Nowadays, more than one hundred extra-solar planets are known, and about a dozen of multi-planetary systems have been discovered. Most of them have been detected by the radial velocity (RV) method. The recovery of orbital parameters from RV data leads to several problems. Usually RV data cover irregularly a short time interval which is frequently shorter than the orbital period of the most distant planet. Moreover, observations contain a noise due to the instabilities of the star. The distribution of this noise is unknown. A precise determination of the dynamical state of a multi-planetary system is important for understanding its stability and evolution. In most cases observers determine the orbital parameters for multi-planetary systems just fitting a sum of Keplerian orbits. The parameters obtained in such a way are in most cases the only accessible data about an extra-solar system because the observes very rarely publish their observations. However, the parameters from a multi-Keplerian fit as it has already been observed by many authors, cannot be interpreted as the osculating elements for actual planetary orbits. Moreover, these parameters can be considered as Keplerian elements of: relative, barycentric or Jacobi orbits. One can find arguments that the interpretation of parameters from a multi-Keplerian fit as elements of Keplerian orbits in the Jacobi coordinates is the most proper one, see [Lee and Peale, 2002; Goździewski et al. 2003].To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

In this study we give a first description of De Haerdtl's 3:7 inequality between the Jovian satellites Ganymede and Callisto and 1:5 inequality between the Saturnian Titan and Iapetus and the resonant arguments associated. For each inequality, 19 arguments are associated. The overlapping of resonant zones induces stochasic layers that the system might have crossed in the past thanks to tidal dissipation.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

When a new Near Earth Asteroid is discovered, it is important to know if there is the possibility of an impact with the Earth in the near future. In these last years second generation software for impact monitoring (CLOMON2 and SENTRY) have been developed and the performances have been significantly increased in comparison to the earlier, simpler and solitary system CLOMON. The two systems use the Line Of Variations (LOV) approach: they sample the LOV, an 1-dimensional subspace, to perform the sampling of the 6-dimensional confidence region. This approach is very useful when the confidence region is elongated and thin, that is an eigenvalue of the covariance matrix is much bigger than the others. When the observed arc is short (1$^\circ$ or less), usually for asteroids observed for few nights, the confidence region is like a flat disk and we propose to use a 2-dimensional sampling. We triangulate the admissible region in the $(r, \dot r)$ plane, using the nodes of triangulations as Virtual Asteroids (VAs). After orbit propagation we project the VAs and the triangulation on the Target Plane (TP) of a given epoch to study the existence of a Virtual Impactor (VI) and complex dynamical behaviors such as folds.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We are witnessing tremendous progress in the nascent multidisciplinary field of astrobiology, encompassing the origin and evolution of life in the cosmic context. One of the key concepts recently introduced in this field is the Galactic Habitable Zone (GHZ): an interval of galactocentric distances convenient for formation of stars possessing habitable planets. The boundaries of the GHZ are still poorly understood, however. Here we present a comparative analysis of various proposals for the mechanisms determining the GHZ boundaries, as well as different numerical values obtained. When joined with the models of Galactic stellar distribution, this gives us a better handle on the number of potential life-bearing sites.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We report on our theoretical and numerical results concerning the transport mechanisms in the asteroid belt. We first derive a simple kinetic model of chaotic diffusion and show how it gives rise to some simple correlations (but not laws) between the removal time (the time for an asteroid to experience a qualitative change of dynamical behavior and enter a wide chaotic zone) and the Lyapunov time. The correlations are shown to arise in two different regimes, characterized by exponential and power-law scalings. We also show how is the so-called “stable chaos” (exponential regime) related to anomalous diffusion. Finally, we check our results numerically and discuss their possible applications in analyzing the motion of particular asteroids.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Interstellar dust grains approaching the Sun are influenced mainly by solar gravity, solar electromagnetic radiation and Lorentz force due to the existence of interplanetary magnetic field. These interactions together with the effect of the solar wind on dust grain and the effect of solar cycle are taken into account when modelling behaviour of interstellar dust in the vicinity of the Sun. As a consequence, nonspherical dust grains can be captured and survive in the solar system – they can orbit the Sun in sufficiently large distances from the Sun not to be thermally destroyed. On the other hand, captured spherical dust grains are practically all destroyed. Detailed numerical simulations showed an interesting behaviour of a quantity of the dimension of length cubed divided by time squared. The quantity behaves practically as an invariant of motion: it is a constant during the process when surviving captured interstellar grain is orbiting the Sun. The constancy is fulfilled with an accuracy better than 1%.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The source of long-period comets can be numerically modeled by means of Monte Carlo simulation of the Oort cloud dynamics. Tracing a comet motion under the galactic perturbations over a long time interval requires taking into account of planetary perturbations. A method for the approximate treating of the planetary perturbations in such simulations is described. Some peculiarities found in planetary action on long-period simulated cometary sample are also discussed.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Meteor streams that form as a result of cometary activity around perihelion consist of both structured and background components. The former are often referred to as trails. A trail is created at each perihelion passage as a result of the meteoroids' range of orbital periods. Trail locations can be precisely calculated by numerical integrations, allowing predictions of meteor outbursts and storms. The initial distribution of meteoroids, which relates to the meteor shower profile, depends on the meteoroid production rate and ejection velocity distribution as functions of heliocentric distance and on solar radiation pressure. The profile can gradually evolve owing to other radiative forces. This paper reviews such work on these aspects of shower predictions.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Gravity is the most important force to affect the motion of bodies in the Solar system. At small sizes, however, additional forces must be taken into account to explain fine details of their translational and rotational motion, as well as parameters of their populations. This is because the strength of the non-gravitational perturbations typically increases as $\simeq 1/D$ toward small sizes $D$. The principal perturbation acting on macroscopic main-belt bodies (sizes up to several kilometers for timescales of about billion years) is due to the anisotropic thermal re-radiation of the absorbed sunlight. In orbital dynamics this is known as the Yarkovsky effect, while in rotational dynamics the same physical phenomenon is called the YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect. We review the main observational implications of the Yarkovsky/YORP effects as understood and evidenced today.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

