We study the population of asteroids inside the 2/1 mean motion resonance with Jupiter, in the so called Hecuba gap. Origin of these bodies is not well understood: (i) the long-lived (stable) population may be primordial, but this contradicts its steep size distribution, while (ii) the short-lived (unstable) population requires an efficient sustaining mechanism. Our working hypothesis is that the unstable asteroids are continuously resupplied from outside the resonance by the Yarkovsky effect. As a first step toward comparison of such model with observations, we report here an update of the observed population of asteroids residing in the 2/1 Jovian resonance, mainly because the number of cataloged orbits increased substantially during the last few years. We found there are 153 numbered and multi-opposition resonant asteroids in total and we classified them into the three sub-populations according to their dynamical lifetime. Our work also allowed us to derive several important parameters such as asteroid locations inside the resonance or size distribution of the sub-populations. As a particular novelty, we identified 6 asteroids located inside the high-eccentricity quasi-regular stable island, which previously seemed empty.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We present an analysis of the reliability of computation of maximum Characteristic Exponents of Lyapunov from the numerical integrations of asteroid orbits over finite intervals of time. We used two complementary approaches - a comparison of the LCE estimates from the backward and forward integrations of orbits, and a comparison of the estimates coming from the integrations of the same initial conditions over different time spans. The main conclusion is that for a vast majority of asteroids ($> 80\%$) the results can be considered as reliable enough to reveal the very nature and basic properties of the motion.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Estimates of the region of Nekhoroshev stability of Jupiter's Trojan asteroids are obtained by a direct (i.e. without use of the normal form) construction of formal integrals near the Lagrangian elliptic equilibrium points. Formal integrals are constructed in the Hamiltonian model of the planar circular restricted three body problem (PCRTBP), and in a mapping model (Sándor et al. 2002) of the same problem for small orbital eccentricities of the asteroids. The analytical estimates are based on the calculation of the size of the remainder of the formal series by a computer program. An analysis is made of the accumulation of small divisors in the series. The most important divisors introduce competing Fourier terms with sizes growing at similar rates as the order of truncation increases. This makes impossible to improve the estimates by considering nearly resonant forms of the formal integrals for particular near-resonances. Improved estimates were obtained in a mapping model of the PCRTBP. The main source of improvement is the use of better variables (Delaunay). Our best estimate represents a maximum libration amplitude $D_p=10.6^0$. This is a quite realistic value which demonstrates the usefulness of Nekhoroshev theory.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We analyze the effect of the temporary capture of comet-like orbits in asteroid mean motion resonance by following the dynamical evolution of 2090 Jupiter-family comet-like orbits over ${\sf 10^7}$ yr under the perturbation of the four major planets. The resonant capture may be related to the phenomenon known as “resonant stickiness” consisting in the temporary stabilization of very eccentric orbits near the separatrices of the mean motion resonances. We found that the population of orbits that were captured at least once during the simulation has a median lifetime larger than that of the complete sample.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

When a celestial body, e.g., an asteroid, has been observed only over a short time, its orbit is not well determined but may be anywhere in a confidence region where the astrometric residuals are acceptable. This region can be sampled by a swarm of Virtual Asteroids (VA) sharing the reality of the asteroid: one of them is real, but we do not know which one. The problem is how to sample the confidence region with a small number of VA, still being able to solve the main problems of asteroid recovery/identification and impact monitoring.

One class of methods uses random sampling of the confidence region to mimic with the VA population the probabilistic distributions of the orbits. This class includes the Monte Carlo and the Statistical Ranging methods. When it is critical to detect a very small probability (e.g., of a catastrophic impact) by computing a small number of VA orbits, and also when a large catalog of asteroids has to be handled, it is more efficient to sample the confidence region with a geometric object, such as a smooth manifold: it can be sampled uniformly, taking into account its dimension. Our group has developed in the last 6-7 years 1-dimensional sampling methods based upon a differentiable curve, the Line Of Variations (LOV), which can represent, in suitable cases, the spine of the confidence region. The LOV is sampled by uniformly spaced VA, thus interpolation between consecutive VA is possible. This is the basis for the current algorithms of Impact Monitoring, used in Pisa and at JPL. The LOV method is also used for recovery of lost asteroids and for identification of independent discoveries of the same object.

