Solar eclipses of Phobos and Deimos observed from the surface of Mars

The small martian satellites Phobos and Deimos orbit in synchronous rotation with inclinations of only 0.01 degrees and 0.92 degrees , respectively, relative to the planet's equatorial plane. Thus, an observer at near-equatorial latitudes on Mars could occasionally observe solar eclipses by these satellites (see ref. 1, for example). Because the apparent angular diameter of the satellites is much smaller than that of the Sun, however, such events are more appropriately referred to as transits. Transit data can be used for correcting and refining the orbital ephemerides of the moons. For example, Phobos is known to exhibit a secular acceleration that is caused by tidal dissipation within Mars. Long-term, accurate measurements are needed to refine the magnitude and origin of this dissipation within the martian interior as well as to refine the predicted orbital evolution of both satellites. Here we present observations of six transits of Phobos and Deimos across the solar disk from cameras on Mars aboard the Mars Exploration Rovers Spirit and Opportunity. These are the first direct imaging observations of satellites transiting the Sun from the surface of another planet.     

Origin of the Moon in a giant impact near the end of the Earth's formation

The Moon is generally believed to have formed from debris ejected by a large off-centre collision with the early Earth. The impact orientation and size are constrained by the angular momentum contained in both the Earth's spin and the Moon's orbit, a quantity that has been nearly conserved over the past 4.5 billion years. Simulations of potential moon-forming impacts now achieve resolutions sufficient to study the production of bound debris. However, identifying impacts capable of yielding the Earth-Moon system has proved difficult. Previous works found that forming the Moon with an appropriate impact angular momentum required the impact to occur when the Earth was only about half formed, a more restrictive and problematic model than that originally envisaged. Here we report a class of impacts that yield an iron-poor Moon, as well as the current masses and angular momentum of the Earth-Moon system. This class of impacts involves a smaller-and thus more likely-object than previously considered viable, and suggests that the Moon formed near the very end of Earth's accumulation.     

Origin of the orbital architecture of the giant planets of the Solar System

Planetary formation theories suggest that the giant planets formed on circular and coplanar orbits. The eccentricities of Jupiter, Saturn and Uranus, however, reach values of 6 per cent, 9 per cent and 8 per cent, respectively. In addition, the inclinations of the orbital planes of Saturn, Uranus and Neptune take maximum values of approximately 2 degrees with respect to the mean orbital plane of Jupiter. Existing models for the excitation of the eccentricity of extrasolar giant planets have not been successfully applied to the Solar System. Here we show that a planetary system with initial quasi-circular, coplanar orbits would have evolved to the current orbital configuration, provided that Jupiter and Saturn crossed their 1:2 orbital resonance. We show that this resonance crossing could have occurred as the giant planets migrated owing to their interaction with a disk of planetesimals. Our model reproduces all the important characteristics of the giant planets' orbits, namely their final semimajor axes, eccentricities and mutual inclinations.     

Discovery of 12 satellites of Saturn exhibiting orbital clustering.

The giant planets in the Solar System each have two groups of satellites. The regular satellites move along nearly circular orbits in the planet's orbital plane, revolving about it in the same sense as the planet spins. In contrast, the so-called irregular satellites are generally smaller in size and are characterized by large orbits with significant eccentricity, inclination or both. The differences in their characteristics suggest that the regular and irregular satellites formed by different mechanisms: the regular satellites are believed to have formed in an accretion disk around the planet, like a miniature Solar System, whereas the irregulars are generally thought to be captured planetesimals. Here we report the discovery of 12 irregular satellites of Saturn, along with the determinations of their orbits. These orbits, along with the orbits of irregular satellites of Jupiter and Uranus, fall into groups on the basis of their orbital inclinations. We interpret this result as indicating that most of the irregular moons are collisional remnants of larger satellites that were fragmented after capture, rather than being captured independently.     