To correctly take into account the solar wind drag equations for secular variations in the meteoroid orbital semimajor axes and eccentricities were obtained. The equations are similar to those derived for the Poynting- Robertson radiation drag (Wyatt and Whipple 1950). An estimation for the Geminid meteoroid stream shows that the ratios of corpuscular to radiation drags are 0.4 – 0.7 for particles of size $> 10 \mu m$, i.e. the effect is much stronger than was assumed before.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We point out two important effects relevant to the information which can be obtained from the distributions of galactic angular elements of new comets. (i) The commonly used criterion for a selection of new comets from a catalog of long-period comets (reciprocal original semi-major axis $a < 1.0^{-4}\,$AU$^{-1}$) is crude as already proved by Dybczyński in 2001. It is more relevant to regard as new the comets with previous perihelion distance $q > 15\,$AU. (ii) The angular orbital elements of Oort-cloud comets referred to the galactic coordinate system undergo large changes at the observed (current) perihelion passage, therefore their values are chaotic enough. Thus the information contained in the distribution of angular elements is dimmed. We suggest constructing the distributions for the elements at other epoch, e.g. for those at the previous perihelion passage.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The contribution of high-eccentricity trans-Neptunian objects to the observed populations of both short-period and long-period comets is estimated. About $10^{10}$ objects with a radius $R>0.7$ km in orbits with perihelion distances $28<q<35.5$ AU and semimajor axes $60<a<1000$ AU are the main source of Jupiter-family comets. If the population of high-eccentricity trans-Neptunian objects formed about 4.5 Gyr ago, the mean near-parabolic flux produced by these objects is on the order of 0.3-1.0 AU$^{-1}$ yr$^{-1}$ for comets with $R>0.7$ km.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The orbital motion of comets is difficult to characterize accurately due to the rocket-like outgassing of material from the cometary nucleus. The resulting nongravitational accelerations often appear to be fundamentally stochastic in nature and thus pose severe modeling challenges in orbit determination, especially when the comet has been observed for many revolutions. Even so, new techniques have arisen in recent years that give new insight, not only into the motion of the comets, but also into their physical characteristics and spin states. These approaches include modeling of spin axis precession over many decades and the consideration of the seasonal variation in the thrust from discrete jets acting on a rotating nucleus. Such advances have been enabled, in part, by the increasing efforts and capabilities of comet observers worldwide as more and more comets with longer and longer observing arcs become available for study. In this review we specifically consider the application of the Rotating Jet Model to several space mission targets, indicating how this model can often be used to infer the orientation of a comet's spin axis.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The trans-Neptunian region is inhabited by multiple dynamical populations, each of which have a complicated structure. For the most part, these structures cannot have been sculpted by the giant planets, once on their current orbital configuration. Thus, they represent important clues to the conditions that existed in the distant past. We argue in this paper, that most of what we see is the result of the outward migration of Neptune. By combining results from various authors, we can reproduce most of the observed properties of the trans-Neptunian region. Several aspects are not yet totally clear, and some may not be totally correct. But, for the first time, we have a view — if not not a detailed model — of how the system formed.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We evaluate asteroid orbital uncertainties from the discovery night onwards using 6D orbit computation tools based on statistical techniques. In particular, we outline a new nonlinear Monte Carlo technique of phase-space sampling that helps us in assessing the nonlinear phase transition from extended orbital-element distributions to well-constrained ones as the observational arc and number of observations grows. We apply the statistical techniques for near-Earth asteroid 2004 AS$_1$ to examine the time evolution of the orbital uncertainties and to assess the asteroid impact risk immediately after discovery. We start with the technique of statistical ranging for exiguous data, continue with the phase-space sampling technique for moderate data, and conclude with the standard least-squares fit for extensive data.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The KLENOT project is a project of the Klet Observatory, Czech Republic, devoted to astrometric observations of Near-Earth objects, distant objects and comets. The improved effort of the large NEO surveys resulting in an increasing number of newly discovered NEOs calls for continuous follow-up astrometry to secure an accurate orbit determination of discovered bodies first in discovery opposition and then during next apparitions. Considering this urgent need of astrometric follow-up, the fact that many of these targets are fainter then magnitude 20.0 V and our results and experience in minor planet and comet CCD astrometry done at Klet since 1993, we decided to bring into operation a new 1-m class facility working on a permanent basis - the KLENOT telescope. The regular observing of the telescope started in March 2002 (the MPC code 246). Beside methods and techniques we use for follow-up astrometry we present most important results of the project.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We approach the dynamics in proto-stellar systems via the two-body problem associated to an anisotropic Schwarzschild-type potential. On the basis of the natural symmetries of the characteristic vector field, and using variational methods (particularly the classical lower-semicontinuity method), we prove the existence of infinitely many families of symmetric periodic orbits.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

