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.     

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.     

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.     

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.     

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.     

Secular love numbers and hydrostatic equilibrium of planets

The secular Love numbers of planets and of the Moon have been computed by use of the recent satellite data. It has been demonstrated that Venus, Mercury, and the Moon are far from the ideal hydrostatic equilibrium; the angular velocities (rotation periods) which correspond to the hydrostatic equilibrium have been computed.     

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.     

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.     

Disharmony of the spheres: Recent trends in planetary surface nomenclature

Inadvisable departures from tradition in naming newly mapped features on Mars, Mercury, and the Moon have been implemented and proposed since 1970. Functional need for place names also has become confused with cartographic convenience. Much of the resulting new nomenclature is neither unique, efficient, nor imaginative. The longstanding classical orientation in Solar System geography needs to be firmly reasserted. The Mädler scheme for designating smaller craters on the Moon should be retained and extended to the farside. Names of surface features on other bodies might best reflect the traditional connotations of planet and satellite names: for example, most crates on Mars would be named for mythical heroes and military personalities in ancient history, craters on Mercury might commemorate explorers or commercial luminaries, and features on Venus would bear the names of famous women.     

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.     

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.     

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.     

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。     

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.     

Numerical investigation of collision orbits of lunar satellites

In the present study an investigation of the collision orbits of natural satellites of the Moon (considered to be of finite dimensions) is developed, and the tendency of natural satellites of the Moon to collide on the visible or the far side of the Moon is studied. The collision course of the satellite is studied up to its impact on the lunar surface for perturbations of its initial orbit arbitrarily induced, for example, by the explosion of a meteorite. Several initial conditions regarding the position of the satellite to collide with the Moon on its near (visible) or far (invisible) side is examined in connection to the initial conditions and the direction of the motion of the satellite. The distribution of the lunar craters-originating impact of lunar satellites or celestial bodies which followed a course around the Moon and lost their stability - is examined. First, we consider the planar motion of the natural satellite and its collision on the Moon's surface without the presence of the Earth and Sun. The initial velocities of the satellite are determined in such a way so its impact on the lunar surface takes place on the visible side of the Moon. Then, we continue imparting these velocities to the satellite, but now in the presence of the Earth and Sun; and study the forementioned impacts of the satellites but now in the Earth-Moon-Satellite system influenced also by the Sun. The initial distances of the satellite are taken as the distances which have been used to compute periodic orbits in the planar restricted three-body problem (cf. Gousidou-Koutita, 1980) and its direction takes different angles with the x-axis (Earth-Moon axis). Finally, we summarise the tendency of the satellite's impact on the visible or invisible side of the Moon.     

基于无量纲的轨道参数开展卫星性质统计研究

目前已发现了285颗围绕太阳系八大行星公转的卫星, 它们的轨道和物理性质呈现了丰富多样性. 目前为止, 几乎所有的卫星研究工作都基于单个卫星系统或者卫星群, 似乎缺少统一的研究. 提出了一个新的与行星性质无关、只与恒星半径有关的轨道参数n, 定义为以太阳半径为单位的轨道半长轴的自然对数. 不同行星的卫星的n值都存在双极分布, 绝大部分卫星在$n\gtrsim2$区间, 其次在$n\lesssim-1$区间, 位于中间区域的行星则很少. 从卫星物理参数和轨道参数与n的关系中发现, 分属六大行星的卫星有明显的共同特征. 首先, 轨道偏心率和轨道倾角偏大的卫星的n值都在3.5左右, 它们都是巨行星的不规则卫星. 其次, n值在-1和1之间的卫星绝大部分体积大、质量大、反照率高、自转速度慢. 从文献中找到11颗系外卫星候选体, 获得了它们轨道n值和卫星质量, 发现后者也是在-1< n< 1区间最大,其他区间偏小.这些统一的 规律暗示,太阳系内不同行星的卫星形成机制以及太阳系外卫星的形成机制可能一样或类似.     

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.     

40Ar/39Ar and (U‐Th)/He model age signatures of elusive Mercurian and Venusian meteorites

No meteorites from Mercury and Venus have been conclusively identified so far. In this study, we develop an original approach based on extensive Monte Carlo simulations and diffusion models to explore the radiogenic argon (⁴⁰Ar*) and helium (⁴He*) loss behavior and the range of ⁴⁰Ar/³⁹Ar and (U‐Th)/He age signatures expected for a range of crystals if meteorites from these planets were ever to be found. We show that we can accurately date the crystallization age of a meteorite from both Mercury and Venus using the ⁴⁰Ar/³⁹Ar technique on clinopyroxene (± orthopyroxene) and that its ⁴⁰Ar/³⁹Ar age should match the Pb‐Pb age. At the surface of Mercury, phases like albite and anorthite will exhibit a complete range of ⁴⁰Ar* loss ranging from 0% to 100%, whereas merrillite and apatite will show 100% ⁴He* loss. By measuring the crystal size and diffusion parameters of a series of plagioclase crystals, one can inverse the ⁴⁰Ar* loss value to estimate the maximum temperature experienced by a rock, and narrow down the possible pre‐ejection location of the meteorite at the surface of Mercury. At the surface of Venus, plagioclase and phosphate phases will only record the age of ejection. The (U‐Th)/He systematics of merrillite and apatite will be, respectively, moderately and strongly affected by ⁴He* loss during the transit of the meteorite from its host planet to Earth. Finally, meteorites from Mercury or Venus will each have their own ⁴⁰Ar/³⁹Ar and (U‐Th)/He isotopic age and ³⁸Ar_c cosmic ray exposure age signatures over a series of different crystal types, allowing to unambiguously recognize a meteorite for any of these two planets using radiogenic and cosmogenic noble gases.