Dynamical behaviour of planetesimals temporarily captured by a planet from heliocentric orbits: basic formulation and the case of low random velocity

Planetesimals encountering with a planet cannot be captured permanently unless energy dissipation is taken into account, but some of them can be temporarily captured in the vicinity of the planet for an extended period of time. Such a process would be important for the origin and dynamical evolution of irregular satellites, short-period comets, and Kuiper-belt binaries. In this paper, we describe the basic formulation for the study of temporary capture of planetesimals from heliocentric orbits using three-body orbital integration, such as the definition of the duration and rate of temporary capture, and present results in the case of low random velocity of planetesimals. In the case of planetesimals initially on circular orbits, we find that planetesimals undergo a close encounter with the planet before they become temporarily captured. When planetesimals are scattered by the planet into the vicinity of one of periodic orbits around the planet, the duration of temporary capture tends to be extended. Typically, these capture orbits are in the retrograde direction around the planet. We evaluate the rate of temporary capture of planetesimals, and find that the ratio of this rate to their collision rate on to the planet increases with increasing semimajor axis of the planet. Similar results are obtained for planetesimals with non-zero but small random velocities, as long as Kepler shear dominates the relative velocity between the planet and planetesimals. For larger initial random velocities of planetesimals, temporary capture in both prograde and retrograde directions with much longer duration becomes possible.     

On the stability of hypothetical satellites coorbital to Mimas or Enceladus

In the present work, we study the stability of hypothetical satellites that are coorbital with Enceladus and Mimas. We performed numerical simulations of 50 particles around the triangular Lagrangian equilibrium points of Enceladus and Mimas taking into account the perturbation of Mimas, Enceladus, Tethys, Dione, Titan and the oblateness of Saturn. All particles remain on tadpole orbits after 10 000 yr of integration. Since in the past the orbit of Enceladus and Mimas expanded due to the tidal perturbation, we also simulated the system with Enceladus and Mimas at several different values of semimajor axes. The results show that in general the particles remain on tadpole orbits. The exceptions occur when Enceladus is at semimajor axes that correspond to 6:7, 5:6 and 4:5 resonances with Mimas. Therefore, if Enceladus and Mimas had satellites librating around their Lagrangian triangular points in the past, they would have been removed if Enceladus crossed one of these first-order resonances with Mimas.     

Dynamical evolution of the Prometheus–Pandora system

The system of Saturn's inner satellites is saturated with many resonances. Its structure should be strongly affected by tidal forces driving the satellites through several orbit–orbit resonances. The evolution of these satellites is investigated using analytic and numerical methods. We show that the pair of satellites Prometheus and Pandora has a particularly short lifetime (<20 Myr) if the orbits of the satellites converge without capture into a resonance. The capture of Pandora into a resonance with Prometheus increases the lifetime of the couple by a few tens of Myr. However, resonances of the system are not well separated, and capture results in a chaotic motion. Secondary resonances also disrupt the resonant configurations. In all cases, the converging orbits of these two satellites result in a close encounter. The implications for the origin of Saturn's rings are discussed.     

The dynamics of Neptune Trojan – I. The inclined orbits

The stability of Trojan type orbits around Neptune is studied. As the first part of our investigation, we present in this paper a global view of the stability of Trojans on inclined orbits. Using the frequency analysis method based on the fast Fourier transform technique, we construct high-resolution dynamical maps on the plane of initial semimajor axis a ₀ versus inclination i ₀. These maps show three most stable regions, with i ₀ in the range of  (0°, 12°), (22°, 36°)  and  (51°, 59°),  respectively, where the Trojans are most probably expected to be found. The similarity between the maps for the leading and trailing triangular Lagrange points L ₄ and L ₅ confirms the dynamical symmetry between these two points. By computing the power spectrum and the proper frequencies of the Trojan motion, we figure out the mechanisms that trigger chaos in the motion. The Kozai resonance found at high inclination varies the eccentricity and inclination of orbits, while the  ν₈  secular resonance around   i ₀∼ 44°  pumps up the eccentricity. Both mechanisms lead to eccentric orbits and encounters with Uranus that introduce strong perturbation and drive the objects away from the Trojan like orbits. This explains the clearance of Trojan at high inclination  (>60°)  and an unstable gap around  44°  on the dynamical map. An empirical theory is derived from the numerical results, with which the main secular resonances are located on the initial plane of  ( a ₀, i ₀)  . The fine structures in the dynamical maps can be explained by these secular resonances.     

