任意倾角的共轨运动研究

共轨运动天体与摄动天体的半长径相同,处于1:1平运动共振中.太阳系内多个行星的特洛伊天体即为处于蝌蚪形轨道的共轨运动天体,其中一些高轨道倾角特洛伊天体的轨道运动与来源仍未被完全理解.利用一个新发展的适用于处理1:1平运动共振的摄动函数展开方式,对三维空间中的共轨运动进行考察,计算不同初始轨道根数情况下共轨轨道的共振中心、共振宽度,分析轨道类型与初始轨道根数的关系.并将分析方法所得结果与数值方法的结果相互比较验证,得到了广阔初始轨道根数空间内共轨运动的全局图景.     

Ultra-low delta-v objects and the human exploration of asteroids

Missions to near-Earth objects (NEOs) are key destinations in NASA's new ‘Flexible Path’ approach. NEOs are also of interest for science, for the hazards they pose, and for their resources. We emphasize the importance of ultra-low delta-v from LEO to NEO rendezvous as a target selection criterion, as this choice can greatly increase the payload to the NEO. Few such ultra-low delta-v NEOs are currently known; only 65 of the 6699 known NEOs (March 2010) have delta-v <4.5 km/s, 2/3 of typical LEO-NEO delta-v. Even these are small and hard to recover. Other criteria – short transit times, long launch windows, a robust abort capability, and a safe environment for proximity operations – will further limit the list of accessible objects. Potentially there is at least an order of magnitude more ultra-low delta-v NEOs, but finding them all on a short enough timescale (before 2025) requires a dedicated survey in the optical or mid-IR, optimally from a Venus-like orbit because of the short synodic period for NEOs in that orbit, plus long arc determination of their orbits.     

Discovery of an asteroid and quasi‐satellite in an Earth‐like horseshoe orbit

Abstract— The newly discovered asteroid 2002 AA₂₉ moves in a very Earth‐like orbit that relative to Earth has a unique horseshoe shape and allows transitions to a quasi‐satellite state. This is the first body known to be in a simple heliocentric horseshoe orbit, moving along its parent planet's orbit. It is similarly also the first true co‐orbital object of Earth, since other asteroids in 1:1 resonance with Earth have orbits very dissimilar from that of our planet. When a quasi‐satellite, it remains within 0.2 AU of the Earth for several decades. 2002 AA₂₉ is the first asteroid known to exhibit this behavior. 2002 AA₂₉ introduces an important new class of objects offering potential targets for space missions and clues to asteroid orbit transfer evolution.     

Asteroids in the Eccentrids meteor system

Among 11 673 of near-Earth objects (NEOs), 52 asteroids are identified, which, together with the Eccentrids meteor system, comprise a single population of small bodies of the Solar System with the smallest orbits of high eccentricity. Some features of this unique system of bodies are discussed in this paper. The distribution of perihelion longitudes is studied for the given group of asteroids and compared to that of the Aten asteroids, which are the most similar to the Eccentrids. The dependence is obtained of the character of perihelion longitude distribution on the eccentricities of the NEO orbits. Eight asteroid stream of the Eccentrids are found. The Eccentrids asteroids approaching the Earth’s orbit along its whole length in their aphelia can pose a certain hazard for the Earth.     

Associations Between Asteroids and Meteoroid Streams

The recent systematic monitoring of the skies has led to the discovery of an increasingly large number of objects on Earth approaching orbits. Not surprisingly, an increasing number of this population have also been associated with meteoroid streams in the literature. We will review the history of this topic. We have also conducted our own search for asteroids moving on orbits that are similar to the orbits of known fireball streams. As NEOs are moving in prograde orbits with low geocentric velocities, any potential streams will have large radiant areas and in consequence, may have been identified as several "sub-streams". This greatly hampers both their detection and their recognition as single meteoroid streams. With the large number of Near Earth Asteroids detected, the probability of two orbits being similar at the present time by coincidence is high. We have therefore also investigated the evolution of the orbits and only include as real asteroid-stream pairs those where the evolution is also similar over 5000 years. We have identified nine pairs, including the well known pair of the Geminid meteoroid stream and asteroid 3200 Phaethon. Currently there are a number of papers being published on the pairing of asteroid 2003 EH1 and the Quadrantid meteoroid stream. Because of the newness of the research and the fact that this is a high inclination pair, we have excluded this pair from our discussions.     

