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.     

A dynamical investigation of the conjecture that Mercury is an escaped satellite of Venus

The possibility that Mercury might once have been satellite of a Venus, suggested by a number of anomalies, is investigated by a series of numerical computer experiments. Tidal interaction between Mercury and Venus would result in the escape of Mercury into a solar orbit. Only two escape orbits are possible, one exterior and one interior to the Venus orbit. For the interior orbit, subsequent encounters are sufficiently distant to avoid recapture or large perturbations. The perihelion distance of Mercury tends to decrease, while the orientation of perihelion librates for the first few thousand revolutions. If dynamical evolution or nonconservative forces were large enough in the early solar system, the present semimajor axes could have resulted. The theoretical minimum quadrupole moment of the inclined rotating Sun would rotate the orbital planes out of coplanarity. Secular perturbations by the other planets would evolve the eccentricity and inclination of Mercury's orbit through a range of possible configurations, including the present orbit. Thus the conjecture that Mercury is an escaped satellite of Venus remains viable, and is rendered more attractive by our failure to disprove it dynamically.     

Characterization of terrestrial exoplanets based on the phase curves and albedos of Mercury, Venus and Mars

The empirically derived phase curves of terrestrial planets strongly distinguish between airless Mercury, cloud-covered Venus, and the intermediate case of Mars. The function for Mercury is steeply peaked near phase angle zero due to powerful backscattering from its surface, while that for Venus has 100 times less contrast and exhibits a brightness excess near 170° due to Mie scattering from droplets in the atmosphere. The phase curve of Mars falls between those of Mercury and Venus, and there are variations in luminosity due to the planet’s rotation, seasons, and atmospheric states. The phase function and geometric albedo of the Earth are estimated from published albedos values. The curves for Mercury, Venus and Mars are compared to that of the Earth as well as theoretical phase functions for giant planets. The parameters of these different phase functions can be used to characterize exoplanets.     

Possibility of self-sustaining bombardment of inner planets

The great strengthening the material undergoes under high confining pressure, and jet pattern of matter outflowing from large impact craters make possible the ejection of asteroid-size bodies from the Earth into space. The ejected bodies, after gaining energy in planetary perturbations, may fall back with a velocity higher than that of their ejection. This solves, in particular, the problem of shower bombardments with ~ 25 Myr interval (Drobyshevski, Sov. Astron. Let. 16(3), 193, 1990), and a question arises whether this process could become self-sustained, like a chain reaction, when secondary impacts release an energy higher than that of primary impact. Estimates show that such a possibility could have been realized for Mercury (Drobyshevski, Lunar Planet. Sci. Conf. Abstr. 23(1), 317, 1992) due to its low escape and high orbital velocities. Self-sustained bombardment can account for the loss of the silicate mantle from Mercury. The energy and angular momentum conservation laws imply that its orbit contracted toward the Sun in the course of ejection of the mantle fragments by Mercury's perturbations beyond its orbit. Straight-forward calculations show the initial orbit to have practically coincided with the Venusian orbit. This puts the old hypothesis of Mercury being a lost satellite of Venus on a solid ground and provides an explanation for many facts from the origin of the Imbrium bombardment to the observed locks in the axial and orbital rotation of Mercury, Venus, and the Earth.     

