Origin of the Moon — Capture by gas drag of the Earth's primordial atmosphere

We propose a new scenario of the lunar origin, which is a natural extension of planetary formation processes studied so far by us in Kyoto. According to these studies, the Earth grew up in a gaseous solar nebula and, consequently, the sphere of its gravitational influence (i.e., the Hill sphere of the Earth) was filled by a gas forming a dense primordial atmosphere of the Earth. In the later stages, this atmosphere as well as the solar nebula was dissipated gradually, owing to strong activities of the early-Sun in a T Tauri-stage.In the present and the subsequent papers, we study a series of dynamical processes where a lowenergy (i.e., slightly unbound) planetisimal is trapped within the terrestrial Hill sphere, under the above-mentioned circumstances that the gas density of the primordial atmosphere is gradually decreasing. It is clear that two conditions must be satisfied for the lunar origin: first, an unbound planetesimal entering the Hill sphere have to dissipate its kinetic energy and come into a bound orbit before it escapes from the Hill sphere and, second, the bound planetisimal never falls onto the surface of the Earth.In this paper we study the first condition by calculating the oribital motion of a planetesimal in the Hill sphere, which is affected both by solar gravity and by atmospheric gas drag. The results show that a low-energy planetisimal with the lunar mass or less can be trapped in the Hill sphere with a high probability, if it enters the Hill sphere at stages before the atmospheric density is decreased to about 1/50 of the initial value.In the subsequent paper, the second condition will be studied and it will be shown that a tidal force, among other forces, is very important for a trapped planetesimal to avoid collision with the Earth and stay eternally in the Hill sphere as a satellite.     

Dynamical Effects of Mars on Asteroidal Dust Particles

Asteroidal dust particles resulting from family-forming events migrate from their source locations in the asteroid belt inwards towards the Sun under the effect of Poynting-Robertson (PR) drag. Understanding the distribution of these dust particle orbits in the inner solar system is of great importance to determining the asteroidal contribution to the zodiacal cloud, the accretion rate by the Earth, and the threat that these particles pose to spacecraft and satellites in near-Earth space. In order to correctly describe this distribution of orbits in the inner solar system, we must track the dynamical perturbations that the dust particle orbits experience as they migrate inwards. In a seminal paper Öpik (1951) determines that very few of the μm-cm sized dust particles suffer a collision with the planet face as they decay inwards past Mars. Here we re-analyze this problem, considering additionally the likelihood that the dust particle orbits pass through the Hill sphere of Mars (to various depths) and experience potentially significant perturbations to their orbits. We find that a considerable fraction of dust particle orbits will enter the Hill sphere of Mars. Furthermore, we find that there is a bias with inclination, particle size, and eccentricity of the particle orbits that enter the Martian Hill sphere. In particular the bias with inclination may create a bias towards higher-inclination sources in the proportions of asteroid family particles that reach near-Earth space.     

The escape of natural satellites from Mercury and Venus

Kumar's (1977) suggestion that the slow rotations of Mercury and Venus are in part due to natural satellites that subsequently escaped is discussed. A more useful criterion for the escape of such satellites than that previously proposed is derived, and it is shown that this distance is sufficiently small for Mercury and Venus to make the escape of satellites a likely possibility.     

The escape of natural satellites from Mercury and Venus

It is suggested that the slow rotations of Mercury and Venus may be connected with the absence of natural satellites around them. If Mercury or Venus possessed a satellite at the time of formation, the tidal evolution would have caused the satellite to recede. At a sufficiently large distance from the planet, the Sun's gravitational influence makes the satellite orbit unstable. The natural satellites of Mercury and Venus might have escaped as a consequence of this instability.     