Chaos-assisted capture of irregular moons

It has been thought that the capture of irregular moons--with non-circular orbits--by giant planets occurs by a process in which they are first temporarily trapped by gravity inside the planet's Hill sphere (the region where planetary gravity dominates over solar tides). The capture of the moons is then made permanent by dissipative energy loss (for example, gas drag) or planetary growth. But the observed distributions of orbital inclinations, which now include numerous newly discovered moons, cannot be explained using current models. Here we show that irregular satellites are captured in a thin spatial region where orbits are chaotic, and that the resulting orbit is either prograde or retrograde depending on the initial energy. Dissipation then switches these long-lived chaotic orbits into nearby regular (non-chaotic) zones from which escape is impossible. The chaotic layer therefore dictates the final inclinations of the captured moons. We confirm this with three-dimensional Monte Carlo simulations that include nebular drag, and find good agreement with the observed inclination distributions of irregular moons at Jupiter and Saturn. In particular, Saturn has more prograde irregular moons than Jupiter, which we can explain as a result of the chaotic prograde progenitors being more efficiently swept away from Jupiter by its galilean moons.     

Chaotic capture of Jupiter's Trojan asteroids in the early Solar System

Jupiter's Trojans are asteroids that follow essentially the same orbit as Jupiter, but lead or trail the planet by an angular distance of approximately 60 degrees (co-orbital motion). They are hypothesized to be planetesimals that formed near Jupiter and were captured onto their current orbits while Jupiter was growing, possibly with the help of gas drag and/or collisions. This idea, however, cannot explain some basic properties of the Trojan population, in particular its broad orbital inclination distribution, which ranges up to approximately 40 degrees (ref. 8). Here we show that the Trojans could have formed in more distant regions and been subsequently captured into co-orbital motion with Jupiter during the time when the giant planets migrated by removing neighbouring planetesimals. The capture was possible during a short period of time, just after Jupiter and Saturn crossed their mutual 1:2 resonance, when the dynamics of the Trojan region were completely chaotic. Our simulations of this process satisfactorily reproduce the orbital distribution of the Trojans and their total mass.     

Stellar encounters as the origin of distant Solar System objects in highly eccentric orbits

The Kuiper belt extends from the orbit of Neptune at 30 au to an abrupt outer edge about 50 au from the Sun. Beyond the edge is a sparse population of objects with large orbital eccentricities. Neptune shapes the dynamics of most Kuiper belt objects, but the recently discovered planet 2003 VB12 (Sedna) has an eccentric orbit with a perihelion distance of 70 au, far beyond Neptune's gravitational influence. Although influences from passing stars could have created the Kuiper belt's outer edge and could have scattered objects into large, eccentric orbits, no model currently explains the properties of Sedna. Here we show that a passing star probably scattered Sedna from the Kuiper belt into its observed orbit. The likelihood that a planet at 60-80 au can be scattered into Sedna's orbit is about 50 per cent; this estimate depends critically on the geometry of the fly-by. Even more interesting is the approximately 10 per cent chance that Sedna was captured from the outer disk of the passing star. Most captures have very high inclination orbits; detection of such objects would confirm the presence of extrasolar planets in our own Solar System.     

地球蛇行轨道运动的研究

本文从有效势能入手,通过理论推导,得出了地球的蛇行轨道运动是地球在太阳作用下的圆周运动和地球在月球作用下径向上的受迫振动的合运动的结论。     

A common mass scaling for satellite systems of gaseous planets

The Solar System's outer planets that contain hydrogen gas all host systems of multiple moons, which notably each contain a similar fraction of their respective planet's mass (approximately 10(-4)). This mass fraction is two to three orders of magnitude smaller than that of the largest satellites of the solid planets (such as the Earth's Moon), and its common value for gas planets has been puzzling. Here we model satellite growth and loss as a forming giant planet accumulates gas and rock-ice solids from solar orbit. We find that the mass fraction of its satellite system is regulated to approximately 10(-4) by a balance of two competing processes: the supply of inflowing material to the satellites, and satellite loss through orbital decay driven by the gas. We show that the overall properties of the satellite systems of Jupiter, Saturn and Uranus arise naturally, and suggest that similar processes could limit the largest moons of extrasolar Jupiter-mass planets to Moon-to-Mars size.     

