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We numerically investigate how an asteroid's elongation controls the sensitivity of its surface to tidal effects during a distant planetary encounter beyond the Roche limit. We analyze the surface slope and its variation by considering the shape elongation, as well as the spin period and orbital conditions. A more elongated asteroid tends to have a higher slope variation, while there may not be a monotonic increase of the total area having such a variation, 12 pages, 1 figures, to be published in Icarus

The Moon migrated to $r_{\leftmoon}\simeq3.8\times10^{10}$ cm over a characteristic time $r/v=10^{10}$ Gyr by tidal interaction with the Earth's oceans at a present velocity of $v=3.8$ cm yr$^{-1}$. We derive scaling of global dissipation that covers the entire history over the past 4.52 Gyr. Off-resonance tidal interactions at relatively short tidal periods in the past reveal the need for scaling {with amplitude}. The global properties of the complex spatio-temporal dynamics and dissipation in broad spectrum ocean waves is modeled by damping $\epsilon = h F/(2Q_0)$, where $h$ is the tidal wave amplitude, $F$ is the tidal frequency, and $Q_0$ is the $Q$-factor at the present time. It satisfies $Q_0\simeq 14$ for consistency of migration time and age of the Moon consistent with observations for a near-resonance state today. It shows a startingly fast eviction of the Moon from an unstable near-synchronous orbit close to the Roche limit, probably in a protolunar disk. Rapid spin down of the Earth from an intial $\sim30\%$ of break-up by the Moon favored early formation of a clement global climate. Our theory suggests moons may be similarly advantageous to potentially habitable exoplanets., Comment: 8 pages, 5 figures

Regions of Hill stability were determined using the full three-body theory for the planetary candidates that were found by the Kepler mission to lie in the Habitable Zone of the host star with radii larger than 3 Earth radii. The values obtained give a more accurate assessment of the sphere of influence of a planet than does the Hill radius using the restricted three-body expression. The values given by the two estimates for circular orbits are compared. The variation in the full three-body Hill regions were examined for a variety of possible moon masses and orbital eccentricities and inclinations. It was found that the critical moon planet separation decreased with increased moon orbital eccentricity and inclination but to a far greater extent when the planetary orbital eccentricity increased suggesting they would lie inside the Roche limit and are unlikely to have formed or exist now. The angular separation of the moon and planet and the radial velocity amplitudes of the planets likely to be observed are also affected. This is important for future observations and missions. It was also found that the giant planets in the habitable zone lie in a narrow band that can be fitted by a linear regression relation between log10(Planet luminosity) and log10 (Planet temperature) with a slope of 3.34.

We address the thermal history of the Earth after the Moon-forming impact, taking tidal heating and thermal blanketing by the atmosphere into account. The atmosphere sets an upper bound of ~100 W/m^2 on how quickly the Earth can cool. The liquid magma ocean cools over 2-10 Myrs, with longer times corresponding to high angular-momentum events. Tidal heating is focused mostly in mantle materials that are just beginning to freeze. The atmosphere's control over cooling sets up a negative feedback between viscosity-dependent tidal heating and temperature-dependent viscosity of the magma ocean. While the feedback holds, evolution of the Moon's orbit is limited by the modest radiative cooling rate of Earth's atmosphere. Orbital evolution is orders of magnitude slower than in conventional constant Q models, which promotes capture by resonances. The evection resonance is encountered early, when the Earth is molten. Capture by the evection resonance appears certain but unlikely to generate much eccentricity because it is encountered early when the Earth is molten and Q_Earth >> Q_Moon. Tidal dissipation in the Earth becomes more efficient (Q_Earth << Q_Moon) later when the Moon is between ~20 R_Earth and ~40 R_Earth. If lunar eccentricity grew great, this was when it did so, perhaps setting the table for some other process to leave its mark on the inclination of the Moon., 34 pages, 10 figures, preprint format

