mass Hayashi model [Hayashi, C., Nakozawa, K., Nakagawa, Y., 1985. In: Black, D.C., Matthews, M.S. (Eds.). Protostars and Planets II. Univ. of Arizona Press, Tucson, AZ] whose inner and outer radii have been truncated at various distances from the Sun. A comet size of 1.7 km was used for most of our simulations. In all of our simulations, the density of the primordial solar nebula decayed exponentially with an e-folding time of 2 Myr. It turns out that when the primordial solar nebula extends much beyond Saturn or Neptune, virtually no material will end up in the Oort cloud (OC) during this phase. Instead, the majority of the material will be on circular orbits inside of Jupiter if the inner edge of the disk is well inside Jupiter's orbit. If the disk's inner edge is beyond Jupiter's orbit, most comets end up on orbits in exterior mean-motion resonances with Saturn when Uranus and Neptune are not present. In those cases where the outer edge of the disk is close to Saturn or Neptune, the fraction of material that ends up in the subsequently formed OC is much less than that found in Brasser et al. [Brasser, R., Duncan, M., Levison, H., 2006. Icarus 184, 59-82] for the same cluster densities. This implies that for comets of roughly 2 km in size, the presence of the primordial solar nebula hinders OC formation. A byproduct of some of our simulations are endresults with a substantial fraction of the comets in the Uranus-Neptune scattered disk. A subsequent followup of this material is planned for the near future. In order to determine the effect of the size of the comets on OC formation efficiency, a set of runs with the same initial conditions but different cometary radii have been performed as well, from which it is determined that the threshold comet size to begin producing significant Oort clouds is roughly 20 km. This implies that the presence of the primordial solar nebula acts as a size-sorting mechanism, with large bodies unaffected by the gas drag and ending up in the OC while small bodies remain trapped in the planetary region, in the models studied.     

W-shaped occultation signatures: Inference of entwined particle orbits in charged planetary ringlets

Observed W-shaped occultation signatures of certain narrow ringlets in the ring systems of Saturn and Uranus imply a concentration of material near their inner and outer radial edges. A model is proposed where edge bunching is a natural consequence of particles in entwined elliptical orbits, with the same particles alternately defining both edges. While such orbits cross over in radius, collisions would not occur if they have small inclinations, the same fixed argument of periapse ω, and other parameters whereby the particles would “fly in formation” along compressed helical paths relative to the core of the ringlet, which is taken to be a circle in the equatorial plane. For this model to match the observed ring thickness and ringlet widths, orbit inclinations i must be much smaller than their eccentricities e, which themselves would be very small compared to unity. Thus, the meridional cross section of the resultant torus would be a very thin ellipse of thickness proportional to i∣cos ω∣, tilted slightly from the equatorial plane by (i/e)∣sin ω∣ radians. However, gravitational perturbations due to the oblateness of the planet would cause a secular change in ω so that this cross section would collapse periodically to a tilted line, and collisions would then occur. If this collapse could be prevented, the torus could remain in a continuous state of nearly zero viscosity. Stabilization against collapse appears possible due to several remarkable characteristics that are added to the model when the particles are electrically charged. First, because of inherent features of the torus structure, a weak electric force could counter the key effect of the vastly larger oblateness force. Second, because the electric perturbation also affects i, there is a large region in ω,i space where stability against cross-sectional collapse is automatic. For this region, the thickness of the elliptical cross section would expand and contract in concert with the way that the major axis of the ellipse rocks back and forth relative to the equatorial plane. The period of these “rocking and breathing” changes would be from 1 to 3 weeks for a torus in the C ring of Saturn, for example. The electric effects could change considerably without driving the parameters of the torus from the stable domain where cross-sectional collapse does not occur. While specialized and in several important ways still incomplete, the proposed model could account for the W-shaped patterns and explain how very dense ringlets might endure without energy loss due to collisions. It also appears to be capable of explaining the observed sorting of particles by size within a ringlet. Several characteristics of the model suggest definitive tests of its applicability, including its prediction that a nonsymmetrical W-shaped occultation signature could be reversed a half orbit away, and that grazing solar illumination of tilted ringlets might cast shadows that change with time in a prescribed way.     