Modeling orbital relative motion to enable formation design from application requirements

While trajectory design for single satellite Earth observation missions is usually performed by means of analytical and relatively simple models of orbital dynamics including the main perturbations for the considered cases, most literature on formation flying dynamics is devoted to control issues rather than mission design. This work aims at bridging the gap between mission requirements and relative dynamics in multi-platform missions by means of an analytical model that describes relative motion for satellites moving on near circular low Earth orbits. The development is based on the orbital parameters approach and both the cases of close and large formations are taken into account. Secular Earth oblateness effects are included in the derivation. Modeling accuracy, when compared to a nonlinear model with two body and J₂ forces, is shown to be of the order of 0.1% of relative coordinates for timescales of hundreds of orbits. An example of formation design is briefly described shaping a two-satellite formation on the basis of geometric requirements for synthetic aperture radar interferometry.     

A survey of orbits of co-orbitals of Mars

Many asteroids with a semimajor axis close to that of Mars have been discovered in the last several years. Potentially some of these could be in 1:1 resonance with Mars, much as are the classic Trojan asteroids with Jupiter, and its lesser-known horseshoe companions with Earth. In the 1990s, two Trojan companions of Mars, 5261 Eureka and 1998 VF₃₁, were discovered, librating about the L₅ Lagrange point, 60° behind Mars in its orbit. Although several other potential Mars Trojans have been identified, our orbital calculations show only one other known asteroid, 1999 UJ₇, to be a Trojan, associated with the L₄ Lagrange point, 60° ahead of Mars in its orbit. We further find that asteroid 36017 (1999 ND₄₃) is a horseshoe librator, alternating with periods of Trojan motion. This asteroid makes repeated close approaches to Earth and has a chaotic orbit whose behavior can be confidently predicted for less than 3000 years. We identify two objects, 2001 HW₁₅ and 2000 TG₂, within the resonant region capable of undergoing what we designate “circulation transition”, in which objects can pass between circulation outside the orbit of Mars and circulation inside it, or vice versa. The eccentricity of the orbit of Mars appears to play an important role in circulation transition and in horseshoe motion. Based on the orbits and on spectroscopic data, the Trojan asteroids of Mars may be primordial bodies, while some co-orbital bodies may be in a temporary state of motion.     

Planet crossing asteroids and parallel computing: Project spaceguard

The orbits of the asteroids crossing the orbit of the Earth and other planets are chaotic and cannot be computed in a deterministic way for a time span long enough to study the probability of collisions. It is possible to study the statistical behaviour of a large number of such orbits over a long span of time, provided enough computing resources and intelligent post processing software are available. The former, problem can be handled by exploiting the enormous power of parallel computing systems. The orbit of the asteroids can be studied as a restricted (N+M)-body problem which is suitable for the use of parallel processing, by using one processor to compute the orbits of the planets and the others to compute the orbits the asteroids. This scheme has been implemented on LCAP-2, an array of IBM and FPS processors with shared memory designed by E. Clementi (IBM). The parallelisation efficiency has been over 80%, and the overall speed over 90 MegaFLOPS; the orbits of all the asteroids with perihelia lower than the aphelion of Mars (410 objects) have been computed for 200,000, years (Project SPACEGUARD). The most difficult step of the project is the post processing of the very large amount of output data and to gather qualitative information on the behaviour of so many orbits without resorting to the traditional technique, i.e. human examination of output in graphical form. Within Project SPACEGUARD we have developed a qualitative classification of the orbits of the planet crossers. To develop an entirely automated classification of the qualitative orbital behaviour-including crossing behaviour, resonances (mean motion and secular), and protection mechanisms avoiding collisions-is a challenge to be met.     