We reconsider two scenarios for the formation of Phobos and Deimos from a circum-martian accretion disk of debris: the strong tide regime for which accretion occurs close to the planet at the Roche limit and the weak tide regime for which accretion occurs farther from the planet. We assume a disk with an initial mass of 10 18 kg (Craddock, R.A. [2011]. Icarus 211, 1150–1161). In the strong tide regime, the disk loses its material by viscous spreading inward to and outward from the planet. When outward moving material crosses the Roche limit, small-sized moonlets are accreted from gravitational instabilities with a shape and density similar to Phobos and Deimos. Due to the gravitational torque exerted by the disk, the moonlets migrate away from the planet, though they cannot reach the synchronous orbit (lying at 6 Mars’ radii). After the disk has lost most of its mass they rapidly fall back onto Mars due to the tidal decay of their orbits. Although, the total mass of moonlets is comparable to the mass of Phobos, their survival time does not exceed 200 Ma, which is incompatible with the formation of Phobos and Deimos early in Mars’ history. In the weak tide regime, moonlets can accrete near the synchronous orbit with the mass of Deimos in a disk of up to 10 18 kg (similarly to planetary embryos formation in the protoplanetary disk). A Phobos-mass embryo can also be formed in the same disk but closer to Mars (at 3–4 Mars’ radii) so that it rapidly falls back onto Mars by tidal decay of its orbit. However, several embryos may accrete together in the disk (similarly to the final stage of terrestrial planet formation), and Phobos and Deimos may be the last two remnants of those bodies formed near the synchronous distance to Mars. Further investigations are still needed to understand such accretion mechanism within a circum-martian disk primarily extending below the synchronous orbit.

Despite many efforts an adequate theory describing the origin of Phobos and Deimos has not been realized. In recent years a number of separate observations suggest the possibility that the martian satellites may have been the result of giant impact. Similar to the Earth–Moon system, Mars has too much angular momentum. A planetesimal with 0.02 Mars masses must have collided with that planet early in its history in order for Mars to spin at its current rate (Dones, L., Tremaine, S. [1993]. Science 259, 350–354). Although subject to considerable error, current crater-scaling laws and an analysis of the largest known impact basins on the martian surface suggest that this planetesimal could have formed either the proposed 10,600 by 8500-km-diameter Borealis basin, the 4970-km-diameter Elysium basin, the 4500km-diameter Daedalia basin or, alternatively, some other basin that is no longer identifiable. It is also probable that this object impacted Mars at a velocity great enough to vaporize rock (>7 km/s), which is necessary to place large amounts of material into orbit. If material vaporized from the collision with the Mars-spinning planetesimal were placed into orbit, an accretion disk would have resulted. It is possible that as material condensed and dissipated beyond the Roche limit forming small, low-mass satellites due to gravity instabilities within the disk. Once the accretion disk dissipated, tidal forces and libration would have pulled these satellites back down toward the martian surface. In this scenario, Phobos and Deimos would have been among the first two satellites to form, and Deimos the only satellite formed—and preserved—beyond synchronous rotation. The low mass of Phobos and Deimos is explained by the possibility that they are composed of loosely aggregated material from the accretion disk, which also implies that they do not contain any volatile elements. Their orbital eccentricity and inclination, which are the most difficult parameters to explain easily with the various capture scenarios, are the natural result of accretion from a circum-planetary disk.

Many new small moons of the giant planets have been discovered recently. In parallel, satellites of several asteroids, e.g., Ida, have been found. Strikingly, a majority of these new-found planetary moons are estimated to have very low densities, which, along with their hypothesized accretionary origins, suggests a rubble internal structure. This, coupled to the fact that many asteroids are also thought to be particle aggregates held together principally by self-gravity, motivates the present investigation into the possible ellipsoidal shapes that a rubble-pile satellite may achieve as it orbits an aspherical primary. Conversely, knowledge of the shape will constrain the granular aggregate's orbit—the closer it gets to a primary, both primary's tidal effect and the satellite's spin are greater. We will assume that the primary body is sufficiently massive so as not to be influenced by the satellite. However, we will incorporate the primary's possible ellipsoidal shape, e.g., flattening at its poles in the case of a planet, and the proloidal shape of asteroids. In this, the present investigation is an extension of the first classical Darwin problem to granular aggregates. General equations defining an ellipsoidal rubble pile's equilibrium about an ellipsoidal primary are developed. They are then utilized to scrutinize the possible granular nature of small inner moons of the giant planets. It is found that most satellites satisfy constraints necessary to exist as equilibrated granular aggregates. Objects like Naiad, Metis and Adrastea appear to violate these limits, but in doing so, provide clues to their internal density and/or structure. We also recover the Roche limit for a granular satellite of a spherical primary, and employ it to study the martian satellites, Phobos and Deimos, as well as to make contact with earlier work of Davidsson [Davidsson, B., 2001. Icarus 149, 375–383]. The satellite's interior will be modeled as a rigid-plastic, cohesion-less material with a Drucker–Prager yield criterion. This rheology is a reasonable first model for rubble piles. We will employ an approximate volume-averaging procedure that is based on the classical method of moments, and is an extension of the virial method [Chandrasekhar, S., 1969. Ellipsoidal Figures of Equilibrium. Yale Univ. Press, New Haven] to granular solid bodies.

