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Ma&#;gorzata Królikowska Grzegorz Sitarski Andrzej M. So&#;tan 《Monthly notices of the Royal Astronomical Society》2009,399(4):1964-1976
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. 相似文献
3.
Analytical description of physical librations of saturnian coorbital satellites Janus and Epimetheus
Janus and Epimetheus are famously known for their distinctive horseshoe-shaped orbits resulting from a 1:1 orbital resonance. Every 4 years these two satellites swap their orbits by a few tens of kilometers as a result of their close encounter. Recently Tiscareno et al. (Tiscareno, M.S., Thomas, P.C., Burns, J.A. [2009]. Icarus 204, 254-261) have proposed a model of rotation based on images from the Cassini orbiter. These authors inferred the amplitude of rotational librational motion in longitude at the orbital period by fitting a shape model to Cassini ISS images. By a quasi-periodic approximation of the orbital motion, we describe how the orbital swap impacts the rotation of the satellites. To that purpose, we have developed a formalism based on quasi-periodic series with long- and short-period librations. In this framework, the amplitude of the libration at the orbital period is found proportional to a term accounting for the orbital swap. We checked the analytical quasi-periodic development by performing a numerical simulation and find both results in good agreement. To complete this study, the results obtained for the short-period librations are studied with the help of an adiabatic-like approach. 相似文献
4.
The situation leading to the determination of the Hale-Bopp orbit is discussed, largely in terms of a procedure that generates
two sequences of parabolic orbits. The comet is also considered in relation to the problem of the possibility of impact on
the earth. The placement of its orbital nodes near the orbits of the earth and Jupiter is clearly an intriguing feature. The
role of the prediscovery observation in 1993 is described, as it appeared both as a boon and a burden. Although evidence has
been put forward that the Hale-Bopp nucleus is unusually large, it seems likely that nongravitational forces are noticeably
affecting the comet's motion. While discussion of the comet's future long-term motion may be amenable to the usual treatment
as a problem of diffusion, it is not entirely improbable that the present situation arose from a recent dramatic approach
to Jupiter. It is shown that such a Jupiter encounter in June -2215 is not inconsistent with the non-existence of records
at the comet's last perihelion passage, which could then have been the first to occur as close as 0.9 AU to the sun. Of course,
the Jupiter encounter might also have given rise to the possible large satellite to Hale-Bopp discussed by Sekanina.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
5.
Pluto and the chaotic satellite system of Neptune may have originated from a single encounter of Neptune with a massive solar system body. A series of numerical experiments has been carried out to try to set limits on the circumstances of such an encounter. These experiments show that orbits very much like those of Pluto, Triton, and Nereid can result from a single close encounter of such a body with Neptune. The implied mass range and encounter velocities limit the source of the encountering body to a former trans-Neptunian planet in the 2- to 5-Earth-mass range. 相似文献
6.
A. Carusi G. B. Valsechi R. Greenberg 《Celestial Mechanics and Dynamical Astronomy》1990,49(2):111-131
Öpik's assumptions on the geometry of particle trajectories leading to and through planetary close encounters are used to compute the distribution of changes in heliocentric orbital elements that result from such encounters for a range of initial heliocentric orbits. Behaviour at encounter is assumed to follow two-body (particle—planet) gravitational scattering, while before and after encounter particle motion is only governed by the force of the Sun. Derivation of these distributions allows precise analysis of the probability of various outcomes in terms of the physical characteristics of the bodies involved. For example, they allow an explanation and prediction of the asymmetry of the extreme energy perturbations for different initial orbits. The formulae derived here may be applied to problems including the original accumulation of planets and satellites, and the continuing evolution of populations of small bodies, such as asteroids and comets. 相似文献
7.
The dynamics of near-Earth asteroids near mean motion resonances with the Earth or other planets is considered. The probability domains of the motion of some near-Earth asteroids close to low-order resonances are presented. The investigations have been carried out by means of a numerical integration of differential equations, taking into account the perturbations from the major planets and the Moon. For each investigated object an ensemble of 100 test particles with orbital elements nearby those of the nominal orbit has been constructed and its evolution has been retraced over the time interval (–3000, +3000 years). The initial set of orbits has been generated on the basis of probable variations of the initial orbital elements obtained from the least square analysis of observations.This revised version was published online in October 2005 with corrections to the Cover Date. 相似文献
8.
