R. Gonczi

FAST LYAPUNOV INDICATORS. APPLICATION TO ASTEROIDAL MOTION

We present a very simple and fast method to separate chaotic from regular orbits for non-integrable Hamiltonian systems. We use the standard map and the Hénon and Heiles potential as model problems and show that this method appears to be at least as sensitive as the frequency-analysis method. We also study the chaoticity of asteroidal motion.

The fast Lyapunov indicator: a simple tool to detect weak chaos. Application to the structure of the main asteroidal belt

A new method is presented, based on the variaiion with time sf the length of vectors evolving in tangential space, which distinguishes very quickly between regular and chaotic motion. This method is closely related to the computation of the Lyapunov characteristic exponents, but because of the speed of computation it can be easily applied to the study of a large set of orbits. This method is tested for the 2- dimensional standard mapping, and the structure of the phase space is explored for the 4-dimensional standard map simulating the conditions of the distribution of asteroids. Then the distribution of the 716 asteroids orbiting between the 3/l and 512 Kirkwood gaps is studied. 0 1997 Elsevier Science Ltd

Meteorites from the Asteroid 6 Hebe

We have numerically integrated the orbits of 18 fictitious fragments ejected from the asteroid 6 Hebe, an S-type object about 200 km across which is located very close to the g = g 6 (or v 6) secular resonance at a semimajor axis of 2.425 AU and a (proper) inclination of 15°.0. A realistic ejection velocity distribution, with most fragments escaping at relative speeds of a few hundreds m/s, has been assumed. In four cases we have found that the resonance pumps up the orbital eccentricity of the fragments to values > 0.6, which result into Earth-crossing, within a time span of ≈ 1M yr; subsequent close encounters with the Earth cause strongly chaotic orbital evolution. The closest Earth and Mars encounters recorded in our integration occur at miss distances of a few thousandths of AU, implying collision lifetimes < 109yr. Some other fragments affected by the secular resonance become Mars-crossers but not Earth-crossers over the integration time span. Two bodies are injected into the 3: 1 mean motion resonance with Jupiter, and also display macroscopically chaotic behaviour leading to Earth-crossing. 6 Hebe is the first asteroid for which a realistic collisional/dynamical evolution route to generate meteorites has been fully demonstrated. It may be the parent body of one of the ordinary chondrite classes.

Probable asteroidal origin of the Tunguska Cosmic Body

The complete characterisation of the Tunguska event of 30th June 1908 is still a challenge for astro- physicists. We studied the huge amount of scientic literature to select data directly available from measurements and we introduced parameters calculated by the application of models, and evaluated other possibilities. We then selected a range of meaningful atmospheric trajectories, from which we extracted a set of possible orbits. We obtained 886 orbits, which were used to estimate the probabilities of the possible origin of the Tunguska Cosmic Body (TCB). We found that the probability that the TCB moved on an asteroidal path is higher than it moved on a cometary one, 83% to 17%, respectively.

Meteorite Delivery and Transport

Understanding how meteorites and near-Earth asteroids reach their Earth-crossing orbits starting as fragments from main-belt asteroids is a basic prerequisite to identifying the original parent bodies of these objects and building a self-consistent cosmogonical interpretation of the observed properties of meteorites. We review the recent progress made in this area and the most important remaining open problems. These concern the physics of asteroidal collisions, the size distribution of small main-belt asteroids, the efficiency of different dynamical routes, and the relationships between asteroid taxonomic types based on spectrophotometry data and meteorite classes having different thermal histories and compositions.

On the Stochasticity of Halley Like Comets

Using mainly Lyapunov characteristic numbers the stochasticity of Halley like cometary orbits has been investigated in the framework of different models of the restricted three body problem.

The accuracy of proper orbital elements and the properties of asteroid families: Comparison with the linear theory

Abstract The accuracy and reliability of the proper orbital elements used to define asteroid families are investigated by simulating numerically the dynamical evolution of families assumed to arise from the “explosion” of a parent object. The orbits of the simulated family asteroids have then been integrated in the frame of the elliptic restricted three-body problem Sun-Jupiter-asteroid, for times of the order of the circulation periods of perihelia and nodes. By filtering out short-periodic perturbations, we have monitored the behavior of the proper eccentricities and inclinations, computed according to the linear secular perturbation theory. Significant long-period variations have been found especially for families having nonnegligible eccentricities and/or inclinations (like the Eos family), and strong disturbances due to the proximity of mean motion commensurabilities with Jupiter have been evidenced (for instance, in the case of the Themis family). These phenomena can cause a significant “noise” on the proper eccentricities and inclinations, probably affecting in some cases the derived family memberships. They can also give rise to a spurious anisotropy in the fragment ejection velocity fields computed from the dispersion in proper elements observed in each family, and this could explain the puzzling anisotropies of this kind actually found in real families by D. Brouwer (1951 , Astron. J. 56 , 9–32) and by V. Zappala, P. Farinella, Z. Kneževic, and P. Paolicchi (1984) , Icarus 59 , 261–285).

Modelling close encounters with Öpik's theory

Abstract The results obtained by numerical integration of the equations of motion of fictitious comets, in the restricted circular three-dimensional three-body problem, are compared with those obtained with Opiks theory of close encounters, for an experimental set-up similar to that used by Froeschle and Rickman (1980, 1981) to model both the infeed of comets from the trans-jovian region into the Jupiter family and their subsequent orbital evolution within the family. The distributions of perturbations in orbital energy E, eccentricity e and inclination i are well reproduced by Opiks theory, as long as the comparison is made on the outcomes of encounters only up to a certain unperturbed distance bmax; several values of the latter are experimented with and it is found that, surprisingly, Opiks theory seems to be still working reasonably well for values of bmax in excess of several times the Hills radius of the planet.

Long—Term Dynamics of the Tunguska Cosmic Body

We performed a detailed analysis of the large amount of the literature on the Tunguska event in order to determine a useful sample of observed data. Then from a selected range of meaningful atmospheric trajectories, we computed a set of 886 possible TCB (Tunguska Cosmic Body) orbits, which were used to estimate the probabilities of the possible origin of the TCB. According to the obtained results, the probability of an asteroidal origin of the TCB is much higher i.e. 83% than the cometary one i.e. 17%.

On the Stochasticity of the Asteroid Belt

The study of the stochasticity of the asteroid belt requires the analysis of a large number of orbits. We detect the dynamical character of a set of 5 400 asteroids using the Fast Lyapunov Indicator, a method of analysis closely related to the computation of the Lyapunov Characteristic Exponents, but cheaper in computational time. For both regular and chaotic orbits we try to associate the motion to the underlying resonances network. For it we consider different methods of classification of rational numbers proposed by number theory, and we choose the one which seems to be strictly related to the dynamical behaviour of a system.