Temporary satellite capture of comets by Jupiter

This paper studies the dynamical evolution of 97 Jupiter-family comets over an 800-year time period. More than two hundred encounters with Jupiter are investigated, with the observed comets moving during a certain period of time in an elliptic jovicentric orbit. In most cases this is an ordinary temporary satellite capture of a comet in Everhart??s sense, not associated with a transition of the small body into Jupiter??s family of satellites. The phenomenon occurs outside the Hill sphere with comets with a high Tisserand constant relative to Jupiter; the comets?? orbits have a small inclination to the ecliptic plane. An analysis of 236 encounters has allowed the determination within the planar pair two-body problem of a region of orbits in the plane (a, e) whose semimajor axes and eccentricities contribute to the phenomenon under study. Comets with orbits belonging to this region experience a temporary satellite capture during some of their encounters; the jovicentric distance function has several minima; and the encounters are characterized by reversions of the line of apsides and some others features of their combination that are intrinsic to comets in this region. Therefore, this region is called a region of comets with specific features in their encounters with Jupiter. Twenty encounters (out of 236), whereby the comet enters an elliptic jovicentric orbit in the Hill sphere, are identified and investigated. The size and shape of the elliptic heliocentric orbits enabling this transition are determined. It is found that in 11 encounters the motion of small bodies in the Hill sphere has features the most important of which is multiple minima of the jovicentric distance function. The study of these 20 encounters has allowed the introduction of the concept of temporary gravitational capture of a small body into the Hill sphere. An analysis of variations in the Tisserand constant in these (20) encounters of the observable comets shows that their motion is unstable in Hill??s sense.     

Hill stability of satellite orbits

Szebehely's criterion for Hill stability of satellites is derived from Hill's problem and a more exact result is obtained. Direct, Hill stable, circular satellites can exist almost twice as far from the planet as retrograde satellites. For direct satellites the new result agrees with Kuiper's empirical estimate that such satellites are stable up to a distance of half the radius of action of the planet. Comparison with the results of numerical experiments shows that Hill 'stability is valid for direct satellites but meaningless for retrograde satellites. Further accuracy for the maximum distance of Hill stable orbits is obtained from the restricted problem formulation. This provides estimates for planetary distances in double star systems.     

On the Inclination Distribution of the Jovian Irregular Satellites

Irregular satellites—moons that occupy large orbits of significant eccentricity e and/or inclination I—circle each of the giant planets. The irregulars often extend close to the orbital stability limit, about 1/3-1/2 of the way to the edge of their planet's Hill sphere. The distant, elongated, and inclined orbits suggest capture, which presumably would give a random distribution of inclinations. Yet, no known irregulars have inclinations (relative to the ecliptic) between 47 and 141°.This paper shows that many high-I orbits are unstable due to secular solar perturbations. High-inclination orbits suffer appreciable periodic changes in eccentricity; large eccentricities can either drive particles with ∼70°<I<110° deep into the realm of the regular satellites (where collisions and scatterings are likely to remove them from planetocentric orbits on a timescale of 10⁷-10⁹ years) or expel them from the Hill sphere of the planet.By carrying out long-term (10⁹ years) orbital integrations for a variety of hypothetical satellites, we demonstrate that solar and planetary perturbations, by causing particles to strike (or to escape) their planet, considerably broaden this zone of avoidance. It grows to at least 55°<I<130° for orbits whose pericenters freely oscillate from 0 to 360°, while particles whose pericenters are locked at ±90° (Kozai mechanism) can remain for longer times.We estimate that the stable phase space (over 10 Myr) for satellites trapped in the Kozai resonance contains ∼10% of all stable orbits, suggesting the possible existence of a family of undiscovered objects at higher inclinations than those currently known.     

Hill stability of the general problem of three bodies

We discuss Hill stability in the general three-body problem. The Hill curves in the general problem are the same as in the planar problem. We show that the bifurcation points correspond to the five equilibrium solutions, and derive the criterion for stability in the general case. Application of this criterion to 19 natural satellites of the Solar system leads to the result that, apart from Neptune 1, all the other 18 satellites are unstable in the sense of Hill. The dominant factor in producing this result is the finite eccentricity of the planetary orbits around the Sun.     

Implications of the Galilean satellites ice envelope explosions. I. The motion of fragments inside and beyond Jupiter's sphere of action

Explosions of the electrolyzed ice envelopes of the Galilean satellites resulted in the appearance of a large number of ice fragments deep inside Jupiter's sphere of action. Gravitational perturbations by the Galilean satellites transferred these fragments from satellite orbits into the periphery of the sphere of action and beyond it. The fragments move initially in the direction of a satellite's motion tangentially to its orbit.The fragments have a small angular momentum since they come from deep inside Jupiter's sphere of action. On reaching the periphery of the sphere, the fragments can acquire retrograde motion (even in the sidereal frame) because of the Sun's action.If ejected from the zone of the Galilean satellites with a sufficient velocity, the fragments can leave Jupiter's sphere of action going both inside and outside its orbit, which leads to a substantial difference in the pattern of their subsequent motion in the vicinity of Jupiter's orbit.The results obtained may be used to shed light on the origin of the irregular satellites (Paper 1) and Trojans (Paper 2).     