Possibility of self-sustaining bombardment of inner planets

The great strengthening the material undergoes under high confining pressure, and jet pattern of matter outflowing from large impact craters make possible the ejection of asteroid-size bodies from the Earth into space. The ejected bodies, after gaining energy in planetary perturbations, may fall back with a velocity higher than that of their ejection. This solves, in particular, the problem of shower bombardments with ~ 25 Myr interval (Drobyshevski, Sov. Astron. Let. 16(3), 193, 1990), and a question arises whether this process could become self-sustained, like a chain reaction, when secondary impacts release an energy higher than that of primary impact. Estimates show that such a possibility could have been realized for Mercury (Drobyshevski, Lunar Planet. Sci. Conf. Abstr. 23(1), 317, 1992) due to its low escape and high orbital velocities. Self-sustained bombardment can account for the loss of the silicate mantle from Mercury. The energy and angular momentum conservation laws imply that its orbit contracted toward the Sun in the course of ejection of the mantle fragments by Mercury's perturbations beyond its orbit. Straight-forward calculations show the initial orbit to have practically coincided with the Venusian orbit. This puts the old hypothesis of Mercury being a lost satellite of Venus on a solid ground and provides an explanation for many facts from the origin of the Imbrium bombardment to the observed locks in the axial and orbital rotation of Mercury, Venus, and the Earth.     

Some unsolved problems in evolutionary dynamics in the solar system

Several unsolved problems in the evolutionary histories leading to current dynamical configurations of the planets and their systems of satellites are discussed. These include the possibilities of rather tight constraints on the primordial rotation states of Mercury and Venus and the stabilizing mechanism for the latter's retrograde spin, a brief mention of the problem of origin of the moons of Earth and Mars, the excessive heat flow from Jupiter's satellite lo which is not compatible with an otherwise self-consistent model of origin of the Laplace three-body libration, the mechanism for the long history of resurfacing of Saturn's satellite Enceladus and the possibly short lifetime of the A ring and the mechanisms for resurfacing the satellites of Uranus, especially Ariel, if the high stability of the mean motion orbital resonances at the 2/1 commensurability involving Ariel and Umbriel precludes a long term occupancy of the resonance. Finally, excessive times of accumulation of the outer planets in current models may possibly be reducible from the effects of nebular gas drag.     

A survey for satellites of Venus

We present a systematic survey for satellites of Venus using the Baade-Magellan 6.5 m telescope and IMACS wide-field CCD imager at Las Campanas observatory in Chile. In the outer portions of the Hill sphere the search was sensitive to a limiting red magnitude of about 20.4, which corresponds to satellites with radii of a few hundred meters when assuming an albedo of 0.1. In the very inner portions of the Hill sphere scattered light from Venus limited the detection to satellites of about a kilometer or larger. Although several main belt asteroids were found, no satellites (moons) of Venus were detected.     

Possible satellites of Mercury and Venus

On the basis of works of King and Innanen, the limiting direct and retrograde orbits around the planets Mercury and Venus have been calculated. Synthesizing this concept with the concept of synchronous orbits around the planets and tidal drags acting within them it is shown that Venus may not have retained any satellite direct or retrograde but Mercury may have retained a retrograde satellite at a distance between 225000 and 252700 km from its center. It is urged that this satellite may be investigated observationally.     

Tectonics of the Venus and the early Precambrian

Analyzing the tectonics of planets and their satellites we use all the information available from the studies of the Earth and other celestial bodies such as the Moon, Mars and Mercury. An important condition in such analysis is naturally the scale of the phenomena compared. Most surface structures of Venus are known to have no direct analogues on the surface of the present Earth, with its global systems of mid-oceanic ridges, deep trenches and vast lithospheric plates. This might be due to the sharp differences in the present thermal regimes of the Earth and Venus. It has already been suggested in numerous papers that the key to the genesis of the Cytherean surficial structures must be looked for in the geodynamics of the Early Precambrian Earth.Such an approach appears very logical indeed since the rheology of the present Cytherean crust must be closer to that of the Precambrian rigid lithosphere of the Earth which is as if floating in the low-viscous asthenosphere. An attempt has therefore been made to evaluate certain elements in the tectonics of Venus through the theological properties of its crust comparing structural formation in the low-viscous layers of the Earth crust in the Early Precambrian with data on the morphology of structures on the surface of Venus.     