Mutual occultations and eclipses of the Galilean satellites of Jupiter in 2002–2003: final astrometric results

The photometry of mutual occultations and eclipses of natural planetary satellites can be used to infer very accurate astrometric data. This can be achieved by processing the light curves of the satellites observed during international campaigns of photometric observations of these mutual events.
This work focuses on processing the complete data base of photometric observations of the mutual occultations and eclipses of the Galilean satellites made during the international campaign in 2002–2003. The final goal is to derive new accurate astrometric data.
We propose the most accurate photometric model of mutual events based on all the data available to date about the satellites, and develop the corresponding method for extracting astrometric data. This method is applied to derive astrometric data from photometric observations of mutual occultations and eclipses of the Galilean satellites.
We process the 371 light curves obtained during the international campaign of photometric observations of the Galilean satellites in 2002–2003. As compared with the theory, the rms 'O-C' residuals with respect to theory is equal to 0.055 and 0.064 arcsec in right ascension and declination, respectively, for the 274 best observations. Topocentric or heliocentric angular differences for satellite pairs are obtained for 119 time instants during the time period from 2002 October 10 to 2003 July 17.     

Geometric characterization of the Arjuna orbital domain

Arjuna‐type orbits are characterized by being Earth‐like, having both low‐eccentricity and low‐inclination. Objects following these trajectories experience repeated trappings in the 1:1 commensurability with the Earth and can become temporary Trojans, horseshoe librators, quasi‐satellites, and even transient natural satellites. Here, we review what we know about this peculiar dynamical group and use a Monte Carlo simulation to characterize geometrically the Arjuna orbital domain, studying its visibility both from the ground and with the European Space Agency Gaia spacecraft. The visibility analysis from the ground together with the discovery circumstances of known objects are used as proxies to estimate the current size of this population. The impact cross‐section of the Earth for minor bodies in this resonant group is also investigated. We find that, for ground‐based observations, the solar elongation at perigee of nearly half of these objects is less than 90°. They are best observed by space‐borne telescopes, but Gaia is not going to improve significantly the current discovery rate for members of this class. Our results suggest that the size of this population may have been underestimated by current models. On the other hand, their intrinsically low encounter velocities with the Earth induce a 10–1000‐fold increase in the impact cross‐section with respect to what is typical for objects in the Apollo or Aten asteroid populations. We estimate that their probability of capture as transient natural satellites of our planet is about 8 %. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Dynamical capture in the Pluto–Charon system

This paper explores the possibility that the progenitors of the small satellites of Pluto got captured in the Pluto?CCharon system from the massive heliocentric planetesimal disk in which Pluto was originally embedded into. We find that, if the dynamical excitation of the disk is small, temporary capture in the Pluto?CCharon system can occur with non- negligible probability, due to the dynamical perturbations exerted by the binary nature of the Pluto?CCharon pair. However, the captured objects remain on very elliptic orbits and the typical capture time is only ~ 100?years. In order to explain the origin of the small satellites of Pluto, we conjecture that some of these objects got disrupted during their Pluto-bound phase by a collision with a planetesimal of the disk. This could have generated a debris disk, which damped under internal collisional evolution, until turning itself into an accretional disk that could form small satellites on circular orbits, co-planar with Charon. Unfortunately, we find that objects large enough to carry a sufficient amount of mass to generate the small satellites of Pluto have collisional lifetimes orders of magnitude longer than the capture time. Thus, this scenario cannot explain the origin of the small satellites of Pluto, which remains elusive.     

Ringlet–satellite interactions

We study the interaction of a satellite and a nearby ringlet on eccentric and inclined orbits. Secular torques originate from mean motion resonances and the secular interaction potential which represents the m  = 1 global modes of the ring. The torques act on the relative eccentricity and inclination. The resonances damp the relative eccentricity. The inclination instability owing to the resonances is turned off by a finite differential eccentricity of the order of 0.27 for nearly coplanar systems. The secular potential torque damps the eccentricity and inclination and does not affect the relative semi-major axis; also, it suppresses the inclination instability that persists at small differential eccentricities. The damping of the relative eccentricity and inclination forces an initially circular and planar small mass ringlet to reach the eccentricity and inclination of the satellite. When the planet is oblate, the interaction of the satellite damps the proper precession of a small mass ringlet so that it precesses at the satellite's rate independently of their relative distance. The oblateness of the primary modifies the long-term eccentricity and inclination magnitudes and introduces a constant shift in the apsidal and nodal lines of the ringlet with respect to those of the satellite. These results are applied to Saturn's F-ring, which orbits between the moons Prometheus and Pandora.     

