On the model of the accumulation of the moon compatible with the data on the composition and the age of lunar rocks

It is suggested that the overall early melting of the lunar surface is not necessary for the explanation of facts and that the structure of highlands is more complicated than a solidified anorthositic ‘plot’. The early heating of the interior of the Moon up to 1000K is really needed for the subsequent thermal history with the maximum melting 3.5 × 10⁹ yr ago, to give the observed ages for mare basalts. This may be considered as an indication that the Moon during the accumulation retained a portion of its gravitational energy converted into heat, which may occur only at rapid processes. A rapid (t < 10³ yr) accretion of the Moon from the circumterrestrial swarm of small particles would give necessary temperature, but it is not compatible with the characteristic time 10⁸ yr of the replenishment of this swarm which is the same as the time-scale of the accumulation of the Earth. It is shown that there were conditions in the circumterrestial swarm for the formation at a first stage of a few large protomoons. Their number and position is evaluated from the simple formal laws of the growth of satellites in the vicinity of a planet. Such ‘systems’ of protomoons are compared with the observed multiple systems, and the conclusion is reached that there could have been not more than 2–3 large protomoons with the Earth. The tidal evolution of protomoon orbits was short not only for the present value of the tidal phase-lag but also for a considerably smaller value. The coalescence of protomoons into a single Moon had to occur before the formation of the observed relief on the Moon. If we accept the age 3.9 × 10⁹ yr for the excavation of the Imbrium basin and ascribe the latter to the impact of an Earth satellite, this collision had to be roughly at 30R, whereR is the radius of the Earth, because the Moon at that time had to be somewhere at this distance. Therefore, the protomoons had to be orbiting inside 20–25R, and their coalescence had to occur more than 4.0x10⁹ yr ago. The energy release at coalescence is equivalent to several hundred degrees and even 1000 K. The process is very rapid (of the order of one hour). Therefore, the model is valid for the initial conditions of the Moon.     

Formation and evolution of planets

Hydrodynamical calculations are becoming increasingly successful at understanding the shapes and kinematics of planetary nebulae (PNs). The most successful models are two-dimensional interacting stellar wind models for which the PN nucleus is assumed to originally expel much or most of its mass in an equatorial waistband. The physics of the ensuing evolution seems to be explained nicely by a combination of hydrodynamics coupled with time-dependent stellar ionization and energy loss through nebular radiation. Recent radiation gas dynamic calculations are shown to yield excellent agreement with data.     

Gas Dissipation from the Protosatellite Disk of Jupiter

We consider the dissipation of the gaseous component from the gas–dust accretion disk of Jupiter in which the Galilean satellites were formed. The thermal dissipation of hydrogen and helium is shown to be ineffective. It could ensure the loss of gas only for a low-mass disk and only if the rarefied outer layers of the disk are heated to 10⁴ K. Such a high disk temperature is not reached through Jupiter's radiation in existing models of its formation, but it could be provided by UV radiation of the early Sun after the dissipation of the protoplanetary disk. The viscous dissipation (with a viscosity parameter 10^–3 in the -disk model) related to disk accretion onto Jupiter could disperse a low-mass disk in 10⁷ years. A magnetocentrifugal mechanism, which produced a disk wind during accretion capable of carrying away 0.1 of the accreted gas mass, was probably also involved in the dispersal of the Jovian disk. Differential dispersion, with the loss of only hydrogen and helium and the retention of water vapor and heavier gases in the disk, is possible only in a low-mass disk model. We conclude that the water contained in the Galilean satellites was brought in mainly by solid planetesimals captured into the disk during mutual inelastic collisions in Jupiter's sphere of influence.     

The origin of Jovian and Saturnian satellites in accretion disks

The properties of gas-dust disks that surrounded Jupiter and Saturn during the final stage of their formation are analyzed. The sizes of the disks are determined by the total planetocentric angular momentum of the matter accreted by planets and correspond to the sizes of the orbits of their largest satellites. The mass of the solid component of disks is limited from below by the total mass of the Galilean satellites of Jupiter (no less than 4 × 10²⁶ g) and the mass of the largest Saturnian satellites (1.4 × 10²⁶ g), whereas the mass of the gaseous component is limited from above by the amount of hydrogen and helium that could have been later lost by the disks. Our analysis of the known mechanisms of dissipation of gas showed that its simultaneous content in the disks relative to the solid component was much lower than the corresponding gas-to-solid ratio in the Sun. A certain amount of solid compounds (including ice) could have been brought into the disks with planetesimals, which had undergone mutual collisions in the neighborhood of giant planets and served as germs of satellites. The bulk of solid matter appears to have been captured into disks when the latter were crossed by smaller and intermediate-sized planetesimals, which then became parts of the satellites.     

On the thermal history of Saturn’s satellites Titan and Enceladus

The thermal histories of two geologically active satellites of Saturn—Titan and Enceladus—are discussed. During the Cassini mission, it was found that there are both nitrogen-containing compounds—NH₃ and N₂-and CO₂ and CH₄ in the water plumes of Enceladus; at that, ammonia is the prevailing form. This may testify that during evolution, the material of the satellite was warmed up to T ∼ 500–600 K, when NH₃ (the form of nitrogen capable of being accreted) could only be partly converted into N₂. Contrary to Enceladus, the temperature inside Titan probably reached values higher than 800 K or even higher than 1000 K, since the process of the chemical dissociation of ammonia was completely finished on this satellite and its atmosphere contains only molecular nitrogen. While the internal heating of Titan up to high temperatures can be explained by its large mass, the heating source for Enceladus’ interior is far from evident. Such traditional heating sources as the energy of gravitational differentiation and the radiogenic heating due to shortliving ²⁶Al and ⁶⁰Fe could not be effective. The first one is because of the small size of Enceladus (RE ≈ 250 km), and the inefficiency of the second one is caused by the fact that the satellite was formed not earlier than 8–10 Myr after the formation of calcium and aluminum-enriched inclusions in carbonaceous chondrites (CAI), i.e., after ²⁶Al had completely decayed. In the present paper, we propose other heating mechanisms-the heat of long-living radioactive elements and tidal heat, which could provide the observed chemical composition of the water plumes of Enceladus rather than only the differentiation of its protomatter into the ironstone core and the ice mantle.     

Dynamical history of coplanar two-satellite systems

One of the possible early states of the Earth-Moon system was a system of several large satellites around the Earth. The dynamical evolution of coplanar three-body systems is studied; a planet (Earth) and two massive satellites (proto-moons) with geocentric orbits of slightly different radii. Such configurations may arise in multiple satellite systems receding from a planet due to tidal friction. The numerical integration of the equations of motion shows that initially circular Keplerian orbits are soon transformed into disturbed elliptic orbits which are intersecting. The life-time of such a coplanar system between two probable physical collisions of satellites is roughly from one day to one year for satellite systems with radii less than 20R⊕, and may reach 100 yr for three-dimensional systems. This time-scale is short in comparison with the duration of the removal of satellites due to tides raised on the planet, which is estimated as 10⁶–10⁸ yr for the same orbital dimensions. Therefore, the life-time of a system of several proto-moons is mainly determined by their tidal interactions with the Earth. For conditions which we have considered, the most probable result of the evolution was coalescence of satellites as the consequence of the collisions.     

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_⊙.