V. Batllo 《Celestial Mechanics and Dynamical Astronomy》1998,71(3):191-201
The objective of this paper is to develop a simple model of an encounter between a comet and a planet, with a subsequent capture
or an escape, and to study the potential consequences. The hypothetical scenario is as follows: a comet with a conic orbit
meets close to one of its vertices (located near the ecliptic plane), a jovian planet, and transforms its orbit. There are
two hypotheses which are made for the shock: this vertex becomes one of the final vertices and the orbital plane of the comet
is unchanged during the encounter as it was the case for Brooks 2 in 1886.
In this model, it was able to find an equation which was then used to obtain the pre‐ and post‐encounter orbits elements and
the kind of orbit (ellipse, hyperbola, parabola) with respect to the initial inclination. The numerical experiments with the
observed comets often provide pre‐encounter orbits with an aphelion point located near another jovian planet farther from
the Sun, and so on with sometimes several planets, or with an aphelion point located beyond the Pluto orbit.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
9.
This study of the orbital evolution and encounters of distant satellites of planets is aimed at determining their origin. It is also important for understanding the distribution of matter in the early stages of evolution of the Solar System. The mutual encounter of satellites is very weak because of their small sizes and masses. However, at very large time intervals, mutual encounter can be quite close to significantly changing the orbits of satellites. In order to study these factors, we have developed a special method and computer programs. For 107 distant satellites of Jupiter, Saturn, Uranus, and Neptune, motion parameters have been determined using observational data. On the basis of these parameters, a numerical integration of the equations of motion of the satellites has been carried out in time intervals of several thousand years. Using the original method of frequency analysis, we found rather simple analytical functions that correspond to the results of the numerical integration and make it possible to calculate orbital parameters at any time during a long interval. These tools make it possible to conduct extensive studies of changes in the form and relative position in space of the orbits of distant satellites of Jupiter, Saturn, Uranus, and Neptune. Several examples illustrate the possibilities offered by these tools. The computer software in the form of a service ephemeris of satellite orbits over a long interval of time is available via the Internet (http://www.sai.msu.ru/neb/nss/evolu0e.htm) on the website of the State Astronomical Institute of the Moscow State University. 相似文献
10.
Numerical integrations of 99 orbits centered on that of comet P/Scotti (P/2000 Y3), and of the nominal orbit, were made 4000 days backwards in time, and 73000 days into the future. The integrations show that this comet has been transferred into its present orbit as recently as 1998. The future orbital evolution indicates a stable period for almost 150 years, when another close encounter with Jupiter may lead to further drastic changes of the present orbit. 相似文献
11.
The stability of the motion of a hypothetical planet in the binary system ?? Cen A?CB has been investigated. The analysis has been performed within the framework of a planar (restricted and full) three-body problem for the case of prograde orbits. Based on a representative set of initial data, we have obtained the Lyapunov spectra of the motion of a triple system with a single planet. Chaotic domains have been identified in the pericenter distance-eccentricity plane of initial conditions for the planet through a statistical analysis of the data obtained. We have studied the correspondence of these chaotic domains to the domains of initial conditions that lead to the planet??s encounter with one of the binary??s stars or to the escape of the planet from the system. We show that the stability criterion based on the maximum Lyapunov exponent gives a more clear-cut boundary of the instability domains than does the encounterescape criterion at the same integration time. The typical Lyapunov time of chaotic motion is ??500 yr for unstable outer orbits and ??60 yr for unstable inner ones. The domain of chaos expands significantly as the initial orbital eccentricity of the planet increases. The chaos-order boundary has a fractal structure due to the presence of orbital resonances. 相似文献
12.
Iwan P. Williams & Collander-Brown 《Monthly notices of the Royal Astronomical Society》1998,294(1):127-138
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. 相似文献
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. 相似文献
13.
The significant orbital eccentricities of most giant extrasolar planets may have their origin in the gravitational dynamics of initially unstable multiple planet systems. In this work, we explore the dynamics of two close planets on inclined orbits through both analytical techniques and extensive numerical scattering experiments. We derive a criterion for two equal mass planets on circular inclined orbits to achieve Hill stability, and conclude that significant radial migration and eccentricity pumping of both planets occurs predominantly by 2:1 and 5:3 mean motion resonant interactions. Using Laplace-Lagrange secular theory, we obtain analytical secular solutions for the orbital inclinations and longitudes of ascending nodes, and use those solutions to distinguish between the secular and resonant dynamics which arise in numerical simulations. We also illustrate how encounter maps, typically used to trace the motion of massless particles, may be modified to reproduce the gross instability seen by the numerical integrations. Such a correlation suggests promising future use of such maps to model the dynamics of more coplanar massive planet systems. 相似文献
14.