Jupiter and Super-Earth embedded in a gaseous disc

In this paper we investigate the evolution of a pair of interacting planets – a Jupiter-mass planet and a Super-Earth with a mass of  5.5 M _⊕  – orbiting a Solar-type star and embedded in a gaseous protoplanetary disc. We focus on the effects of type I and II orbital migrations, caused by the planet–disc interaction, leading to the capture of the Super-Earth in first-order mean-motion resonances by the Jupiter. The stability of the resulting resonant system in which the Super-Earth is on the internal orbit relative to the Jupiter is studied numerically by means of full 2D hydrodynamical simulations. Our main aim is to determine the Super-Earth behaviour in the presence of the gas giant in the system. It is found that the Jupiter captures the Super-Earth into the interior 3:2 or 4:3 mean-motion resonance, and that the stability of such configurations depends on the initial positions of the planets and on the evolution of the eccentricity. If the initial separation of the orbits of the planets is larger than or close to that required for the exact resonance, the final outcome is the migration of the pair of planets at a rate similar to that of the gas giant, at least for the time of our simulations. Otherwise, we observe a scattering of the Super-Earth from the disc. The evolution of planets immersed in a gaseous disc is compared with their behaviour in the case of the classical three-body problem when the disc is absent.     

The young long-period comet family of Saturn

The distributions of long-period comets with respect to the minimum distance Δ between their orbits and the orbit of Saturn or Jupiter, constructed by Konopleva using data up to 1972, exhibit a sharp peak at Δ<0.5 au for the Saturnian family, while being fairly monotonic for Jupiter. Hence, in view of the appreciable eccentricity of Saturn's orbit and the rotation of its perihelion longitude with a period of 47 kyr, the conclusion was drawn by Drobyshevski that the objects belonging to this peak are young (10 kyr).
Similar distributions constructed using more recent data show less pronounced differences between one another. Analysis of the distributions for various epochs shows that the initially noted difference is due to observational selection, being inherent to brighter comets. Since on average the cometary activity fades with age, the conclusion that the Saturnian family comets, forming the peak at Δ<0.5 au, are young is all the more substantiated. The question concerning the origin of these comets, which in all likelihood were ejected over a period of a decade from deep inside the Saturnian sphere of influence , is still open. The only self-consistent hypothesis that we see now is that of their appearance as a result of an explosion of the electrolysed ice envelope of Titan. We encourage the development of other explanations.     

Adiabatic chaos in the Prometheus–Pandora system

The chaotic orbital motion of Prometheus and Pandora, the 16th and 17th satellites of Saturn, is studied. Chaos in their orbital motion, as found by Goldreich & Rappaport and Renner & Sicardy, is due to interaction of resonances in the resonance multiplet corresponding to the 121:118 commensurability of the mean motions of the satellites. It is shown rigorously that the system moves in adiabatic regime. The Lyapunov time (the 'time horizon of predictability' of the motion) is calculated analytically and compared to the available numerical–experimental estimates. For this purpose, a method of analytical estimation of the maximum Lyapunov exponent in the perturbed pendulum model of non-linear resonance is applied. The method is based on the separatrix map theory. An analytical estimate of the width of the chaotic layer is made as well, based on the same theory. The ranges of chaotic diffusion in the mean motion are shown to be almost twice as big compared to previous estimates for both satellites.     

天体运动的轨道偏心率研究概述---从恒星系统到行星系统

偏心率是描述天体运动轨道的重要参数之一, 能够为揭示天体的动力学演化提供重要线索, 进而帮助理解天体形成与演化的过程及背后的物理机制. 随着天文观测技术的不断发展, 人们对于天体运动轨道的研究已经走出太阳系, 包含的系统也从大质量端的恒星系统延伸到了低质量端的行星系统. 聚焦天体轨道偏心率研究, 回顾了目前在恒星系统(包括主序恒星、褐矮星以及致密星)和行星系统(包括太阳系外巨行星以及``超级地球''、``亚海王星''等小质量系外行星)方面取得的进展, 总结了不同尺度结构下偏心率研究的一些共同之处和待解决的问题. 并结合当下和未来的相关天文观测设备和项目, 对未来天体轨道偏心率方面的研究工作进行了展望.     