面向全球变化探测的月基对地观测覆盖性能分析

从全球变化的空间观测需求出发,设想了一个依靠载人月球基地的对地观测望远镜,通过模拟地球静止轨道,太阳轨道和月球轨道,利用逐点计算法,从空间、时间和角度三个方面分析月球对地观测的覆盖特点,同时与现有的静止轨道卫星和日地L1点对地观测作比较.分析结果表明,月基对地观测具有良好的时空覆盖性能,尤其是角度覆盖度优点突出,有助于完善多角度遥感以及全球能量平衡观测系统.     

人造月球卫星的运动及其稳定性

得到了人造月球卫星在月球、地球和太阳引力作用下的运动:1)除轨道根数a,e,i外都有长期项;2)所有根数都有短周期变化,但是变化周期很短,振幅很小;3)除轨道半长径a以外都有长周期项。长周期项可以分为3部分:第一部分是由于月球扁率摄动造成的;第二部分是由于地球引力造成的;第三部分是二者联合摄动造成的。其中以第二种影响最大;它的周期约半个恒星月,振幅约3km和3ms~(-1)。还讨论了人造月球卫星以及相应的同步卫星的运动稳定性。     

A high-velocity black hole on a Galactic-halo orbit in the solar neighbourhood

Only a few of the dozen or so known stellar-mass black holes have been observed away from the plane of the Galaxy. Those few could have been ejected from the plane as a result of a 'kick' received during a supernova explosion, or they could be remnants of the population of massive stars formed in the early stages of evolution of the Galaxy. Determining their orbital motion should help to distinguish between these options. Here we report the transverse motion (in the plane of the sky) for the black-hole X-ray nova XTE J1118+480 (refs 2, 3, 4, 5), from which we derive a large space velocity. This X-ray binary system has an eccentric orbit around the Galactic Centre, like most objects in the halo of the Galaxy, such as ancient stars and globular clusters. The properties of the system suggest that its age is comparable to or greater than the age of the Galactic disk. Only an extraordinary 'kick' from a supernova could have launched the black hole into an orbit like this from a birthplace in the disk of the Galaxy.     

Improving the accuracy of GRACE Earth’s gravitational field using the combination of different inclinations

In this paper, the GRACE Earth＇s gravitational field complete up to degree and order 120 is recovered based on the combination of different inclinations using the energy conservation principle. The results show that because different inclinations of satellite are sensitive to the geopotential coefficients with different degrees l and orders m, the design of GRACE exploiting 89° inclination can effectively improve the accuracy of geopotential zonal harmonic coefficients. However, it is less sensitive to the geopotential tesseral harmonic coef- ficients. Accordingly, the second group of GRACE exploiting lower inclination is required to determine high-accurately the geopotential tesseral harmonic coefficients and cover the shortage of the single group of GRACE exploiting 89° inclination. Two groups of GRACE individually exploiting 89° ＋ （82°-84°） inclinations are the optimal combination of the Earth＇s gravitational field recovery complete up to degree and order 120. In the degree 120, the joint accuracy of cumulative geoid height based on two groups of GRACE individually exoloiting 89° and 83° inclinations is averagely two times higher than the accuracy of a group of GRACE exploiting 89~ inclination.     