On the internal structures of mercury and venus

Recent radar measures of the radius and mass of Mercury imply a composition for the planet containing about 60% iron. One or other of two conclusions seems inescapable: either that Mercury is a highly exceptional object among terrestrial planets, or that all measures to date of the planet involve substantial systematic error. In either case the situation is such that independent checking of the radius and mass of Mercury by some entirely different means has become of the greatest importance to planetary physics and cosmogony.The recent radar and other determinations of the solid radius of Venus imply an internal structure similar to that of the Earth, namely a liquid core surrounded by a solid mantle and outer-shell zone. The theory also implies that the temperatures within Venus should be slightly higher than at the corresponding parts of the Earth. The proportion of mass in the core of Venus (about 25% of the whole) is entirely consistent with the phase-change hypothesis as to its nature, as of course is also the absence of any liquid or iron core in both Mars and the Moon. On the older iron-core hypothesis, Venus with considerably less iron content by mass than the Earth, and Mars and the Moon with none, would all present problems in different degrees to account for the differences of composition.If Venus began as an all-solid planet, the initial radius would have been about 6300 km, and the total amount of surface reduction to date owing to contraction of the planet would have been almost 40 million km², and as a proportion of the total area only slightly less than the contraction of the Earth. The theory thus predicts the existence of folded and thrusted mountain-systems of terrestrial type at the surface of Venus.     

Collisional breakup of particles in a planetary ring

Jeffreys (1947) estimated the size of fragments resulting from breakup of a satellite inside the Roche limit, obtaining a result of ～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 ?3 km for rock, or ?1 km for ice. This result affects not only Jeffrey's 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.     

Mercurian impact ejecta: Meteorites and mantle

Abstract— We have examined the fate of impact ejecta liberated from the surface of Mercury due to impacts by comets or asteroids, in order to study 1) meteorite transfer to Earth, and 2) reaccumulation of an expelled mantle in giant‐impact scenarios seeking to explain Mercury's large core. In the context of meteorite transfer during the last 30 Myr, we note that Mercury's impact ejecta leave the planet's surface much faster (on average) than other planets in the solar system because it is the only planet where impact speeds routinely range from 5 to 20 times the planet's escape speed; this causes impact ejecta to leave its surface moving many times faster than needed to escape its gravitational pull. Thus, a large fraction of Mercurian ejecta may reach heliocentric orbit with speeds sufficiently high for Earth‐crossing orbits to exist immediately after impact, resulting in larger fractions of the ejecta reaching Earth as meteorites. We calculate the delivery rate to Earth on a time scale of 30 Myr (typical of stony meteorites from the asteroid belt) and show that several percent of the high‐speed ejecta reach Earth (a factor of 2–3 less than typical launches from Mars); this is one to two orders of magnitude more efficient than previous estimates. Similar quantities of material reach Venus. These calculations also yield measurements of the re‐accretion time scale of material ejected from Mercury in a putative giant impact (assuming gravity is dominant). For Mercurian ejecta escaping the gravitational reach of the planet with excess speeds equal to Mercury's escape speed, about one third of ejecta reaccretes in as little as 2 Myr. Thus collisional stripping of a silicate proto‐Mercurian mantle can only work effectively if the liberated mantle material remains in small enough particles that radiation forces can drag them into the Sun on time scale of a few million years, or Mercury would simply re‐accrete the material.     

Planetary perturbations on Mercury’s libration in longitude

Two space missions dedicated to Mercury (MESSENGER and BepiColombo) aim at understanding its rotation and confirming the existence of a liquid core. This double challenge requires much more accurate models for the spin-orbit resonant rotation of Mercury. The purpose of this paper is to introduce planetary perturbations on Mercury’s rotation using an analytical method and to analyse the influence of the perturbations on the libration in longitude. Applying a perturbation theory based on the Lie triangle, we were able to re-introduce short periodic terms into the averaged Hamiltonian and to compute the evolution of the rotational variables. The perturbations on Mercury’s forced libration in longitude mainly come from the orbital motion of Mercury (with an amplitude around 41 arcsec that depends on the momenta of inertia). It is completed by various effects from Jupiter (11.86 and 5.93 year-periods), Venus (with a 5.66 year-period), Saturn (14.73 year-period), and the Earth (6.58 year-period). The amplitudes of the oscillations due to Jupiter and Venus are approximately 33% and 10% of those from the orbital motion of Mercury and the amplitudes of the oscillations due to Saturn and the Earth are approximately 3% and 2%. We compare the analytical results with the solution obtained from the spin-orbit numerical model SONYR.     