Theoretical meteor radiants for macroscopic Taurid Complex objects

The calculation of theoretical meteor radiants is discussed for comets and asteroids whose orbits pass within, but at present do not necessarily intersect, that of the Earth, in particular from the perspective of developing a suitable method for application to Taurid Complex orbits. The main question addressed here is how to allow for dynamical evolution between epochs when an orbit isnot Earth-intersecting (as at present in most cases for macroscopic bodies) and those when itis (i.e., when meteors can actually be observed). This should be understood in terms of evolution in the past, such that meteoroids released some time ago have evolved differentially from the putative parents, allowing meteors to be detected now. Theoretical radiants for macroscopic Taurid objects are then presented and compared with observations of the nighttime and daytime Taurid meteor showers. These are found to be broadly similar in form, given the sparsity of some of the data, adding weight to the hypothesis that this sub-jovian complex contains kilometre-plus asteroids. A similar conclusion results for the group of objects in similar orbits to (2212) Hephaistos.     

Rotational excitation and damping as probes of interior structures of asteroids and comets

Abstract— Rotational excitation and damping are discussed in the context of inferring structural properties of asteroids and comets. Opportunities for carrying out deterministic experiments are outlined and basic concepts involving space missions are discussed. Spacecraft carrying an impactor or explosives together with an orbiter are suggested as effective probes of the interiors of asteroid and comets. The feasibility of such missions, especially to near‐Earth objects (NEOs), is highlighted as NEOs provide an appropriate cost‐effective path to explore interiors of asteroids and comets.     

Mining the CFHT Legacy Survey for known Near Earth Asteroids

The Canada‐France‐Hawaii Legacy Survey (CFHTLS) comprising about 25 000 MegaCam images was data mined to search for serendipitous encounters of known Near Earth Asteroids (NEAs) and Potentially Hazardous Asteroids (PHAs). A total of 143 asteroids (109 NEAs and 34 PHAs) were found on 508 candidate images which were field corrected and measured carefully, and their astrometry was reported to Minor Planet Centre. Both recoveries and precoveries (apparitions before discovery) were reported, including data for 27 precovered asteroids (20 NEAs and 7 PHAs) and 116 recovered asteroids (89 NEAs and 27 PHAs). Our data prolonged arcs for 41 orbits at first or last opposition, refined 35 orbits by fitting data taken at one new opposition, recovered 6 NEAs at their second opposition and allowed us to ameliorate most orbits and their Minimal Orbital Intersection Distance (MOID), an important parameter to monitor for potential Earth impact hazard in the future (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Mostly Dormant Comets and their Disintegration into Meteoroid Streams: A Review

The history of associating meteor showers with asteroidal-looking objects is long, dating to before the 1983 discovery that 3200 Phaethon moves among the Geminids. Only since the more recent recognition that 2003 EH1 moves among the Quadrantids are we certain that dormant comets are associated with meteoroid streams. Since that time, many orphan streams have found parent bodies among the newly discovered Near Earth Objects. The seven established associations pertain mostly to showers in eccentric or highly inclined orbits. At least 35 other objects are tentatively linked to streams in less inclined orbits that are more difficult to distinguish from those of asteroids. There is mounting evidence that the streams originated from discrete breakup events, rather than long episodes of gradual water vapor outgassing. If all these associations can be confirmed, they represent a significant fraction of all dormant comets that are in near-Earth orbits, suggesting that dormant comets break at least as frequently as the lifetime of the streams. I find that most pertain to NEOs that have not yet fully decoupled from Jupiter. The picture that is emerging is one of rapid disintegration of comets after being captured by Jupiter, and consequently, that objects such as 3200 Phaethon most likely originated from among the most primitive asteroids in the main belt, instead. They too decay mostly by disintegration into comet fragments and meteoroid streams. The disintegration of dormant comets is likely the main source of our meteor showers and the main supply of dust to the zodiacal cloud. Editorial handling: Frans Rietmeijer.     