Photometric data on 17 binary near-Earth asteroids (15 of them are certain detections, two are probables) were analysed and characteristic properties of the near-Earth asteroid (NEA) binary population were inferred. We have found that binary systems with a secondary-to-primary mean diameter ratio D s / D p ⩾ 0.18 concentrate among NEAs smaller than 2 km in diameter; the abundance of such binaries decreases significantly among larger NEAs. Secondaries show an upper size limit of D s = 0.5 – 1 km . Systems with D s / D p ⩽ 0.5 are abundant but larger satellites are significantly less common. Primaries have spheroidal shapes and they rotate rapidly, with periods concentrating between 2.2 to 2.8 h and with a tail of the distribution up to ∼4 h. The fast rotators are close to the critical spin for rubble piles with bulk densities about 2 g/cm3. Orbital periods show an apparent cut-off at P orb ∼ 11 h ; closer systems with shorter orbital periods have not been discovered, which is consistent with the Roche limit for strengthless bodies. Secondaries are more elongated on average than primaries. Most, but not all, of their rotations appear to be synchronized with the orbital motion; nonsynchronous secondary rotations may occur especially among wider systems with P orb > 20 h. The specific total angular momentum of most of the binary systems is similar to within ±20% and close to the angular momentum of a sphere with the same total mass and density, rotating at the disruption limit; this suggests that the binaries were created by mechanism(s) related to rotation near the critical limit and that they neither gained nor lost significant amounts of angular momentum during or since formation. A comparison with six small asynchronous binaries detected in the main belt of asteroids suggests that the population extends beyond the region of terrestrial planets, but with characteristics shifted to larger sizes and longer periods. The estimated mean proportion of binaries with D s / D p ⩾ 0.18 among NEAs larger than 0.3 km is 15 ± 4 % . Among fastest rotating NEAs larger than 0.3 km with periods between 2.2 and 2.8 h, the mean proportion of such binaries is (66+10−12)%.

The plasma density gradients in the outer drift shells of the plasmasphere are generally stable with respect to convective instability during quiet geomagnetic–geoelectric conditions. When the IMF turns southward before the onset of a magnetic substorm, this situation gradually changes: the magnetospheric convection electric field is then enhanced and penetrates deeper in the nightside plasmasphere. The sunward and eastward magnetospheric convection velocity is enhanced in the post-midnight local time sector at L>4, and occasionally down to L=2.5. As a result of this enhancement of the azimuthal component of the convection velocity, centrifugal effects are augmented in the distant region of the magnetosphere; the field-aligned potential energy of ions and electrons is reduced along the equatorial portion of magnetic field lines; the field-aligned plasma density distribution, initially in mechanical equilibrium, is accelerated and becomes convectively unstable. As a consequence, a field-aligned polar-wind-like flow of H+-ions (and He+-ions) is driven upward and the mid-latitude ionosphere gets depleted of its light ions. The plasma density at high altitudes diminishes in all flux tubes whose angular speed has been enhanced. It does not change significantly, however, on lower L-shells where the convection velocity has not changed. As a result of the shear in the upward ionization flow, a “knee” develops in the cross-L plasma density distribution along the drift shell which is tangent to a surface which has been called the Roche limit surface or zero-parallel-force surface. As a result of Coulomb collisions and wave–particle interaction, the upflowing particles that are able to overcome the reduced potential barrier may become trapped, and will tend to accumulate in the equatorial potential well beyond this zero-parallel-force surface. But, quasi-interchange — a type of ballooning instability driven by gravitational force or centrifugal effects — prevents this accumulation from taking place; it detaches from the plasmasphere any equatorial plasma cloud of trapped ions and electrons with negative gradients of the density and kinetic pressure beyond the Roche limit surface. The detached plasma is driven away from the unperturbed plasmasphere by quasi-interchange motion and by ballooning instability.

New expressions for the Roche limit for solid biaxial ellipsoids are derived, taking the size, shape, density, material strength, and rotational period of the object into account. It is shown that the shape has a significant effect on the tidal splitting distance, so that spherical bodies are more stable than oblate spheroids, which in turn are more stable than prolate spheroids. New expressions for the critical rotational breakup period (for objects in free space) are derived, and are used to put constraints on the density and material strength of a collection of comets, for which size, shape, and period have been estimated. This investigation shows that the notion of very low cometary material strengths (≲100 Pa) is consistent with observational data.