Silicon in the Earth's core

Small isotopic differences between the silicate minerals in planets may have developed as a result of processes associated with core formation, or from evaporative losses during accretion as the planets were built up. Basalts from the Earth and the Moon do indeed appear to have iron isotopic compositions that are slightly heavy relative to those from Mars, Vesta and primitive undifferentiated meteorites (chondrites). Explanations for these differences have included evaporation during the 'giant impact' that created the Moon (when a Mars-sized body collided with the young Earth). However, lithium and magnesium, lighter elements with comparable volatility, reveal no such differences, rendering evaporation unlikely as an explanation. Here we show that the silicon isotopic compositions of basaltic rocks from the Earth and the Moon are also distinctly heavy. A likely cause is that silicon is one of the light elements in the Earth's core. We show that both the direction and magnitude of the silicon isotopic effect are in accord with current theory based on the stiffness of bonding in metal and silicate. The similar isotopic composition of the bulk silicate Earth and the Moon is consistent with the recent proposal that there was large-scale isotopic equilibration during the giant impact. We conclude that Si was already incorporated as a light element in the Earth's core before the Moon formed.     

Forming the lunar farside highlands by accretion of a companion moon

The most striking geological feature of the Moon is the terrain and elevation dichotomy between the hemispheres: the nearside is low and flat, dominated by volcanic maria, whereas the farside is mountainous and deeply cratered. Associated with this geological dichotomy is a compositional and thermal variation, with the nearside Procellarum KREEP (potassium/rare-earth element/phosphorus) Terrane and environs interpreted as having thin, compositionally evolved crust in comparison with the massive feldspathic highlands. The lunar dichotomy may have been caused by internal effects (for example spatial variations in tidal heating, asymmetric convective processes or asymmetric crystallization of the magma ocean) or external effects (such as the event that formed the South Pole/Aitken basin or asymmetric cratering). Here we consider its origin as a late carapace added by the accretion of a companion moon. Companion moons are a common outcome of simulations of Moon formation from a protolunar disk resulting from a giant impact, and although most coplanar configurations are unstable, a ～1,200-km-diameter moon located at one of the Trojan points could be dynamically stable for tens of millions of years after the giant impact. Most of the Moon's magma ocean would solidify on this timescale, whereas the companion moon would evolve more quickly into a crust and a solid mantle derived from similar disk material, and would presumably have little or no core. Its likely fate would be to collide with the Moon at ～2-3?km?s(-1), well below the speed of sound in silicates. According to our simulations, a large moon/Moon size ratio (～0.3) and a subsonic impact velocity lead to an accretionary pile rather than a crater, contributing a hemispheric layer of extent and thickness consistent with the dimensions of the farside highlands and in agreement with the degree-two crustal thickness profile. The collision furthermore displaces the KREEP-rich layer to the opposite hemisphere, explaining the observed concentration.     

Late formation and prolonged differentiation of the Moon inferred from W isotopes in lunar metals

The Moon is thought to have formed from debris ejected by a giant impact with the early 'proto'-Earth and, as a result of the high energies involved, the Moon would have melted to form a magma ocean. The timescales for formation and solidification of the Moon can be quantified by using 182Hf-182W and 146Sm-142Nd chronometry, but these methods have yielded contradicting results. In earlier studies, 182W anomalies in lunar rocks were attributed to decay of 182Hf within the lunar mantle and were used to infer that the Moon solidified within the first approximately 60 million years of the Solar System. However, the dominant 182W component in most lunar rocks reflects cosmogenic production mainly by neutron capture of 181Ta during cosmic-ray exposure of the lunar surface, compromising a reliable interpretation in terms of 182Hf-182W chronometry. Here we present tungsten isotope data for lunar metals that do not contain any measurable Ta-derived 182W. All metals have identical 182W/184W ratios, indicating that the lunar magma ocean did not crystallize within the first approximately 60 Myr of the Solar System, which is no longer inconsistent with Sm-Nd chronometry. Our new data reveal that the lunar and terrestrial mantles have identical 182W/184W. This, in conjunction with 147Sm-143Nd ages for the oldest lunar rocks, constrains the age of the Moon and Earth to Myr after formation of the Solar System. The identical 182W/184W ratios of the lunar and terrestrial mantles require either that the Moon is derived mainly from terrestrial material or that tungsten isotopes in the Moon and Earth's mantle equilibrated in the aftermath of the giant impact, as has been proposed to account for identical oxygen isotope compositions of the Earth and Moon.     