This paper reviews recent results on the dynamics of multiple-planet extra-solar systems, including main sequence stars and the pulsar PSR B1257+12 and, comparatively, our own Solar System. Taking into account the degree of gravitational interaction of the planets, the known planetary systems may be separated into four main groups: (Ia) Planets in Mean-motion resonance (Ib) Low-eccentricity near-resonant pairs; (II) Non-resonant planets with a significant secular dynamics; and (III) Weakly interacting planet pairs. Different analytical and numerical tools can help to understand the structure of the phase space, to identify stability mechanisms and to categorize different types of motions in the cases of more significant dynamical interaction. The origin of resonant configurations is discussed in the light of the hypothesis of planetary migration.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The results of a numerical simulation of the tidal evolution of the Earth-Moon system during the Phanerozoic epoch (the last 600 million years) are given. In most of the researches devoted to the solution of the problem the authors simplified and parametrized very complicated tidal phenomena to a primitive integral hump on the Earth's surface. As distinct from these the numerical model of the ocean tides in its most complete form is the core of the present study: the problem is solved for a viscous liquid in a paleoocean with variable outlines and depth allocations stimulated by the drift of the lithospheric platforms; the global interaction between the ocean and earth tides and the fluctuations of the gravitational field of the planet caused by them are taken into account. The astronomical component of the model is simplified. It is assumed that the Earth-Moon system is isolated, the Moon's orbit circular and the moment of inertia of the Earth constant during the Phanerozoic epoch. It is shown that the evolution of the Earth-Moon system during the Phanerozoic was nonuniform and that the primary role in this process belongs to the geodynamic factor.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

In the framework of the restricted three body problem, the resonant periodic orbits associated with the Kuiper belt dynamics are studied. Particularly, all the first, second and third order exterior mean motion resonances with Neptune located up to 50A.U. and the asymmetric resonances (beyond the 48 A.U.) are considered. We present the bifurcation points of families of periodic orbits of the planar circular problem from which families of periodic orbits are generated in the planar elliptic and in the 3D circular problem. Similarities and differences between the various resonant cases are noticed. The relation between the distribution of the bifurcation points and the population of small bodies at the particular resonances is discussed.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html