On the origin and initial temperature of Jupiter and Saturn

A two-stage growth of the giant planets, Jupiter and Saturn, is considered, which is different from the model of contraction of large gaseous protoplanets. In the first stage, within a time of ～3 × 10⁷ years in Jupiter's zone and ～2 × 10⁸ years in Saturn's zone, a nucleus forms from condensed (solid) material having the mass, ～10²⁸ g, necessary for the beginning of acceleration. The second stage may gravitating body, and a relatively slow accretion begins until the mass of the planet reaches ～10 m_⊕. Then a rapid accretion begins with the critical radius less than the radius of the Hill lobe, so that the classical formulae for the rate of accretion may be applied. At a mass m > m₁ ≈ 50 m_⊕ accretion proceeds slower than it would according to these formulae. When the planet sweeps out all the gas from its nearest zone of feeding (m = m₂ ≈ 130 m_⊕), the width of the exhausted zone being $\text{～}\text{built1}\text{3}$ of the whole zone of the planet) growth is provided the slow diffusion of gas from the rest of the zone (time scale increases to 10⁵?10⁶ years and more). The process is terminated by the dissipation of the remnants of gas. In Saturn's zone m₁ > m₂ ≈ 30 m_⊕. The initial mass of the gas in Jupiter's zone is estimated. Before the beginning of the rapid accretion about 90% of the gas should have been lost from the solar system, and in the planet's zone less than two Jupiter masses remain. The highest temperature of Jupiter's surface, ≈5000°K, is reached at the stage of rapid accretion, m < 100 m_⊕, when the luminosity of the planet reaches 3 × 10^?3 L_⊙. This favors an effective heating of the inner parts of the accretionary disk and the dissipation of gas from the disk. The accretion of Saturn produced a temperature rise up to 2000?2400° K (at m ≈ 20?25 m_⊕) and a luminosity up to 10^?4 L_⊙.     

Angular momentum drain: A mechanism for despinning asteroids

It is proposed that a new mechanism—angular momentum drain—helps account for the relatively slow rotation rates of intermediate-sized asteroids. Impact ejecta on a spinning body preferentially escape in the direction of rotation. This material systematically drains away spin angular momentum, leading to the counterintuitive result that collisions can reduce the spin of midsized objects. For an asteroid of mass M spinning at frequency ω, a mass loss δM correspond to an average decrease in rotation rate $\text{δω ≈}\text{ωδM}\text{M}$. A. W. Harris' (1979), Icarus40, 145–153) theory for the collisional evolution of asteroidal spins is significantly altered by inlusion of this effect. While the modified theory is still somewhat artificial, comparison of its predictions with the data of S. F. Dermott, A. W. Harris, and C. D. Murray (1984, Icarus57, 14–34) suggests that angular momentum drain is essential for understanding the statistics of asteroidal rotations.     

The angular momenta of solar system bodies: Implications for asteroid strengths

The angular momentum H is plotted versus mass M for the planets and for all asteroids with known rotation rates and shapes, primarily taken from D. C. McAdoo and J. A. Burns [Icarus18, 285–293 (1973)]. An asteroid's angular momentum is derived from its rotation rate as determined by the period of its lightcurve, its shape as indicated by the lightcurve amplitude, and where possible its size as given by polarimetry or radiometry. The asteroid is assumed to be rotating about its axis of maximum moment of inertia. As previously found by F. F. Fish [Icarus7, 251–256 (1967]) and W. K. Hartmann and S. M. Larson [Icarus7, 257–260 (1967)], H is approximately proportional to $\text{M}{}^{\mathrm{<mtext>5</mtext><mtext>3</mtext>}}$, which shows that the asteroids and most planets spin with nearly the same rate. The very smallest asteroids on the plot deviate from the above reaction, usually containing excess angular momentum. This suggests that collisions have transferred substantial angular momentum to the smallest asteroids, perhaps causing their internal stress states to be substantially modified by centrifugal effects.The forces produced by gravitation are then compared to centrifugal effects for a rotating, triaxial ellipsoid of density 3 g cm^?3. For all asteroids with known properties the gravitational attraction is shown to be larger than the centrifugal acceleration of a particle on the surface: thus the observed asteroid regoliths are gravitationally bound. Poisson's equation for the gravitational potential is investigated and it is shown by mathematical and physical arguments that any arbitrarily shaped ellipsoid with the attractive surface force boundary condition found above will have only attractive internal forces. Thus the internal stress states in asteroids are always compressive so that asteroids could be internally fractured without losing their integrity.     