水（金）星凌日的程序化预报方法

本文介绍了预报水(金)星凌日的计算方法和凌日图的绘制方法,建立了一套完整的预报程序。作为该程序的一个简单应用,我们结合DE200历表及美国海军天文台提供的岁差章动程序,给出了1999年水星凌日的预报结果。     

Upstream proton cyclotron waves at Venus

Data from the magnetometer MAG aboard the Venus Express S/C are investigated for the occurrence of cyclotron wave phenomena upstream of the Venus bow shock. For an unmagnetized planet such as Venus and Mars the neutral exosphere extends into the on-flowing solar wind and pick-up processes can play an important role in the removal of particles from the atmosphere. At Mars upstream proton cyclotron waves were observed but at Venus they were not yet detected. From the MAG data of the first 4 months in orbit we report the occurrence of proton cyclotron waves well upstream from the planet, both outside and inside of the planetary foreshock region; pick-up protons generate specific cyclotron waves already far from the bow shock. This provides direct evidence that the solar wind is removing hydrogen from the Venus exosphere. Determining the role the solar wind plays in the escape of particles from the total planetary atmosphere is an important step towards understanding the evolution of the environmental conditions on Venus. The continual observations of the Venus Express mission will allow mapping the volume of escape more accurately, and determine better the present rate of hydrogen loss.     

Some aspects of the solar radiation incident at the top of the atmospheres of Mercury and Venus

A formalism has been developed for the calculation of the insolation on the planets Mercury and Venus neglecting any atmospheric absorption. For Mercury, the instantaneous insolation curves are repeated in a 2-tropical year cycle, the distribution of the solar radiation being perfectly symmetric between both hemispheres. In addition to latitudinal variations, one observes a longitudinal effect expressed by different instantaneous insolation distributions during the course of the time; on the equator, the relative diurnal insolation variability may attain a factor of 3. The small obliquity of Venus results in a nearly symmetric solar radiation distributions with respect to the equator except at the poles, where an important seasonal effect has been found. It has to be noted that no longitudinal dependence exists. Finally, the insolation curves are repeated in a nearly half-year cycle.     

Size distribution of particles in planetary rings

Harris (Icarus24, 190–192) has suggested that the maximum size of particles in a planetary ring is controlled by collisional fragmentation rather than by 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 Roche's 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 ～100 km but with most cross-section in cm-scale particles.     

One-millimeter brightness temperatures of the planets

New values for the 1-mm brightness temperatures of Mercury, Venus, Jupiter, Saturn, Uranus, and Neptune have been determined using Mars as the absolute photometric standard.     

Large scale chaos and marginal stability in the solar system

Large scale chaos is present everywhere in the solar system. It plays a major role in the sculpting of the asteroid belt and in the diffusion of comets from the outer region of the solar system. All the inner planets probably experienced large scale chaotic behavior for their obliquities during their history. The Earth obliquity is presently stable only because of the presence of the Moon, and the tilt of Mars undergoes large chaotic variations from 0° to about 60°. On billion years time scale, the orbits of the planets themselves present strong chaotic variations which can lead to the escape of Mercury or collision with Venus in less than 3.5 Gyr. The organization of the planets in the solar system thus seems to be strongly related to this chaotic evolution, reaching at all time a state of marginal stability, that is practical stability on a time-scale comparable to its age.This lecture was given at the XIth International Congress of Mathematical Physics, Paris, july 1994