Three-body capture of irregular satellites: Application to Jupiter

We investigate a new theory of the origin of the irregular satellites of the giant planets: capture of one member of a ∼100-km binary asteroid after tidal disruption. The energy loss from disruption is sufficient for capture, but it cannot deliver the bodies directly to the observed orbits of the irregular satellites. Instead, the long-lived capture orbits subsequently evolve inward due to interactions with a tenuous circumplanetary gas disk.We focus on the capture by Jupiter, which, due to its large mass, provides a stringent test of our model. We investigate the possible fates of disrupted bodies, the differences between prograde and retrograde captures, and the effects of Callisto on captured objects. We make an impulse approximation and discuss how it allows us to generalize capture results from equal-mass binaries to binaries with arbitrary mass ratios.We find that at Jupiter, binaries offer an increase of a factor of ∼10 in the capture rate of 100-km objects as compared to single bodies, for objects separated by tens of radii that approach the planet on relatively low-energy trajectories. These bodies are at risk of collision with Callisto, but may be preserved by gas drag if their pericenters are raised quickly enough. We conclude that our mechanism is as capable of producing large irregular satellites as previous suggestions, and it avoids several problems faced by alternative models.     

New confirmation of image-processing techniques for astrometry of Saturn and its satellites

The image-processing techniques used by Peng et al. are further improved to measure precisely the positions of Saturn and its satellites. 495 CCD images taken with the 1-m telescope at the Yunnan Observatory during the years 2002–2004 are processed with these techniques. These measured pixel positions are compared to their theoretical positions computed with the ephemerides of TASS1.7 for the satellites and JPL DE405 for Saturn itself. Analysis of the data for the intersatellite positions among four bright Saturnian satellites (S3–S6) and for Saturn–satellite (i.e. Saturn–Titan) positions shows that these measured positions have the same dispersions, i.e. about 0.05 and 0.06 arcsec in right ascension and declination, respectively. However, for the fainter satellites, Enceladus and Mimas, poorer residuals up to 0.1 and 0.2 arcsec, respectively, in both directions are found mainly due to their small separations from the primary planet and short exposure time in order to obtain useful images of Saturn.     

The parent of the Quadrantid meteoroid stream

The Quadrantid meteor shower is one of the major showers that produces reliable displays every January. However, it is unique amongst the major showers in still not having its parent uniquely identified. One of the reasons for this may be because the stream, and presumably the parent, lies in a region of the Solar system where near-resonant motion with Jupiter, coupled with potential close encounters, is possible. Such a combination can lead to a rapid dynamical evolution of an orbit. In particular, it may be possible that the orbit of the parent both satisfies the condition for a close encounter and is in resonant motion, while most of the meteoroids cannot satisfy both conditions. This results in the parent evolving away from the bulk of the stream.
To date, two suggestions have been made regarding possible parents for the Quadrantid stream, these being Comet 1491 I and Comet 96P/Machholz. The argument in favour of the first named being the parent is because of the general similarity between the orbits around 1491. The argument for comet 96P/Machholz being the parent is based on the similarity in orbital evolution coupled with a similarity in orbits phase-shifted by 2000 yr. In this paper we suggest that on both counts asteroid 5496 (1973 NA) is more similar to the Quadrantids, and that even if 5496 is not the actual parent in the strict sense that meteoroids are currently being ejected, it is either likely to be a fragment of the parent or the dormant remains of the parent.     

How selection and weighting of astrometric observations influence the impact probability. The case of asteroid (99942) Apophis

The aim of this paper is to show that in the case of a low probability of asteroid collision with the Earth, the appropriate selection and weighting of the data are crucial for the impact investigation and for analysing the impact possibilities using extensive numerical simulations. By means of the Monte Carlo special method, a large number of 'clone' orbits have been generated. A full range of orbital elements in the six-dimensional parameter space, that is, in the entire confidence region allowed by the observational material, has been examined. On the basis of 1000 astrometric observations of (99942) Apophis, the best solutions for the geocentric encounter distance of  6.065 ± 0.081 R_⊕  (without perturbations by asteroids) or  6.064 ± 0.095 R_⊕  (including perturbations by the four largest asteroids) were derived for the close encounter with the Earth on 2029 April 13. The present uncertainties allow for special configurations ('keyholes') during this encounter that may lead to very close encounters in future approaches of Apophis. Two groups of keyholes are connected with the close encounter with the Earth in 2036 (within the minimal distance of  5.7736−5.7763 R_⊕  on 2029 April 13) and 2037 (within the minimal distance of  6.3359–6.3488 R_⊕  ). The nominal orbits for our most accurate models run almost exactly in the middle of these two impact keyhole groups. A very small keyhole for the impact in 2076 has been found between these groups at the minimal distance of 5.97347   R_⊕  . This keyhole is close to the nominal orbit. The present observations are not sufficiently accurate to eliminate definitely the possibility of impact with the Earth in 2036 and for many years after.     