Inner Solar System dynamical analogs of plutinos

By studying orbits of asteroids potentially in 3:2 exterior mean motion resonance with Earth, Venus, and Mars, we have found plutino analogs. We identify at least 27 objects in the inner Solar System dynamically protected from encounter through this resonance. These are four objects associated with Venus, six with Earth, and seventeen with Mars. Bodies in the 3:2 exterior resonance (including those in the plutino resonance associated with Neptune) orbit the Sun twice for every three orbits of the associated planet, in such a way that with sufficiently low libration amplitude close approaches to the planet are impossible. As many as 15% of Kuiper Belt objects share the 3:2 resonance, but are poorly observed. One of several resonance sweeping mechanisms during planetary migration is likely needed to explain the origin and properties of 3:2 resonant Kuiper Belt objects. Such a mechanism likely did not operate in the inner Solar System. We suggest that scattering by the next planet out allows entry to, and exit from, 3:2 resonance for objects associated with Venus or Earth. 3:2 resonators of Mars, on the other hand, do not cross the paths of other planets, and have a long lifetime. There may exist some objects trapped in the 3:2 Mars resonance which are primordial, with our tests on the most promising objects known to date indicating lifetimes of at least tens of millions of years. Identifying 3:2 resonant systems in the inner Solar System permits this resonance to be studied on shorter timescales and with better determined orbits than has been possible to date, and introduces new mechanisms for entry into the resonant configuration.     

Atlas of the mean motion resonances in the Solar System

The aim of this work is to present a systematic survey of the strength of the mean motion resonances (MMRs) in the Solar System. We know by applying simple formulas where the resonances with the planets are located but there is no indication of the strength that these resonances have. We propose a numerical method for the calculation of this strength and we present an atlas of the MMRs constructed with this method. We found there exist several resonances unexpectedly strong and we look and find in the small bodies population several bodies captured in these resonances. In particular in the inner Solar System we find one asteroid in the resonance 6:5 with Venus, five asteroids in resonance 1:2 with Venus, three asteroids in resonance 1:2 with Earth and six asteroids in resonance 2:5 with Earth. We find some new possible co-orbitals of Earth, Mars, Saturn, Uranus and Neptune. We also present a discussion about the behavior of the resonant disturbing function and where the stable equilibrium points can be found at low and high inclination resonant orbits.     

A search program for objects in the vicinity of the Earth

Using a Super-Schmidt camera installed at the Cesco Observatory we are developing a program conducted to detect asteroids (especially members of the Aten Group) and comets approaching the Earth. The search strategy is based on simulations of the population of objects in this kind of orbits.     

Orbital maneuver optimization using time-explicit power series

Orbital maneuver transfer time optimization is traditionally accomplished using direct numerical sampling to find the mission design with the lowest delta-v requirements. The availability of explicit time series solutions to the Lambert orbit determination problem allows for the total delta-v of a series of orbital maneuvers to be expressed as an algebraic function of only the individual transfer times. The delta-v function is then minimized for a series of maneuvers by finding the optimal transfer times for each orbital arc. Results are shown for the classical example of the Hohmann transfer, a noncoplanar transfer as well as an interplanetary fly-by mission to the asteroids Pallas and Juno.     

Transient co-orbital asteroids

We analyze the orbital behavior of four new co-orbital NEOs and the Earth horseshoe object 2002 AA29. The new objects are 2001 CK32, a 3753 Cruithne-like co-orbital of Venus, 2001 GO2 and 2003 YN107, two objects with motion similar to 2002 AA29. 2001 CK32 is on a compound orbit. The asteroid reverses its path when the mean longitude difference is −50°. Its motion is chaotic. 2001 GO2 is an Earth HS orbiter with repeated transitions to the QS phase, the next occurring 200 years from now. The HS libration period is 190 years and the QS phases last 45 years. For 2002 AA29, our simulations permit us to find useful theoretical insights into the HS-QS transitions. Its orbit can be simulated with adequate accuracy for 4400 years into the future and 1483 years into the past. The new co-orbital 2003 YN107 is at present an Earth QS. It has entered this phase in 1997 and will leave it again in 2006, completing one QS cycle. Like 2002 AA29, it has frequent transitions between HS and QS. One HS cycle takes 133 years.     