We investigate the evolution of a circumterrestrial disk of debris generated by a giant impact on Earth and the dynamical characteristics of the moon accreted from the disk by using high-resolution N -body simulation. We find that in most cases the disk evolution results in the formation of a single large moon on a nearly circular orbit close to the equatorial plane of the initial disk just outside the Roche limit, which is consistent with the previous work by S. Ida et al. (1997, Nature 389 , 353–357). The efficiency of incorporation of disk material into a moon is 10–55%, which increases with the initial specific angular momentum of the disk. These results hardly depend on the initial condition of the disk as long as the mass of the disk is 2 to 4 times the present lunar mass and most mass of the disk exists inside the Roche limit. The timescale of the disk evolution is determined mainly by the surface density of the disk because mass transfer to the outside of the Roche limit and formation of lunar seeds are regulated by collective behavior of disk particles. The evolution of the disk is summarized as follows: The disk contracts through collisional damping. As the velocity dispersion of disk particles decreases, particle clumps grow inside the Roche limit. The clumps become elongated due to Keplerian shear, which forms spiral arm-like structure. Particles are transfered to the outside of the Roche limit through the gravitational torque exerted by the spiral arms. When a tip of a spiral arm goes beyond the Roche limit, it collapses into a small moonlet. The rapid accretion of these small moonlets forms a lunar seed. The seed exclusively grows by sweeping up particles transfered over the Roche limit. When the moon becomes large enough to gravitationally dominate the disk, it pushes the rest of the inner disk to Earth. The formation timescale of the moon is of the order of 1 month if a particulate disk is assumed and the effect of melting/vaporization is not included.

A number of new expressions for the Roche limit are derived in order to investigate the splitting behavior of cometary nuclei when passing close to massive bodies. These expressions handle both ten ...

We present the first published numerical calculations of accretion of an impact-generated protolunar disk into a single large Moon. Our calculations are based on the model developed by R. M. Canup and L. W. Esposito ( Icarus 113, 331–352, 1995) to describe accretion in the Roche zones around the giant planets. Previous numerical simulations of a large impact event predict the formation of a disk of material centered near or within the Roche limit (∼2.9 R ⊕ ). A natural expectation based on our previous results and comparison with the satellite systems of the outer planets would be for multiple small moons to arise from such a protolunar disk. Multiple moonlets could accrete to form a single Moon if they evolved into crossing orbits due to tidal interaction with the Earth. This would occur if the innermost moonlet in the disk were also the most massive, so that it evolved outward at the relatively fastest rate and swept up all exterior material. Our calculations, which include both moonlet accretion and orbital evolution, demonstrate that forming massive moonlets in the inner disk near the Roche limit is extremely difficult. We conclude that an Earth system with multiple moons is the final result unless some particularly severe constraints on initial conditions in the disk are met. A disk with a lunar mass of material exterior to a ∼ 3.5–4 R ⊕ or an extremely steep radial surface density profile at the onset of collisional growth is required for a single, lunar-sized body to result from accretion of silicate density material in a protolunar disk. The former corresponds most closely to disks produced by impactors with nearly twice the mass of Mars and about twice the angular momentum of the current Earth/Moon system. Other processes, such as gravitational instability or primary accretion of an iron core in the inner disk, might be able to “seed” accretional growth and allow for the formation of a single Moon if disk temperature and compositional requirements are met. Our analysis demonstrates the need for more detailed, higher resolution impact simulations.

The Voyager spacecraft discovered that small moons orbit within all four observed ring systems coincident with the discovery of narrow and dusty rings around Jupiter, Saturn, Uranus and Neptune. These moons can provide the source for new rings if they are catastrophically disrupted by a comet or large meteoroid impact. This hypothesis for ring origins provides a natural mechanism for the ongoing creation of planetary rings. While it relieves somewhat the problem of explaining the continued existence of rings with apparently short evolutionary lifetimes, it raises the problem of explaining the continued existence of small moons, and the coexistence of moons and rings at comparable locations within the Roche zones of the giant planets. This problem has been studied in some detail recently, and the present work is a review of our current understanding of the processes in satellite disruption that pertain to the creation of planetary rings and the collisional cascade of circumplanetary bodies. Significant progress has been made. Narrow rings are produced by disruption of small moons in numerical simulations, and a self-consistent model of the collisional cascade can explain present-day moon populations. Absolute timescales and initial moon populations remain uncertain due to our poor knowledge of the impactor population and uncertainties in the strength of planetary satellites. More pressing are the qualitative issues that remain to be resolved including the nature of reaccretion of the debris and the origin of Saturn's rings.

The apparent tidal disruption of Periodic Comet Shoemaker-Levy 9 (1993e) during a close encounter within approximately 1.62 planetary radii of Jupiter can be used along with theoretical models of tidal disruption to place an upper bound on the density of the predisruption body. Depending on the theoretical model used, these upper bounds range from rho(sub c) less than 0.702 +/- 0.080 g/cu cm for a simple analytical model calibrated by numerical smoothed particle hydrodynamics (SPH) simulations to rho(sub c) less than 1.50 +/- 0.17 g/cu cm for a detailed semianalytical model. The quoted uncertainties stem from an assumed uncertainty in the perijove radius. However, the uncertainty introduced by the different theoretical models is the major source of error; this uncertainty could be eliminated by future SPH simulations specialized to cometary disruptions, including the effects of initially prolate, spinning comets. If the SPH-based upper bound turns out to be most appropriate, it would be consistent with the predisruption body being a comet with a relatively low density and porous structure, as has been asserted previously based on observations of cometary outgassing. Regardless of which upper bound is preferable, the models all agree that the predisruption body could not have been a relatively high-density body, such as an asteroid with rho approximately = 2 g/cu cm.