Constructive analytical solution of the evolution hill problem

A new analytical solution of the system of differential equations describing secular perturbations and long-period solar perturbations of mean orbits of outer satellites of giant planets was obtained. As distinct from other solutions, the solution constructed using von Zeipel’s method approximately takes into account, in the secular part of the perturbing function, the totality of fourth order with respect to the small parameter m of the ratio of the mean motions of the primary planet and the satellite. This enables us to describe more accurately the evolution of satellite orbits with large apocentric distances, which in the course of evolution may exceed the halved radius of the Hill sphere of the planet with respect to the Sun. Among these are the orbits of the two outermost Neptunian satellites N10 (Psamathe) and N13 (Neso). For these satellites, the parameter m amounts to 0.152 and 0.165, respectively. Different from a purely analytical solution, the proposed solution requires preliminary calculations for each satellite. More precisely, in doing so, we need to construct some simple functions to approximate more complex ones. This is why we use the phrase “constructive analytical.” To illustrate the solution, we compare it with the results of the numerical integration of the strict motion equations of the satellites N10 and N13 over time intervals 5–15 thousand years.     

Time-varying transformations for Hill–Clohessy–Wiltshire solutions in elliptic orbits

The relative motion of chief and deputy satellites in close proximity with orbits of arbitrary eccentricity can be approximated by linearized time-periodic equations of motion. The linear time-invariant Hill–Clohessy–Wiltshire equations are typically derived from these equations by assuming the chief satellite is in a circular orbit. Two Lyapunov–Floquet transformations and an integral-preserving transformation are here presented which relate the linearized time-varying equations of relative motion to the Hill–Clohessy–Wiltshire equations in a one-to-one manner through time-varying coordinate transformations. These transformations allow the Hill–Clohessy–Wiltshire equations to describe the linearized relative motion for elliptic chief satellites.     

High resolution interferometric observations of Venus at three radio wavelengths

We present new 6.0 and 21.1 cm interferometric observations of Venus. When combined with our previous 3.12 cm work they provide s self-consistent set of high-resolution observations at three wavelengths covering a range in which the opacity of the Venus atmosphere varies by a factor of 50. Model calculations indicate that a model atmosphere of CO₂ in adiabatic equilibrium containing uniformly mixed gaseous absorbers surrounding a dielectric sphere cannot simultaneously and adequately predict the radio interferometric measurements at all wavelengths together with the radar and radio occultation measurements.     

Venus Express—The first European mission to Venus

Venus Express is the first European mission to planet Venus. The mission aims at a comprehensive investigation of Venus atmosphere and plasma environment and will address some important aspects of the surface physics from orbit. In particular, Venus Express will focus on the structure, composition, and dynamics of the Venus atmosphere, escape processes and interaction of the atmosphere with the solar wind and so to provide answers to the many questions that still remain unanswered in these fields. Venus Express will enable a breakthrough in Venus science after a long period of silence since the period of intense exploration in the 1970s and the 1980s.The payload consists of seven instruments. Five of them were inherited from the Mars Express and Rosetta projects while two instruments were designed and built specifically for Venus Express. The suite of spectrometers and imaging instruments, together with the radio-science experiment, and the plasma package make up an optimised payload well capable of addressing the mission goals to sufficient depth. Several of the instruments will make specific use of the spectral windows at infrared wavelengths in order to study the atmosphere in three dimensions. The spacecraft is based on the Mars Express design with minor modifications mainly needed to cope with the thermal environment around Venus, and so a very cost-effective mission has been realised in an exceptionally short time.The spacecraft was launched on 9 November 2005 from Baikonur, Kazakhstan, by a Russian Soyuz-Fregat launcher and arrived at Venus on 11 April 2006. Venus Express will carry out observations of the planet from a highly elliptic polar orbit with a 24-h period. In 3 Earth years (4 Venus sidereal days) of operations, it will return about 2 Tbit of scientific data.Telecommunications with the Earth is performed by the new ESA ground station in Cebreros, Spain, while a nearly identical ground station in New Norcia, Australia, supports the radio-science investigations.     