Numerical experiments on the stability of preplanetary disks

Gravitational stability of gaseous protostellar disks is relevant to theories of planetary formation. Stable gas disks favor formation of planetesimals by the accumulation of solid material; unstable disks allow the possibility of direct condensation of gaseous protoplanets. We present the results of numerical experiments designed to test the stability of thin disks against large-scale, self-gravitational disruption. The disks are represented by a distribution of about 6 × 10⁴ point masses on a two-dimensional (r, φ) grid. The motions of the particles in the self-consistent gravity field are calculated, and the evolving density distributions are examined for instabilities. Two parameters that have major influences on stability are varied: the initial temperature of the disk (represented by an imposed velocity dispersion), and the mass of the protostar relative to that of the disk. It is found that a disk as massive as 1M_⊙, surrounding a 1M_⊙ protostar, can be stable against long-wavelength gravitational disruption if its temperature is about 300°K or greater. Stability of a cooler disk requires that it be less massive, but even at 100°K a stable disk can have an appreciable fraction ($\text{～}\text{1}\text{3}$) of a solar mass.     

On the mechanism of catastrophic destruction of minor planets by high-velocity impact

For the study of the collisional breakup of minor planets, semiquantitative interpretations of the catastrophic destruction of cubic rock targets by high-velocity impact reported by A. Fujiwara, G. Kamimoto, and A. Tsukamoto (1977, Icarus31, 277–288) are attempted. The conditions for transition and core-type destruction are derived from consideration of the side surface spallation, or central spallation, and the back surface spallation caused by the rarefaction pulses. In the derivation, the strengths of the original P-pulse at the crater rim and the bottom are given by application of the failure criterion. As the condition for complete destruction, an empirical rule is proposed. It is found that the critical sizes for these destructions vary as E^0.40 and the previously reported $\text{E}\text{M}\text{-}\text{scaling}$ is only an approximate rule (E, impact energy; M, target mass). The possibilities of extending of these results to larger bodies of any other shape are discussed.     

A co-accretional model of satellite formation

Numerical calculation of a simple accretion model including the effects of tidal friction indicate that coformation is tenable only if the planet's Q is less than about 10³. The parameter which most strongly affects the final mass ratio of the pair is the time at which the secondary embryo is introduced. Our model yields the proper Moon-Earth mass ratio if the Moon embryo is introduced when the Earth is only about $\text{1}\text{10}$ of its final mass. The lunar orbit remains at about 10 Earth radii throughout most of the growth.This model of satellite formation overcomes two difficulties of the “circumterrestrial cloud” model of Ruskol (1960, 1963, 1972): (1) The difficulty of accumulating a mass as great as the entire Moon before gravitational instability reduces the cloud to a small number of moonlets is removed. (2) The differences between terrestrial and outer planet satellite systems is easily understood in terms of the differences in Q between these planets. The high Q of the outer planets does not allow a satellite embryo to survive a significant portion of the accretion process, thus only small bodies which formed very late in the accumulation of the planet remain as satellites. The low Q of the terrestrial planets allows satellite embryos of these planets to survive during accretion, thus massive satellites such as the Earth's Moon are expected. The present lack of such satellites of the other terrestrial planets may be the result of tidal evolution, either infall following primary despinning (Burns, 1973) or escape due to increase in orbit eccentricity.     

Observations of Saturn's outer ring and new satellites during the 1980 edge-on presentation

Observations of Saturn's satellites and external rings during the 1980 edge-on presentation were obtained with a focal coronograph. A faint satellite traveling in the orbit of Dione and leading it by 72° has been detected, together with the two inner satellites already suspected (cf. J. W. Fountain and S. M. Larson, 1978,Icarus36, 92–106). The external ring has been observed on both east and west sides; it may extend up to $\text{?8.3}$ Saturn radii, and appears structured.     

The Effect of Tidal Interaction with a Gas Disk on Formation of Terrestrial Planets