An evaluation is conducted of the possibility that the tidal disruption of a population of contact binary asteroids can account for terrestrial-impact 'doublet' craters. Detailed orbital integrations indicate that while such asteroids are often disrupted by tidal forces outside the Roche limit, the magnitude of the resulting separations is too small to account for the observed doublet craters. It is hypothesized that an initial population of km-scale earth-crossing objects encompassing 10-20 percent binaries must be responsible for doublet impacts, as may be verified by future observations of earth-approaching asteroids.

Gravitational torques and erosion by micrometeoroids may cause rapid evolution of Saturn's rings, possibly suggesting formation of the rings within the last 108 years. Optically thin and/or narrow rings at Jupiter, Uranus, and Neptune may form repeatedly by disruption of inner satellites. However, present-day creation of Saturn's more massive rings in this way is unlikely. An alternative scenario for ring origin is tidal disruption of a large comet, such as Chiron, passing within Saturn's Roche radius. Subsequent collisions among the fragments lead to a flat, equatorial ring, while collisions with inner satellites produce a Population II-like set of craters on the moons. Assuming a nominal flux of Saturn-crossing bodies, 10–100 close passages occur in 4.5 Gyr. Most close passages leave no bound debris, so that approximately one ring capture event occurs in the age of the solar system. This rate is comparable to the expected frequency of disruption of ring parent satellites by cometary bombardment. These results imply that the rings result from a recent unlikely tidal or collisional event, or that the arguments for rapid evolution of Saturn's rings are erroneous and the rings are primordial. However, the flux of Saturn-crossers is highly uncertain; if the flux is much higher, the rings are probably the recent result of tidal disruption. Ongoing searches for outer Solar System planetesimals and future data from Cassini will help determine the rings' age and origin.

In view of previous efforts' demonstration that strongly dissipative planetesimals are immune to tidal disruption, an examination is presently conducted of the complementary case of inviscid planetesimals arising from collisions that are sufficiently energetic to entirely melt the resulting planetesimal and debris. The tidal disruption is numerically simulated by means of the smoothed particle hydrodynamics (SPH) code of Cameron and Benz (1991), concentrating on the tidal disruption of 0.01 earth-mass planetesimals passing by the earth with variations in the impact parameter at perigee and velocity at infinity. The SPH models show that tidal forces during a close encounter can efficiently convert orbital angular momentum into spin angular momentum, thereby initiating equatorial mass-shedding to inviscid planetesimals that have been spun up beyond the limit of rotational stability.

We use the Wilson-Devinney program to solve anew the light and radial velocity curve of WX Cnc, confirming it to be a detached binary. By adding a spot to the surface of the secondary star, the asymmetry in the light curve revealed in the new solution is satisfactorily explained. The new solution shows the secondary to be a G4V star and not a G8V star, as previously thought. The absolute parameters are given in TABLE 2. Both stars show evolution in the main sequence.

We carried out a statistical study of 107 semi-detached with combined light curve solutions. 1. We derived an empirical period-dependent mass-radius relation, thereby revealing the impossibility of having evolved semi-detached systems with very short periods. 2. Statistically, the near-contact semi-detached systems have the common properties of nearly equal mass densities of the components, larger mass-ratios, shorter periods and smaller specific angular momenta and their A- F-type secondaries generally have greater densities than the secondaries of classical Algol systems of the same spectral types. A detailed discussion is also made in this paper on the evolution of near-contact semi-detached binaries.

The discovery of the strong Galactic X-ray sources (Giacconi et al., 1962; Giacconi, 1974; Gursky and Schreier, 1975) and the suggestion that these sources may be powered by accretion onto a compact object orbiting a ‘normal’ stellar companion (Hayakawa and Matsouko, 1964; Zel'dovich and Guseynov, 1965) has, over the past twenty years or so, led to renewed interest in the processes of mass transfer and accretion in close binary stars.