Tetrahedron formation of nanosatellites with single-input control

The present paper studies the formation flight of four nanosatellites forming a tetrahedron. The main goal of this research is to find the relative orbits of these satellites that, at least in the linear Hill–Clohessy–Wiltshire model, ensure finite relative motion and keep the volume and shape of the tetrahedron configuration. Since real motions of these satellites will differ from the linear ones, especially under the influence of the \(J_{2}\) perturbation, active control is necessary. In addition, the limited size of the satellites does not allow us to use a complex 3-axis attitude control system. In the present paper we consider the passive magnetic attitude control system and suppose that the thrust direction is always aligned with the local geomagnetic field. In order to increase mission lifetime the control algorithm that minimizes the propellant consumption and keeps the tetrahedron volume and shape is investigated.     

Quasi-satellite orbits in the general context of dynamics in the 1:1 mean motion resonance: perturbative treatment

Our investigation is motivated by the recent discovery of asteroids orbiting the Sun and simultaneously staying near one of the Solar System planets for a long time. This regime of motion is usually called the quasi-satellite regime, since even at the times of the closest approaches the distance between the asteroid and the planet is significantly larger than the region of space (the Hill’s sphere) in which the planet can hold its satellites. We explore the properties of the quasi-satellite regimes in the context of the spatial restricted circular three-body problem “Sun–planet–asteroid”. Via double numerical averaging, we construct evolutionary equations which describe the long-term behaviour of the orbital elements of an asteroid. Special attention is paid to possible transitions between the motion in a quasi-satellite orbit and the one in another type of orbits available in the 1:1 resonance. A rough classification of the corresponding evolutionary paths is given for an asteroid’s motion with a sufficiently small eccentricity and inclination.     

The thermosphere of Venus and its exploration by a Venus Express Accelerometer Experiment

The forthcoming observations by Venus Express provide an ideal opportunity to comprehensively study the atmosphere of Venus for the first time since Pioneer Venus (1978–1992), and for the first time ever in detail at polar latitudes. This article reviews some of our current knowledge from space and ground-based observations about the upper atmosphere of Venus, such as its thermal structure, the global distribution of gases and dynamics. We discuss the processes most likely responsible for phenomena such as the cold nightside cryosphere, the cloud top superrotation and waves, and highlight outstanding scientific challenges for Venus Express measurements. In particular, we describe an experiment to measure atmospheric drag using the on-board accelerometers.     

The composition and vertical structure of the lower cloud deck on Venus

The opportunity to determine the planetwide temperature and cloud structure of Venus using radio occultation techniques arose with Pioneer Venus. Amplitude and Doppler data provided by the radio occultation experiment offered a unique and powerful means of examining the atmospheric properties in the lower cloud region.Absorption due to gaseous components of the atmosphere was subtracted from the measured absorption coefficient profiles before they were used to compute cloud mass contents. This absorption was found to represent a small part of the total absorption, depending on the latitude. In the main cloud deck, gaseous absorption contributes 10 to 20%, however, at the bottom of the detected absorption layer the sulfuric acid vapor contributes up to 100% due to increased vapor pressures. The clouds are the primary contributing absorbers in the 1- to 3-bar level of the Venus atmosphere. Below about 3 bars, depending on the latitude, absorption due to sulfuric acid vapor dominates.If a cloud particle model consisting of a solid nonabsorbing dielectric sphere with a concentric liquid sulfuric acid coating is invoked, the absorptivity of the particles increases from that of a pure sulfuric acid liquid sphere, and the mass content derived from the absorption coefficient profiles decreases. As the ratio of the core radius to the total radius (q) increases, absorption increases by more than a factor of 10 for high values of q. In the case of pure sulfuric acid droplets, the conductivity is sufficiently high that some of the field is excluded from the interior of the droplet thereby reducing the absorption. When a dielectric core of nonabsorbing material is introduced, the surface charge density is reduced and the absorption increases.The mass contents for all orbits in the equatorial region of Venus were calculated using values of q from 0 to 1. The resulting profiles match the probe mass content profiles at similar locations when a q of 0.97 is chosen.The wavelength dependence of the absorption for the spherical shell model varies with q from 1/λ² for pure liquid to λ^0.2 for a large core. A q of from 0.96 to 0.98 results in a wavelength dependence of 1/λ^1.0 to 1/λ^1.4 which matches the radio occultation absorption wavelength dependence and the microwave opacity wavelength dependence.Mass content profiles using a q of 0.97 were determined for occultations in the polar, collar, midlatitudinal, and equatorial regions assuming q remains constant over the planet. The results show considerable variability in both the level and the magnitude of the lower cloud deck. The cloud layer is lowest in altitude in the polar region. This might be expected as the temperature profile is cooler in the polar region than over the rest of the planet. The mass content is greatest in the polar and collar regions; however, many of the collar profiles were cut off due to fluctuations resulting from increased turbulence in the collar region. The mass contents are least dense in the midlatitude regions. There is a sharp lower boundary at about 1.5 bars in the equatorial and midlatitude regions and at about 2.5 bars in the polar region. Measurements made by the Particle Size Spectrometer and nephelometers also showed sharp lower cloud boundaries at this level.     