We have performed N-body simulation on final accretion stage of terrestrial planets, including the effect of damping of eccentricity and inclination caused by tidal interaction with a remnant gas disk. As a result of runway and oligarchic accretion, about 20 Mars-sized protoplanets would be formed in nearly circular orbits with orbital separation of several to ten Hill radius. The orbits of the protoplanets would be eventually destabilized by long-term mutual gravity and/or secular resonance of giant gaseous planets. The protoplanets would coalesce with each other to form terrestrial planets through the orbital crossing. Previous N-body simulations, however, showed that the final eccentricities of planets are around 0.1, which are about 10 times higher than the present eccentricities of Earth and Venus. The obtained high eccentricities are the remnant of orbital crossing. We included the effect of eccentricity damping caused by gravitational interaction with disk gas as a drag force (“gravitational drag”) and carried out N-body simulation of accretion of protoplanets. We start with 15 protoplanets with 0.2M⊕ and integrate the orbits for 10⁷ years, which is consistent with the observationally inferred disk lifetime (in some runs, we start with 30 protoplanets with 0.1M⊕). In most runs, the damping time scale, which is equivalent to the strength of the drag force, is kept constant throughout each run in order to clarify the effects of the damping. We found that the planets' final mass, spatial distribution, and eccentricities depend on the damping time scale. If the damping time scale for a 0.2M⊕ mass planet at 1 AU is longer than 10⁸ years, planets grow to Earth's size, but the final eccentricities are too high as in gas-free cases. If it is shorter than 10⁶ years, the eccentricities of the protoplanets cannot be pumped up, resulting in not enough orbital crossing to make Earth-sized planets. Small planets with low eccentricities are formed with small orbital separation. On the other hand, if it is between 10⁶ and 10⁸ years, which may correspond to a mostly depleted disk (0.01-0.1% of surface density of the minimum mass model), some protoplanets can grow to about the size of Earth and Venus, and the eccentricities of such surviving planets can be diminished within the disk lifetime. Furthermore, in innermost and outermost regions in the same system, we often find planets with smaller size and larger eccentricities too, which could be analogous to Mars and Mercury. This is partly because the gravitational drag is less effective for smaller mass planets, and partly due to the “edge effect,” which means the innermost and outermost planets tend to remain without collision. We also carried out several runs with time-dependent drag force according to depletion of a gas disk. In these runs, we used exponential decay model with e-folding time of 3×10⁶ years. The orbits of protoplanets are stablized by the eccentricity damping in the early time. When disk surface density decays to ?1% of the minimum mass disk model, the damping force is no longer strong enough to inhibit the increase of the eccentricity by distant perturbations among protoplanets so that the orbital crossing starts. In this disk decay model, a gas disk with 10⁻⁴-10⁻³ times the minimum mass model still remains after the orbital crossing and accretional events, which is enough to damp the eccentricities of the Earth-sized planets to the order of 0.01. Using these results, we discuss a possible scenario for the last stage of terrestrial planet formation.     

Evolution of Planetesimal Velocities Based on Three-Body Orbital Integrations and Growth of Protoplanets

We obtain the viscous stirring and dynamical friction rates of planetesimals with a Rayleigh distribution of eccentricities and inclinations, using three-body orbital integration and the procedure described by Ohtsuki (1999, Icarus137, 152), who evaluated these rates for ring particles. We find that these rates based on orbital integrations agree quite well with the analytic results of Stewart and Ida (2000, Icarus 143, 28) in high-velocity cases. In low-velocity cases where Kepler shear dominates the relative velocity, however, the three-body calculations show significant deviation from the formulas of Stewart and Ida, who did not investigate the rates for low velocities in detail but just presented a simple interpolation formula between their high-velocity formula and the numerical results for circular orbits. We calculate evolution of root mean square eccentricities and inclinations using the above stirring rates based on orbital integrations, and find excellent agreement with N-body simulations for both one- and two-component systems, even in the low-velocity cases. We derive semi-analytic formulas for the stirring and dynamical friction rates based on our numerical results, and confirm that they reproduce the results of N-body simulations with sufficient accuracy. Using these formulas, we calculate equilibrium velocities of planetesimals with given size distributions. At a stage before the onset of runaway growth of large bodies, the velocity distribution calculated by our new formulas are found to agree quite well with those obtained by using the formulas of Stewart and Ida or Wetherill and Stewart (1993, Icarus106, 190). However, at later stages, we find that the inclinations of small collisional fragments calculated by our new formulas can be much smaller than those calculated by the previously obtained formulas, so that they are more easily accreted by larger bodies in our case. The results essentially support the previous results such as runaway growth of protoplanets, but they could enhance their growth rate by 10-30% after early runaway growth, where those fragments with low random velocities can significantly contribute to rapid growth of runaway bodies.     

Satellite formation,II

The satellite formation model of Harris and Kaula (Icarus24, 516–524, 1975) is extended to include evolution of planetary ring material and elliptic orbital motion. This model is more satisfactory than the previous one in that the formation of the moon begins at a later time in the growth of the earth, and that 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.     

