The origin of stony meteorites landing on Earth today is directly linked to the history of the main belt, which evolved both through collisional evolution and dynamical evolution/depletion. In this paper, we focus our attention on the main belt dynamical evolution scenario discussed in Petit et al. (2001). According to Petit et al., during the planet formation epoch, the primordial main belt contained several Earth masses of material, enough to allow the asteroids to accrete on relatively short timescales.

After a few My, the accretion of planetary embryos in the main belt zone dynamically stirred the remaining planetesimals to high enough velocities to initiate fragmentation. After a short interval, perhaps as long as 10 My, the primordial main belt was dynamically depleted of $>99$% of its material via the combined perturbations of the planetary embryos and a newly-formed Jupiter. The small percentage of objects that survived in the main belt zone became the asteroid belt. It has been shown that the wavy-shaped size-frequency distribution of the main belt is a “fossil” left over from this violent period (Bottke et al. 2004).

Using a collisional/dynamical model of this scenario, we tracked the evolution of stony meteoroids produced by catastrophic disruption events over the last several Gy. We show that most stony meteoroids are a byproduct of a collisional cascade derived from large and ancient asteroid families or smaller, more recent breakup events. The meteoroids are then delivered to Earth by drifting in semimajor axis via Yarkovsky thermal drag forces until they reach a resonance powerful enough to place them on an Earth-crossing orbit.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

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

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

In view of the possibility of employing Cassini's experiments for the diagnosis of the Saturnian ring system, local $N$-body simulations of low and moderately high optical depth regions of Saturn's main rings are presented. A special emphasis is made on fine-scale spiral structures (irregular cylindric wave-type structures of the order of 100 m or so) of Saturn's A, B, and C rings. It is predicted that Cassini spacecraft high-resolution images of Saturn's rings will reveal this kind of small-scale irregular density wave structure.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Nonspherical dust grains orbiting the Sun are influenced by solar electromagnetic radiation. Interaction of electromagnetic radiation with nonspherical grains is complex and analogy with spherical grains may not be physically justified. As a consequence, equation of motion for nonspherical grain is more general than the equation of motion for spherical particle. Application of this more general interaction to possible trapping of the grain in resonances with planet Neptune is investigated. Approximation of the planar circular restricted three-body problem with action of solar electromagnetic radiation on nonspherical grain is used.

The orbital evolution of nonspherical dust grains of radius $\approx$ 2 micrometers is numerically calculated. Attention is payed to exterior resonances with the Neptune, and the numerical experiments are concentrated on their possible high capture efficiency. Physical difference between possibilities for resonant captures for spherical and nonspherical dust particles is pointed out.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Yarkovsky effect (YE), a tiny nongravitational force due to radiative recoil of the anisotropic thermal emission, is known to secularly affect the orbital semimajor axis. Therefore, angular phases such as longitude in orbit or proper longitude of node undergo a quadratic perturbation. This is fast enough to allow direct detection of the YE. The first positive case was obtained for (6489) Golevka in 2003 and prospects are very good for many more detections in the near future. To make productive scientific use of the YE detections, we need to accurately compute its strength for a given body. Simple models, available so far, will likely not be adequate in many of the forthcoming YE detection possibilities. We thus developed a complex numerical approach capable of treating most of them. Here we illustrate its power by discussing the cases of: (i) Toutatis, with a tumbling (non-principal-axis) rotation state, and (ii) 2000 DP107, a binary system.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

In the beginning we review briefly the evolution of the ideas on the motion of the bodies in our solar system, from Newton's clockwork Universe to the presently accepted ubiquity of chaotic transport in the asteroid belt. Then we discuss the result of chaotic motion, which is transport in phase space, and we introduce the concept of diffusion of an asteroid in action space. We proceed by reviewing recent work on numerical as well as analytical study of asteroids following chaotic trajectories and we summarize the main results. We present several applications of the theoretical modelling of asteroid motion as diffusion in action space, to problems of specific interest.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