The composition of the atmosphere of Venus below 100 km altitude: An overview

We review the progress in our understanding of the composition of the Venus atmosphere since the publication of the COSPAR Venus International Reference Atmosphere volume in 1985. Results presented there were derived from data compiled in 1982–1983. More recent progress has resulted in large part from Earth-based studies of the near-infrared radiation from the nightside of the planet. These observations allow us to probe the atmosphere between the cloud tops and the surface. Additional insight has been gained through: (i) the analysis of ultraviolet radiation by satellites and rockets; (ii) data collected by the Vega 1 and 2 landers; (iii) complementary analyses of Venera 15 and 16 data; (iv) ground-based and Magellan radio occultation measurements, and (v) re-analyses of some spacecraft measurements made before 1983, in particular the Pioneer Venus and Venera 11, 13 and 14 data. These new data, and re-interpretations of older data, provide a much better knowledge of the vertical profile of water vapor, and more information on sulfur species above and below the clouds, including firm detections of OCS and SO. In addition, some spatial and/or temporal variations have been observed for CO, H₂O, H₂SO₄, SO₂, and OCS. New values of the D/H ratio have also been obtained.     

Venus express: Highlights of the nominal mission

Venus Express is the first European (ESA) mission to the planet Venus. Its main science goal is to carry out a global survey of the atmosphere, the plasma environment, and the surface of Venus from orbit. The payload consists of seven experiments. It includes a powerful suite of remote sensing imagers and spectrometers, instruments for in-situ investigation of the circumplanetary plasma and magnetic field, and a radio science experiment. The spacecraft, based on the Mars Express bus modified for the conditions at Venus, provides a versatile platform for nadir and limb observations as well as solar, stellar, and radio occultations. In April 2006 Venus Express was inserted in an elliptical polar orbit around Venus, with a pericentre height of ～250 km and apocentre distance of ～66000 km and an orbital period of 24 hours. The nominal mission lasted from June 4, 2006 till October 2, 2007, which corresponds to about two Venus sidereal days. Here we present an overview of the main results of the nominal mission, based on a set of papers recently published in Nature, Icarus, Planetary and Space Science, and Geophysical Research Letters.     

Geology of terrestrial planets with dynamic atmospheres

Geological exploration of the solar system shows that solid-surfaced planets and satellites are subject to endogenic processes (volcanism and tectonism) and exogenic processes (impact cratering and gradation). The present appearance of planetary suffaces is the result of the complex interplay of these processes and is the linked to the evolution of planets and their environments. Terrestrial planets that have dynamic atmospheres are Earth, Mars, and Venus. Atmospheric interaction with the surfaces of these planets, oraeolian activity, is a form of gradation. The manifestation of aeolian activity is the weathering and erosion of rocks into sediments, transportation of the weathered debris (mostly sand and dust) by the wind, and deposition of windblown material. Wind-eroded features include small-scale ventifacts (wind-sculptured rocks) and large-scale landforms such as yardangs. Wind depositional features include dunes, drifts, and mantles of windblown sediments. These and other aeolian features are observed on Earth, Mars, and Venus.