Structure of the satellitary accretion disk of Saturn

A detailed computation on the equilibrium structure of an accretion disk around Saturn from which the regular satellites presumably originated is reported. Such a disk is the predecessor of the self-dissipating disk that is formed when the mass infall stops (Cassen and Moosman, 1981, Icarus48, 353–376). When determining the disk structure local energy balance was assumed. Convention was taken into account by introducing local energy dissipation and, in an approximate manner, sonic convection. Changes in the disk structure were investigated by varying the free parameters, i.e., the external flux from both the protosun and the protoplanet, the abundance of dust and the strength of turbulence. It has been verified that the external energy flux does not play an important role in the evolution of the disk structure. Models characterized by either longer times (?3 10³ year) or a noticeable depletion of condensable elements (10^?2 times less than the solar value) have a total mass of the order of 0.34?0.1 times the mass of the regular satellites increased by the mass of the light elements. Low turbulence models (Reynolds critical number $\text{Re}{}^1\text{= 150}$) are characterized approximately by a total mass twice as large the mass of the regular satellites. All the studied models present a temperature distribution that allows the condensation of iron, silicate, and, in the outer regions, ice grains. All models but the one with 10^?2 of the solar value of condensable elements are characterized by a wide convective region that contains the formation zone of the regular satellites.     

Orientation and shape of the Earth's bow shock in three dimensions

Nearly 2500 shock crossings from HEOS-1, HEOS-2 and 5 IMP spacecraft, covering most of the northern and part of the southern bow shock surface for X values X > ? 20 R_E, have been used to carry out a detailed study of the three-dimensional shape and location of the bow shock. The influence of the different solar wind conditions has been reduced by normalising the observed crossings to an average solar wind dynamical pressure (N₀ = 9.4 cm^?3, V₀ = 450 kms^?1). It has been shown that the shock surface is symmetric with respect to the ecliptic plane and intersects the coordinate axes at 11.9 R_E (X), + 27.0 and ? 22.9 R_E (Y), + 23.9 and ? 24.5 R_E (Z) for the average dynamical pressure (N₀ = 9.4 cm^?3, V₀ = 450kms^?1, with $\text{M}{}_{\mathrm{A}}\text{= 9.3}$, $\text{M}{}_{\mathrm{MS}}\text{= 6.1)}$. The observed aberration of the shock surface is 8.9° ± 1°, i.e. 5.1° larger than the aberration predicted from the Earth's motion. This asymmetry around the solar wind apparent direction is described by equation (6) for different Mach numbers M_A and confirms the predictions of Walters [J. geophys. Res. 71, 1319 (1964)] and Michel [J. geophys. Res. 70, 1 (1965)].The magnetosheath thickness is 3.3 R_E along the X-axis, 11.4 R_E (+ Y), 8.7 R_E (? Y), 9.9 R_E (+Z) and 10.9 R_E along the negative Z axis.     

Airborne spectroscopy and spacecraft radiometry of Venus in the far infrared

In March 1979, the spectrum of Venus was recorded in the far infrared from the G.P. Kuiper Airborne Observatory when the planet subtended a phase angle of 62°. The brightness temperature was observed to be 275°K near 110 cm^?1, dropping to 230°K near 270 cm^?1. Radiance calculations, using temperature and cloud structure formation from the Pioneer Venus mission and including gaseous absorption by the collision-induced dipole of CO₂, yield results consistently brighter than the observations. Supplementing the spectral data, Pioneer Venus OIR data at similar phase angles provide the constraint that any additional infrared opacity must be contained in the upper cloud, H₂SO₄ to the Pioneer-measured upper cloud structure serves to reconcile the model spectrum and the observations, but cloud microphysics strongly indicates that such a high particle density haze $\text{(N ? 1.6 × 10}{}^7\text{cm}{}^{\mathrm{?3}}\text{)}$ is implausible. The atmospheric environment is reviewed with regard to the far infrared opacity and possible particle distribution modifications are discussed. We conclude that the most likely possibility for supplementing the far-infrared opacity is a population of large particles $\text{(}\text{r}\text{? 1 μm)}$ in the upper cloud with number densities less than 1 particle cm^?3 which has remained undetected by in situ measurements.     