F. MarzariS.J. Weidenschilling 《Icarus》2002,156(2):570-579
Most extrasolar planets discovered to date are more massive than Jupiter, in surprisingly small orbits (semimajor axes less than 3 AU). Many of these have significant orbital eccentricities. Such orbits may be the product of dynamical interactions in multiplanet systems. We examine outcomes of such evolution in systems of three Jupiter-mass planets around a solar-mass star by integration of their orbits in three dimensions. Such systems are unstable for a broad range of initial conditions, with mutual perturbations leading to crossing orbits and close encounters. The time scale for instability to develop depends on the initial orbital spacing; some configurations become chaotic after delays exceeding 108 y. The most common outcome of gravitational scattering by close encounters is hyperbolic ejection of one planet. Of the two survivors, one is moved closer to the star and the other is left in a distant orbit; for systems with equal-mass planets, there is no correlation between initial and final orbital positions. Both survivors may have significant eccentricities, and the mutual inclination of their orbits can be large. The inner survivor's semimajor axis is usually about half that of the innermost starting orbit. Gravitational scattering alone cannot produce the observed excess of “hot Jupiters” in close circular orbits. However, those scattered planets with large eccentricities and small periastron distances may become circularized if tidal dissipation is effective. Most stars with a massive planet in an eccentric orbit should have at least one additional planet of comparable mass in a more distant orbit. 相似文献
15.
A number of extrasolar planets have been detected in close orbits around nearby stars. It is probable that these planets did
not form in these orbits but migrated from their formation locations beyond the ice line. Orbital migration mechanisms involving
angular momentum transfer through tidal interactions between the planets and circumstellar gas-dust disks or by gravitational
interaction with a residual planetesimal disk together with several means of halting inward migration have been identified.
These offer plausible schemes to explain the orbits of observed extrasolar giant planets and giant planets within the Solar
System. Recent advances in numerical integration methods and in the power of computer workstations have allowed these techniques
to be applied to modelling directly the mechanisms and consequences of orbital migration in the Solar System. There is now
potential for these techniques also to be applied to modelling the consequences of the orbital migration of planets in the
observed exoplanetary systems. In particular the detailed investigation of the stability of terrestrial planets in the habitable
zone of these systems and the formation of terrestrial planets after the dissipation of the gas disk is now possible. The
stability of terrestrial planets in the habitable zone of selected exoplanetary systems has been established and the possibility
of the accretion of terrestrial planets in these systems is being investigated by the author in collaboration with Barrie
W. Jones (Open University), and with John Chambers (NASA-Ames) and Mark Bailey of Armagh Observatory, using numerical integration.
The direct simulation of orbital migration by planetesimal scattering must probably await faster hardware and/or more efficient
algorithms.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
16.
Using statistical orbital ranging, we systematically study the orbit computation problem for transneptunian objects (TNOs). We have automated orbit computation for large numbers of objects, and, more importantly, we are able to obtain orbits even for the most sparsely observed objects (observational arcs of a few days). For such objects, the resulting orbit distributions include a large number of high-eccentricity orbits, in which TNOs can be perturbed by close encounters with Neptune. The stability of bodies on the computed orbits has therefore been ascertained by performing a study of close encounters with the major planets. We classify TNO orbit distributions statistically, and we study the evolution of their ephemeris uncertainties. We find that the orbital element distributions for the most numerous single-apparition TNOs do not support the existence of a postulated sharp edge to the belt beyond 50 AU. The technique of statistical ranging provides ephemeris predictions more generally than previously possible also for poorly observed TNOs. 相似文献
17.
We systematically investigate the encounters between the Sun and neighbouring stars and their effects on cometary orbits in the Oort cloud, including the intrinsic one with the star Gl 710 (HIP 89 825), with some implications to stellar and cometary dynamics. Our approach is principally based on the combination of a Keplerian‐rectilinear model of stellar passages and the Hipparcos Catalogue (ESA 1997). Beyond the parameters of encounter, we pay particular attention to the observational errors in parallaxes and stellar velocities, and their propagation in time. Moreover, as a special case of this problem, we consider the collision probability of a star passing very closely to the Sun, taking also into account the mutual gravitational attraction between the stars. In the part dealing with the influence of stellar encounters on the orbital elements of Oort cloud comets, we derive new simple formulae calculating the changes in the cometary orbital elements, expressed as functions of the Jeans impulse formula. These expressions are then applied to calculate numerical values of the element changes caused by close encounters of neighbouring stars with some model comets in the Oort cloud. Moreover, the general condition for an ejection of comets from the cloud effected by a single encounter is derived and discussed. 相似文献
18.