We present a model of the self-regulating growth of a single protoplanet in the planetesimal disk. Acceration of disk material onto the protoplanet is driven by the protoplanet's gravitational perturbations and the trapping of planetesimals within its Roche lobe, due to protoplanet's extended primordial atmosphere and/or protosatellite disk. We formulate and solve the explicitly time-dependent equations of planet growth. The most distinctive features of the analytical model, which also find the confirmation in our direct numerical simulations of protoplanet growth, are the division of the accretion process into two phases (the first corresponding to initial self-accelerating disk destructions, and the second phase of subsequent accretion slow-down or stopping due to slow increase of Roche lobe radius with planet's mass) and the short time scales of growth (≲104 orbital periods, independent of disk characteristics). The mass of the protoplanet at the moment of transition between the above two phases of accretion is proportional to σ 3 2 R 3 , where σ is the local disk surface density and R is the heliocentric distanced. For the Solar System planets the end of the early runaway embryo growth occurs after 0.3–0.6 of the present radius of the planet (or planet's core) is achieved. By applying the model to the problem of gas accretion onto the core of Jupiter we predict the substantial reduction of the accretion rate after it achieves about one-half of its present mass, which takes only several hundreds of orbital periods. As intermediate results, we present among others the geometry of Hill-stable disk regions near the protoplanet and the numerical determination of time scales for the clearing of a gap out to 2·3 1 2 Roche lobe radii around the fixed mass protoplanet.

The plasmapause position is determined by the innermost equipotential surface which is tangent to the ‘Roche-Limit’ surface of the ionospheric plasma filling the magnetosphere. When the thermal particles corotate with the Earth's angular velocity, the ‘Roche-Limit’ equatorial distance is L c =5.78 [ R E ]. When the angular convection velocity is evaluated from the quiet time electric field distribution E3 of McIIwain (1972), L c depends on the local time. Its minimum value is then L C =4.5Near 2400 LT, and the plasmapause shape and position satisfactorily fit the observations. The diffusive equilibrium dnesity distribution appropriated inside the plasmasphere, becomes convectively unstable beyond L = L c , where the collisions type of model satisfactorily represents the observations. In the intermediate region between the plasmapause and the last closed magnetic field line, contimues ionization fluxes are expected to flow out of the midlatitude ionosphere

A satellite formation model is extended to include evolution of planetary ring material and elliptic orbital motion. In this model the formation of the moon begins at a later time in the growth of the earth, and a significant fraction of the lunar material is processed through a circumterrestrial debris cloud where volatiles might have been lost. Thus, the chemical differences between the earth and moon are more plausibly accounted for. Satellites of the outer planets probably formed in large numbers throughout the growth of those planets. Because of rapid inward evolution of the orbits of small satellites, the present satellite systems represent only satellites formed in the last few percent of the growths of their primaries. The rings of Saturn and Uranus are most plausibly explained as the debris of satellites disrupted within the Roche limit. Because such a ring would collapse onto the planet in the course of any significant further accretion by the planet, the rings must have formed very near or even after the conclusion of accretion.

An improved model of the Saturn magnetosphere and of the locations of known moons and rings is invoked in the present reconsideration of Pioneer 11 observations of five abrupt depletions in the flux of trapped magnetospheric electrons within a 2000-km-wide band around the F ring. It is inferred that the observed depletions of charged particles are caused by clumps of material with low optical depth; it is further hypothesized that these clumps are composed of regolith ejecta, are generated by collisions occurring within a belt of unseen, moonlet-scale (or smaller) objects occupying the entire radial region between Pandora and Prometheus. Attention is given to a self-consistent scenario in which these debris clouds are created, longitudinally spread, swept up onto belt object surfaces, and then thrown off by a subsequent collision.

It is shown how it is possible to explain the low abundance of iron and siderophiles in the Moon in a natural way. This is done by an extension of Opik's mechanism, whereby one or more planetoids pass through Earth's Roche zone, are broken up, and have part of their material captured. Assuming the planetoids are differentiated, the iron core can easily escape capture. This process does not involve any dissipation mechanisms and goes a long way toward explaining the peculiar bulk composition of the Moon. The picture is consistent with that of Urey, in which the early solar system contained more (and smaller) planets than it does today. In the second part of the paper, dynamical considerations are applied for two models, and it is shown that capture from one (or a few) planetoids is quite feasible, whereas a large number of contributors is highly unlikely.

Considerations related to the angular momentum of the earth-moon system have led Ward and Cameron (1978) to the suggestion of a collisional origin of the moon. The required projectile would be about the mass of Mars (i.e., about 0.1 earth masses). The possibility has been considered that both the proto-earth and the projectile would be remnants of the formation of giant gaseous protoplanets. Processes of lunar formation studied take into account the viscous dissipation of an accretion disk. The present paper is concerned with the formation of the prelunar accretion disk. The hydrodynamics of a compressible viscous gas are simulated with the aid of the particle-in-cell method. The obtained results imply that the projectile is in an elliptical earth-crossing orbit.