Hyperion: Collisional disruption of a resonant satellite

Hyperion is an irregularly shaped object of about 285 km in mean diameter, which appears as the likely remmant of a catastrophic collisional evolution. Since the peculiar orbit of this satellite (in $\text{4}\text{3}$ resonance locking with Titan) provides an effective mechanism to prevent any reaccretion of secondary fragments originated in a breakup event, the present Hyperion is probably the “core” of a disrupted precursor. This contrasts with the other, regularly shaped small satellites of Saturn, which, according to B.A. Smith et al. [Science215, 504–537 (1982)], were disrupted several times but could reaccrete from narrow rings of collisional fragments. The numerical experiments performed to explore the region of the phase space surrounding the present orbit show that most fragments ejected with a relative velocity $\text{?0.1}\text{km}\text{/}\text{sec}$ rapidly attain chaotic-type orbits, having repeated close encounters with Titan. Ejection velocities of this order of magnitude are indeed expected for a collision at a velocity of ～ 10 km/sec with a projectile-to-target mass ratio of the order of 10^?3; similar effects could be produced by less energetic but nearly grazing collisions. Such events are not likely to displace the largest remnant (i.e., the present Hyperion) outside the stable region of the phase space associated with the resonance, but could be responsible for the large amplitude of the observed orbital libration.     

A possible rotation period for the minor planet 164 Eva

The minor planet 164 Eva passed through opposition on December 1, 1975 with a magnitude B_opp = 11.3 mag. Photoelectric observations at the Observatory of Torino, Italy, were carried out in two nights on Oct. 27/28 and Nov. 11, each with a run of about 3 hr. Two further successful photoelectric observations were carried out at the OHP, France, each with a run of about 6 hr. From all observed parts of the lightcurve a resulting synodic period of rotation of about 27.3 hr can be deduced, with a range of the total amplitude of at least Δm = 0.07 mag. With this period of 27.3 hr the minor planet 164 Eva is one more long period object, falling now between 654 Zelinda (H. J. Schober, 1975, Astron. Astrophys.44, 85–89) and 139 Juewa (J. Goguen et al., 1976, Icarus29, 137–142), at the high end in the histogram of the distribution of minor planet rotation periods.     

The partial volatilization of Mercury

During recent years my research on the primitive solar nebular has followed two main themes: (1) Very early in the development of the nebula conditions probably favored the occurence of major gaseous instabilities leading to the formation of giant gaseous protoplanets, but the rapid rise of the external temperature soon evaporated the envelopes of these protoplanets, possibly leaving behind precipitated solids which formed the cores and mantles of the terrestrial planets. (2) Models of the nebula indicate a later stage when conditions in the inner Solar System became very hot; at the position of Mercury the temperature was probably in the range 2500–3500°K. This leads to the hypothesis that the original protomercury was a body substantially more massive than the present planet and of normal composition, but that when it was immersed in the high-temperature field of the dissipating solar nebula, most of the rocky mantle was vaporized and mixed into the solar nebula gases and carried away by them. This hypothesis is investigated in the present paper. For simplicity the vaporization of a mantle composed of enstatite, MgSiO₃, was computed for a planet with 2.25 the mass of Mercury at a temperature of 3000°K. It is argued that the mantle could probably be largely removed in the available time of 3 × 10⁴ years. Subsequent accretion would restore some magnesium silicates to the mantle of the planet.     

Collisional processes among interplanetary dust grains: An unlikely origin for the β meteoroids

The question of the collisional production of the β meteoroids is reexamined incorporating recent experimental results (A. Fugiwara, G. Kamimoto, A. Tsukamoto, 1977, Icarus31, 277–288). The collisional model yields a flux of fragments supported by the conservation of mass flux which does not account by far for the observed flux of submicron grains. Particles larger than about 100 μm will be destroyed by collisions inside 1 AU, well before they can get near the Sun. The existence of two independent populations of interplanetary dust grains as proposed by L. B. Le Sergeant and Ph. L. Lamy (1978, Nature266, 822–824; 1980, Icarus43, 350–372) appears reinforced. It is proposed that the bulk of submicron grains does not necessarily travel in hyperbolic orbits and that β meteoroids may be a phenomenon—possibly transitory—of limited importance.     

Discrete calculations of interstellar migration and settlement

Monte Carlo calculations of the expansion of space-faring civilizations are presented for a wide range of values of the population growth coefficient (α) and emigration coefficient (γ). Even for the very low values proposed by Newman and Sagan (α = 10^?4per year; γ = 10^?8per year) the migration wavefront expands at 1.4 × 10^?5 pc per year. Even with this low expansion velocity, such a civilization would fill the Galaxy in about 10⁹ years. Filling times of the order of 60 million years seem probable. The wavefront velocity is approximated by $\text{υ =}\text{Δr}\text{[(}\text{Δx}\text{υ}{}_{\mathrm{<mtext>s</mtext>}}\text{)}\text{+ (}\text{1}\text{α}\text{)}\text{ln}\text{(}\text{2α}\text{γ}\text{)]}$, where $\text{Δr}$ is the average radial distance traveled, $\text{δx}$ the average distance traveled, and υ_s the ship speed. This approximation was derived by Newman.