Saturn's moon Phoebe as a captured body from the outer Solar System

The orbital properties of Phoebe, one of Saturn's irregular moons, suggest that it was captured by the ringed planet's gravitational field rather than formed in situ. Phoebe's generally dark surface shows evidence of water ice, but otherwise the surface most closely resembles that of C-type asteroids and small outer Solar System bodies such as Chiron and Pholus that are thought to have originated in the Kuiper belt. A close fly-by of Phoebe by the Cassini-Huygens spacecraft on 11 June 2004 (19 days before the spacecraft entered orbit around Saturn) provided an opportunity to test the hypothesis that this moon did not form in situ during Saturn's formation, but is instead a product of the larger protoplanetary disk or 'solar nebula'. Here we derive the rock-to-ice ratio of Phoebe using its density combined with newly measured oxygen and carbon abundances in the solar photosphere. Phoebe's composition is close to that derived for other solar nebula bodies such as Triton and Pluto, but is very different from that of the regular satellites of Saturn, supporting Phoebe's origin as a captured body from the outer Solar System.     

Volatile accretion history of the Earth

It has long been thought that the Earth had a protracted and complex history of volatile accretion and loss. Albarède paints a different picture, proposing that the Earth first formed as a dry planet which, like the Moon, was devoid of volatile constituents. He suggests that the Earth's complement of volatile elements was only established later, by the addition of a small veneer of volatile-rich material at ～100 Myr (here and elsewhere, ages are relative to the origin of the Solar System). Here we argue that the Earth's mass balance of moderately volatile elements is inconsistent with Albarède's hypothesis but is well explained by the standard model of accretion from partially volatile-depleted material, accompanied by core formation.     

Obliquity pacing of the late Pleistocene glacial terminations

The 100,000-year timescale in the glacial/interglacial cycles of the late Pleistocene epoch (the past approximately 700,000 years) is commonly attributed to control by variations in the Earth's orbit. This hypothesis has inspired models that depend on the Earth's obliquity (approximately 40,000 yr; approximately 40 kyr), orbital eccentricity (approximately 100 kyr) and precessional (approximately 20 kyr) fluctuations, with the emphasis usually on eccentricity and precessional forcing. According to a contrasting hypothesis, the glacial cycles arise primarily because of random internal climate variability. Taking these two perspectives together, there are currently more than thirty different models of the seven late-Pleistocene glacial cycles. Here we present a statistical test of the orbital forcing hypothesis, focusing on the rapid deglaciation events known as terminations. According to our analysis, the null hypothesis that glacial terminations are independent of obliquity can be rejected at the 5% significance level, whereas the corresponding null hypotheses for eccentricity and precession cannot be rejected. The simplest inference consistent with the test results is that the ice sheets terminated every second or third obliquity cycle at times of high obliquity, similar to the original proposal by Milankovitch. We also present simple stochastic and deterministic models that describe the timing of the late-Pleistocene glacial terminations purely in terms of obliquity forcing.     

A low density of 0.8 g cm(-3) for the Trojan binary asteroid 617 Patroclus

The Trojan population consists of two swarms of asteroids following the same orbit as Jupiter and located at the L4 and L5 stable Lagrange points of the Jupiter-Sun system (leading and following Jupiter by 60 degrees ). The asteroid 617 Patroclus is the only known binary Trojan. The orbit of this double system was hitherto unknown. Here we report that the components, separated by 680 km, move around the system's centre of mass, describing a roughly circular orbit. Using this orbital information, combined with thermal measurements to estimate the size of the components, we derive a very low density of 0.8(- 0.1)+0.2 g cm(-3). The components of 617 Patroclus are therefore very porous or composed mostly of water ice, suggesting that they could have been formed in the outer part of the Solar System.