Near-Sun asteroids

As follows from dynamical studies, in the course of evolution, most near-Earth objects reach orbits with small perihelion distances. Changes of the asteroids in the vicinity of the Sun should play a key role in forming the physical properties, size distribution, and dynamical features of the near-Earth objects. Only seven of the discovered asteroids are currently moving along orbits with perihelion distances q < 0.1 AU. However, due to the Kozai–Lidov secular perturbations, the asteroids, having recently passed near the Sun, could by now have moved to orbits farther from the Sun. In this study, we found asteroids that have been recently orbiting with perihelion distances q < 0.1 AU. Asteroids may be on such orbits for hundreds to tens of thousands of years. To carry out astrophysical observations of such objects is a high priority.     

A concept for providing warning of earth impacts by small asteroids

The atmospheric detonation of a 17 m-asteroid above Chelyabinsk, Russia on 2013 February 15 shows that even small asteroids can cause extensive damage. Earth-based telescopes have found smaller harmless objects, such as 2008 TC3, a 4 m-asteroid that was discovered 20h before it exploded over northeastern Sudan (Jenniskens, 2009). 2008 TC3 remains the only asteroid discovered before it hit Earth because it approached Earth from the night side, where it was observed by large telescopes searching for near-Earth objects (NEO’s). The larger object that exploded over Chelyabinsk approached Earth from the day side, from too close to the Sun to be detected from Earth. A sizeable telescope in an orbit about the Sun-Earth L1 (SE-L1) libration point could find objects like the “Chelyabinsk” asteroid approaching approximately from the line of sight to the Sun about a day before Earth closest approach. Such a system would have the astrometric accuracy needed to determine the time and impact zone for a NEO on a collision course. This would give at least several hours, and usually 2–4 days, to take protective measures, rather than the approximately two-minute interval between the flash and shock wave arrival that occurred in Chelyabinsk. A perhaps even more important reason for providing warning of these events, even smaller harmless ones that explode high in the atmosphere with the force of an atomic bomb, is to prevent mistaking such an event for a nuclear attack that could trigger a devastating nuclear war. A concept using a space telescope similar to that needed for an SE-L1 monitoring satellite, is already conceived by the B612 Foundation, whose planned Sentinel Space Telescope could find nearly all 140 m and larger NEO’s, including those in orbits mostly inside the Earth’s orbit that are hard to find with Earth-based telescopes, from a Venus-like orbit (Lu, 2013). Few modifications would be needed to the Sentinel Space Telescope to operate in a SE-L1 orbit, 0.01 AU from Earth towards the Sun, to find most asteroids larger than about 5 meters that approach the Earth from the solar direction. The spacecraft would scan 165 square degrees of the sky around the Earth every hour, finding asteroids when they are brightest (small phase angle) as they approach Earth. We will undertake Monte Carlo studies to see what fraction of asteroids 5 m and larger approaching from the Sun might be found by such a mission, and how much warning time might typically be expected. Also, we will check the overall coverage for all Earth-approaching NEO’s, including ground-based observations and observations by the recently-launched NEOSSat, which may best fill any gaps in coverage between that provided by an SE-L1 telescope and ground-based surveys. Many of the objects as large as 50 m, like the one that created Meteor Crater in Arizona, will not be found by current NEO surveys, while they would usually be seen by this possible mission even if they approached from the direction of the Sun. We should give better warning for future “Bolts out of the blue.”     

Properties of collision trajectories of asteroids with the earth

Close encounters of asteroids with the Earth can lead to a transition to resonant orbits, close encounters, and collisions in the future. The structure of the sets of possible collisions of asteroids with the Earth is similar to a fractal structure thanks to resonant returns of asteroids. Areas of semi-major axes and positions and sizes of gaps leading to collisions with the Earth for Apophis asteroids 2007 VK184 and 2011 AG5 are given.