The model of this object as a masssive eclipsing binary system with titled “precessing “ (slaved ) accretion disk surrounding tivistic object has been proposed by Van den Heuvel et al. 1980, Cherepaschuckuk 1981,.This model has been confirmed by recent X—ray observations of 99 433 which indicate partial X—ray eclipses in SS 433 and moving “blue “ X—ray line Fe XXV at 6.7 key (Stewart et al. 1987,Watson et al.,1986.)Now it is proved thaat emission line He II 4686 is formed irs the accretion click and correctness of the determination of the mass function (Crampton and Hutchings, 1981) . i.;: ~ “~“ ‘ =

In the Jupiter-Saturn region of the nebular disk, grains accumulated to form planetary cores. When the masses of planetary cores increased to the order of 10 25 grams, they started to accrete gas, and around the cores were gradually formed flat rotating gaseous envelopes. When grains and small ice particles entered the gaseous envelopes, the bulk fell into the cores, but a small part had the e , i values of their orbits decreased because of gas drag, and formed around the cores very flat planetesimal disks, from which regular satellites were later formed. The gaseous envelopes finally collapsed to become the intermediate layers and the outer layers of Jupiter and Saturn. Owing to the increase in the masses of central bodies, the orbits of the regular satellites contracted to a fraction of their original dimensions, the satellite nearest Saturn fell inside the Roche Limit, and broke up to form the rings of Saturn. No gaseous envelope was formed around Uranus. A residual large planetesimal with about 5% of Uranus' mass collided with Uranus, causing Uranus to rotate in its present peculiar fashion, and also causing the ejection of large amounts of matter. Part of this matter revolved around Uranus in its equatorial plane, cooled and condensed rather rapidly, formed the five satellites and the ring system which has recently been discovered.

Starting from the concept of vibrational stability, the Roche limit for a uniform incompressible liquid sphere is derived. It is shown how this method can be generalized to the case where there is a non-uniform matter distribution in the radial direction.

Harris (1975) has suggested that the maximum size of particles in a planetary ring is controlled by collisional fragmentation rather than 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 the Roche 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 about 100 km but with most of the cross section in centimeter-scale particles.

We made observations of SS433 covering the entire primary optical minimum phase in the binary period X-ray astronomy satellite Ginga. The light curve obtained by the present observations revealed ingress and egress of the compact X-ray source. If the duration of the eclipse is due to occultation of the blue jet by the normal companion star, we can determine the radius of the companion star to be about 60% of the binary spearation. Assuming the companion star to be filling its Roche lobe, the ratio of the mass of the compact object to that of the companion star is found to be 0.1. Combined with the previous results from optical spectroscopy, the mass of the compact object in SS433 is determined to be 1–2 M⊙.

Periodic variations of the X- and gamma-ray flux from Geminga are interpreted as being caused by an orbital motion in a close binary system consisting of a degenerate dwarf and a black hole. The dwarf is supposed to fill its Roche lobe. The observed period P≃60 s fits the model and fixes the mass of the dwarf on Md = = 0,6 M⊙. Gravitational radiation together with the mass transfer explain observed increase of the period, the total mass of the system M = 5M⊙ being determined by the value of P. The energy flux in gravitational waves with = 130 Hz is ∼ 5.10−3 erg s−1 cm−2 at a distance of 100 pc which is seven orders of magnitude greater than from any other known stationary source. Gamma-ray sources similar to Geminga must have periods from several minutes to several hours. Poor photon statistics makes it difficult to obtain a reliable value of P from gamma-observations. The identification of gamma- and associated X-ray sources may be improved by better localization of the formers.

A self-consistent numerical model is developed for the tidal disruption of a solid planetesimal. The planetesimal is treated as a highly viscous, slightly compressible fluid whose disturbed parts are an inviscid, pressureless fluid undergoing distortion and disruption. The distortions were constrained to being symmetrical above and below the equatorial plane. The tidal potential is expanded in terms of Legendre polynomials, which eliminates the center of mass acceleration effects, permitting definition of equations of motion in a noninertial frame. Consideration is given to viscous dissipation and to characteristics of the solid-atmosphere boundary. The model is applied to sample cases in one, two and three dimensions.

A study of the dynamics of nearby debris from impact craters was made to explain the distinctive features seen on Phobos, Deimis, and Amalthea. The planetary tides and satellite rotation were considered, and the usual pseudo-energy (Jacobi) integral was numerically calculated in the framework of a restricted body problem where satellites are modelled as triaxial ellipsoids rather than point masses. Iso-contours of this integral show that Deimos and Amalthea are entirely closed by Roche lobes, and the surfaces of their model ellipsoids lie nearly along equipotentials. Presently, the surface of Phobos overflows its Roche lobe, except for regions within a few km of the sub-Mars and anti-Mars points. The behavior of crater ejecta from the satellites of Mars were also examined by numerical integration of trajectories for particles leaving their surfaces in the equatorial plane.