When the asteroid has moved on the sky while being observed by $<1^\circ$, the confidence region is wide in two directions and the LOV may be an inappropriate way of sampling it. We have recently developed 2-dimensional sampling methods based upon the concept of Admissible Region, a 2-dimensional manifold parameterized by a compact subset of the range/range-rate plane. This region is then sampled by triangulation, with each node used as a VA. This allows to define methods for asteroid identification/recovery and for impact monitoring starting from very poor data, such as the ones collected during a single night of observations.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Despite of the large number of detections of new asteroids, both in the main belt and in the near-Earth space, our observational knowledge of the asteroid populations is not quite complete. Our catalogs are affected by observational biases. Thus, a modeling work is required in order to infer the real distributions of the asteroid populations.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

A novel method for the preliminary identification of asteroids at discovery and a few days thereafter is being developed in Helsinki. Having two different sets of asteroid observations, the goal is to identify all possible pairs of objects between the sets. An arbitrary asteroid can either remain unidentified, or be preliminary linked to one or more asteroids. In the case of ambiguity, the final decision must usually be based on additional observations. We use a multistep approach, during which possible pairs of objects are first selected by comparing ephemerides that have been generated for three common epochs. The method has been successfully tested using both Very Large Telescope observations, and simulated observations of near-Earth and main-belt objects. Identification results of simulated observations indicate that the observing strategy promoted by the Minor Planet Center might not be the best one, at least for the purposes of identification. The ultimate goal is to produce a real-time asteroid identification tool for ESA's astrometric space observatory Gaia, the Lowell Observatory Near-Earth-Object Search, the Near-Earth Space Surveillance mission, and the Nordic Near-Earth Object Network. The tool could also benefit large-scale surveys done with the Large Synoptic Survey Telescope, and the Discovery Channel Telescope.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

In the framework of the analytical theory of close encounters, and under suitable assumptions, we compute the size of the region in orbital elements space containing collisions solutions. In the linearized approximation in the semimajor axis/eccentricity plane the collision region is the interior of an ellipse. Examples are given from past cases of Near Earth Asteroids having the possibility of impacting our planet.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We show the utility of the Systematic Ranging technique by analyzing the orbit determination of asteroid 2004 FU$_{162}$, which passed approximately 6400 km from the surface of the Earth on March 31, 2004. The limited observations introduce strong nonlinearities that must be accounted for when estimating the actual encounter distance.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

This paper explores the advantages of using gravity assisted trajectories to perform flyby and rendezvous missions to accessible near-Earth asteroids (NEAs), in terms of the total velocity budget required for the mission. Combining the Opik's formalism of close encounters with the Monte Carlo sampling technique and Lambert trajectories, we give a general picture of the accessibility regions for NEAs in phase space of orbital elements, without considering the phasing requirements between bodies.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

Recent years have seen a revolution in the possibility to understand cometary capture, i.e., the origin of the cometary population that moves in orbits confined to the inner Solar System. This is due to the discovery of the major source populations: the Edgeworth-Kuiper belt, and the scattered disk. We review the current understanding of the links between the distant sources, including the Oort cloud, and the observed, short-period population, and the problems that remain. Some highlights of present research in this field will serve to illustrate recent progress and major issues that are currently arising.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

In the late stage of planet formation, planetesimals are perturbed by large (proto) planets. There are four fates of planetesimals, (1) to collide with planets, (2) to escape from the planetary region, (3) to survive in the planetary region, and (4) to fall onto the central star. The ratios of these fates depend on initial orbital parameters. We performed numerical simulations of gravitational scattering of planetesimals by a planet. We obtained the escape rate of planetesimals and its dependence on the orbital parameters of the planetesimals and the planet. We also calculated the rate for increasing the semimajor axis to more than 3000AU. Using these results, we discuss the relative efficiency of the four giant planets of the solar system in the formation of the Oort cloud.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

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