The composition of Saturn's E ring

We present the first in situ direct measurement of the composition of particles in Saturn's rings. The Cassini cosmic dust analyser (CDA) measured the mass spectra of nearly 300 impacting dust particles during the 2004 October E ring crossing. An initial interpretation of the data shows that the particles are predominantly water ice, with minor contributions from possible combinations of silicates, carbon dioxide, ammonia, molecular nitrogen, hydrocarbons and perhaps carbon monoxide. This places constraints on both the composition of Enceladus, the main source of the E ring, as well as the grain formation mechanisms.     

Yarkovsky origin of the unstable asteroids in the 2/1 mean motion resonance with Jupiter

The 2/1 mean motion resonance with Jupiter, intersecting the main asteroid belt at ≈3.27  au, contains a small population of objects. Numerical investigations have classified three groups within this population: asteroids residing on stable orbits (i.e. Zhongguos), those on marginally stable orbits with dynamical lifetimes of the order of 100 Myr (i.e. Griquas), and those on unstable orbits. In this paper, we reexamine the origin, evolution and survivability of objects in the 2/1 population. Using recent asteroid survey data, we have identified 100 new members since the last search, which increases the resonant population to 153. The most interesting new asteroids are those located in the theoretically predicted stable island A, which until now had been thought to be empty. We also investigate whether the population of objects residing on the unstable orbits could be resupplied by material from the edges of the 2/1 resonance by the thermal drag force known as the Yarkovsky effect (and by the YORP effect, which is related to the rotational dynamics). Using N -body simulations, we show that test particles pushed into the 2/1 resonance by the Yarkovsky effect visit the regions occupied by the unstable asteroids. We also find that our test bodies have dynamical lifetimes consistent with the integrated orbits of the unstable population. Using a semi-analytical Monte Carlo model, we compute the steady-state size distribution of magnitude   H < 14  asteroids on unstable orbits within the resonance. Our results provide a good match with the available observational data. Finally, we discuss whether some 2/1 objects may be temporarily captured Jupiter-family comets or near-Earth asteroids.     

Weak lensing signal in unified dark matter models

This paper is an extension of the work done by Pierens & Nelson in which they investigated the behaviour of a two-planet system embedded in a protoplanetary disc. They put a Jupiter mass gas giant on the internal orbit and a lower mass planet on the external one. We consider here a similar problem taking into account a gas giant with mass in the range 0.5 to  1 M _J  and a Super-Earth (i.e. a planet with mass  ≤10 M _⊕  ) as the outermost planet. By changing disc parameters and planet masses, we have succeeded in getting the convergent migration of the planets which allows for the possibility of their resonant locking. However, in the case in which the gas giant has the mass of Jupiter, before any mean-motion first-order commensurability could be achieved, the Super-Earth is caught in a trap when it is very close to the edge of the gap opened by the giant planet. This confirms the result obtained by Pierens & Nelson in their simulations. Additionally, we have found that, in a very thin disc, an apsidal resonance is observed in the system if the Super-Earth is captured in the trap. Moreover, the eccentricity of the small planet remains low, while the eccentricity of the gas giant increases slightly due to the imbalance between Lindblad and corotational resonances. We have also extended the work of Pierens & Nelson by studying analogous systems in which the gas giant is allowed to take sub-Jupiter masses. In this case, after conducting an extensive survey over all possible parameters, we have succeeded in getting the 1:2 mean-motion resonant configuration only in a disc with low aspect ratio and low surface density. However, the resonance is maintained just for a few thousand orbits. Thus, we conclude that for typical protoplanetary discs the mean-motion commensurabilities are rare if the Super-Earth is located on the external orbit relative to the gas giant.