The 1978 photoeletric observations of the late type close binary RZ Dra were reanalyzed with the Wilson and Devinney approach. Photometric parameters were determined (in Tab. 1.). The system is found to be semi-detached where the less massive component fills its Roche surface, whereas the other component almost does so. The configuration of the system is shown in Fig. 1. The absolute dimensions of the system are found to be M1 = 0.61M⊙, M 2 = 0.41 M ⊙ R 1 = 1.15 R , and R 2 = 0.96 R ⊙ . Both components appear to be overluminous and oversized for their masses and spectral types. Its evolutionary stage is also discussed. The variability in the brightness of the primary mlnimum(Fig. 4) indicates mass loss from the vicinity of L2, which would be mainly responsible for the long-term decrease in its period.

Some sixty years ago, G.K. Gilbert wrote a remarkable paper on the structure and origin of the Moon's surface, and subsequent students of the subject with various scientific backgrounds have come to similar conclusions, often without knowing of the previous work. Gilbert's ideas and those of other investigators are reviewed and some new points are added. It is contended that the Moon was formed at predominantly low temperatures, that the face of the Moon was fashioned mostly at the terminal stage of its formation and during a period of 105 years or less, that it was always at a distance substantially greater than the Roche limit, and that the craters, mountains, and maria are mostly the result of collisions of satellites of the Earth-Moon system with its surface.

Fundamental equations are derived for the secular changes of the elliptic orbit of a satellite under the action of tidal friction. We restrict ourselves to the two-body problem and consider radial tides and “weak” tidal friction. Equations are developed to account for temporal changes of the moment of inertia of the planet caused by changes in the structure and size of its core. The eccentricity of the Moon's orbit at 10 Earth radii is numerically calculated; it depends on two quantities, n and βm, accounting, respectively, for changes of core dimensions and for the rate of dissipation in the interior of the Moon. Especially for the cases n = 1 (no changes in the core) and n = 1.125 (relatively large changes), the fundamental equations are integrated with the aid of a computer for a set of selected values of βm. In all cases an increase of e towards 1 results within less than 5 × 103 years. Furthermore, it is shown that shorter distances of the perigee than 1.4–1.6 R do not occur regardless of the values of n and βm. The maximum energy dissipation in the body of the Moon results for βm ≈ 10−30, increasing the lunar temperature by more than 103°K. The Moon entered the Roche limit for some years, but in all cases it did so only for extremely short times; therefore a complete disruption could not have occured. The limits of the possible values of βm permit one to conclude that the ratio of the relaxation times τMoon/τEarth should have been about 10−1 to 10−2. The value of τMoon has been restricted to 0.5−10 sec. This small value is regarded as a hint of a relatively “hot” Moon at the time of its capture. The capture of the Moon by the Earth is investigated, supposing that dissipation takes place only in the body of the Moon by radial tides. An expression for the total amount of dissipation ΔEB is given: ΔE B ∼ l −15 2 , where l is the distance of the perigee. From this follows an upper limit of 1km/sec for the velocity νt8 of the Moon relative to the Earth before its capture by tidal friction. In a simplified discussion of statistics of near encounters between a planetoid and the Earth, an expression is derived for the mean “encounter time” TC depending on the ratios of the masses M⊙/M, of the velocities ν∞/νEarth = N, and on the angle 2θ between the asymptotes of the hyperbola of the original orbit of this planetoid relative to the Earth. Within this time TC occurs—in a statistical average—at least one encounter resulting in a deflection of the planetoid of more than δ = 180° − 2θ. We find that a planetoid with a relative velocity ν∞ = 1 km/sec could resolve around the Sun in an independent orbit no longer than 106 years at most. After this time it would collide with the Earth or be captured. To clear this discrepancy, the development of masses being created in the asteroidal belt at any time is investigated. Agreement with the derived time scale can be achieved only if the formation of masses in suvh orbits took place no earlier than 0.5–1 × 109 years before the Moon was captured.

Jeffreys (1947) estimated the size of fragments resulting from breakup of a satellite inside the Roche limit, obtaining a result of about 100 km. This result does not allow for the further breakup of the fragments due to collisions among themselves, which should reduce the maximum size to less than about 3 km for rock, or less than about 1 km for ice. This result affects not only Jeffreys' speculations as to the origin of Saturn's rings, but also recent speculations on the origin of the moon by capture and the possible tidal destruction of satellites of Mercury or Venus.