Saturn's nonaxisymmetric ring edges at 1.95 Rs and 2.27 Rs

The outer edges of Saturn's A and B rings, at 2.27 R_s and 1.95 R_s, have been examined using data acquired by four Voyager experiments. The shapes and kinematics of these features are influenced by their proximity to strong low-order Lindblad resonances. The data for the A-ring edge are consistent with a seven-loded radial distortion of amplitude 6.7 ± 1.5 km which rotates with the mass-weighted mean angular velocity of the coorbital satellite system. The B-ring edge has essentially a double-lobed figure of radial amplitude 74 ± 9 km which rotates with the mean motion of Mimas, though there is an indication that it is not completely described withe a simple Saturn-centered ellipse. An upper limit of 10 m has been placed on the vertical thickness in the unperturbed region of the B ring.     

Lava flooding of ancient planetary crusts: Geometry,thickness, and volumes of flooded lunar impact basins

Estimates of lava volumes on planetary surfaces provide important data on the lava flooding history and thermal evolution of a planet. Lack of information concerning the configuration of the topography prior to volcanic flooding requires the use of a variety of techniques to estimate lava thicknesses and volumes. A technique is described and developed which provides volume estimates by artificially flooding unflooded lunar topography characteristic of certain geological environments, and tracking the area covered, lava thicknesses, and lava volumes. Comparisons of map patterns of incompletely buried topography in these artificially flooded areas are then made to lava-flooded topography on the Moon in order to estimate the actual lava volumes.This technique is applied to two areas related to lunar impact basins; the relatively unflooded Orientale basin, and the Archimedes-Apennine Bench region of the Imbrium basin. Artificially flooding the Orientale basin to the Cordillera Mountains (outer basin ring) produces a lava fill geometry with two components; (a) thebasin interior (within the inner Rook ring) where the area covered is small but lava thicknesses are large (6–8 km), and (b) thebasin, edges where larger areas are covered but thicknesses are less, averaging about 2 km. Detailed examination of the Archimedes-Apennine Bench area (Imbrium basin edge) also shows average thicknesses in this region of basins of approximately 2 km.On the basis of these analyses it is concluded that early flooding of the basin interior places a major load on the lithosphere in the same geographic region where mascon gravity anomalies are concentrated. Mare ridges and arches are concentrated at the outer edge of the region of thickset fill and appear to be related to tectonic activity accompanying basin loading and downwarping. Lava thicknesses in most areas of flooded, impact basins (>2 km) exceed the thickness of lava where vertical mixing of underlying non-mare material is possible. Thus, vertical mixing is not likely to have been an important process in mare deposits within flooded impact basins. Thickness estimates derived from this technique exceed those derived from the morphometry of buried or partially buried craters by at least a factor of two. Examination of the assumptions employed in the latter technique show several sources of variability (e.g., initial rim height variability in a fresh crater) which may result in significant underestimation of lava thicknesses.     

Formation of neutral current sheet and loop coronal transients

An eruption of opposite magnetic flux into a bipolar background field is likely to lead to the formation of a natural current sheet between the new emerging field and the background. A numerical study is made on this process, based on the ideal MMD equations, taking into account the interaction between the magnetic field and the coronal plasma. The result shows that a subsonic eruption will give rise to a four region structure; 1) a cool and dense prominence made of the erupting material in the innermost region; 2) a cool and tenuous region further out; 3) a hot and dense loop formed by the concentration of both the erupting material and the coronal material in the neutral current sheet; and 4) a forerunner region outside the loop with density slightly above the background, due to fast magneto-acoustic waves. This structure agrees with the observed features of typical loop coronal transients. Therefore the eruption of opposite magnetic flux into a bipolar background is probably an important mechanism for triggering off such transients.     

Saturn's rings: II. Condensations of light and optical thickness of Cassini's division

“Condensations” of light have been observed when Saturn's rings are seen almost edge on, and the Sun and the Earth are on opposite sides of the ring plane. These condensations are associated with ring C and Cassini's division. If the relative brightness between the two condensations and the optical thickness of ring C are known, we can calculate the optical thickness of Cassini's division, τ_CASS. Using Barnard's and Sekiguchi's measurements, we have obtained 0.01 ? τ_CASS ? 0.05. A brightness profile of the condensations which agrees well with visual observations is also presented.We are able to set an upper limit of about 0.01 for the optical thickness of any hypothetical outer ring. This rules out a ring observed by C. Cragg in 1954, but does not eliminate the D′ ring observed by Feibelman in 1967.It is known that the outer edge of ring B is almost at the position of the 1/2 resonance with Mimas. Franklin, Colombo, and Cook explained this fact in 1971, postulating a total mass of ring B of 10^?6M_SATURN. We have derived a formula for the mass of the rings, which is a linear function of the mean particle size. We find that 10^?6M_SATURN implies large particles (～70m). If the particles are small (～10cm), as currently believed, the total mass of ring B is not enough to shift the outer edge. We conclude that the above explanation and current size estimates are inconsistent.     