In the standard scenario of planet formation, solid planets are formed through accretion of small bodies called planetesimals. The dynamics of planetesimals is important since it controls their growth mode and timescale. Here, I briefly explain the basic dynamics of planetesimals due to the two-body gravitational relaxation process. The important roles of two-body relaxation in a planetesimal system are viscous stirring and dynamical friction. Due to viscous stirring, the random velocities (eccentricities and inclinations) of planetesimals increase, while dynamical friction realizes the energy equipartition of the random energy. I also explain the orbital repulsion of protoplanets which is the coupling effect of two-body scattering and dynamical friction.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The orbital evolution of planetary systems similar to our Solar one represents one of the most important problems of Celestial Mechanics. In the present work we use Jacobian coordinates, introduce two systems of osculating elements, construct the Hamiltonian expansions in Poisson series for all the elements for the planetary three-body problem (including the problem Sun–Jupiter–Saturn). Further we construct the averaged Hamiltonian by the Hori–Deprit method with accuracy up to second order with respect to the small parameter, the generating function, the change of variables formulae, and the right-hand sides of the averaged equations. The averaged equations for the Sun–Jupiter–Saturn system are integrated numerically over a time span of 10 Gyr. The Liapunov Time turns out to be 14 Myr (Jupiter) and 10 Myr (Saturn).To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

This paper presents recent results concerning the planet formation, planet migration, and the long term stability of planetary systems. Most stars are found in binary systems and binary companions can disrupt both planet formation and stability. We first consider the effects of outer binary companions on the late stages of terrestrial planet formation and show how planet formation depends on the binary periastron. We then consider migration mechanisms for giant planets. In this case, planet scattering produces the full range of orbital eccentricities, but is less effective in moving planets inward (decreasing their semi-major axes). Disk torques are effective at moving planets inward, but not at increasing the eccentricities. We explore a scenario in which disk torques act in concert with planet scattering to provide the full range of orbital elements observed in extrasolar planetary systems. Finally, we consider the longer term stability of Earth-like planets in binary systems; we find that nearly 50 percent of binaries allow for Earth-like planets to remain stable over the current (4.6 Gyr) age of our solar system.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

More than 300 000 artificial debris particles with diameter larger than 1 cm are orbiting the Earth. The space debris population is similar to the asteroid belt, since it is subject to a process of high-velocity mutual collisions that affects the long-term evolution of its size distribution. The near–Earth space can be divided in three major regions where orbital debris is of concern: Low Earth Orbits (LEOs), below about 2000 km, Geosynchronous Orbits (GEOs), at an altitude of about 36000 km and the Medium Earth Orbits (MEOs) in between. The issues are in principle the same in the three regions, nevertheless they require different approaches and solutions. The space debris are composed by several different populations according to their source and their orbital region. A description of the nature and dynamics of the different populations in the low, medium and high orbital regimes is given. The impact risk posed by these debris is then briefly outlined.

The long term evolution of the whole debris population can be studied with computer models allowing the simulation of all the known source and sinks mechanisms. One of these codes is described and the evolution of the debris environment, over the next 100 years, under different traffic scenarios is shown, pointing out the possible measures to mitigate the growth of the orbital debris population.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

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

The problem of escape/capture is encountered in many problems of the celestial mechanics – the capture of the giants planets irregular satellites, comets capture by Jupiter, and also orbital transfer between two celestial bodies as Earth and Moon. To study these problems we introduce an approach which is based on the numerical integration of a grid of initial conditions. The two-body energy of the particle relative to a celestial body defines the escape/capture. The trajectories are integrated into the past from initial conditions with negative two-body energy. The energy change from negative to positive is considered as an escape. By reversing the time, this escape turns into a capture. Using this technique we can understand many characteristics of the problem, as the maximum capture time, stable regions where the particles cannot escape from, and others. The advantage of this kind of approach is that it can be used out of plane (that is, for any inclination), and with perturbations in the dynamics of the n-body problem.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

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