Cezary Migaszewski Krzysztof Go&#;dziewski Tobias C. Hinse 《Monthly notices of the Royal Astronomical Society》2009,395(3):1204-1212
We investigate the dynamics of putative Earth-mass planets in the habitable zone (HZ) of the extrasolar planetary system OGLE-2006-BLG-109L, a close analogue of the Solar system. Our work is inspired by the work of Malhotra & Minton. Using the linear Laplace–Lagrange theory, they identified a strong secular resonance that may excite large eccentricity of orbits in the HZ. However, due to uncertain or unconstrained orbital parameters, the subsystem of Jupiters may be found in a dynamically active region of the phase space spanned by low-order mean-motion resonances. To generalize this secular model, we construct a semi-analytical averaging method in terms of the restricted problem. The secular orbits of large planets are approximated by numerically averaged osculating elements. They are used to calculate the mean orbits of terrestrial planets by means of a high-order analytic secular theory developed in our previous works. We found regions in the parameter space of the problem in which stable, quasi-circular orbits in the HZ are permitted. The excitation of eccentricity in the HZ strongly depends on the apsidal angle of jovian orbits. For some combinations of that angle, eccentricities and semimajor axes consistent with the observations, a terrestrial planet may survive in low eccentric orbits. We also study the effect of post-Newtonian gravity correction on the innermost secular resonance. 相似文献
19.
A. E. Nazarov 《Solar System Research》2014,48(7):523-530
The control of the orbital structure of the satellite constellation (SC) of continuous service with spacecraft in highly elliptical orbits of the Molniya type is considered. For ensuring the SC dynamic stability, it is proposed to use passive, active, and combined approaches to the SC orbital structure control. A statement of the problem to ensur e dynamic stability is given and results of its solution for a particular variant of the orbital construction of the Arktika-M space system are presented for the passive control approach. The proposed orbital structure control is based on minimizing the evolution-induced space-time deformation of the orbital structure by means of differentiated selection of initial parameters of orbits at the stages of the SC deployment and replenishment and by means of control of the spacecraft’s ground track at the SC operation stage. Using this control method is especially important with long active life spans of spacecraft and limitations on propellant margins for orbit correction. 相似文献
20.
《Chinese Astronomy and Astrophysics》2022,46(4):346-390
The 1:1 mean motion resonance may be referred to as the lowest order mean motion resonance in restricted or planetary three-body problems. The five well-known libration points of the circular restricted three-body problem are five equilibriums of the 1:1 resonance. Coorbital motion may take different shapes of trajectory. In case of small orbital eccentricities and inclinations, tadpole-shape and horseshoe-shape orbits are well-known. Other 1:1 libration modes different from the elementary ones can exist at moderate or large eccentricities and inclinations. Coorbital objects are not rare in our solar system, for example the Trojans asteroids and the coorbital satellite systems of Saturn. Recently, dozens of coorbital bodies have been identified among the near-Earth asteroids. These coorbital asteroids are believed to transit recurrently between different 1:1 libration modes mainly due to orbital precessions, planetary perturbations, and other possible effects. The Hamiltonian system and the Hill’s three-body problem are two effective approaches to study coorbital motions. To apply the perturbation theory to the Hamiltonian system, standard procedures involve the development of the disturbing function, averaging and normalization, theory of ideal resonance model, secular perturbation theory, etc. Global dynamics of coorbital motion can be revealed by the Hamiltonian approach with a suitable expansion. The Hill’s problem is particularly suitable for the studies on the relative motion of two coorbital bodies during their close encounter. The Hill’s equation derived from the circular restricted three-body problem is well known. However, the general Hill’s problem whose equation of motion takes exactly the same form applies to the non-restricted case where the mass of each body is non-negligible, namely the planetary case. The Hill’s problem can be transformed into a “canonical shape” so that the averaging principle can be applied to construct a secular perturbation theory. Besides the two analytical theories, numerical methods may be consulted, for example the approach of periodic orbit, the surface of section, and the computation of invariant manifolds carried by equilibriums or periodic orbits. 相似文献