Bending waves and the structure of Saturn's rings

The surface mass density profiles at four locations within Saturn's rings are calculated using Voyager spacecraft images of spiral bending waves. Bending waves are vertical corrugations in Saturn's rings which are excited at vertical resonances of a moon, e.g., Mimas, whose orbit is inclined with respect to the mean plane of the rings. Bending waves propagate toward Saturn by virtue of the rings' self-gravity; their wavelength depends on the local surface mass density of the rings. Observations of bending waves can thus be used to determine the surface density in regions of Saturn's rings near vertical resonances. The average surface density of the outer B ring near Mimas' 4:2 inner vertical resonance is 54 ± 10 g cm^?2. Surface density in this region probably varies by ～ 30% over radial length scales of tens of kilometers; and irregular radial structure is present on similar length scales in this region. Surface densities ranging from 24 g cm^?2 to 45 g cm^?2 are found in the A ring. Small scale variations in surface density are not seen in the A ring, consistent with its more uniform optical appearance.     

A 3D dynamical model of the colliding winds in binary systems

We present a three-dimensional (3D) dynamical model of the orbital-induced curvature of the wind–wind collision region in binary star systems. Momentum balance equations are used to determine the position and shape of the contact discontinuity between the stars, while further downstream the gas is assumed to behave ballistically. An Archimedean spiral structure is formed by the motion of the stars, with clear resemblance to high-resolution images of the so-called 'pinwheel nebulae'. A key advantage of this approach over grid or smoothed particle hydrodynamic models is its significantly reduced computational cost, while it also allows the study of the structure obtained in an eccentric orbit. The model is relevant to symbiotic systems and γ-ray binaries, as well as systems with O-type and Wolf–Rayet stars.
As an example application, we simulate the X-ray emission from hypothetical O+O and WR+O star binaries, and describe a method of ray tracing through the 3D spiral structure to account for absorption by the circumstellar material in the system. Such calculations may be easily adapted to study observations at wavelengths ranging from the radio to γ-ray.     

Formation of planetary systems by successive contractions of the solar nebula

The theory discussed in the present paper is a solar nebula-type theory which assumes the initial existence of a big disk-shaped gas cloud in rotational motion around the Sun. At the outer edge of the gas cloud there is a steady loss of angular momentum, which is mainly caused by the diffusion induced by turbulence and shock waves. This leads to the formation of a doughnutshaped gas ring at the edge of the cloud, outside of which there is plasma in a state of partial corotation. The gas ring is then slowly shifted towards the Sun, whereby the grains of solid matter within the gas cloud are also transported and collected within the gas torus. During the contraction process the following two situations arise: First, due to the small amount of friction, the angular momentum of the inner part of the ring rapidly exceeds that of the outer part. Second, the angle between the orbits of the inner and outer part of the gas ring increases gradually. When, during contraction, a certain distance is covered, the gas ring turns over, i.e. there is a sudden interchange of the inner and outer parts of the gas ring, where two adjacent rings of solid matter (jet streams) are formed. Immediately after the turn-over process the speed of contraction is at first drastically reduced, but then the gas ring is shifted once more towards the Sun. This process is then repeated periodically. The planets originate from the outer rings of solid matter, which contain much more matter than their adjacent inner rings. The inclination between the inner and outer rings is roughly 5°. In particular, Mercury, the Moon, Titan as well as Triton result from the innermost rings of matter. Having gone through the formation process, most of the planets acquire a rotating gas disk out of which the regular satellites are also created by the same periodic contraction process (hetegonic principle). This theory is the first that can explain all noteworthy facts about our planetary system and the satellite systems in a qualitative yet conclusive way.     

Application of the Gauss' Method to the Stellar Three Body Problem

In this paper, we deal with the stellar three body problem, that is one star is far away from the other two stars. The outer orbit is assumed to be Keplerian. To analyze the effect of the distant star on the orbit of the close stars, we use the Gauss method; this method consist in replacing the gravitational attraction of the third star by the gravitational attraction of an infinitesimal non-homogeneous elliptic ring. We obtain the force vector for the Gauss method in terms of elliptic integrals. Finally we compare the results obtained by this model with the classical third body model. This revised version was published online in August 2006 with corrections to the Cover Date.