In this work, we review the analytical and semi-analytical tools introduced to deal with resonant proper elements and their applications to the Trojan asteroids, the numerical computation of synthetic proper elements for resonant and non resonant asteroids, and the introduction of proper elements for planet crossing asteroids. We discuss the applications and accuracy of these methods and present some comparisons between them.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Regularity and chaos of “quasi-stable” (i.e. appearing stable during a finite interval of time) planetary orbits around one component of binary stars is investigated for different values of the binary's mass ratio and orbital eccentricity $e$. The behavior of fictitious planetary orbits around 16 Cyg B-like stars is presented. Among the quasi-stable orbits we found that there exists a (“stability zone”) for every values of $e$, but that the existence of nearly-circular planetary orbits is restricted to values of $e$ less than 0.8. However, not all the quasi-stable orbits are regular: emergence of chaos when $e$ increases is shown in two sets of quasi-stable orbits (each set has fixed initial conditions for the planet, but varying values for $e$ from 0 to 0.99). In the first set, which lies in the “heart” of the stability zone, chaos appears only when $e$ approaches 1. The second one is near the border of the stability zone, and chaos appears as soon as $e$ reaches 0.7. The influence of the binary's orbital eccentricity on the limit between regularity and chaos is therefore stronger in the latter case (wider planetary orbits) than for the former one (closer planetary orbits).To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

The paper presents a review of the recent contributions and open questions concerning the families of asteroids. Due to the availability of very large catalogues (synthetic and analytical proper elements of the asteroids and large observational surveys of their spectra) and to the introduction of non gravitational forces in their determination, the concept of static family has disappeared, to be replaced by this of dynamical families. The proper elements are not constant anymore but are ageing on very long timescales. The size distributions of the populations of asteroids, in and out the families, their ages, the ejection velocities of the fragments after an impact, have been reconsidered by several teams of research, with this new approach. Parallel numerical simulations of collisions and fragmentations of bodies have showed that most of the asteroids are likely rubble piles or agglomerates than monolithic blocks. The methods of classification have been refined and combine, in their newest versions, the dynamics and the observations, working now on 5 dimensional space instead of 3. A series of sub families of the large well-known families have been recently identified, using catalogues with more than 100 000 asteroids (the cluster Karin for example).To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We form a sample of nearby single stars. Their masses are estimated on the basis of the mass-luminosity relation. Our aim is to specify a reasonable space limit, i.e. a heliocentric volume, as small as possible, but to contain a sufficient number of stars so that an application of statistical laws becomes possible. Among the quantities calculated by us a special attention is paid to the mean mass of a single star and, also, to the local value of Agekyan's factor.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

We integrated the orbital evolution of 30,000 Jupiter-family comets, 1300 resonant asteroids, and 7000 asteroidal, trans-Neptunian, and cometary dust particles. For initial orbital elements of bodies close to those of Comets 2P, 10P, 44P, and 113P, a few objects got Earth-crossing orbits with semi-major axes $a<2$ AU and moved in such orbits for more than 1 Myr (up to tens or even hundreds of Myrs). Three objects (from 2P and 10P runs) even got inner-Earth orbits (with aphelion distance $Q<0.983$ AU) and Aten orbits for Myrs. Our results show that the trans-Neptunian belt can provide a significant portion of near-Earth objects, or the number of trans-Neptunian objects migrating inside the solar system can be smaller than it was earlier considered, or most of 1-km former trans-Neptunian objects that had got near-Earth object orbits for millions of years disintegrated into mini-comets and dust during a smaller part of their dynamical lifetimes. The probability of a collision of an asteroidal or cometary particle during its lifetime with the Earth was maximum at diameter $d\sim 100\,\mu$m. At $d<10\,\mu$m such probability for trans-Neptunian particles was less than that for asteroidal particles by less than an order of magnitude, so the fraction of trans-Neptunian particles with such diameter near Earth can be considerable.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

Among more than 120 discovered exo-planets, less than 20 were found in double star systems. Out of this sample we studied the planetary motion in those systems that can be regarded as close binaries, i.e. HD41004 AB, $\gamma$ Cephei and Gliese 86. In this study we concentrate on the first two systems, where the secondaries are M4 V dwarfs at about 20 AU from the host-star. A comparison of previous studies – where the dynamical behavior was studied in the (semi-major axis, inclination) plane (see Dvorak et al. 2003a) for $\gamma$ Cephei and Pilat-Lohinger & Funk (2004) for HD41004 A) – shows significant differences in the stability maps. Our numerical investigation examines the region between 0.5 and 1.2 AU, which is influenced mainly by mean motion resonances when the initial position of the detected planet $a_{gp} < 1.5$ AU. If we move the planet farther away from the host-star (to distances $> 1.5$ AU) we observe an arc-shaped chaotic structure in the dynamical map.To search for other articles by the author(s) go to: http://adsabs.harvard.edu/abstract_service.html

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